=== === ============= ==== === ==== == == == == == ===== == == = == ==== === == == == == == == == = == == == == == == == == == ==== M U S I C T H E O R Y O N L I N E * * MTO ELECTRONIC DISCUSSION FORUM * * Copyright (c) 1996 Society for Music Theory ============================================================================== mto-talk is a moderated discussion forum sponsored by the Society for Music Theory, a non-profit scholarly society devoted to the promotion of quality research and teaching in music theory. All messages are checked by the list editor for format and appropriateness prior to being forwarded to subscribers. Send messages for posting to . Please include your name, affiliation (optional), and email address at the end of the message. Policies exist regulating the posting of advertisements and the reprinting of items that appear on this list. See the mto-talk Guide for details. ============================================================================= From rjudd@sas.upenn.edu Mon Aug 5 11:50:19 1996 Received: from mail1.sas.upenn.edu (rjudd@MAIL1.SAS.UPENN.EDU [165.123.26.32]) by boethius.music.ucsb.edu (8.7.1/8.7.1) with ESMTP id LAA03664 for ; Mon, 5 Aug 1996 11:50:18 -0700 (PDT) Received: (from rjudd@localhost) by mail1.sas.upenn.edu (8.7.5/SAS 8.06) id OAA14393 for mto-talk@boethius.music.ucsb.edu; Mon, 5 Aug 1996 14:49:45 -0400 (EDT) From: rjudd@sas.upenn.edu (Robert F Judd) Posted-Date: Mon, 5 Aug 1996 14:49:45 -0400 (EDT) Message-Id: <199608051849.OAA14393@mail1.sas.upenn.edu> Subject: Re: Wibberley, MTO 2.5 To: mto-talk@boethius.music.ucsb.edu (MTO -Talk) Date: Mon, 5 Aug 1996 14:49:45 -0400 (EDT) X-Mailer: ELM [version 2.4 PL23-upenn3.1] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: mua01rw@gold.ac.uk (Roger Wibberley) Subject: Re: Wibberley, MTO 2.5 Having returned today from a week's vacation to find Cristle Collins Judd's further message dated 26 July, I feel that we may after all be talking only at cross purposes. We seem to be essentially agreed at least on how the Josquin extract should actually sound. It may be that by using MTO-talk we can move even closer together, and possibly encourage other interested parties to contribute to the discussion. One crucial area of misunderstanding that may explain some of our initial differences could perhaps be explored. Judd wrote the following: >The reason that I went on at length in my response about the "theoretical >status of mode" was to suggest that according a priority to mode will >*not* as Wibberley argues yield a totally different musical result (and it >was here that I understood him to be posing what appears to me an >artificial "opposition" of mode and ficta). The differences seem, to me, very clear: when the Josquin extract is accorded a "priority of mode" the end-product will yield something like my original Example 2 (whose musical result Judd agrees with essentially). This is, surely, because the melodic lines follow the simple diatonic steps of the mode in question. It is not to do with things like "range", "last note of tenor", or any other such thing. It is just that the tonality (yes!) that arises from this particular succession of tones and semitones - melodically AND harmonically - yield the particular "affect" of mode 12. There seems to me no other possible justification for arriving at this solution (diminished-fifths, warts and all) except via the argument of *mode*. This sole element of musical fabric (and recognized as such by Glareanus) provides, in my view, the ONLY counter to those (including Bent) who hold out against the "perpetration" of any diminished fifths which, of course, are (in their view) always to be considered as candidates for *ficta* adjustment. If, however, modal priority is subjugated by what might be called *ficta*-priority, the end product will accord with my original Example 1 (i.e. Bent's proposal, based not upon anything to do whatsoever with mode, but conceptualized purely in terms of interval-perfection). I cannot understand how it is possible to view these two different manifestations of the same phrase as being anything other than of totally different musical substance: one identifies aurally and visually with a designated mode, and contains (as an inevitable result) imperfect fifths; the other does NOT identify aurally (even if it "does" visually) with a single mode, and does NOT contain any imperfect fifths. If anybody is unable to hear the different musical results, they need only click the appropriate hotspots to activate the midi files attached to my article. We may (as I hope) still be slightly at cross-purposes, but I am still completely gob-smacked by the above quotation! It may be that we do not agree upon what is implied by "priority of mode". What I meant by this term is explained (I hope) clearly in the above paragraph. I am not, of course, meaning to imply that music would always assume this priority - it is clear from other works by Josquin (to name only one) that it didn't. (One only has to look at a piece like *Absolon fili mi* to see MODULATION as a powerful rhetorical device. This might have been an example for Glareanus to offer of a piece where the composer DOES "move the harmony from its base" - and very successfully too.) It is just that in the particular case in question "priority of mode" would seem to me to provide a suitable solution to a difficult extract that not only "sounds" appropriate (as Judd seems to agree) but also has the support of a fairly important Renaissance musical theorist. I think Miller's translation of "non emota sua sede harmonia" IS OK, surely? What is clear to me is that Glareanus is telling us something quite definitely about the way the COMPOSER has composed the music, rather than about the way