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See the mto-talk Guide for details. ============================================================================= From rothfarb@smt.ucsb.edu Mon Aug 31 10:36:33 1998 Received: from boethius (boethius [128.111.94.30]) by smt.ucsb.edu (8.7.1/8.7.1) with SMTP id KAA09830 for ; Mon, 31 Aug 1998 10:36:33 -0700 (PDT) Message-Id: <199808311736.KAA09830@smt.ucsb.edu> Date: Mon, 31 Aug 1998 10:36:33 -0700 (PDT) From: Lee Rothfarb Reply-To: Lee Rothfarb Subject: Re: Solmization To: mto-talk@smt.ucsb.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: ajU3HZoxkn5mbYVNdwMyzg== X-Mailer: dtmail 1.2.0 CDE Version 1.2 SunOS 5.6 sun4m sparc Sender: stefano mengozzi Subject: Re: Solmization David Lewin's analysis of the Subject of Bach's D-major Fuge from WTC II raises the important issue of hexachord as a diatonic structure that is supposedly capable of shaping the way one hears music. At [12], Lewin wonders whether Bach could have heard (or sung) either the mutated, or one of the unmutated versions of the subject, and at [16] he writes that "[he is] (at present) happy to hear the Subject by itself 'in D,' [understanding] the "D" at issue to be the UT of a pertinent hexachord, rather than the tonic note of a common-practice tonality." It seems to me that to hear a piece hexachordally can only mean hearing musical pitch in terms of hexachordal (as opposed to heptachordal) scale degrees or functions. In principle, this is quite possible, although I suspect that modern listeners will find it quite hard to hear a major sixth as *the* main structural segment of the diatonic space, as opposed to a mere portion of the octave. I would be curious to know how Lewin has trained himself to hear Bach's Subject in hexachordal terms and how he has dealt with the problem of the cognitive discrimination between the two "kinds of sixth." Of course, it is the mutated version of the Subject that raises problems from a listener's perspective, if the assumption is that mutations are there to be heard. Let us assume, for example, that Bach did hear the opening high D as the fifth scale degree (SOL) of a G hexachord, and the closing low D as the first scale degree (UT) of a D hexachord, and that he may even have felt a certain aural pleasure when mutating between the two 6-note segments at some point along the way. But then, shall we also conclude that he heard both the suspended A in the alto part of measure 5 and the following high D in the top part as the SOL degrees of two simutaneous D and G hexachords? I am puzzled by the idea of two different pitches having the same hexachordal function, again if hexachord is taken to be a structural (read: audible) element of musical space. The opposite, but equally puzzling, case, is that of the D on the second beat of bar 8 in the left hand, which would seem to function as both UT and FA at the same time. The question for us is not only, "was Bach accustomed to Guidonian solmization," as Lewin asks, but also what was (or were) the precise function(s) of Guidonian solmization for singers and composers across the centuries? This may sound like going back to Adam and Eve, yet surprisingly little thought has been given to this issue. There is of course little doubt that the six Guidonian syllables were widely used from the Middle Ages onwards as a way to label or recognize diatonic intervals and their various species; but from here to assert that, because Guidonian solmization was widely used with this function, it also superimposed a grid of hexachordal scale degrees onto the diatonic space, is a huge step that is supported by little, if any, corroborating evidence. Finally, I would like to comment on Nicolas Meeus's point that "a 'mutated' reading [of the Subject] necessarily must be based on the soft G hexachord, because the second note of the subject (G) already lies outside the hard A hexachord." I am not sure that the choice of the G hexachord is really a *necessity,* although I agree that it represents perhaps the most obvious way to solmize the opening fifth. Just as 17th-century French singers used the "method du SI" in their "solfege mobile," so a "Guidonian" singer, as a rule of thumb, would immediately translate any sharp appearing in key signature into MI. Thus, it is at least conceivable for an hypothetical singer to solmize Bach's Subject beginning on FA of the A hexachord, and to sing again FA (of the D hexachord) on the following G, as follows: FA FA FA / FA LA RE SOL FA MI UT It is admittedly a little bizarre to mutate after only one note, yet the solmization FA/FA was customarily suggested, if I am not mistaken, as appropriate for the "Lydian" (or third species of) fifth. Besides, this solmization requires only one mutation, like the others that have been suggested. In sum: I am skeptical about the idea that solmization may provide a solution to the problem of pitch ambiguities, because pitch ambiguities also increase the number of possible solmizations. This is precisely why the problem of so-called *musica ficta* in medieval and Renaissance music is so frustrating: it is always possible to solmize alternative versions of the same passage, regardless of whether or not you decide to flatten your B's or to sharpen your F's. Stefano Mengozzi University of Chicago men8@midway.uchicago.edu ------------- End Forwarded Message ------------- From rothfarb Mon Aug 31 14:15:05 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id OAA18146; Mon, 31 Aug 1998 14:15:04 -0700 (PDT) Date: Mon, 31 Aug 1998 14:15:04 -0700 (PDT) From: Lee Rothfarb To: mto-talk@smt.ucsb.edu Subject: Re: Solmization (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: "nicolas meeus" Subject: Re: Solmization Stefano Mengozzi makes the most interesting point that solmization may not have been very practical when reading polyphonic music polyphonically -- i.e., when reading more than one part at a time -- because mutations occur differently in the different part and if a note belongs to two parts at the same time, it may have two hexachordal functions at the same time. More specifically, it must have been quite uncomfortable for keyboardists. This may explain why Schlick, for instance, stated that musica ficta was so difficult for organists. I never realized that before, and I am quite grateful. The situation was different, of course, for singers or players of monodic instruments when they read only one part. These, in the Middle Ages and the early Renaissance at least, must have conceived the diatonic space as a complex concatenation of hexachords (rather than a simple concatenation of octaves). They must have thought in terms of what I proposed to call "hexachordal classes" (see my communication at the European Congress of Music Analysis in Trento), akin to our modern pitch classes. Is that what Stefano doubts when he speaks of a "superimposed grid of hexachordal scale degrees"? in that case, we probably should pursue the discussion. A hexachordal perception (or a tetrachordal one, for that matter) is characterized by the importance given to very local events; it is quite incompatible with large scale perception. To hear Bach's subject as SOL SOL SOL UT MI=LA SOL FA MI UT, with a mutation on MI=LA, is to perceive that something changes at that very point -- that, in a way, the subject begins "in G" and continues "in D" (and this, in addition, with respect to the diatonic space itself, not the mode). Now, if such a conception included nothing of the truth, David Lewin wouldn't have had to write his article. Stefano is right that a reading of the subject in the durum/naturale combination of hexachords is not utterly unthinkable. It seems to me quite improbable, however, because it imposes a mutation "in the air", so to speak, i.e. between notes rather than on one note that would assume two functions in succession. It is true that the lydian fifth must be read FA FA, and that the two sharps in the signature at first may suggest such a reading. My impression, however, is that the reader having said FA on the initial D (because of the C sharp in the signature) would immediately be quite puzzled about how to name the G. The situation would have been different if the intermediate notes had been heard before, establishing a lydian context and allowing a mutation on an implicit degree -- but these previous notes would also have established a D major context, of course, so that, once again, we wouldn't be discussing today. I am not sure that this discussion can lead us to hear Bach's subject as less ambiguous (why should we, it IS ambiguous); but it does help pointing where the ambiguity arises, in the first two notes. Nicolas Meeus Universite de Paris-Sorbonne nicolas.meeus@paris4.sorbonne.fr From rothfarb Mon Aug 31 21:43:30 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id VAA29774; Mon, 31 Aug 1998 21:43:30 -0700 (PDT) Date: Mon, 31 Aug 1998 21:43:29 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: Re: Solmization (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: Joel Lester Subject: Re: Solmization Stefano Mengozzi touches on a crucial point when he notes that "There is of course little doubt that the six Guidonian syllables were widely used from the Middle Ages onwards as a way to label or recognize diatonic intervals and their various species;" and goes on to argue "but from here to assert that, because Guidonian solmization was widely used with this function, it also superimposed a grid of hexachordal scale degrees onto the diatonic space, is a huge step that is supported by little, if any, corroborating evidence." I wonder. What COULD it mean for a musician to be fully comfortable with mutating hexachordal solmization and NOT relate that to diatonic space? Well into the "common-practice era," it seems, "tonal" musicians freely used such solmization -- a practice documented well after Bach's death. I confess that I am still as astonished now as I was over a decade ago when I realized that Albrechtsberger, in his _Gru"ndliche Anweisung zur Composition" (Leipzig, 1790), published just two years before the 22-year-old Beethoven studied with him, gave the following alternatives for solmizing the major and minor scales on p. 1 of his text: MAJOR: or: do re mi fa do re mi fa sol la mi fa G A B C D E F# G MINOR: or: do re mi fa re mi fa sol la re mi fa E F# G A B C# D# E Here, the tonic of major appears as "do" and "fa," and "do" denotes both tonic and dominant; and in minor "re" denotes both tonic and the raised submediant. Albrechtsberger must have referred to pitches in this hexachordal manner when he taught Beethoven species counterpoint (in major/minor keys, not in the modes!). Did the Beethoven whose works formed the foundation for most tonal theories of the past two centuries conceptualize the tonic equally as "do" and "fa"? I join Mengozzi when he notes, "I am puzzled by the idea of two different pitches having the same hexachordal function, again if hexachord is taken to be a structural (read: audible) element of musical space." But how could the hexachord NOT have been meant to be an "audible element of musical space," since the whole point of solmizing was (is!) to make the intervals "audible" conceptually? I do not know exactly when such hexachordal solmization finally faded from pedagogy. But I do know that "late" instances such as Albrechtsberger's do point to a pitch-spatial conceptual universe quite different from ours -- yet one in which Beethoven was probably quite at home. (We can also be quite certain that Haydn conceptualized in such terms, since he virtually certainly learned hexachordal solmization when he was a choirboy at St. Stephan's at the end of the lifetime of Fux, 6 decades before Albrechtsberger continued that tradition. Fux, after all, had argued vociferously in defense of hexachordal solmization in the mid 1710s in his dispute with Mattheson.) Joel Lester Mannes College of Music jlester@email.gc.cuny.edu From rothfarb@smt.ucsb.edu Tue Sep 1 08:22:38 1998 Received: from boethius (boethius [128.111.94.30]) by smt.ucsb.edu (8.7.1/8.7.1) with SMTP id IAA10476 for ; Tue, 1 Sep 1998 08:22:38 -0700 (PDT) Message-Id: <199809011522.IAA10476@smt.ucsb.edu> Date: Tue, 1 Sep 1998 08:22:38 -0700 (PDT) From: Lee Rothfarb Reply-To: Lee Rothfarb Subject: Re: Solmization To: mto-talk@smt.ucsb.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=US-ASCII Content-Transfer-Encoding: QUOTED-PRINTABLE Content-MD5: PE+km7dGKC8UsXib/9LcNg== X-Mailer: dtmail 1.2.0 CDE Version 1.2 SunOS 5.6 sun4m sparc ------------- Begin Forwarded Message ------------- Date: Tue, 1 Sep 1998 03:22:15 -0700 (PDT) Originator: mto-talk@boethius.music.ucsb.edu From: "nicolas meeus" To: rothfarb@smt.ucsb.edu Subject: Re: Solmization X-Listprocessor-Version: 6.0c -- ListProcessor by Anastasios Kotsikonas Mime-Version: 1.0 This message was submitted by "nicolas meeus" to list mto-talk@boethius.music.ucsb.edu= . If you forward it back to the list, it will be distributed without the paragra= phs above the dashed line. You may edit the Subject: line and the text of the message before forwarding it back. If you edit the messages you receive into a digest, you will need to remove these paragraphs and the dashed line before mailing the result to the list. Finally, if you need more information from the author of this message, you should be able to do so by simply replying to this note. ----------------------- Message requiring your approval -------------------= --- Sender: "nicolas meeus" Subject: Re: Solmization 1. David Lewin is right that issues of solmization may be conceptualized quite differently in French and in English/German. It is a problem of which we have been aware in Paris, when working on solmization last year: we decided to use the alphabetical names in our discussions, which otherwise would have turned quite impossible. I have used the alphabet as a musical shorthand since years, so that I trust I can conceptualize solmization much as in English or German. There are other cultural splits, however. 2.1 One of them concerns "pitch class", an expression which has no satisfactory translation in French ("classe de hauteur" is awkward). I think, as a matter of fact, that there is something unsatisfactory in the concept itself, because it tends to calling a "class" something that is but a member of a class. As a class, pitch class "C" includes some eight or nine members, e.g. from C0 to C8 in American pitch notation. When we speak of "a C", or "in C", we actually think of none of these nine C's in particular, but rather of an abstract C without register. It is this abstraction that the expression "pitch class" rather improperly tries to denote. I have proposed the French "hauteur nominale", "nominal pitch", meaning the pitch insofar as it is designated by its name, without any implication of register. 