others might have performed it. So I believe that Judd's statement "... one could (perversely) I suppose even argue that it is Bent's solution, with its absence of diminished fifths, which preserves the "harmonia." is, as was suggested, "perverse". ______________________ Roger Wibberley Head of Studies Music Department Goldsmiths College New Cross London SE14 6NW Tel: 0171 919 7661 Fax: 0171 919 7644 JANET: mua01rw@uk.ac.gold InterNet: mua01rw@gold.ac.uk Web page- http://ludwig.gold.ac.uk/rwibberley/ ______________________ From rjudd@sas.upenn.edu Wed Aug 7 22:01:40 1996 Received: from mail2.sas.upenn.edu (rjudd@MAIL2.SAS.UPENN.EDU [165.123.26.33]) by boethius.music.ucsb.edu (8.7.1/8.7.1) with ESMTP id WAA16550 for ; Wed, 7 Aug 1996 22:01:40 -0700 (PDT) Received: (from rjudd@localhost) by mail2.sas.upenn.edu (8.7.5/SAS 8.06) id BAA16055 for mto-talk@boethius.music.ucsb.edu; Thu, 8 Aug 1996 01:01:03 -0400 (EDT) From: rjudd@sas.upenn.edu (Robert F Judd) Posted-Date: Thu, 8 Aug 1996 01:01:03 -0400 (EDT) Message-Id: <199608080501.BAA16055@mail2.sas.upenn.edu> Subject: Re: Wibberley, MTO 2.5 (fwd) To: mto-talk@boethius.music.ucsb.edu (MTO -Talk) Date: Thu, 8 Aug 1996 01:01:03 -0400 (EDT) X-Mailer: ELM [version 2.4 PL23-upenn3.1] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: Victor Grauer Subject: Re: Wibberley, MTO 2.5 At 12:04 PM 8/5/96 -0700, Roger Wibberley wrote: >Judd wrote the following: > >>The reason that I went on at length in my response about the "theoretical >>status of mode" was to suggest that according a priority to mode will >>*not* as Wibberley argues yield a totally different musical result (and it >>was here that I understood him to be posing what appears to me an >>artificial "opposition" of mode and ficta). > Wibberley: >The differences seem, to me, very clear: when the Josquin extract is >accorded a "priority of mode" the end-product will yield something like my >original Example 2 (whose musical result Judd agrees with essentially). >This is, surely, because the melodic lines follow the simple diatonic >steps of the mode in question. It is not to do with things like "range", >"last note of tenor", or any other such thing. It is just that the >tonality (yes!) that arises from this particular succession of tones and >semitones - melodically AND harmonically - yield the particular "affect" >of mode 12. There seems to me no other possible justification for arriving >at this solution (diminished-fifths, warts and all) except via the >argument of *mode*. Some comments and questions regarding the above dispute. First, I see only one diminished fifth in Wibberley's version, on the last quarter of m. 48, between e and b flat. There is also a false relation in measure 51 (b flat in the bass followed by b natural in the alto). The effect of this is exacerbated by the presence of e in the soprano, a tritone away from the "offending" b flat. This bothers me more than the tritone in m. 48, but perhaps it wouldn't have bothered Josquin. I find it most interesting that the tritone in m. 48 has a distinctly "modern" ring, interpretable as a vii6 of IV in C major, though with the "wrong" voice leading. Given Wibberley's "tonality (yes!)" (see above), I wonder if he'd like to comment on this touch of what would become routine practice in the era of major/minor tonality. In a similar spirit, I'd like to ask if either Wibberley or Judd could consider the viability of the passage without any ficta alterations, as plain old white note music in "C major." Here again, literally all the tritones (all are between b and f) would be interpretable in "modern," i.e., tonal, terms as part of the V 6/5 chord, also (like the vii6 of IV) a "dominant" harmony (though, again, with the "wrong" voice leading). And we'd get rid of that false relation. Given that Josquin's contemporary, Obrecht, is know for excursions into what often sounds like quite "modern" realms, would it not be likely that Josquin, too, might have "looked ahead" occasionally? Might I dare to speculate a bit further to suggest that the difficulties entailed in the sort of ficta vs. mode problems revealed here could have led (dare one say "inevitably") to the major/minor system? (Perhaps inevitably *is* the wrong word, since an entirely different, though equally logical path, that of the Bent version, was just as possible, but became "the path not taken" -- though, as Lowinsky has shown, it was not a path completely neglected either). These moments in history where fundamental contradictions, traditionally hidden or adroitly smoothed over, begin to emerge and create real problems that lead to the invention of new "paradigms" are very interesting and have become, thanks to the sort of post structuralist thinking we have been examining lately on this list, rather timely. Any "new musicologists" out there who might care to comment? (I must add that I realize perfectly well that the sort of speculation I am indulging in here is not new and existed, along with so much else of similar interest, long before the "new" musicology -- only I think the time for a re-examination and maybe a "rethinking" of such ideas may now have come.) Victor Grauer No academic affiliation grauer@pps.pgh.pa.us From rjudd@sas.upenn.edu Thu Aug 8 06:38:34 1996 Received: from mail2.sas.upenn.edu (rjudd@MAIL2.SAS.UPENN.EDU [165.123.26.33]) by boethius.music.ucsb.edu (8.7.1/8.7.1) with ESMTP id GAA20096 for ; Thu, 8 Aug 1996 06:38:33 -0700 (PDT) Received: (from rjudd@localhost) by mail2.sas.upenn.edu (8.7.5/SAS 8.06) id JAA06815 for mto-talk@boethius.music.ucsb.edu; Thu, 8 Aug 1996 09:37:59 -0400 (EDT) From: rjudd@sas.upenn.edu (Robert F Judd) Posted-Date: Thu, 8 Aug 1996 09:37:59 -0400 (EDT) Message-Id: <199608081337.JAA06815@mail2.sas.upenn.edu> Subject: Re: Wibberley, MTO 2.5 (fwd) To: mto-talk@boethius.music.ucsb.edu (MTO -Talk) Date: Thu, 8 Aug 1996 09:37:59 -0400 (EDT) X-Mailer: ELM [version 2.4 PL23-upenn3.1] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: mua01rw@gold.ac.uk (Roger Wibberley) Subject: Re: Wibberley, MTO 2.5 I read Victor Grauer's contribution to this debate with interest. However, his gloss demonstrates to me clearly that I am far more in agreement with Judd's position than with the ideas he has interrogatively suggested. Indeed, I would have to move into a completely different orbit to meet him, whereas with Judd I feel that it is only a simple adjustment of trajectory that is needed! There is no way that I could accept his proposal for eliminating all accidentals - this would leave diminished fifths exposed with the bass line, which is completely alien (in my view) with all we know about theory and practice in the Renaissance. It is also inappropriate to "justify" such moves by applying anachonistic chord symbols that apply to a fundamentally different and later tonal system. When I used the term "tonality", I was applying it in a sense figuratively to make a distinction between *mode* viewed as an apparatus for musical design, and what the living aural EFFECT of the application of *mode* yields. I can see no actual connection between this and what Grauer is implying be "tonality". It is an interesting idea that a composer like Josquin can - as a soothsayer - peep into the minds of composers not to be born for over 100 years, and emulate the ideas they will come up with. I don't personally regard this as a tenable "justification" for seeking to interpret his music in a particular way, and would much rather view his eminence in terms of the effect HE had on those who followed him. Nonetheless, I found much of interest in some of Grauer's ideas, and thank him very much for sending them. ______________________ Roger Wibberley Head of Studies Music Department Goldsmiths College New Cross London SE14 6NW Tel: 0171 919 7661 Fax: 0171 919 7644 JANET: mua01rw@uk.ac.gold InterNet: mua01rw@gold.ac.uk Web page- http://ludwig.gold.ac.uk/rwibberley/ ______________________ From rjudd@sas.upenn.edu Fri Aug 9 11:38:17 1996 Received: from mail1.sas.upenn.edu (rjudd@MAIL1.SAS.UPENN.EDU [165.123.26.32]) by boethius.music.ucsb.edu (8.7.1/8.7.1) with ESMTP id LAA08649 for ; Fri, 9 Aug 1996 11:38:16 -0700 (PDT) Received: (from rjudd@localhost) by mail1.sas.upenn.edu (8.7.5/SAS 8.06) id OAA00561 for mto-talk@boethius.music.ucsb.edu; Fri, 9 Aug 1996 14:37:44 -0400 (EDT) From: rjudd@sas.upenn.edu (Robert F Judd) Posted-Date: Fri, 9 Aug 1996 14:37:44 -0400 (EDT) Message-Id: <199608091837.OAA00561@mail1.sas.upenn.edu> Subject: Re: Wibberley, MTO 2.5 (fwd) To: mto-talk@boethius.music.ucsb.edu (MTO -Talk) Date: Fri, 9 Aug 1996 14:37:43 -0400 (EDT) X-Mailer: ELM [version 2.4 PL23-upenn3.1] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: Victor Grauer Subject: Re: Wibberley, MTO 2.5 At 06:44 AM 8/8/96 -0700, Roger Wibberley wrote: >I read Victor Grauer's contribution to this debate with interest. However, >his gloss demonstrates to me clearly that I am far more in agreement with >Judd's position than with the ideas he has interrogatively suggested. >Indeed, I would have to move into a completely different orbit to meet >him, whereas with Judd I feel that it is only a simple adjustment of >trajectory that is needed! > >There is no way that I could accept his proposal for eliminating all >accidentals - this would leave diminished fifths exposed with the bass >line, which is completely alien (in my view) with all we know about theory >and practice in the Renaissance. This was not really a proposal. I just wondered why you were willing to accept certain awkwardnesses and not others. Your answer makes this very clear and reminds me of what I already "knew" and should have remembered. ( I hope I did not give the impression that I was attempting to speak as an authority on the theory of this period, which I am certainly not.) Meanwhile, the passage does remain a conundrum. >It is also inappropriate to "justify" >such moves by applying anachonistic chord symbols that apply to a >fundamentally different and later tonal system. When I used the term >"tonality", I was applying it in a sense figuratively to make a >distinction between *mode* viewed as an apparatus for musical design, and >what the living aural EFFECT of the application of *mode* yields. I can >see no actual connection between this and what Grauer is implying be >"tonality". Again, I think you are interpreting what I said more strongly than it was intended. I mainly wanted to sound you out on this topic, particularly as I was intrigued by your use of the word "tonal." >It is an interesting idea that a composer like Josquin can - as a >soothsayer - peep into the minds of composers not to be born for over 100 >years, and emulate the ideas they will come up with. I don't personally >regard this as a tenable "justification" for seeking to interpret his >music in a particular way, and would much rather view his eminence in >terms of the effect HE had on those who followed him. New ideas, in music and elsewhere, do not simply come out of nowhere. When I said that Josquin might have "looked ahead" this was a metaphor for something that we find everywhere in history. Please don't take it literally. The problem exposed in your paper is not limited to this particular piece. What I was suggesting was 1. that the difficulties entailed in avoiding the "Diabolus in Musica" were of a nature that they created a "pressure" which eventually led to the tonal system; 2. the "pressure" in question was already present in the 15th century and could have led to practices that look like "anticipations" of