2.2 Because of this, I had not fully grasped David's point whether UT was a pitch class for Bach. I do believe that that really is a matter of what you understand by "pitch class". In one way, a pitch class (or a nominal pitch) can exist only in a fixed solfege, because that is the only case where the name always refers to the same pitch or class of pitches. In 18th-century Germany, pitch classes in this first sense were denoted by the alphabetical pitch names. Solmization syllables, on the other hand, in both hexachordal and heptachordal solmization, were pitch classes (or nominal pitches) in another sense. Hexachordal classes included various degrees in each octave, in a rather complex and unstable way; and heptachordal nominal pitches applied to various degrees of the system, depending on the key. The ambiguity also is in the word "pitch" itself (for which, again, there is no simple French equivalent) which denotes either that characteristic which we associate with frequency, or a degree in a scalar unit (a hexachord, the diatonic system, and the like). 3.1 David indicates that his questions about the D major fugue were not historical. I feel however that we cannot avoid historical considerations, if only because our knowledge of solmization is second hand. If Bach's own manner of solmizing in any way is of concern to us, then the history of solmization must be taken in account. 3.2 The difficulties inherent in hexachordal solmization were strongly felt in the 17th century and various devices (among which the SI) were proposed to simplify it. One such device was to abandon the UT altogether (and the LA, or the RE, to a lesser extent), with the practical result that one returned to tetrachordal solmization. The rule of thumb was, for instance, that any note above SOL or LA (depending on whether the hexachords were a 4th or a 5th apart) was to be sung MI, and any note under MI was to be sung SOL or LA. Let me quote Thomas Morley (1597; I quote the Playford edition of 1730): "Now to sing your notes, you cannot use the words GAMUT, Are, etc., they being too long; therefore their meaning is contracted to these several short syllables, Sol, La, Mi, Fa; Ut and Re being left out, and are with less Confusion supplied with Sol, and La. It was the Ancient Practice [Morley, or Playford, probably means: to sing six syllables], and the French generally use it now, but this Modern Way [i.e. of singing four syllables only] is found less difficult to the young practicioner". J. Wallis mentions this practice in his edition of Ptolemy in 1682. And Burney (1789): "The ancients [i.e. the Greek] used likewise four different monosyllables ending with different vowels, by way of solmization, for the exercise of the voice in singing, like our mi, fa, sol, la". [This system apparently sometimes has been called the "Lancashire system": does anyone have information about that?] 3.3 I am not sure whether solmization was practiced with four syllables in Germany, but even singing with six syllables, it could happen that a major scale be solmized FA RE MI FA SOL RE MI FA, or FA SOL MI FA SOL LA MI FA, with the same name for the low and the high notes. 3.4 If I wrote that "a true hexachordal reading necessarily implies a (missing) C NATURAL", it is because I believed that the structure of Bach's subject necessarily implied a soft hexachord. I have been corrected on this point by Stefano, but I still believe that this reading is the more probable. It not only implies a C natural but, in hexachordal solmization, it also results in that the name of the G is (or may be) the same as that of the D, namely, FA or UT (depending on how you solmize). That is: G and D must have been felt as belonging to the same hexachordal class -- i.e. as sharing the same hexachordal function; in this way also, solmization may have stressed the tonal ambiguity of the subject. 3.5 David's argument, on the contrary, is to the effect that D3 and D4 (d and d' in English register notation) may have been perceived as belonging to different hexachordal classes, or that they were different nominal pitches. I am afraid this really is a question on which we cannot decide. 4.1 About the establishment of tonality, I would hate to have given the impression that I despise Schoenberg. On the contrary, I am quite interested in the idea of diatonic saturation because I believe that it has a long and interesting history. My own view of tonality is different, but it also stems from Schoenberg (namely from his classification of harmonic progressions, another idea which also makes a fascinating history). 4.2 I agree that "weak" may not be the right term to describe the initial statement of tonality. My point is that the key is first proposed in a veiled way (is that better?). The first four measures of Prelude I in WTCI expose a full "functional cycle", as Yizhak Sadai calls it, but sort of veiled by the fact that the voice progressions are conjunct and that the subdominant parallel and the dominant chords are not in root position. (To pretend that these chords are but the result of voice leading would neglect the fact that voice leading, in free writing, must conform to the rules of harmonic progression.) Note, by the way, that the D major subject in WTCII also implicitly proposes a "weak" functional cycle, tonic (D D D), subdominant (G B [E]), dominant seventh (A G) and tonic (F#). The last three notes, A G F#, certainly sound as 5 4 3 (or, as Christoph Wolff hears them, SOL FA MI), not 2 1 7. Nicolas Meeus Universite de Paris Sorbonne nicolas.meeus@paris4.sorbonne.fr=1A ------------- End Forwarded Message ------------- From rothfarb Tue Sep 1 11:19:22 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id LAA16401; Tue, 1 Sep 1998 11:19:21 -0700 (PDT) Date: Tue, 1 Sep 1998 11:19:21 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: (Fwd) Fugue and tonality (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: "Murray Dineen" Subject: (Fwd) Fugue and tonality Subject: Fugue and tonality Reply-to: pdineen@uottawa.ca Date: Mon, 31 Aug 1998 12:17:08 -0500 David Lewin's article on WTC II, no. 5, and Nicholas Meeus' comments are the subject of the following comments: 1. Rhetoric and Bach. By Bach's time, and presumably long before, any hexachord would have a certain ambiguity: should the next tone above la be a soft fa or hard mi? I wonder if this question--certainly a commonplace among composers and listeners of the day--took on a rhetorical dimension (and by the term rhetoric, I mean the current sense of a conscious conceit or literary technique, like irony). Like the flat 6th scale degree in 19th century music, implicit hexachordal usage (and there is no doubt in my mind that Bach's fugal subject imply somisation by their structure) takes on formulaic dimensions, measured against other, less formulaic structures, such as the system of evolving chromaticism that temperament is beginning to allow. In other words, any good composer in Bach's milieu (and presumably many a good listener) would have recognized the particular manifestation of the generic mi-or-fa-above-la problem in this fugue: "Ah, this is how Bach is framing the old question." The initial descending fifth might have proved startling in this respect, but there is much good expressionism in Bach, after all. 2. Fugal elucidation. If we allow the subject to be a rhetorical device, we might profit by considering the remainder of the work as a supplement--as an elucidation of the ambiguity, or a solution of the problem posed by the subject. Our listening composer might, having heard the subject and recognized the ambiguity, query inwardly: "Now I wonder how Bach will elaborate and effect an elucidation, how he will fill in this gap?" Since there are at least two possible supplements to the initial hexachord--mutation to a soft fa or to a hard mi--and these might, in Bach's day, be carried out at various transposition levels, this elucidation could take up the remainder of the fugue (indeed could be carried out in parallel in other fugues, with ambiguities or problems of a similar kind). I know little of the considerable rhetorical practices of Baroque music, and the notion of rhetoric I invoke here, accordingly, draws nothing from that conception. There are several threads in both Lewin's and Meeus' thoughts that suggest an informal rhetoric, of the kind I have mentioned, specifically Lewin para. 5 and 10, and Meeus' Greimasian notion of isotopy (although I think there is too much human calculation in rhetoric for it to work simply by recurrence). My suggestion is tie this rhetoric directly to the ambiguity of the single hexachord: to invoke a hexachord is a gesture that invokes with it a complex set of understandings (much like the initial move in a game of chess). 3. Fugal tonality. Bach's tonality I think of as being particularly complex and subtle--multifaceted with at least the following faces: 3a. A pitch-class gamut like that invoked by Lewin, but also a non-pitch class gamut, akin to medieval and Renaissance prototypes, with sometimes tripartite solmization indications, like C sol-fa-ut. The latter might bear some influence upon the questions raised by the composer in Bach's day, so that we might envision this composer querying: "Is this initial descending fifth D an ut-fa or an ut-sol?" Again, the remainder of the work might be considered an elucidation of this initial predicament. We take our modern pitch-class gamut for granted in application to modern music, but we need not do so for Bach's time, since the various temperaments and tunings then gave a rather unequal division of musical space. Here I refer not simply to the unequal temperaments themselves but moreso to the notion that a wolf sounding low on a keyboard or in some other scoring sounds quite different when compared with its counterpart transposed into much higher registers. There is an intriguing article in an early issue of Early Music that traces Bach's registral placement with regard to the wolves in a Werkmiester temperament, I believe. With a quick perusal of my Tovey edition, I find many supplementary sharps but not a flat. Does this mean that the keyboard would have been tuned with more sharps in mind (presumably D) than flats (presumably G)? Would a good, contemporary ear, hearing the rather low G# in m. 3, have detected this inclination toward the sharp side in the tuning, and added this to the list of clues in Bach's elucidation of the hexachord problem? 3b. Mode (but here I decline, leaving this to my betters, including my colleague Lori Burns, cited by Lewin in his MTO talk reply to Meeus). 3c. Hexachord (and possibly heptachord). Perhaps enough has been said on this for the moment. 3d. Species of tetrachord (and pentachord). These interval species are, perhaps, as rhetorical as the hexachord. They lie at the heart of modal distinctions with regard to a final, but by Bach's time modal distinction is sufficiently petrified to lend it the status of a rhetorical device, perhaps. More important, I believe, is the use of tetrachordal outlines to obtain variety in a work, and in particular to obtain chromatic variety. The rising fourth that spans beats one and two of m. 1 is, to me, a rhetorical gesture: what hexachordal syllables ought we to assign these notes? The subsequent two notes establish the tetrachord as a tone-semitone-tone type (E F# G A) with only one possible location in hexachordal space, re-mi-fa-sol, in a hexachord where ut is D. How ingenious of Bach to follow this hexachord immediately with two others, one involving G# (suggesting accordingly a hexachord on E) and then C# (suggesting a hexachord on A). In this way Bach, presumably, deepens the initial conceit (D or G; or Lewin's C natural or C sharp?). This kind of tetrachordal manipulation is produced by transposition, but it is an offshoot of invertible counterpoint at intervals other than the octave (since at these intervals tonal inversion often involves a change of tetrachord type), which would be second hand to a master of invertible counterpoint such as Bach. Familial obligations require me to interrupt this letter, but I shall try to conclude my comments in another posting. I need to discuss species of pentachord, the tenor-superius cadence, cross-relation, and then falling fifth basses, and a note about Schoenberg. Murray Dineen pdineen@uottawa.ca Department of Music University of Ottawa From rothfarb Tue Sep 1 11:19:54 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id LAA16408; Tue, 1 Sep 1998 11:19:54 -0700 (PDT) Date: Tue, 1 Sep 1998 11:19:53 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: (Fwd) Fugue and tonality (2) (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: "Murray Dineen" Subject: (Fwd) Fugue and tonality (2) Subject: Fugue and tonality (2) Reply-to: pdineen@uottawa.ca Date: Tue, 1 Sep 1998 13:00:18 -0500 Re: Solmization and fugal tonality Yesterday, Aug. 31, I posted a note with remarks about David Lewin's MTO article on the WTC II, no. 5, which I interrupted. Herewith the continuation of my remarks. Lee Rothfarb reminds me that this should fall under the rubric of MTO-Talk, so I shall copy my letters to that list. In essence, my suggestion is that hexachordal solmization might be looked upon not simply as a pedagogic or technical device by the time of Bach, but that it might have assumed a rhetorical import, as a conceit or "subject" proposed in the fugal subject to which the remainder of the work relates as elucidation. In this sense, the question that underpins Professor Lewin's discussion--C natural or C sharp (fa or mi) ?--captures the rhetorical hexachordal import of the subject. In my section 3, which I shall continue, I suggest that there are many other facets, apart from hexachord, that inform Bach's tonality, and some of these might well have been used in this rhetorical manner. 3e. Tenor-superius cadence. There are two obvious tenor-superius cadences later in the work, merely fortuitously in soprano and tenor voices on the first two beats of m. 27 and over the bar line between mm.32-33, and of course the ornamentation of the final cadence--the suspension in the alto voice against the soprano, which is a residue of the tenor-superius framework. Just why Bach invokes this cadence (as opposed to the fifth-falling-in-bass cadence, see m. 15 to m. 16) at these points is again a matter of conjecture, but I wonder if they are rhetorical flourishes designed to highlight various corners or regions of Bach's tonal space. Although the point is still moot, I believe the leading tone to which the suspended superius resolves would have necessitated a hexachordal "mi". In this (by now cliche) manner, Bach might have lent special emphasis to certain tones, such as the E sharp and F sharp of m. 27. Here I think I begin to approximate (and I recognize the tenuous nature of the approximation) something like Schoenberg's notion of an enriched and expanded musical space. The invocation of the tenor-superius cadence invokes as well a hexachordal context--new hexachords, in m. 27 one on C sharp and one on F sharp--that can be used to enrich the tonality (if indeed such was Bach's plan, caveat emptor). As I have suggested (and as Lewin and Meeus have suggested too), the fugal subject poses an ambiguity about musical space, by invoking rhetorically the hexachord. The tenor-superius cadences that I have pointed out, and their truncated counterparts (mm. 12-13 in bass and alto) take up that initial rhetorical gesture--C natural fa or C sharp mi? In m.27 Bach's answer is C sharp, but C sharp ut (and E sharp mi!). A scant six measures later Bach's answer would be C natural fa, if one argues from the tenor superius cadence to G. Bach the expressionist, again! 3f. Cross relations. Let me provisionally define "cross-relation" as the juxtaposition of two pitches belonging obviously to two different pitch collections. So for instance, F and F sharp must be cross related in a diatonic context. Accordingly we might call mi-contra-fa, B flat and B natural, cross related, or false related in a hexachordal context. I think of a cross relation as another type of ambiguity, akin to the missing note above a hexachordal la. It follows that Bach could have posed the question " C fa or C sharp mi?" by cross relation in his subject, instead of by omission. And I find it interesting that he takes up a tonally close cross relation--G natural and G sharp--in the continuation of his subject, mm. 2-3, which seems merely to deepen the rhetorical question C or C sharp. Now the cross-relation of mm. 2-3 is so benign as to hardly merit the label. But if we afford it rhetorical status, so that a composer in Bach's day might have wondered what Bach was about to make of it, the chromatically rich closing measures, starting circa m. 43 are rife with similar cross relation (see bass and soprano in m. 46 in particular). Rhetorically they form a kind of contracted catalogue of the principal chromatics touched upon in the fugue: to the flat side--D natural, F natural, G natural, and finally C natural; to the sharp side--D sharp, F sharp, G sharp, and finally C sharp. I wonder if a contemporary of Bach might not have admired this rhetorical flourish, built(as much of it is) on the ascending tetrachordal motive of mm. 2-3 (see the alto, last eighth of m. 45 to the downbeat of m. 46). I am enough of a post-structuralist to recognize humour and irony in this closing passage, but humour and irony are the offspring of rhetorical excess: the cross relation of mm.2-3 is demure; those of mm. 43ff uproariously humourous. 3g. Falling-fifth-in bass. I have already noted the cadential import of the falling fifth with regard to mm. 15-16, for example. In combination with the resolution of the tritone, the two would single mechanically (to follow Professor Lewin's citation of Browne, and of Brown and Butler) the tonality. But there is not a little rhetoric and humour I think in opening a subject with a descending fifth, enough so as to lift Marpurg's crust enladen eyes, as Christoph Wolff relates. Presumably our contemporary of Bach would have pondered the first notes: "D to G: sol to ut or ut to fa, now what will Bach make of this?" The real fifth of the answer would merely deepen the problem, especially with the G sharp in the subject's continuation shortly thereafter. If we return to Browne, and Butler and Brown, we have a problem in the opening measures: where's the tonally defining tritone? The problem is created by omission (Lewin's C or C sharp?) and by cross relation (my G or G sharp?) We need not be mechanistic about this, however, since I think Bach planned this rhetorically in his subject, and then appended a resolution in the last four measures (a resolution that would have made his contemporary smile perhaps), again rhetorically. To drive home the tonality, a composer must place the tritone correctly with respect to the framing fifth of the tonic and fifth scale degrees. I think it is, again, a rhetorical gesture on Bach's part to allude to the subject in the bass of m. 43 but to alter the descending fifth to a tritone (especially amid all the cross relation: the thing begins to sound uproariously funny--right out of Falstaff, both Shakespeare and Verdi). Tritones abound here (so much so that my Tovey edition can't quite decide the tenor part of m. 45), as if in lieu of that missing tritone which the subject poses (C natural-Fsharp or C sharp-G natural?), this coda seems to burst with them! I think the pentachord downward runs starting with the tenor in m. 47 elucidate both the tonality and the rhetoric, since the true tritone G-C sharp is given an outlined prominence across the bar line mm. 47-48, and the errant C natural is sequestered nicely by being buried in both pentachord and tetrachord in the latter half of m. 48. The falling fifth cadence of m. 50 is redundant rhetorically, because the tritone has already been fixed. _______________________ In my spontaneous comments above I have merely tried to extend the notion of rhetoric, which yesterday I tried to frame in light of the hexachord. It will be abundantly clear to some that I could have phrased my comments in terms of a narrative, and read Bach like a detective story (pace Cone): who done it, C or C sharp? Detective stories are, of course, filled with rhetorical gestures (as indeed are all genres, although not styles). Let me conclude with brief remarks about that most rhetorical of theorists, Schoenberg. Saturation is no doubt one way of expanding or filling a Schoenbergian tonality. But one aspect of the quarrel with Schenker, which surfaces in Schoenberg's Harmonielehre, deals with imitation. In the Roy Carter translation, on p. 385, Schoenberg notes that imitation is a primary process in the development of harmonic resources. I take him to mean by this that saturation is achieved by imitating diatonic events through non-diatonic tones. The crucial point--and here, correctly or otherwise, he takes Schenker to task--is that imitation need not be slavish. A secondary dominant need not resolve to a secondary tonic to expand the tonality. I take this to mean that the secondary dominant is a cliche--a rhetorical gesture--that achieves its purpose by mere allusion. Functioning rhetorically we need only here the secondary dominant to sense its potential resolution and recognize the allusion to a secondary region. Accordingly, tonality is produced not by mechanics alone--the correct resolution of the correct tritone--but also by a consciousness that treats mechanics critically. I think that Bach the retrogressive inherited a wealth of devices from the rich heritage of his ancestors, many of which he subjected to a kind of bricolage. In this he has much in common with Schoenberg. As a result I put rhetoric and the notion of ambiguity at the heart of my reading of the fugue. And, quite unlike Professor Lewin in his conclusion, I think the "idea that the Subject is 'missing' some C-or-C#" is anything but "tangential." Murray Dineen pdineen@uottawa.ca Department of Music Universite d' Ottawa PS: With respect to Joel Lester's posting, the Mizler translation of Fux (1742?) and Mizler's Anfangs-Gruende des General-Basses (1739?) I believe might elucidate the role of solmization in Bach's conception, although it has been some years since I perused those volumes. From rothfarb Tue Sep 1 11:27:48 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id LAA17504; Tue, 1 Sep 1998 11:27:48 -0700 (PDT) Date: Tue, 1 Sep 1998 11:27:47 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: Fw: Solmization (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: "nicolas meeus" Subject: Re: Solmization 1. David Lewin is right that issues of solmization may be conceptualized quite differently in French and in English/German. It is a problem of which we have been aware in Paris, when working on solmization last year: we decided to use the alphabetical names in our discussions, which otherwise would have turned quite impossible. I have used the alphabet as a musical shorthand since years, so that I trust I can conceptualize solmization much as in English or German. There are other cultural splits, however. 2.1 One of them concerns "pitch class", an expression which has no satisfactory translation in French ("classe de hauteur" is awkward). I think, as a matter of fact, that there is something unsatisfactory in the concept itself, because it tends to calling a "class" something that is but a member of a class. As a class, pitch class C includes some eight or nine members, e.g. from C0 to C8 in American pitch notation. When we speak of "a C", or "in C", we actually think of none of these nine C's in particular, but rather of an abstract C without register. It is this abstraction that the expression "pitch class" rather improperly tries to denote. I have proposed the French "hauteur nominale", "nominal pitch", meaning the pitch insofar as it is designated by its name, without any implication of register. 2.2 Because of this, I had not fully grasped David's point whether UT was a pitch class for Bach. I do believe that that really is a matter of what you understand by "pitch class". In one way, a pitch class (or a nominal pitch) can exist only in a fixed solfege, because that is the only case where the name always refers to the same pitch or class of pitches. In 18th-century Germany, pitch classes in this first sense were denoted by the alphabetical pitch names. Solmization syllables, on the other hand, in both hexachordal and heptachordal solmization, were pitch classes (or nominal pitches) in another sense. Hexachordal classes included various degrees in each octave, in a rather complex and unstable way; and heptachordal nominal pitches applied to various degrees of the system, depending on the key. The ambiguity also is in the word "pitch" itself (for which, again, there is no simple French equivalent) which denotes either that characteristic which we associate with frequency, or a degree in a scalar unit (a hexachord, the diatonic system, and the like). 3.1 David indicates that his questions about the D major fugue were not historical. I feel however that we cannot avoid historical considerations, if only because our knowledge of solmization is second hand. If Bach's own manner of solmizing in any way is of concern to us, then the history of solmization must be taken in account. 3.2 The difficulties inherent in hexachordal solmization were strongly felt in the 17th century and various devices (among which the SI) were proposed to simplify it. One such device was to abandon the UT altogether (and the LA, or the RE, to a lesser extent), with the practical result that one returned to tetrachordal solmization. The rule of thumb was, for instance, that any note above SOL or LA (depending on whether the hexachords were a 4th or a 5th apart) was to be sung MI, and any note under MI was to be sung SOL or LA. Let me quote Thomas Morley (1597; I quote the Playford edition of 1730): "Now to sing your notes, you cannot use the words GAMUT, Are, etc., they being too long; therefore their meaning is contracted to these several short syllables, Sol, La, Mi, Fa; Ut and Re being left out, and are with less Confusion supplied with Sol, and La. It was the Ancient Practice [Morley, or Playford, probably means: to sing six syllables], and the French generally use it now, but this Modern Way [i.e. of singing four syllables only] is found less difficult to the young practicioner". J. Wallis mentions this practice in his edition of Ptolemy in 1682. And Burney (1789): "The ancients [i.e. the Greek] used likewise four different monosyllables ending with different vowels, by way of solmization, for the exercise of the voice in singing, like our mi, fa, sol, la". [This system apparently sometimes has been called the "Lancashire system": does anyone have information about that?] 3.3 I am not sure whether solmization was practiced with four syllables in Germany, but even singing with six syllables, it could happen that a major scale be solmized FA RE MI FA SOL RE MI FA, or FA SOL MI FA SOL LA MI FA, with the same name for the lowest and the highest notes. 3.4 If I wrote that "a true hexachordal reading necessarily implies a (missing) C NATURAL", it is because I believed that the structure of Bach's subject necessarily implied a soft hexachord. I have been corrected on this point by Stefano, but I still believe that this reading is the more probable. It not only implies a C natural but, in hexachordal solmization, it also results in that the name of the G is (or may be) the same as that of the D, namely, FA or UT (depending on how you solmize). That is: G and D must have been felt as belonging to the same hexachordal class -- i.e. as sharing the same hexachordal function; in this way also, solmization may have stressed the tonal ambiguity of the subject. 3.5 David's argument, on the contrary, is to the effect that D3 and D4 (d and d' in English register notation) may have been perceived as belonging to different hexachordal classes, or that they were different nominal pitches. I am afraid this really is a question on which we cannot decide. 4.1 About the establishment of tonality, I would hate to have given the impression that I despise Schoenberg. On the contrary, I am quite interested in the idea of diatonic saturation because I believe that it has a long and interesting history. My own view of tonality is different, but it also stems from Schoenberg (namely from his classification of harmonic progressions, another idea which also makes a fascinating history). 4.2 I agree that "weak" may not be the right term to describe the initial statement of tonality. My point is that the key is first proposed in a veiled way (is that better?). The first four measures of Prelude I in WTCI expose a full "functional cycle", as Yizhak Sadai calls it, but sort of veiled by the fact that the voice progressions are conjunct and that the subdominant parallel and the dominant chords are not in root position. (To pretend that these chords are but the result of voice leading would neglect the fact that voice leading, in free writing, must conform to the rules of harmonic progression.) Note, by the way, that the D major subject in WTCII also implicitly proposes a "weak" functional cycle, tonic (D D D), subdominant (G B [E]), dominant seventh (A G) and tonic (F#). The last three notes, A G F#, certainly sound as 5 4 3 (or, as Christoph Wolff hears them, SOL FA MI), not 2 1 7. Nicolas Meeus Universite de Paris Sorbonne nicolas.meeus@paris4.sorbonne.fr ------------- End Forwarded Message ------------- From rothfarb Wed Sep 2 10:32:43 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id KAA04765; Wed, 2 Sep 1998 10:32:42 -0700 (PDT) Date: Wed, 2 Sep 1998 10:32:41 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: Re: Solmization (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: stefano mengozzi Subject: Re: Solmization I would like to contribute further to this discussion by addressing two questions asked by Joel Lester: "What COULD it mean for a musician to be fully comfortable with mutating hexachordal solmization and NOT relate that to diatonic space?" and "How could the hexachord NOT have been meant to be an audible element of musical space, since the whole point of solmizing was (is!) to make the intervals 'audible' conceptually?" I think the answers to these questions depend on what we mean by the expression "making the intervals audible conceptually." I believe we have two options, which I would preliminary call "weak" and "strong," which entail two different ways of relating hexachord to diatonic space. One may view hexachords in the "weak" sense that Guidonian syllables were attached to pitches regardless of where these pitches occur in the diatonic space. Take the two syllables RE-MI: they could designate the interval D-E, regardless of whether it falls between 1 and 2 in the D mode, 2 and 3 in the C mode, 4 and 5 in the A mode, and so forth. According to this reading, the fact that the syllables RE and MI