tonal practice; and 3. such "anticipations" could be understood also as subtle influences on the future course of music (what makes them appear to be anticipations would actually be due to their influence on the future). In other words, we might want to recognize that there could be a certain *logic* (word of horror to post structuralists, I admit it) to the evolution of music practice and theory, a logic which by its very nature, need not be confined to a particular period. The existence of such a logic would not "justify" a particular practice when seen in terms of the traditions of its own time, but could help us understand why a piece like this motet "violates" certain rules in a certain way rather than some other way. (It could also, I must admit, cause us to retrospectively prefer certain solutions on the basis of what sounds "natural" to us in terms of our own traditions, so we must be very cautious in this respect.) Victor Grauer no academic affiliation grauer@pps.pgh.pa.us From rjudd@sas.upenn.edu Mon Aug 19 09:27:23 1996 Received: from mail2.sas.upenn.edu (rjudd@MAIL2.SAS.UPENN.EDU [165.123.26.33]) by boethius (8.7.1/8.7.1) with ESMTP id JAA14523 for ; Mon, 19 Aug 1996 09:27:22 -0700 (PDT) Received: (from rjudd@localhost) by mail2.sas.upenn.edu (8.7.5/SAS 8.06) id MAA25575 for mto-talk@boethius.music.ucsb.edu; Mon, 19 Aug 1996 12:26:54 -0400 (EDT) From: rjudd@sas.upenn.edu (Robert F Judd) Posted-Date: Mon, 19 Aug 1996 12:26:54 -0400 (EDT) Message-Id: <199608191626.MAA25575@mail2.sas.upenn.edu> Subject: Re: Wibberley, MTO 2.5 (fwd) To: mto-talk@boethius.music.ucsb.edu (MTO -Talk) Date: Mon, 19 Aug 1996 12:26:53 -0400 (EDT) X-Mailer: ELM [version 2.4 PL23-upenn3.1] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: mua01rw@gold.ac.uk (Roger Wibberley) Subject: Re: Wibberley, MTO 2.5 I find much to agree with in Victor Grauer's second message, and I did not want to interpret what he originally said in a more literal manner than he intended. However, I do not regard my views on the "tonality" of 15th c. music as being quite the conundrum suggested. Cristle Collins Judd's initial reprimand suggested that my use of such words as "tonal" belied a modernistic view of early music. Possibly the same sentiment is distantly echoed in the following snippet from Grauer: > What I was suggesting was 1. that the difficulties >entailed in avoiding the "Diabolus in Musica" were of a nature that they >created a "pressure" which eventually led to the tonal system; 2. the >"pressure" in question was already present in the 15th century and could >have led to practices that look like "anticipations" of tonal practice; By "THE tonal system", it must be assumed that reference is being made only to a particular one - i.e. the later major/minor system. Similarly, the "tonal practice" referred to (which may supposedly have been "anticipated") must be the practice of using this particular system (which was not, of course, in use at the time of Josquin). None of this should, however, suggest that other tonal systems did not exist at various times, and my view of tonality with regard to the 15th c. is more related to that of the Middle Ages where, as we know, there were four recognised tonalities: Protus, deuterus, tritus and tetrardus, each of which gave rise to two alternative modes (an authentic and a plagal). The later system was quite different: there were 24 tonalities grouped into two modes (12 major modes, and 12 minor). Furthermore, since 22 of these were simply transpositions of the remaining two, it is obvious that the practice being developed relied upon the progressive use of key and key-relationship. Moving back to the distant world of Josquin, however, tonality was a very different beast, and its practical and theoretical evolution offers an interesting comparison with the later system towards which it must (as Grauer suggests) inexorably have moved. In my view, the key to unravelling this development lies in an understanding of the way in which composers married the two theoretically alien concepts of Mode and Ficta. (While Judd is quite correct in stating that these occupied completely different theoretical concepts, it is quite simple to prove that composers provided their own solutions when faced with the inevitable PRACTICAL interraction of the two phenomena.) Three of the above four modes are quite straightforward: Protus (arising from the Dorian modes), Deuterus (the Phrygians), and Tetrardus (the Mixolydians). The third tonality (Tritus) however demonstrated something quite remarkable: composers started placing a one-flat partial signature in the lower voice(s) in the LOWEST octave of the gamut. Two factors are immediately obvious (one practical, and one theoretical): a) the sole purpose was to eliminate the diminished fifth which would otherwise sound above the low B-mi recurring in the lower voice(s) and the final on F higher in the texture; and b) this partial signature was a direct and unambiguous written use of Ficta. (B-fa did not, remember, exist in the recta gamut in the lowest octave.) It is therefore not correct to state that Ficta and Mode are SIMPLY unrelated theoretical concepts (*pace* Judd). Neither is it correct to state that the sole purpose of using a signature is to transpose to another location the same intervals that would have occurred without the signature but in their "proper" (untransposed) position (*pace* Berger). The reality is that compositions written according to the Tritus tonality (adopting the Lydian modes) now as a matter of custom DID have a one-flat signature, but purely to eliminate a defective interval. The really interesting point, however, is that Glareanus (surely?) did an important and clever double-take! At a time when composers