correspond to the 2nd and 3rd positions within the hexachord was all but irrelevant, because the location of the major second within the diatonic space is determined by other factors, such as cadences, melodic contour, or mode. One may reasonably wonder, what is the point of using hexachords if the position of pitches within them is irrelevant? My answer is that the first and foremost goal of solmization was to help untrained singers execute intervals correctly, and that it was good enough for these syllables to get a novice to sing correctly whatever interval after identifying it on the page. Alternatively, one may argue that the function of hexachord was to "make the intervals audible conceptually" in the "strong" sense that, by assigning specific syllables to those intervals, it also superimposed a grid of hexachordal scale degrees onto them, a theory which leads directly to the conclusion that hexachords were also *audible* structures. I would like to question this interpretation Nicolas Meeus understood me right as the result of misconceptions that are unsupported by historical evidence (as I have tried to argue in my review of Lionel Pike's *Hexachords in Late-Renaissance Music* in the April issue of MTO). For example, I cannot find any secure indication in the theoretical literature that mutations were *embodied* in the musical notation, as if waiting to be recognized and "savored" by the performer, just as centuries later we hear tonal modulations. On the contrary, performers were customarily instructed on how to *make* mutations in the most convenient way, following certain rules of thumb, which is why there is nothing wrong with different singers mutating at different points. It seems to me that mutations were perceived in the Middle Ages and Renaissance as a shortcoming of the system, rather than as a meaningful musical event. Someone like Johannes Gallicus [1460's] spoke very clearly of "mutationum deliramenta," and it seems to me that one can read subsequent contributions to solmization theory, from Ramos to Heyden, from Waelrant to Banchieri, as attempts to minimize, or bypass, the *problem* of mutating between hexachords. Prof. Meeus embraces a "strong" view of hexachord when he claims that "singers and players of monodic instruments... in the Middle Ages and the early Renaissance at least, must have conceived the diatonic space as a complex concatenation of hexachords (rather than a simple concatenation of octaves)." Again, I wonder what reasoning is behind that categorical "must have conceived." By the time Guidonian solmization comes onto the stage, beginning from ca. 1100, there is a whole repertory of chant and polyphony that was still performed daily (and will be so for centuries afterwards, in some cases until today), as well as theories of intervals, consonance and dissonance, counterpoint, and modes. All of this came into being without hexachords. If we accept the thesis that "Guidonian" singers of, say, 1200 began conceptualizing the diatonic space hexachordally as a result of their daily solmizing practices, then the conclusion is that they also started hearing mutations where there was none in other words, that they completely mis-heard the pre-Guidonian repertory just as, today, we are supposedly missing a lot in pre-18th-century music by failing to hear hexachords and mutations. But then, how can you hear something that does not exist? Furthermore, if I understand correctly Prof. Meeus's argument, then I have conclude that my sense of musical hearing as a 20th-century Western listener makes me more qualified to listen to early Indian music, based on the seven svaras, sa, ri, ga, ma, pa, dha, ni, than J.S.Bach's WTC. (I see the problem of adjusting to the Indian tuning system as much more manageable than that of reconstructing my diatonic mindset in terms of overlapping 6-note segments.) Forgive me if I am missing something here, but I find this to be simply grotesque. We know that J.S.Bach refers to solmization syllables in the preface of WTC 1, as Prof. Meeus has already pointed out. But shall we conclude from this, following the "strong" reading of hexachord that I have outlined above, that exactly half of Bach's preludes and fugues in WTC namely, all of those in a minor key end on the second degree of some 6-note segment namely, RE? By which rationale is hexachord able to define as tonic now its first degree (UT), and now its second (RE)? If we agree that a tritone is needed to define a tonic, how can a tritone-less diatonic segment do just that? Since when does a tonic fall on 2? Are hexachordally-aware Roman numeral analyses just around the corner? Are Guido 101 classes going to be part of the undergraduate ear-training curriculum any time soon? In the subject of the D major fugue, I agree that the opening interval tends to suggest G as tonic, but I disagree with Prof. Meeus that it is so because it would most likely be solmized SOL-UT in the G hexachord, because the collection of pitches of the G hexachord (G-A-B-C-D-E, accepting for a moment the problematic statement that Guidonian hexachords consist of actual *pitches*) is also found in scales other than G major, notably C major, A minor, if only in part, and (descending) E minor. Again, UT is not necessarily the tonic, nor the only "seat" of a tonic, in Guidonian solmization. So, it seems to me that our perceiving G as a temporary tonic at the beginning of the Subject of this fugue cannot depend exclusively on hexachordal considerations. Rather, it is possible that the relationship should be reversed: because the opening two notes of the Subject (due either to their rhythmic placement, as Prof. Meeus has observed, or to our being used to hear a descending fifth as implying a V-I progression, or both) suggest a passing tonicization of G i.e., the pitches D-C-B-A-G it makes sense to solmize that opening interval in the G hexachord, if for whatever reason we decide to solmize that Subject hexachordally. Stefano Mengozzi University of Chicago men8@midway.uchicago.edu From rothfarb Fri Sep 4 08:20:23 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id IAA03572; Fri, 4 Sep 1998 08:20:22 -0700 (PDT) Date: Fri, 4 Sep 1998 08:20:22 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: solmization (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: "Murray Dineen" Subject: solmization With regard to strong and weak views of hexachords and solmization: 1. The lack of collaborative theoretical contemporaries is a well meant caution, for which we thank Professor Mengozzi. But whether we must treat theorists' testimony as exhaustive--or lack thereof as proscriptive--is surely a moot point. Having met theorists and their preoccupations in our time, I know it quite possible that great parts of a musical work's being elude theoretical discussion, but are worked out theoretically in the field by composers and performers, often under the influence of long lapsed theoretical assumptions. There are at least two kinds of history--one of which Collingwood disparages as armchair, the other he lauds as fieldwork, if I recall correctly. The two are not incompatible--or need not be--but can be complimentary. 2. It seems not unthinkable that a practice of hexachordal solmization might have largely eluded theoretical notice as a commonplace, only to resurface here and there--Joel Lester's Albrechtsberger citation being a case in point. Neither first (c. 1825) nor second (c. 1837) edition of Albrechtsberger's "...saemmtliche Schriften ueber Generalbass, Harmonie-Lehre, and Tonsetzkunst...." makes reference to solmization, as far as I can tell in a brief perusal. But that may, perhaps, be the product of both editions' editor, Ignaz von Seyfried, who might have sanitized solmization references, finding them too arcane for a developing readership of amateurs. If such it the case, then so much for the accuracy of the historical record. Theorists of history could well apportion their grains of salt equally between testimony and projection--the two being the twin pans of the scales of historical justice. Murray Dineen pdineen@uottawa.ca From rothfarb Fri Sep 4 08:21:12 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id IAA03579; Fri, 4 Sep 1998 08:21:11 -0700 (PDT) Date: Fri, 4 Sep 1998 08:21:10 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: somization (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: nicolas.meeus@paris4.sorbonne.fr (Nicolas Meeus) Subject: somization Stefano Mengozzi is perfecly right that I embrace a "strong" view of hexachord when claiming that "singers and players of monodic intruments, in the Middle Ages and the early Renaissance at least, must have conceived the diatonic space as a complex contatenation of hexachords". My wording "must have conceived" was meant to convey that this is a conviction rather than a certitude, as in the French equivalent, "doivent avoir conc,u". I'd be very sorry if this sounds "categorical" in English: that was not my intention. On the other hand, I can but confirm my conviction. Stefano Mengozzi is aware that several medieval and Renaissanc theorists state that the finals of the modes are RE, MI, FA, and SOL (rather than D, E, F, and G). It is true that they form only a minority, but the medieval doctrine of the *affinitas* proves that other theorists similarly thought that notes sharing the same hexachordal properties as D, E, F and G could be used as alternative finals. I believe, therefore, that the "strong" reading of hexachordal theory is amply supported by historical evidence. As to Bach's mention of solmization syllables in WTC I, I fail to see how it could mean anything else than that "exactly half of [his] preludes and fugues in WTC, namely all those in a minor key, end on [...] RE". I also believe that cases exist where mutations clearly are embodied in medieval or Renaissance notation. More than once, accidentals are placed at the point of mutation, instead of next to the note they concern. More generally, an accidental flat or sharp, denoting a FA or a MI, often is a token of mutation; and it could be argued that accidentals were notated mainly in such cases where the mutation was not obvious. It is striking, besides, that the "rule of the last flat or sharp" that I mentioned before has almost exactly the same effect -- but for the essential fact that, in a heptachordal context, it means a change of octave, thus of key, instead of hexachord. To view solmization as an 11th century theory grafted upon a repertory where it had no place is in my opinion a gross misunderstanding of the role of theory in general, and of solmization in particular. I won't even discuss the first point (we all know, say, that the validity of Schenkerian theory does not depend on the knowledge that tonal composers had of it). As to the second point, it must be realized that hexachordal solmization is but one formulation of a particular way of thinking that, at some point in the history of music, may have been almost universal: tetrachordal thinking. The history of Occidental theories of the diatonic system could be written as the history of a tension between tetrachordal and heptachordal thinking. Both are documented at an early stage in history, so that it is not too difficult to find evidence for or against any of them. But no historical account would be complete that would dismiss one in favour of the other. The tetrachord is the least group of intervals, the repetition of which allows describing the diatonic scale as a whole; the price paid for this economy is that the concatenation of tetrachords forming the scale must be alternatively conjunct and disjunct. The hexachord is the maximum extension that can be given to this basic unit without destroying the principle of alternative conjunction and disjunction (which, in particular contexts, had its advantages). The heptatonic conception simplifies the principle of concatenation, but at the price of being based on a unit of seven notes instead of four. That this is conception prevails today by no means renders the other one "grotesque". >From a tetrachordal point of view, the diatonic scale is a (complex) concatenation of four tetrachordal "qualities". Guido discusses these qualities at great length in the *Micrologus*, where he names them *modi vocum*, "modes of the voices". It appears, then, that the modal classification of a melody depends on the *modus*, the tetrachordal quality, of its final (which, of course, determines the quality of the other notes). And the reason why our Occidental theory knew four (groups of) modes is that there are four qualities in a tetrachord. This conception stresses characteristics of the diatonic system and of its degrees before those of individual modes. Our modern conception on the contrary, because it takes the chromatic scale as its background, tends to view the modes as sub-sets of the background system (the degrees of which hardly could be differentiated by individual intervallic characteristics) and the intervallic qualities as characteristics of each of the modes. This is one cause of our difficulty to understand modality. For a modern conception that is closer to the ancient one, see Jacques Handschin, *Der Toncharakter*. Bach belongs to a transitional period of this history, so that it is difficult to ascertain exactly what his position was. I like Murray Dineen's idea that the reference to hexachordal solmization, that seems unescapable in several of his composition, may have been a rhetorical quotation of something considered archaic. Nicolas Meeus Universite de Paris-Sorbonne nicolas.meeus@paris4.sorbonne.fr From rothfarb Sun Sep 6 15:34:09 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id PAA24482; Sun, 6 Sep 1998 15:34:08 -0700 (PDT) Date: Sun, 6 Sep 1998 15:34:07 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: Schenker and fugue Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: David Lewin Subject: Schenker and fugue NOTE: David Lewin sent the following message recently directly to a "hypermail" address, and it was entered on the mto-talk hypermail page. The figures in [2] and [8] are misaligned in the hypermail posting because the HTML tagging done by the hypermail software does not, unfortunately, observe multiple spaces (or tabs) to create table-like figures. mto-talk subscribers should refer to the version below in order to understand Professor Lewin's comments. Professor Lewin sent two other postings which were not distributed to mto-talk subscribers. They will follow soon. Please send all mto-talk postings to mto-talk@smt.ucsb.edu rather than to a hypermail address. -- Lee A. Rothfarb, Boethius System Administrator (interim 'talk' manager for Jay Rahn) Lewin's most recent posting: [1] I'm somewhat surprised that nobody has yet advanced a Schenkerian rationale for hearing the fugue subject "in D," so I shall try to supply some pertinent commentary here. [2] Taking as a model Schenker's analysis of the cm fugue subject from Book I, one might try to claim that the melody "proposes" the key of D by outlining the following harmonic progression: D (C# D) B A A G G F# E D DM: IV ii V I (As in Schenker's model, the parenthesized notes of the progression, "implied" by the harmony, materialize in the appropriately transposed-and-inverted counterpoint for the answer.) [3] I think there is no doubt that "we" (in 20th-century European-American culture) do hear the indicated harmony in the melody, and that this has a good deal to do with our hearing the G-F# of the Subject as a FA-MI (of some D structure), not an UT-SI (of some G structure). [4] The progression, however, does not determine in itself, to what extent its final D harmony is an overall tonic for the phrase as a whole, or an overall dominant. In paragraph [2], I tendentiously slanted the fundamental-bass (Roman numeral) analysis, to assert _a priori_ that the D harmony was a tonic. But there is nothing in the progression-of-the-phrase itself, to indicate that the Roman numerals might not equally well (or perhaps even better) be read as GM: I, vi= DM:ii, V, I. Or even as GM: I, vi, V/V, V. [5] The progression-in-itself thus seems to me to project D as the weightiest Stufe of the phrase, but not necessarily as the overall tonic. Not, that is, unless one tries to add a rule to the effect that the most-heavily-tonicized Stufe of a WTC fugue subject (or the last-tonicized one) is de facto to be heard as a tonic. But that rule would be difficult to maintain in the face of other subjects, that clearly end on heavily tonicized dominants (e.g. EbM Book I). [6] All this said, I think one gets a lot of value for analysis of the (entire) fugue itself, from a Schenkerian approach to the progression of paragraph [2] (or paragraph [4]) above. The ambiguous Roman-numeral analyses are not so much the point -- indeed one finds talk already in Kirnberger and Marpurg, of inferring such harmonic structures from fugue subjects. The special value of Schenker's work here, for me, lies rather in his inferring and discussing, from such a harmonic progression, _thematic middleground voice-leading gestures_. [7] I would like to comment a bit on Schenker's discussion of the cm fugue subject from Book I, from that point of view. Schenker criticizes A.B. Marx for inferring, from the regular metrically accented notes of the subject, a sort of "cantus firmus" linear gesture of Ab - G - F - Eb. Schenker does not consider that gesture relevant to a good hearing of voice leading. I recall, when I was first learning to play the fugue, how disappointing it sounded when -- hearing like Marx -- I heard the opening Ab of Marx's cantus firmus "resolving" to the motivically parallel G that comes next in his cantus firmus. No _Spannung_ (tension) remains, and one vaguely wonders,while playing: what need continue from here? [8] Schenker's analysis addresses exactly that point. He reads: D (C) C C (C B C) G Ab Ab G G G(p!) G(p) F F Eb cm: i iv! ------(ii?)------- V i [9] The G in the third column of the figure above -- Marx's cantus-firmus G -- is heard by Schenker as a _passing tone_ within a dominant-preparation harmony. Rather than resolve the preceding Ab, the G passes on down to F, maintaining the _Spannung_ of the Zug Ab-G-F within the iv (or ii) harmony. Hearing the G _this_ way, no performer will feel "why continue?"! The Zug is highly thematic for Schenker: it prepares the rising figure F-G-Ab that follows in the foreground, and the immediate response to that figure by the foreground cadential gesture G-F-Eb. David Lewin lewin@fas.harvard.edu Music Dept., Harvard, Cambridge, MA 02138 617/495-2791 fax 617/496-8081 From rothfarb Sun Sep 6 16:37:36 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id QAA27916; Sun, 6 Sep 1998 16:37:35 -0700 (PDT) Date: Sun, 6 Sep 1998 16:37:34 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: Re: Meeus's reply to my fugue article (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: David Lewin Subject: Re: Meeus's reply to my fugue article [1] Thanks to Nicolas Meeus for his lively interest in my Bach fugue article, and for his many suggestive and informative remarks. [2] In my article, I meant to propose Issues (A) and (B) below for consideration. Issue A: How might _I_ (DL), in my own historical - cultural context, be able to hear the subject of this particular fugue (in itself, as a rhetorical "proposition") to be "based on D" in some sense, rather than "based on G"? Issue B: Is it conceivable that _Bach_, in _his_ historical - cultural context, might have listened to the subject in a manner related, in some way, to the mode-of-listening I find suggestive as I respond to Issue A? [3] In approaching those issues, I do not feel that historical norms from 17th and 18th century France can offer decisive assistance, though the story of their development is important and interesting. As Nicolas points out himself, his "... information concerning Germany probably is incomplete ... ." In this regard I have relied for advice on Professor Wolff, being myself quite hopelessly inexpert on such matters. [4] But there is a more general problem, in an appeal to contemporaneous historical norms of _any_ sort. The problem is that Bach's treatment of the subject-and-answer, in this fugue, was considered to be _abnormal_ by such a sympathetic contemporary and follower as Marpurg. My quotations from Marpurg were not just for local flavor. The point is that Marpurg finds Bach's procedure inexplicable, and specifically warns students away from it. And Marpurg is not just any old writer, in this connection. His _Abhandlung_ was the definitive text on fugue-writing for German readers for many years -- indeed Schenker's article on the c minor fugue from Book I specifically cites Marpurg, and treats Marpurg with respect. Marpurg's acquaintance with German 18th-century theory and theorists was certainly much more than adequate. Reference to the critical literature will make that very clear. Then, too, Marpurg was regarded in his own time as a particular authority on the practice of J.S. Bach. The heirs of Bach, for example, asked Marpurg to write the preface for _The Art of the Fugue_, upon the first publication of that composition. [5] So if Marpurg was unable to find, in the canonical music theory of his own time and place, a theoretical reason for the behavior of Bach's fugue subject, I doubt that we shall do much better by searching that and other canons ourselves. It seems to me that, in approaching Issue B above, we must take note of such canons insofaras they might have been _influencing_ the ways in which Bach heard and thought about what he was doing -- e.g. providing terminology and syntax within which he might have been formulating his musical and intellectual ideas. On the other hand, I do not see that we can suppose he was _obeying_ some particular canon of the sort -- in that case, Marpurg would surely have had more to say on the particular subject. [6] The French convention of "the last SI," that Nicolas discusses, is very interesting, but again it does not seem quite to address the Issues of paragraph [2] above. It certainly tells one how to _perform_ solf'ege, given a score. But it does not address how to solf'ege what one _hears without looking at a score_ -- a matter central to my Issue A. Nor does it address how to solf'ege a tune one is _composing_, in particular what key signature to visualize -- a matter central to my Issue B. So Nicolas's remark, that "the C sharp in the signature would have determined the first D to be read UT ...," is somewhat beside the point: Bach _wrote_ the signature; he didn't "read" it; I used to _hear_ the theme "in G," without visualizing either a one-sharp or a two-sharp signature as I was listening in my imagination. (At least so I believe in reminiscence.) I should say that I am not opposed to the idea of "Augenmusik" as such, but I don't think it approaches Issues B or A very adequately here. [7] Nicolas thinks I seem confused, when I ask "Was UT a pitch class for Bach, in the way that DO is for us in modern solf'ege?" He goes on to talk about fixed-DO versus moveable-DO, as if this were the issue. I did not mean to create that impression. What I meant was that for us, a "DO" is a "DO" in any register. So, e.g., in singing up a major scale, we will solf'ege DO-RE-MI-FA-SOL-LA-SI-DO, giving the high DO at the end of the performance the same syllable as the low DO at the beginning. A hexachordal performance might, however, proceed as UT-RE-MI-FA-SOL-RE-MI-FA, or as UT-RE-MI-FA-UT-RE-MI-FA. Other sorts of mutation are possible under other mutational conventions, and that issue is quite complex, especially spread over history and geography. Regardless of the particular mutation used, though, the highest hexachordal note would always be a FA, because the semitone at the high end of this passage would have to be a MI-FA (there being no SI in the hexachordal picture). Thus from a hexachordal point of view, the octave above the low UT of this (complete) scale would be not an UT-in-a-different-register, but a FA. So "UT" is not a pitch class in _that_ sense: if one sings a note as hexachord-UT, and then sings a note an octave higher, the higher note will be not an UT, but some other _vox_. (In case we are imagining filling in a complete major heptachord, the _vox_ must be a FA; if we do not fill in the complete modern-major scale, the _vox_ might be something else -- e.g. a SOL of the plagally related hexachord, as I suggest in my article.) In contrast, if we sing a DO in modern solf'ege and then sing a note an octave higher, we will sing it as DO, whether or not we are mentally supplying the filling-in of the octave through a major scale. In this connection, it is irrelevant whether we are using "fixed DO" or "movable DO." [Hexachordal] "UT," in sum, means not a note some number of octaves away from a given "UT", but rather a note at the bottom of some (any) pertinent hexachord. [8] That is what I was getting at in the way I was mulling over my "unmutated" and "mutated" versions of Bach's theme. I like very much Nicolas's discussion of the problems they raise, which engage from his point of view my questions as to whether a C-or-C# is "missing," or rather whether we may not be in some sort of _musica recta_ situation, where either C or C# is equally available, but equally non-obligatory. I am not sure, though, in what sense "a true hexachordal reading necessarily implies a (missing) C NATURAL, instead of a C sharp." The "implication" seems to be the rather Schenkerian idea that a leap somehow implies all the passing tones that fill it in diatonically (here, within the pertinent hexachord). I wonder to what extent hexachordal _voces_ (in this or that historical period and place -- or in Bach's own ear) can be supposed to behave in that fashion. [9] In his second posting, Nicolas follows this up very brilliantly, by suggesting: "should one not wonder whether avoiding the 7th degree is not a "mixolydian" gesture ... ?" The idea occurred to me too, as I was pondering Nicolas's first posting. It makes me think of a topic covered by Lori Burns, in her study of Bach's harmonizations for "modal" chorale melodies. Not infrequently, as she observes, one finds some harmonization of a Mixolydian melody as if it were in modern major -- in which case Bach generally writes the extra sharp in the key signature (e.g. one sharp for "G major"). And not infrequently too, one finds another harmonization of the same melody as if it were in a strict Mixolydian mode -- in which case Bach generally writes one less sharp in the key signature (e.g. no accidentals for "G Mixolydian"). At times it is difficult, even within one particular harmonization, to pin the modality down to "modern major" or "Mixolydian," and it is not always clear why the key signature has one more or one less accidental. The behavior that Burns describes, vis-'a-vis chorale harmonization, seems to resonate very well with the idea of Bach's leaving the 7th degree out of his fugue subject at its initial appearance. [10] I am moving on now, generally, to Nicolas's second posting. Nicolas states my positions too strongly when he refers to my assumptions, past and present. The title of my article has a question mark at the end of it, and I put it there with some deliberation. So I wouldn't say that the title of my article makes "evident" my "more general assumption" that "tonality, in general, is a matter of the saturation of a 'tonal space' of some kind." Indeed the question-mark of the title hedges my bets even as specifically regards the subject of the fugue under discussion. The title means to suggest something like this: Do we get a sense, in "The D Major Fugue Subject from WTC II," that some sort of metaphorical space is being "saturated"? The title is _not_ "Tonality as Spatial Saturation." I cannot imagine ever wanting to write such an article. Nor is the title even "Spatial Saturation in the Subject of the D Major Fugue ... " Rather, the title points to the D major fugue-subject from WTCII, and then _asks_, "Spatial Saturation?" My intent was not to prove anything about how one "ought to" hear the tune (much less about The Nature of Tonality), but rather to stimulate thought and listening among readers -- exactly the sorts of thought and listening that Nicolas's remarks exemplify. [11] In referring to my "covert assumption that traditional Tonality is expressed by exposing a complete diatonic gamut," I meant to indicate that my assumption had not been conscious, that it had made me think of C-or-C# as somehow "missing," and that it had led me to think in ways I later considered inadequate, when I listened to and analyzed the opening of the fugue. Far from trying to promulgate this "covert assumption," I meant to _repudiate it_ as a generality about Tonality, and even to suggest repudiating it as an aid for analyzing the fugue subject. (I think I sense that Nicolas is less willing than I am, to "let go" of the "missing" C-or-C#.) [12] I quoted from Schoenberg because he was an influential source for me at an early age. Surely we should regard Schoenberg's ideas with respect and interest, however we come to modify or reject this or that one over the course of our lives. I am now 65 years old, and have been teaching music theory -- at undergraduate and graduate levels -- for thirty-seven years; I have changed my attitudes to a number of things that profoundly influenced me from fifty-five to forty-eight years ago, though I think it would be _falsch_ to pretend to myself, that by modifying my attitudes I have completely freed myself from such influences. Schoenberg's own idea about diatonic "saturation" is still interesting for me, not only because Schoenberg himself is, and because his music is as thrillingly compelling for me as ever, but also because the idea I quoted interacts for me in a suggestive way with Schoenberg's involvement in total chromaticism. [13] All that said, it is manifest that many of Bach's fugue subjects (for keyboard in particular) _do_ "define the key" in some way, and that the subject for the DM fugue of WTCII is quite unusual in that regard, not only because it does not adequately "define the key (of D)" but even more because it ambivalently suggests a different key. The quotation from Marpurg speaks directly to those points -- and refers specifically to a "rule that requires a fugue theme to indicate the key unambiguously ([eine] Regel, welche einen deutlichen und die Tonart gehoerig anzeigenden Fugensatz erfordert)." [14] Well, how _does_ a typical (Bach) fugue subject "indicate the