were now adopting the one-flat signature in all voices (instead of laboriously inserting all the upper b-flats as accidentals, thereby "fixing" otherwise superfluous octaves arising from the low B-fa ficta partial signature and b-mi steps higher up in the texture), he now decided to REGARD this as a "transposed mode"! This, surely, caused him to give theoretical recognition to a *new* beast: the Ionian mode (i.e. an "untransposed" version of what had previously been the accepted Tritus (Lydian) tonality with an inserted signature to fix the diminished fifth). This provided a theoretical ratification of something rather like (to us) the later major-key tonality, but it was NOT really "new" because composers *had* been using it as a result of *ficta imposition upon mode* (which was the main focus of my argument against Bent's proposal). What WAS new, however, was that Glareanus was ratifying (and indeed exemplifying) a "mode" that had no theoretical connection whatsoever with the traditional 4 tonalities other than being an "untransposition" of what used to be the Tritus with an added *ficta* signature to fix an unsatisfactory vertical interval (and which had never been transposed in the first place!). In order to answer Rosemary Killam's query, dated 31 July, about the pre-1550 use of Ionian "tonality" (which I suppose we will have to call it, since it does not seem to have arisen from anything other than a clever piece of jiggery-pokery on the part of Glareanus), problems have to be faced: a) which pieces do not appear to be in this mode but WERE?; b) which compositions appear to be written in this mode but were NOT?; and c) which not only appear to have been but also WERE? It is a complex situation to unravel, having various dimensions (theoretical, practical, aesthetic, historical, chronological etc...). There is, of course, no shortage of compositions from Dunstable onwards that might "seem" to be appropriate candidates, but it is difficult to argue that they are all valid ones. The presumption underlying my article was that the Josquin motet WAS, especially since Glareanus said so. ______________________ Roger Wibberley Head of Studies Music Department Goldsmiths College New Cross London SE14 6NW Tel: 0171 919 7661 Fax: 0171 919 7644 JANET: mua01rw@uk.ac.gold InterNet: mua01rw@gold.ac.uk Web page- http://ludwig.gold.ac.uk/rwibberley/ ______________________ From rjudd@sas.upenn.edu Mon Aug 19 09:31:34 1996 Received: from mail2.sas.upenn.edu (rjudd@MAIL2.SAS.UPENN.EDU [165.123.26.33]) by boethius (8.7.1/8.7.1) with ESMTP id JAA14878 for ; Mon, 19 Aug 1996 09:31:33 -0700 (PDT) Received: (from rjudd@localhost) by mail2.sas.upenn.edu (8.7.5/SAS 8.06) id MAA26088 for mto-talk@boethius.music.ucsb.edu; Mon, 19 Aug 1996 12:31:05 -0400 (EDT) From: rjudd@sas.upenn.edu (Robert F Judd) Posted-Date: Mon, 19 Aug 1996 12:31:05 -0400 (EDT) Message-Id: <199608191631.MAA26088@mail2.sas.upenn.edu> Subject: Re: Wibberley, MTO 2.5 (fwd) To: mto-talk@boethius.music.ucsb.edu (MTO -Talk) Date: Mon, 19 Aug 1996 12:31:05 -0400 (EDT) X-Mailer: ELM [version 2.4 PL23-upenn3.1] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: meeus@musi.ucl.ac.be (Nicolas Meeus) Subject: Re: Wibberley, MTO 2.5 Roger Wibberley's article in MTO 2.5 and the following discussion in mto-talk raises interesting issues, some of which I'd like to address. First, a matter of acoustics. Both Margaret Bent and Roger Wibberley seem to imply that Josquin's or today's singers would sing the passage under discussion in just intonation, i.e., that they would sing pure octaves, fifths, fourths and thirds (major or minor), corresponding to the superparticular ratios of 2:1, 3:2, 4:3, 5:4 and 6:5, or to 1200, 702, 498, 386 and 316 cents, respectively. It is easy to compute relative values for all the consonant notes in the passage, but something odd happens. Consider for instance how the first C in the tenor, m. 44, connects to the second, in the altus, m. 46, by a string of consonances: C (tenor) - F (bass) - D (tenor) - G (bass) - E (tenor) - C (altus). Values in cents can be given to these pitches: C (0) - F (498) - D (498-316=182) - G (182+498=680) - E (680-316=364) - C (364-386=-22). The second C, in short, is a syntonic comma lower than the first (this is due to the way in which fifths and thirds combine in the string of consonances). But the phenomenon repeats: I leave it up to you to check that, on the same premises, the C in the altus in m. 52 is five commas, 110 cents, more than a semitone, lower than the first. I doubt that any theory of frequency instability reasonably can account for such a situation which, nevertheless, is quite common (although it probably tends to become more frequent in tonal music). Just intonation is an utopia and, in actual practice, frequent pitch adjustments are required, which will be less obnoxious if the music includes some level of dissonance. This may be considered an argument against Bent's solution. Let's not jump to conclusions, however: the definition of consonance is a complex affair. My sole purpose here is to propose matter for reflection. Wibberley's analysis of Bent's version views the addition of ficta flats as causing the mode to change to transposed Aeolian. Cristle Collins Judd takes this to issue, stating (in substance) that, in the 16th century, the addition of ficta notes was not necessarily viewed as modifying the mode. This is a very old discussion that can be traced back at least to Guido of Arezzo. It first concerned the B flat which, in protus and tritus modes, was considered a mere alternative to B natural but which in tetrardus, Guido says, might produce a confusion with the protus transposed. Glarean settled the matter, stating that the Dorian and the Lydian with B flat had