key"? I do not see any easy generalization on this. In some cases one particular diminshed interval seems to be sufficient. I am thinking of the c#m fugue in BookI; the remarks on diatonic tritones in Note 2 of my article seem also appropriate in this regard -- e.g. the E#-B in the d#m fugue of BookI "indicates the key" of its RE, d#, even though the B must be solf'eged as a "FA super LA." In some cases, a hexachord seems sufficient in itself (CM Book I, DM Book I). In some cases a complete major or minor heptachord of some species -- allowing "harmonic minor" -- is presented (cm BookI, C#M Book I, dm Book 1). And so forth. Other cases seem mixed: for example, the EbM fugue in Book I first presents the complete Eb hexachord, and then modulates to present the complete BbM scale. Here the _low_ UT at the beginning seems important, in its capacity as the low note of its hexachord (and of the subject); by the time we get to what _would_ be a "SI" in Eb major, we are hearing the tone as a MI, not a SI. The example nicely illustrates Nicolas's law of "the last SI": A-natural, in the middle of the subject, pre-empts the SI function from the later D. [15] In this context I do not find it farfetched to think that _one_ of Bach's devices, for "indicating a major key" via a fugue subject, is to expose the hexachord of which the tonic is the low UT. And such an exposition is indeed manifest in the DM fugue subject of BookII, once we are past its problematical opening leap. That noted, all sorts of solf'ege questions and complications come into the picture, as I suggested and as Nicolas has discussed in great detail at greater length. [16] Nicolas refers to a D hexachord, transposed beyond the C, F, and G hexachords, as "a concept utterly foreign to medieval solmization." This is not much to the point as regards Bach's practice. The Hughes article on Solmization in _The New Grove_ (cited in NOTE 5 of the present document) includes discussion of "ficta hexachords" during the Renaissance, necessitated by solmizing conventions observed in Ockeghem's _Missa Mi-mi_, and other such compositions (p.462). [17] "My own view of tonality is that it is never decisively determined. Tonality is a dynamic process; it builds up ... I believe that a tonality can never be established in a few notes or a few measures. .. tonal compositions often begin with a weak statement of the tonality, a statement that is late confirmed, then put to test." Well, yes; sure. We are living after Hegel, Moritz Hauptmann, and Schenker. But Bach was living before them. In Nicolas's observations above, I think the key word is "established," and I think its source, in his discourse, is my Schoenberg quotation -- or rather the title of the section in the _Harmonielehre_ ("Establishment of Tonality") from which the quotation comes. [18] Rather than "_inidicating_ a key" (my translation of Marpurg's "[eine Tonart] anzeigen") or "Establishing a Tonality" (Schoenberg), I suggest here that a Bach fugue subject typically "proposes" a key. I like that term better than Nicolas's idea of beginning with a "weak statement". "Weak" carries unfortunate metaphorical baggage in this context -- one wouldn't want to begin performing a piece with the idea that there is something "weak" about the music one is playing. The idea that a Bach subject "proposes" a key fits in well with the ideas and categories of rhetoric, and the term is not very far from a possible alternate translation of Marpurg's "anzeigen." The problem at hand, then, is that theSubject of the fugue under discussion seems either to propose a key of G that is not later confirmed (even and particularly by the real Answer!), or else to waver ambivalently between two different keys, unambiguously "proposing" neither the one nor the other. My Issue A, then, becomes this: (a)is the Subject "proposing" _something_ about the organization of its tones? (b)Something that makes the tone D referential in any sense? (c)And if so, what is the "proposal," and what is the "sense"? I draw readers' attentions to the question marks in the immediately preceding text above, and to the posing of three separate (serially posed) questions. [19] A note on Christoph Wolff's hearing: he tells me that a very determinative thing for him, is that he hears the G-F# in the final figure of the Subject completely unambiguously, as a FA-MI (and not a possible UT-SI). He then solmizes that figure to himself, wherever and whenever it appears in the fugue -- which is all over the place -- as a motivic movable-DO (or movable-UT) RE-SOL-FA-MI. [20] In the course of studying Nicolas's remarks I became aware of a interesting cultural split, in the ways he and I are thinking about and listening to, the matters under discussion. The split is not so much between the idea of fixed-DO and moveable-DO. After all, the U.S. theoretical and pedagogical literature has many examples of both kinds of systems, extending up through atonal and serial theory. Rather, I am thinking of the difference in conceptual background, between the way a French (or Italian) speaker approaches solf'ege, and the way an English (or German) speaker does. [21] I think the difference is best approched through an example. I reach into my Marpurg bag again, and pull out this phrase: " ... der hier vorhandene Fuehrer [zeigt] nicht die Tonart d dur, sondern vielmehr g dur an ... ." No solf'ege is involved in this discourse. Nor is any solf'ege involved in an English translation: " ... the Subject at hand does not proclaim the key of D major, but rather much more G major." But the situation in French is quite something else: " ... le sujet en question n'annonce pas la tonalite' de RE majeur, mais beaucoup plus celle de SOL majeur." [22] In the French above, "d" and "g" have disappeared from the German, and "RE" and SOL" have appeared in their places. If we now want to ask, "is the G an UT or a FA?" there is no linguistic awkwardness in English (or German), but there is a very tricky sort of linguistic "musical transposition" (so to speak) involved in the French, where we have to work our conceptual way around the idea, "le SOL, est-ce qu'il est un UT, ou un FA?" [23] No doubt this matter imposes certain differences in the ways German/English speakers conceptualize issues of solmization, and the way French/Italian speakers do. The French and Italian conventions certainly pertain to issues of fixed-DO in a heptachordal context, where "SOL" translates German/English "G," but I think they involve more than that as well. I am not sure exactly how or where the matter has impinged upon the discussion between Nicolas and myself, but I sense it as a somewhat covert (!) presence in that discussion, underlying in particular the special significance, for Nicolas as for any French speaker, of the way in which French heptachordal fixed-DO solmization developed historically. Since I think of G as "G," rather than as "SOL," I can feel such a significance only as an intellectual exercise, rather than as a perpetual cognitive and aural-conceptual presence. [24] Not particularly germane to all the above, but amusing by way of coda, is a passage in Shakespeare which I have found useful to bring hexachordal solmization to life for counterpoint students. (I can't think of any better occasion to put it on line or into print.) The passage is Edmund's second solilioquy in _King Lear_ ("This is the excellent foppery of the world ... ," Act I, scene 2, lines 128-48). At the end of the soliloquy the bastard Edmund, plotting against his "legitimate" brother Edgar, notices Edgar approaching. He remarks, "My cue is villainous melancholy ... ," and assumes an air of "serious contemplation," (as Edgar subsequently describes it). The soliloquy ends with the text "Fa, sol, la, mi." The idea, of course, is that the actor is to sing an appropriate few notes "to himself." I have attended quite a few productions of the play. In some the solf'ege was cut; in others the actor recited the syllables without singing; in still others the actor did sing, but sang (some transposition of) F-G-A-E, as if the solmization were of the modern heptachordal sort. I have never heard an actor sing what Shakespeare obviously intended, that is, (some transposition of) F-G-A-B natural. Edmund is mutating from the top of the natural hexachord (F-G-A-)into the MI of the hard hexachord (B natural), rather than into the FA of the soft hexachord (B flat). In doing so, he is deliberately and self-consciously violating the rule "una nota super LA semper est canendum FA." Thus he is deliberately and self-consciously presenting himself to the world at large as jestingly "diabolical," a pose he assumes throughout the first act of the play. Specifically, his "MI contra FA" presents him as "the diabolus in musica." I am not sure whether Edgar hears Edmund's song or not. In any case, Edgar seems to be be a pretty unmusical fellow. NOTES <1> My metaphorical "based," here, is deliberate and somewhat tendentious. I am suggesting that a _low_ D has an idiomatic role in this connection. The suggestion is consistent with traditional figured-bass and fundamental-bass theories, but it is also consistent with the idea of the final note in the Subject, its lowest note, as projecting the UT of a pertinent hexachord. I am self-conciously avoiding the more usual metaphor of "_in_ D", as e.g. "filling out the _interior_ of a Schenkerian _Ursatz_ that prolongs a DM triad." <2> I have always been surprised at that. I would have expected Schenker to be more sympathetic with Kirnberger/Schultz, and less so with Marpurg. But I am thinking of Marpurg's _Handbuch bey dem Generalbasse und der Composition_, when I have such thoughts. Schenker, in his fugue article, is clearly thinking of the _Abhandlung_ -- and / or the _Anhang_ on fugue from the Composition book, and I suspect that he used Marpurg's work on fugue as a text for his own early studies in fugue, and used it with enjoyment. <3> Serwer, Howard J., _Friedrich Wilhelm Marpurg (1718-1795): Music Critic in a Galant Age_, Ph.D. dissertation, Yale University, 1969; Ann Arbor, Michigan: University Microfilms 70-2801. idem, "Marpurg, Friedrich Wilhelm," _The New Grove Dictionary of Music and Musicians, 20 vols., ed. Stanley Sadie (London: Macmillan, 1980), XI, 697-99. Sheldon, David A., _Marpurg's Thoroughbass and Composition Handbook, A Narrative Translation and Critical Study_ (Stuyvesant, New York: Pendragon Press, 1989. <4> Serwer's _Grove_ article notes in particular Marpurg's published " .. translations of French essays in musical aesthetics such as Grandval's _Essai sur le bon goust en musique_ (1732)." The full title of Marpurg's fugue treatise is "Abhandlung von der Fuge nach dem Grundsaetzen der besten deutschen _und auslaendischen_ Meister" (emphasis mine). A French translation of the treatise appeared 3 years after the first German publication. Marpurg's treatise on keyboard practice was originally published in French, as _Principes de Clavecin_ (1756). Marpurg lived in Paris for some time during the 1740's (how much time is not clear), and was known to have had friendly personal relations with (Voltaire and) D'Alembert. So we cannot suppose Marpurg ignorant of French theoretical traditions, though his "translation" of D'Alembert's _Elemens_ does lead one to question how well he might have understood them. He was certainly familiar with Rameau's study of fugue in the _Traite'_ (III, 44). (Rameau does not employ solf'ege in that discussion.) He was also very familiar with Mattheson's work -- Part I of the _Handbuch_ is in fact dedicated to Mattheson. <5> Andrew Hughes's article on "Solmization (European)," in the _New Grove_ (XVII, 458-62), is enlightening and intimidating on issues of mutation. <6>"B fa and B mi are both equally available in the _recta_ system, and .. neither of them has priority over, or is merely a modification of, the other ... ." Maraget Bent, "Diatonic Ficta." _Early Music History 4 (1984), 1-48. The quote is from page 10. <7> The relation between the (musica mundana) "intervals" of Book I and the (musica humana) "intervals" of Book 3 in Zarlino's _Istitutioni_ is suggestive in this connection, lending some support to the idea of filling in consonant leaps -- though allowing various species of diatonic fillers for most intervals. The idea of filling in a leap through various species of diatonic series came up in paragraph [7] of this document, where I discussed possible hexachordal solmizations of an octave leap up from a low UT. If one fills in the octave leap stepwise through a modern-major scale (or imagines doing so), then the high note must be a FA; if one does not do so (or imagine doing so), then other possible solmizations exist for the high note. If one specifically fills in the octave leap through a Mixolydian scale (or imagines doing so), then the high note will be a SOL (because the two notes below it, forming a semitone, must be MI and FA). That particular point will be taken up in paragraph [9] of this document, immediately following the present note. <8> Lori Burns, _Bach's Modal Chorales_, (Stuyvesant, NY: Pendragon Press, 1995) <9> Allen Forte's system, for instance, is fixed-DO: the number zero _always_ labels the pitch class C; C# is labelled by the number one, etc. etc. In contrast, the systems proposed by George Perle and Milton Babbitt are moveable-DO: the number zero labels the first pitch class of a motif or a series that is taken to be thematically privileged in some way; the numbers one through 11 then label the other pitch-classes according to the intervals they form with pitch-class "zero". <10> Hughes's article in the _New Grove_ (cited in note 5 above) discusses the provenance of this saying (page 460). The doggerel itself is not recorded explicitly before Praetorius (1614-15), but the rule was very much in circulation during the middle of the 16th Century, as Hughes shows, and Shakespeare was clearly aware of it when he wrote _Lear_ (considerably later). David Lewin lewin@fas.harvard.edu Music Dept., Harvard, Cambridge, MA 02138 617/495-2791 fax 617/496-8081 From rothfarb Sun Sep 6 16:38:04 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id QAA27964; Sun, 6 Sep 1998 16:38:02 -0700 (PDT) Date: Sun, 6 Sep 1998 16:38:01 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: Re: Killam"s response to my fugue article (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: David Lewin Subject: Re: Killam"s response to my fugue article [1] I'm not sure what Prof. Killam means by a "comparative table of subjects for JSB's WTC I and II." What sort of "comparison" is meant? If it is simply a matter of displaying the individual subjects in musical notation, one after another, then such displays can be found in the Henle ("Urtext") edition -- listing the subjects for Book I at the beginning of that volume, and then the subjects for Book II at the beginning of _that_ volume. I imagine there are other editions that have such lists. [2] In paragraph [14] of my response to Meeus I try to "compare" various subjects more technically, in the ways they seem to me variously to "indicate" or "propose" (Marpurg's "anzeigen") their keys. Is this perhaps the sort of thing Killam has in mind? If so, I think one learns a lot more by going through the subject of each fugue for