to be considered transpositions. Throughout the Middle Ages, the Gamut had been octotonic (including the B flat). In the 16th century, it was split into two intertwined heptatonic systems, the *cantus durus* and the *cantus mollis* or, in Praetorius' terminology, the *regular* and the *transposed* systems. The octotonic conception allowed for one note, the B, to know two forms, B natural of B flat. From there, it was but a little conceptual step to admit that any note similarly could know more than one form. This is the principle of ficta notes, viewed as possible alternatives to recta ones. Replacing a diatonic note by its ficta alternative was not viewed as modifying the essential "diatonicity" of a composition. (The worm was in the fruit from the start, however, for ficta notes were described as belonging to transposed hexachords.) In the Renaissance, a composition may easily have made use of the twelve notes of the chromatic scale and nevertheless remain basically diatonic -- and modal (Gesualdo). However, once the B flat came to be considered as the token of a transposition, the same conception a fortiori applied to more remote ficta notes. Eventually, the system appeared as a "dodecaphonic" (chromatic) interlacing of twelve heptatonic scales. In other terms, there exists in my opinion a "modal" conception of the pitch system where the (dodecaphonic) scale consists in two tiers, with the ficta notes ancillary to the recta ones, and a "tonal" one where chromatic notes are tokens of transpositions (or modulations). This is the scalar aspect of modality and tonality (to which a full description should add considerations of centripetal and/or centrifugal forces). In short, the reference system of modality is the diatonic system (with chromatic notes added), that of tonality the chromatic one (within which diatonic subsets are chosen). Bent's version of the passage discussed involves ten different pitch classes, from A flat to B natural in the cycle of fifths, while Wibberley's version involves only eight, from B flat to B natural. However, Bent's version appears to consist in two heptatonic sections, the first (m. 44-47) based on the "natural" notes (F to B), the second (m. 48-52) making use of the seven pitch classes from A flat to D. Wibberley's version is identical in the first section, but the second one is more difficult to describe in terms of a heptatonic set, because of the alternation of B flat and B natural. In short, Wibberley's version is more adequately described as octotonic, while Bent's is bi-heptatonic (with the two heptatonic sets separated by four steps in the cycle of fifths). These two versions evidence widely different conceptions of diatonicism, Bent's version being, in a way, closer to a "tonal" conception than Wibberley's. The alternation of B flat and B natural in Wibberley's version stresses the ancillary position of the first. Bent, on the other hand, carefully avoids any such alternation and actually introduces ficta notes dictated by considerations of horizontal euphony: from a purely vertical point of view, all the flats in m. 50 could be dispensed with. Any solution that would reduce the number of flats in the second line (m. 49-52) of Bent's version, by creating "false relations" (i.e. by stretching the pitch set to more than seven pitches) would tend to restore the ficta additions to their hierarchically lower position. The problem with Bent's version, in other words, may not be that there are too much ficta alterations, but rather that they are added "quasi diatonically", which tends to produce an effect of transposition (should I dare say "modulation"?). I would not there say whether one of the version can be judged better than the other on these premises, but I think we must be aware of this difference in conception. I also wonder in what sense Cristle Collins Judd argued that Wibberley understood mode "as a tonal system" and whether the same criticism could apply to the above. I'd be happy to hear any objection in this direction. I'd like to stress, however, that to speak of a systematic organization of pitches (such as that of the Greek transposition systems, or of the Gamut, or of the 24 major and minor scales) as a "tonal system" is to use the expression in a totally different meaning as when one says that composers from the 17th to the 19th century composed in the tonal system. To confuse tonality with a system of pitches and of scales has been a common mistake in the 19th and early 20th century. Renaissance modality, if it existed, certainly was based on some system of pitches, the conception of which was quite different from that of the tonal period in the following centuries, even although the resulting pitches and pitch classes basically were the same. Depending on this underlying conception, a composition may be said generally "modal" or "tonal", in some sense of these terms. To determine to what particular mode (or what particular tonality) a composition belongs is another matter. Nicolas Meeus Universite de Paris Sorbonne Universite Catholique de Louvain a Louvain-la-Neuve meeus@musi.ucl.ac.be From rjudd@sas.upenn.edu Mon Aug 19 19:25:34 1996 Received: from mail1.sas.upenn.edu (rjudd@MAIL1.SAS.UPENN.EDU [165.123.26.32]) by boethius (8.7.1/8.7.1) with ESMTP id TAA21844 for ; Mon, 19 Aug 1996 19:25:33 -0700 (PDT) Received: (from rjudd@localhost) by mail1.sas.upenn.edu (8.7.5/SAS 8.06) id WAA27327 for mto-talk@boethius.music.ucsb.edu; Mon, 19 Aug 1996 22:25:03 -0400 (EDT) From: rjudd@sas.upenn.edu (Robert F Judd) Posted-Date: Mon, 19 Aug 1996 22:25:03 -0400 (EDT) Message-Id: <199608200225.WAA27327@mail1.sas.upenn.edu> Subject: Re: Wibberley, MTO 2.5 (fwd) To: mto-talk@boethius.music.ucsb.edu (MTO -Talk) Date: Mon, 19 Aug 1996 22:25:02 -0400 (EDT) X-Mailer: ELM [version 2.4 PL23-upenn3.1] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: r-cohn@uchicago.edu (Richard Cohn) Subject: Re: Wibberley, MTO 2.5 Consider for instance how the first C in the tenor, m. 44, >connects to the second, in the altus, m. 46, by a string of consonances: C >(tenor) - F (bass) - D (tenor) - G (bass) - E (tenor) - C (altus). Values >in cents can be given to these pitches: C (0) - F (498) - D (498-316=182) >- G (182+498=680) - E (680-316=364) - C (364-386=-22). The second C, in >short, is a syntonic comma lower than the first (this is due to the way in >which fifths and thirds combine in the string of consonances). But the >phenomenon repeats: I leave it up to you to check that, on the same >premises, the C in the altus in m. 52 is five commas, 110 cents, more than >a semitone, lower than the first. I doubt that any theory of frequency >instability reasonably can account for such a situation which, >nevertheless, is quite common (although it probably tends to become more >frequent in tonal music). Just intonation is an utopia and, in actual >practice, frequent pitch adjustments are required, which will be less >obnoxious if the music includes some level of dissonance. In his book *Studies in Musical Science in the Late Renaissance*, D.P. Walker draws attention to a passage from the 17th-century theorist Christiaan Huygens. Huygens cites an example quite similar to the melody cited above by Prof. Meeus, and then comments to the effect that the second C ought to be out of tune with the first, but that the singer mentally retains the initial pitch throughout the melody, matching it at the end, so that in fact no flatting takes place. An early account the same cognitive faculties that were later recognized by Schenker as underlying "prolongation." Richard Cohn Acting Chair, Dept. of Music University of Chicago 1010 E 59th St. Chicago IL 60637 (312) 702-8500 r-cohn@uchicago.edu From rjudd@sas.upenn.edu Tue Aug 20 06:39:11 1996 Received: from mail1.sas.upenn.edu (rjudd@MAIL1.SAS.UPENN.EDU [165.123.26.32]) by boethius (8.7.1/8.7.1) with ESMTP id GAA28106 for ; Tue, 20 Aug 1996 06:39:11 -0700 (PDT) Received: (from rjudd@localhost) by mail1.sas.upenn.edu (8.7.5/SAS 8.06) id JAA29439 for mto-talk@boethius.music.ucsb.edu; Tue, 20 Aug 1996 09:38:44 -0400 (EDT) From: rjudd@sas.upenn.edu (Robert F Judd) Posted-Date: Tue, 20 Aug 1996 09:38:44 -0400 (EDT) Message-Id: <199608201338.JAA29439@mail1.sas.upenn.edu> Subject: Re: Wibberley, MTO 2.5 (fwd) To: mto-talk@boethius.music.ucsb.edu (MTO -Talk) Date: Tue, 20 Aug 1996 09:38:44 -0400 (EDT) X-Mailer: ELM [version 2.4 PL23-upenn3.1] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: rnkillam@gte.net (Rosemary N. Killam) Subject: Re: Wibberley, MTO 2.5 Prof. Meeus' points raise some questions that I haven't considered in some years, and on which there is probably newer information than mine--help anyone? I was taught in performance practice that decisions on just/mean intonation lay not only in the historical period and culture, but also in the architectural space for which a work was planned? As I recall, just intonation was considered more appropriate for large spaces such as the Gothic cathedrals, and that likelihood of brass or wind doubling had to be taken into account? What's the current thought on this? Also, my limited experience in singing Gesualdo was done totally unaccompanied, since any instrumental doubling at the time of composition was considered unlikely, if not impossible--that the compositions were designed for very small performance venues, if performed at all at the time written? Thanks, Rosemary Killam, UNT-COM !NEW EMAIL ADDRESS, STARTING JUNE 30!(please report any problems?) rnkillam@gte.net (Rosemary N. Killam) and/or rkillam@music.unt.edu (Rosemary N. Killam) School Phone: 817-565-3761 School FAX: 817-565-2002 From rjudd@sas.upenn.edu Tue Aug 20 06:40:37 1996 Received: from mail1.sas.upenn.edu (rjudd@MAIL1.SAS.UPENN.EDU [165.123.26.32]) by boethius (8.7.1/8.7.1) with ESMTP id GAA28220 for ; Tue, 20 Aug 1996 06:40:36 -0700 (PDT) Received: (from rjudd@localhost) by mail1.sas.upenn.edu (8.7.5/SAS 8.06) id JAA29695 for mto-talk@boethius.music.ucsb.edu; Tue, 20 Aug 1996 09:40:10 -0400 (EDT) From: rjudd@sas.upenn.edu (Robert F Judd) Posted-Date: Tue, 20 Aug 1996 09:40:10 -0400 (EDT) Message-Id: <199608201340.JAA29695@mail1.sas.upenn.edu> Subject: Re: Wibberley, MTO 2.5 (fwd) To: mto-talk@boethius.music.ucsb.edu (MTO -Talk) Date: Tue, 20 Aug 1996 09:40:09 -0400 (EDT) X-Mailer: ELM [version 2.4 PL23-upenn3.1] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: rnkillam@gte.net (Rosemary N. Killam) Subject: Re: Wibberley, MTO 2.5 Although, once again, I'm out of my depth, my experience with modal identification in 15th and 16th c. literature, at least pre-Glarean, is that it involves not only mode and ficta but also hexachords as interrelated on the various forms of the Guidonian hand. My question/guess--I can find no composer/theorist prior to Morley who had not learned music reading as a choir boy (think of Tinctoris' and Gafori's extensive explanations and illustrations of use of hand and hexachord?). Once I started singing/pointing to the appropriate point on my hand, a lot of modal ambiguities seemed to be clarified? My guess is that the way one learns(ed) music influences(ed) one's modal sense? What think y'all? Also, improvising in rhythmic modes to cantus firmi tends to confirm certain modal assignments? Rosemary Killam, !NEW EMAIL ADDRESS, STARTING JUNE 30!