oneself, and then trying to summarize ones findings in ones own terms, than one learns by inspecting a table drawn up by somebody else, on the basis of that other person's thinking and hearing. [3] Killam's remarks about Walther are excellent and suggestive in the context of my article and Meeus's response (and my subsequent response to him). By way of caution, though, I should draw attention here to paragraphs [4] and [5] of my response to Meeus -- stressing the fact that Marpurg (who ought to be speaking with authority) considers the subject of the DM fugue from Book II to be _abnormal_, warning students away from it. So far as what Bach's contemporaneous and/or personal "norms" might have been, I have relied on Prof. Wolff's expertise, feeling that I have very little myself. [4] The best way to learn to read Fraktur, I think, is to practice writing Schrift. It doesn't take long to get the hang of it, and one gets a fair amount of enjoyment from the calligraphy. It also helps one read a fair amount of handwritten material from the 19th and first-half-of-the-20th centuries-- though some people were such slobs that their particular hands remain undecipherable except through long and sustained study. Besides, it's a vanishing art and should be kept alive if only by artificial respiration. German students no longer learn to write Schrift, and many have trouble reading it. In 1991 I was standing in front of Brecht's theater, where there was a poster announcing a future production of "die Dreigroschenoper," that title being written in Schrift. A couple of college-age German students were standing next to me, and one had to ask the other what the words were -- even in _that_ milieu! David Lewin lewin@fas.harvard.edu Music Dept., Harvard, Cambridge, MA 02138 617/495-2791 fax 617/496-8081 From rothfarb Mon Sep 7 16:38:37 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id QAA07087; Mon, 7 Sep 1998 16:38:36 -0700 (PDT) Date: Mon, 7 Sep 1998 16:38:35 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: Re: Solmization--Comments on Comments? (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: rnkillam@gte.net (Rosemary Killam) Subject: Re: Solmization--Comments on Comments? from Prof Meeus, subsequent NM; comments, Rosemary Killam subsequent RK: NM:>Stefano Mengozzi makes the most interesting point that solmization may not >have been very practical when reading polyphonic music polyphonically -- it may have two hexachordal functions at the same time. RK: I need to reread Stefano M's point, but does not any note serving as a mutation point have two hexachordal functions? NM: specifically, it must have been quite uncomfortable for keyboardists. RK: Was this one of the reasons that so much early kb music was written in tableture (forgive me, all, please? My spelling is poor. Spellcheck on Eudora Pro is rudimentary--I need to expand, but it's far down the list of "To Do's". Any solutions so that y'all don't have to wince at my misspellings?--I save/n/send all docs but email thru a much better Spellcheck?) RK: Wild guess--would the prob. of multiple functioning of notes in hexachords have been a partial reason that so many blind musicians were trained to be organists, who would handle reading/memorization quite differently than sighted musicians? I'll cc email this for commentary to an organist friend who specializes in Fr. repertoire? NM:>The situation was different, of course, for singers or players of monodic >instruments when they read only one part. These, in the Middle Ages and the >early Renaissance at least, must have conceived the diatonic space as a >complex concatenation of hexachords (rather than a simple concatenation of >octaves). RK: Also 20th c. ones? After years of performance, the modal 5ths, 4ths & relationship hexachords including transposed ones, I find that I consider octaves as resultant rather than causal in interpretation? RK: Horseley's position was that hexachordal usage, combined w/ modal 5ths & 4ths, est'd the mode of a polyphonic work, determined primarily by tenor, all the more strictly when correlated w/ date of compositions/1st performances? Most 3- & >3&vc. polyphony was written w/ 2 voices in modal pairs? Performers grasp(ed) the mode from the first phrase? As one who has sung/played this literature, I've found her methodology practical and persuasive. To what extent has her research been superseded? RK: Yet another silly question: the mathematical possibilities for equivalent acceptable vertical sonorities vary with the placement of the melody in tenor or later in cantus--what is a simple arithmetic statement of that relationship? NM: >A hexachordal perception (or a tetrachordal one, for that matter) is >characterized by the importance given to very local events; RK: As a performer of the music, I question this? If the incipit I'm playing opens with the "mi-mi" 5th, I have a VERY good idea of the final cadence, as well as significant tones within the composition. Should a section of the work move to "re-fa-sol-la" in the c.f. or as a melody underlying ornamentation, I'll expect that segment to have a different intent and interpretive needs? NM: because it imposes a mutation "in the air", so to >speak, i.e. between notes rather than on one note that would assume two >functions in succession. RK: Isn't there a case to be made for the influence of the acoustical space of the area performance area intended? Small spaces with shorter reverb times supported clear chromaticism, and the inverse. Romanesque and Gothic architecture of large spaces support different overtones in their reverbs. I'm not suggesting that every harried composer of yet one more setting for the next feast took this into conscious account, but until the time of the international movement of composers during their compositional lifetimes, most composers wrote for specific spaces and fairly specific ensembles, with their group strengths & weaknesses. Also, musical vibration remained a part of the core education into the 16th c.? >Nicolas Meeus >Universite de Paris-Sorbonne >nicolas.meeus@paris4.sorbonne.fr Rosemary N. Killam Visiting Scholar Assoc. Prof.Music Theory UMA-Amherst, academic yr 98-99 UNT-COM, Denton TX 76203 Amherst ad: #305,Puffton Vil. UNT email: RKILLAM@MUSIC.UNT.EDU 1040 N. Pleasant St (dbls. to email below) Amherst, MA 01002 travelling email: rnkillam@gte.net Amherst Home Ph: 314-549-7146 Home Address: 414 Seward Sq SE #403 MORE INFO AS AVAILABLE Washington, D.C. 20003, DC Ph: 202-546-8433 From rothfarb Mon Sep 7 16:51:51 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id QAA08633; Mon, 7 Sep 1998 16:51:49 -0700 (PDT) Date: Mon, 7 Sep 1998 16:51:49 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: Re: Solmization--re Lester's Comments on Late use (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: rnkillam@gte.net (Rosemary Killam) Subject: Re: Solmization--re Lester's Comments on Late use Will someone whose specialties include theories of colonial Am. music comment on late use of hexachordal mutation in compositions and theoretical treatises by composers such as Daniel Read, esp. in light of Read's late-in-lifeconfessions that he didn't understand how to write in the "new scientific method"? All of his music I've studied keeps melody in tenor? Hexachordal/septachordal scales and treatises used to teach music in the early 18th c. Am. Revival are a mixed lot, with wide influence. Memory fails, but I hink Gay's 1728 Beggar's Opera, with its many modal-infl melodies, was performed on most of the New World opera circuits as well as English colonies on other continents before death of JSB, Handel, D. Scarlatti? (One of the standard "why don't polar bears eat penguins" questions we've all asked our classes? Why weren't JSB Chorale setting included in the early NA Colonial Psalmbooks?--music composition, history, theory & performance are a lot more historically mixed than 20th c. elementary theory texts tend to present?) Also, what of 17th-18th c. compositional schools and treatises dealing with hexachordal performance/compositional usage, surrounding cathedrals of Mexico City, Santa Fe, and CA Missions? Hasn't recent research shown this music to have more reciprocal European influence than previously believed, rather than being just derivative offshoot? Don't some of the 17th c. dance forms and harmoniec structures seem now to have New World origin, in part? I've been doing specialized reading on perception/cognition for past several years & am behind in areas above. What are y'all's standard reference articles, books on hexachordal-modal-tonal theories, published in the last 5 years? Thanks, Rosemary Rosemary N. Killam Visiting Scholar Assoc. Prof.Music Theory UMA-Amherst, academic yr 98-99 UNT-COM, Denton TX 76203 Amherst ad: #305,Puffton Vil. UNT email: RKILLAM@MUSIC.UNT.EDU 1040 N. Pleasant St (dbls. to email below) Amherst, MA 01002 travelling email: rnkillam@gte.net Amherst Home Ph: 314-549-7146 Home Address: 414 Seward Sq SE #403 MORE INFO AS AVAILABLE Washington, D.C. 20003, DC Ph: 202-546-8433 From rothfarb Mon Sep 7 18:55:46 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id SAA13807; Mon, 7 Sep 1998 18:55:45 -0700 (PDT) Date: Mon, 7 Sep 1998 18:55:44 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: Re: Solmization (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: rnkillam@gte.net (Rosemary Killam) Subject: Re: Solmization Again NM=Prof. Meeus; RK=Rosemary Killam NM:>1. David Lewin is right that issues of solmization may be conceptualized >quite differently in French and in English/German. It is a problem of which >we have been aware in Paris, when working on solmization last year: RK: Your work on the French system has yielded results I've been hoping for, for years. I assume both indirect & indirect infl. on Boulanger and her teachers' methods of solfege? Where have you reported your findings, and how can we all get copies, please? NM:. Let me quote Thomas Morley (1597; I quote the Playford edition >of 1730): "Now to sing your notes, you cannot use the words GAMUT, Are, >etc., . . . [This system apparently sometimes has been called the >"Lancashire >system": does anyone have information about that?] RK: I don't know the term "Lancashire system", but Morley's solmization system was quite atypical for his time in England. (I did a bit of work on this some year ago, superseded by others I'm sure, who will update the following?) RK1. I think of the "Lancashire system" as named the "fa-sol-la" system?. In part its use can be traced (and more perhaps inferred) thru the excellent pay records of the English church, court and town musicians--who sang what where and with whom, born, educated, died when and where? RK2. Morley appears to have been the first English composer/writer on solmization who was not taught it as a child through a religious foundation, since those were dissolved by Henry VIII before his childhood studies began. Therefore, he wrote of a system which he personally hadn't learned. RK3. Morley's writings coincided w/ heavy English Migration to N. Am, and N.A.influenced music publication and solmization treatises often inserted w/ music. What is the relationship of European Fr. practices to those established and maintained in Fr. Canadian music studies and religious schools/foundations? RK: Finally, my problem with incorporation of Schoenberg, Schenker, Schillenger, into a "belief system" of music theory: Isn't "truth" partial and subject to change with new information? Do we denigrate Rutherford because we've refined the speed of light multiple times, or Curie because of our expanded experience with radium? Whatever my respect for B.C.E. Greek philosophers, I wouldn't want them prescribing my medical treatment? How do we continue to respect work of previous theorists without deifying them and canonizing their findings, yet incorporate their knowledge into our current (& everchanging) concepts of music theory? >Nicolas Meeus >Universite de Paris Sorbonne >nicolas.meeus@paris4.sorbonne.fr=1A > > >------------- End Forwarded Message ------------- Rosemary N. Killam Visiting Scholar Assoc. Prof.Music Theory UMA-Amherst, academic yr 98-99 UNT-COM, Denton TX 76203 Amherst ad: #305,Puffton Vil. UNT email: RKILLAM@MUSIC.UNT.EDU 1040 N. Pleasant St (dbls. to email below) Amherst, MA 01002 travelling email: rnkillam@gte.net Amherst Home Ph: 314-549-7146 Home Address: 414 Seward Sq SE #403 MORE INFO AS AVAILABLE Washington, D.C. 20003, DC Ph: 202-546-8433 From rothfarb@smt.ucsb.edu Tue Sep 8 16:27:00 1998 Received: from boethius (boethius [128.111.94.30]) by smt.ucsb.edu (8.7.1/8.7.1) with SMTP id QAA21633 for ; Tue, 8 Sep 1998 16:27:00 -0700 (PDT) Message-Id: <199809082327.QAA21633@smt.ucsb.edu> Date: Tue, 8 Sep 1998 16:27:00 -0700 (PDT) From: Lee Rothfarb Reply-To: Lee Rothfarb Subject: WTK II-5 fuga To: mto-talk@smt.ucsb.edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: r278XwCFIFu34nCnnwpkkQ== X-Mailer: dtmail 1.2.0 CDE Version 1.2 SunOS 5.6 sun4m sparc Sender: Piet Vos Subject: WTK II-5 fuga It may be relevant to add to the discussion around David Lewin's paper about the WTC II-5 D major Fugue subject the following two points. 1. A recently developed computational key-finding model, the Parallel Processing Model, PPM (Vos & Van Geenen, Music perception, 1996, vol 14, pp 185-224), tested with all WTK fugue themes, came also up with G major in this case, and a perceptual test of PPM's plausibility (same article) showed that listeners interpreted the subject unequivocally as G. 2. Recently, I discovered the origin of the exceptionality (Vos, "Tonal implications of ascending fourth and descending fifth openings", submitted to Psychology of Music). Since the latter paper is still under review, I delay its content here, but interested collegues may consult my homepage in which the discovery is essentially formulated as a rule). Piet Vos Piet G. Vos section Perception NICI, U. Nijmegen P.O.Box 9104 6500 HE Nijmegen NL tel: +31 24 36126 31/20; fax: +31 24 361 59 38; vos@nici.kun.nl home-page: http://www.nici.kun.nl/~vos "et altissimus humilissimum facere debet" ------------- End Forwarded Message ------------- From rothfarb Tue Sep 8 20:06:42 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id UAA25088; Tue, 8 Sep 1998 20:06:41 -0700 (PDT) Date: Tue, 8 Sep 1998 20:06:41 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: Re: (Fwd) Fugue and tonality (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: rnkillam@gte.net (Rosemary Killam) Subject: Re: (Fwd) Fugue and tonality Re Prof. Dineen's commentaries-- Would members of the MTO-list conside rposting their favorite citations (preferably recent) on comparisons/contrasts within the whole of WTCI and WTCII? Obviously, WTCII has less variety of voices--no 2- or 5-vc. fugues & as I recall, a difference of some 20 yrs. between completion of the volumes. I'm working from a deficit of knowledge, which many of you have? Would JSB have changed/reworked his use of modes/hexachords between the two volumes, as per the paper from someone at the Goethe Institute, given at the Van Couver meeting, showing a definite change in JSB's 4-vc. chorale cadence writing, ~1728, as I recall? The only possible analogy I can make is to those early chorale preludes rediscovered in the Yale lib. by Wolff in the mid-80's. I've checked the underlying key/mode of those c.p's with JSB's chorale settings of the same melodies, datable from the Leipzig period and contained in cantatas--not just individual chorale settings.. The interior key/mode relationships of those I've checked remain the same between c.p.s and chorales, even when a more "tonal" choice for the later chorales was available, logical and possibly more in JSB's "later" harmonic styles. Tentative conclusion? JSB harmonized the chorale melodies, whether as highly figured c.p.'s or relatively simple 4-vc. chorales, from a pre-existant interior harmonic concept, certainly not dictated by any agreement with or among the many chorale books he owned? Can such a tentative conclusion be expanded to other segments of JSB's sacred works? Can it, possibly, be expanded to his secular works, such as the WTCI and II. As someone who studied WTCI & II, (preludes esp. but w/ some ref to the fugues) for their dance form derivations (hey, Dan Harrison? who else amongst us did this at Stanford?) I wonder what other influences on JSB's fugal writing I'm missing? With curiosity, Rosemary Rosemary N. Killam Visiting Scholar Assoc. Prof.Music Theory UMA-Amherst, academic yr 98-99 UNT-COM, Denton TX 76203 Amherst ad: #305,Puffton Vil. UNT email: RKILLAM@MUSIC.UNT.EDU 1040 N. Pleasant St (dbls. to email below) Amherst, MA 01002 travelling email: rnkillam@gte.net Amherst Home Ph: 314-549-7146 Home Address: 414 Seward Sq SE #403 MORE INFO AS AVAILABLE Washington, D.C. 20003, DC Ph: 202-546-8433 From rothfarb Tue Sep 8 20:11:17 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id UAA25673; Tue, 8 Sep 1998 20:11:16 -0700 (PDT) Date: Tue, 8 Sep 1998 20:11:15 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: Fugue and tonality, solmization Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: rnkillam@gte.net (Rosemary Killam) Subject: Fugue and tonality, solmization Re Prof. Dineen's ref. to Brown & Butler's work on the perceptual/cognitive nature of tonally-defining tritones (suppored theoretically by Ratner): their work presumes 20th c. listeners. David B, Helen B, how comfortable are you with extending your findings back three centuries? Best, Rosemary Re Solmization: Ref Prof. Mengozzi's first segment on the meaning of "re-mi": perhaps I'm not reading deeply enough into his argument, but the consistency and importance of "mi-fa" as a half step throughout the historical use of solmization seems the more important and basic? "Mi-fa" generalizes outside JSB's usage and was one of the points on which all of the solmization texts and practices agreed? Rosemary N. Killam Visiting Scholar Assoc. Prof.Music Theory UMA-Amherst, academic yr 98-99 UNT-COM, Denton TX 76203 Amherst ad: #305,Puffton Vil. UNT email: RKILLAM@MUSIC.UNT.EDU 1040 N. Pleasant St (dbls. to email below) Amherst, MA 01002 travelling email: rnkillam@gte.net Amherst Home Ph: 314-549-7146 Home Address: 414 Seward Sq SE #403 MORE INFO AS AVAILABLE Washington, D.C. 20003, DC Ph: 202-546-8433 From rothfarb Tue Sep 8 20:12:52 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id UAA25920; Tue, 8 Sep 1998 20:12:50 -0700 (PDT) Date: Tue, 8 Sep 1998 20:12:49 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: Re: Killam"s response to my fugue article (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: rnkillam@gte.net (Rosemary Killam) Subject: Killam"s response to my fugue article DL = David Lewin; RK = Rosemary Killam DL: [1] I'm not sure what Prof. Killam means by a "comparative table >of subjects for JSB's WTC I and II." What sort of "comparison" is meant? RK: I was thinking ore of the sort of graph I have somewhere, that I should put into an edb, from the days when I taught 15-18 hrs/wk & had to be able to come up with comparable examples in a hurry? Someplace I've a 2-dimensional graph listing each fugue by length of subject, characterization of answer, meter, number of subsequent appearances of subject, number of mod/non-mod sequences & 4-5 other characteristics. I've the same for the 2-vc. inventions, and lists for the JSB chorale settings: (exs: chorales with: no modulations, 4 phrases only, ending in imperfect authentic cadences, borrowed/mixed mode harmony--the sort of lists I guess we've all made at one time or another during enforced quiet such as hospital stays? Such handy for lesson planning, but only suggestions toward analyses? DL: [2] In paragraph [14] of my response to Meeus I try to "compare" >various subjects more technically, in the ways they seem to me variously >to "indicate" or "propose" (Marpurg's "anzeigen") their keys. Is this >perhaps the sort of thing Killam has in mind? RK: I was thinking far more superficially? DL: [3] Killam's remarks about Walther . . .I should draw attention here to . . . stressing the fact that Marpurg (who ought to be speaking with authority) >considers the subject of the DM fugue from Book II to be _abnormal_, warning students away from it. RK: Good point--but should there perhaps be a corollary to Boorstin's Law": "History belongs to the winners" of, "and to the writers?" Is one of our problems with analyzing JSB the relative lack of treatises written by him or his contemporaries, and the plethora of treatises written by his students and his children? DL: The best way to learn to read Fraktur, I think, is to practice >writing Schrift. It doesn't take long to get the hang of it, and one gets >a fair amount of enjoyment from the calligraphy. . . . RK: Ach, David, I'm gonna have to live to at least 120 to meet your minimum standards of scholarship? Best, Rosemary Rosemary N. Killam Visiting Scholar Assoc. Prof.Music Theory UMA-Amherst, academic yr 98-99 UNT-COM, Denton TX 76203 Amherst ad: #305,Puffton Vil. UNT email: RKILLAM@MUSIC.UNT.EDU 1040 N. Pleasant St (dbls. to email below) Amherst, MA 01002 travelling email: rnkillam@gte.net Amherst Home Ph: 314-549-7146 Home Address: 414 Seward Sq SE #403 MORE INFO AS AVAILABLE Washington, D.C. 20003, DC Ph: 202-546-8433 From rothfarb Tue Sep 8 20:16:26 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id UAA26381; Tue, 8 Sep 1998 20:16:24 -0700 (PDT) Date: Tue, 8 Sep 1998 20:16:24 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: Re: Solmization (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: Elizabeth Crownfield Subject: Re: Solmization Just a few notes about some recent comments on Morley, which I hope are not getting too far off topic. At 07:03 PM 9/7/98 -0700, Rosemary Killam wrote: >Again NM=Prof. Meeus; RK=Rosemary Killam >NM:. Let me quote Thomas Morley (1597; I quote the Playford edition >>of 1730): "Now to sing your notes, you cannot use the words GAMUT, Are, >>etc., . . . EC: I will re-paste the whole quote here, since I didn't respond when NM originally posted it: "Now to sing your notes, you cannot use the words GAMUT, Are, etc., they being too long; therefore their meaning is contracted to these several short syllables, Sol, La, Mi, Fa; Ut and Re being left out, and are with less Confusion supplied with Sol, and La. It was the Ancient Practice [Morley, or Playford, probably means: to sing six syllables], and the French generally use it now, but this Modern Way [i.e. of singing four syllables only] is found less difficult to the young practicioner". This quote is not actually from Morley. Perhaps the closest he comes is: Ma. Take this for a general rule, that in one deduction of the six notes, you can have one name but once used, although indeed (if you could keep right tune) it were no matter how you named any note. But this we use commonly in singing, that except it be in the lowest note of the part we never use ut. Phi. How then? Do you never sing ut but in Gam ut? Ma. Not so: But if either Gam ut, or C fa ut, or F fa ut, or G sol re ut, be the lowest note of the part, then we may sing ut there. >RK: I don't know the term "Lancashire system", but Morley's solmization >system was quite atypical for his time in England. (I did a bit of work on >this some year ago, superseded by others I'm sure, who will update the >following?) Jessie Ann Owens's recent article, "Concepts of Pitch in English Music Theory, c.1560-1640" in _Tonal Structures in Early Music_, ed. Cristle Collins Judd (NY: Garland, 1998) discusses this question at length and very lucidly. The English system (imperfectly represented by Morley) was indeed distinct from the traditional continental one. >RK2. Morley appears to have been the first English composer/writer on >solmization who was not taught it as a child through a religious >foundation, since those were dissolved by Henry VIII before his childhood >studies began. Therefore, he wrote of a system which he personally hadn't >learned. I think this may be a bit of an exaggeration: although Morley was not trained in one of the old religious foundations, he surely studied with people who were, or were at any rate trained according to the old traditions. As far as I know there have been no better suggestions than Shaw's that he was a chorister at Norwich. (If I am missing something, someone please tell me!) The music training there and elsewhere surely did not come to a sudden halt; Morley would have been a child in the early 1560s, not long after Elizabeth assumed the throne and re-established Protestantism. Remember, too, that at this point nobody knew she was going to live so long and that this change would last; many people hoped or feared that Catholicism would be back any minute. My own hypothesis, though this is getting farther away from Bach, is that a practical, oral tradition of theory may have grown up in England, largely isolated from the international written tradition. I think of it as analogous to the difference between the "classical" theory I learned and the "guitar theory" that my stepson is learning as a performer: so many terms and concepts overlap that it appears at first to be the same system, but when you get down to details you find that it really is not. My hypothesis is that Morley was attempting to reconcile these two systems (oral and written) without being entirely clear on the difficulties and inconsistencies in doing this. Those who followed him made the distinctions a bit clearer. I would very much welcome any thoughts that anyone has on this subject -- privately would be fine, since they are getting farther away from the topic under discussion here. ----------------------------------------------------------------- Elizabeth Crownfield New York University eec@midcoast.com From rothfarb Wed Sep 9 08:47:32 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id IAA09778; Wed, 9 Sep 1998 08:47:31 -0700 (PDT) Date: Wed, 9 Sep 1998 08:47:31 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers Subject: Re: Solmization (answers to RK) (fwd) Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: "Nicolas Meeus" Subject: Re: Solmization (answers to RK) In answer to (some of) Rosemary Killam's comments and questions. (The points that I do not comment are those on which I have no opinion -- or at least no informed one.) 1. Notes having two hexachordal functions at the same time. It is true that any note serving as a mutation point has two hexachordal functions, but, conceptually at least, these follow each other. The case that Prof. Mengozzi pointed is that of a note belonging to two polyphonic parts at the same time and having a different function in each. This is the case with the D in the left hand, m. 8 of fugue 5 in WTCII, which is a FA in the bass part and an UT in the tenor part. 2. Was solmization one of the reasons that keyboard music was written in tablature? Yes, I think so. Staff notation is more a notation of intervals than of pitches, and keyboardists really needed to read pitches, not intervals. Note, by the way, that a change of clefs when reading a score reduces to a change of hexachords (an UT on the line of the clef is a C-UT in C-clef, a G-UT in G-clef, an F-UT in F-clef). This has direct consequences on how transposition was conceived; to keyboardists, it may have been an advantage and/or a drawback, depending on the circumstances. 3. Establishment of the mode of a polyphonic work. There are two issues here, as with modern tonality: one is of knowing in what key or mode a piece is (i.e., a matter of classification), the other of knowing HOW it is in that key or mode (a matter of perception). The fact that Bach's fugue under discussion bears number 5 in the WTC allows us to classify it in D major as surely as if Bach had labeled it "Fugue in D major". But David Lewin's question is "how do we know, how do we perceive that it is in D major?" Similarly, hexachordal usage, species of 5ths and 4ths, the tenor, the first phrase, and so on, may allow to classify the piece in a given mode, but we still don't know how, nor even, in the case of Renaissance polyphony, _whether_ we perceive the mode. This is the core of the discussion between Bernhard Meier and Dahlhaus: is modality something belonging to the inner structure of the piece, or merely something external? Or, as Powers puts the question: is mode a pre-compositional category? And the question implicitly asked by David Lewin is similar. 4. Hexachordal perception as local perception. If you can deduce the final cadence of a work from its opening gesture, it certainly is the result of an acculturation (I mean, you seem to be refering to chant formulas, which obviously belong to your musical culture); what you do is that you identify the mode. But is solmization as such concerned with that?. Singing solmization syllables tells you which are the intervals surrounding the note you sing, but not what kind of mutation will follow. To take an example in a totally different context, when in anhemitonic pentatonic music you hear the characteristic interval of the "augmented second", you know the intervals closely surrounding it, but you don't know at what distance the other augmented second will be within the octave, whether it will be a 4th or a 5th higher or lower. The uncertainty, more generally, is whether the next trichord, tetrachord, hexachord or whatever, will be conjunct or disjunct. Note that the first mode, in the middle ages, can be formed either of conjunct or of disjunct hexachords -- which is another way of saying that it can include either the B flat or the B natural. The hexachordal structure does not determine the mode. 5. Our work on the French system. Our intention is to publish an article, which I hope may be ready within weeks or a few months at most. It will then be proposed to one of the (few) French journals, probably *Musurgia*, where it may appear, say, in 1999 or 2000. In the meanwhile, I'll be ready to answer specific questions. 6. The term "Lancashire system" is given, without explanation, in S. Kleinman, *La solmisation mobile de Jean-Jacques Rousseau a John Curwen*, Paris, 1974. 7. "Truth"? Never heard of such a thing. Didn't Popper state that the only thing that is sure about scientific theories, is that they eventually will be proved false? Nicolas Meeus Universite de Paris-Sorbonne nicolas.meeus@paris4.sorbonne.fr From rothfarb Wed Sep 9 09:15:47 1998 Received: (from rothfarb@localhost) by smt.ucsb.edu (8.7.1/8.7.1) id JAA13744; Wed, 9 Sep 1998 09:15:46 -0700 (PDT) Date: Wed, 9 Sep 1998 09:15:45 -0700 (PDT) From: Lee Rothfarb To: mto-talk Subscribers