(please report any problems?) rnkillam@gte.net (Rosemary N. Killam) and/or rkillam@music.unt.edu (Rosemary N. Killam) School Phone: 817-565-3761 School FAX: 817-565-2002 From rjudd@sas.upenn.edu Wed Aug 21 20:09:09 1996 Received: from mail2.sas.upenn.edu (rjudd@MAIL2.SAS.UPENN.EDU [165.123.26.33]) by boethius (8.7.1/8.7.1) with ESMTP id UAA12946 for ; Wed, 21 Aug 1996 20:09:09 -0700 (PDT) Received: (from rjudd@localhost) by mail2.sas.upenn.edu (8.7.5/SAS 8.06) id XAA20826 for mto-talk@boethius.music.ucsb.edu; Wed, 21 Aug 1996 23:08:42 -0400 (EDT) From: rjudd@sas.upenn.edu (Robert F Judd) Posted-Date: Wed, 21 Aug 1996 23:08:42 -0400 (EDT) Message-Id: <199608220308.XAA20826@mail2.sas.upenn.edu> Subject: Re: Wibberley, MTO 2.5 (fwd) To: mto-talk@boethius.music.ucsb.edu (MTO -Talk) Date: Wed, 21 Aug 1996 23:08:42 -0400 (EDT) X-Mailer: ELM [version 2.4 PL23-upenn3.1] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: mua01rw@gold.ac.uk (Roger Wibberley) Subject: Re: Wibberley, MTO 2.5 I read Professor Meeus' penetrating and clinical discussion with great interest, and much appreciated his clear appraisal of the issues underlying the differing interpretations (each inevitably having its own respective pros and cons). There is one important issue, however, that needs to be clarified: I have certainly unwittingly erred if I so much as even implied that just intonation was a factor in my argument. Certainly perfect octaves, fifths and fourths are pure. Thirds, however, are quite another matter. Although it has some attributes to commend it, just intonation can never have had any real *practical* application in vocal music. How could it, since it yields two quite different whole-tone intervals (9/8 and 10/9 respectively)? Its total incompatibility with medieval and Renaissance theory is manifest in crucial ways: 1) We know that all whole-tone steps of the gamut are equivalent (9/8), and upon this fact rests the whole concept of mutation (e.g. g-a is variously "re-mi", "ut-re" or "sol-la", depending upon the hexachord in use). Since all hexachords are equivalent (including *ficta* ones) it must follow that all whole-tone steps are equivalent. This requirement is completely abrogated by just intonation. 2) Medieval and Renaissance theory (and practice) predicate the existence of differing semitones: *major* and *minor*. The difference between the two is the Pythagorean comma. Hence the "diatonic" semitone of the normal hexachord (i.e. e-f, a-b flat and b-c), being the *minor* semitone, is a smaller actual interval than the "chromatic" semitone (e.g. b flat-b natural, or f-f sharp) which is *major*. Just intonation, however, requires an opposite evaluation of semitones: the interval of, say, c-d flat (16/15) is now *greater* than that of c-c sharp (135/128), the difference between the two amounting to 20 cents. 3) Since major thirds in just intonation are pure, this cannot (as a consequence) be the case in theory using the gamut: this is because a pure major third can arise only from two *unequal* whole-tones. Thus, in just intonation, c-d (9/8) + d-e (10/9) will yield 90/72 (=5/4, being a pure third). In contradistinction, hexachordal structure requires that a major third must be a much larger "impure" interval: thus c-d (9/8) + d-e (9/8) will yield 81/64 which is considerably wider even than an equally-tempered major third (equivalent indeed to 408 cents, as opposed to 400 cents in equal temperament, and only 386 in just intonation). This means that the overall difference between a "gamut" major third and that of just intonation is the comma (22 cents). So, what does this mean for the Josquin example (and all others like it)? As Professor Meeus has clearly demonstrated, were just intonation to be applied (by what technical means I cannot imagine, at least within medieval and Renaissance theoretical limitations), the sung pitch of the motet would inexorably sink. As the rising melodic lines attained their perfect fifths (which would be pure), the thirds (also pure) would be narrowed downwards. Against these narrowed pure thirds further successions of perfect fifths would accrue. After only two measures, the difference would be at least a syntonic comma; within only eight measures, this would expand to at least a semitone. I have to admit, however, that this state of affairs would do far more harm to my argument than to Margaret Bent's (Bent, remember, argued *against* the notion of pitch stability while I argued strongly for it). But to be realistic, if the singing of 8 measures of a motet can depress the pitch by a semitone, what kind of voices would have been expected to continue singing for up to ten minutes?!! Happily, however, we can be fairly certain that these difficulties are only illusory, and did not actually exist. By what technical means would singers have maintained the pitch while being obedient to the laws of consonance (as they understood them)? A clue is apparent immediately in the melodic movement from the last beat of m. 44 to the first beat of m. 45. While voice 1 moves upwards from gg to aa, voice 4 accompanies with a move from E to F. Since E-F is a *minor* semitone, the upward movement of voice 1 (the whole-tone step gg-aa) must be equivalent to *more than twice* this amount. This means not only that the third is NOT pure, but that singers of the time would have expected as a matter of course (from their training derived through the gamut and its solmization) to pitch major thirds as wide intervals (indeed *very* wide by our standards). It therefore would follow that when in m. 45 voice 3 moves up to the d (to form its perfect fifth with voice 1) this d would also be protected from pitch-depression. A similar tempering of thirds and fifths would continue throughout the sequence. In short, not only does this mean that after two measures the note c in voice 2 is identical in pitch with that two measures earlier in voice 3, but also that this same pitch is maintained at bar 50 in voice 2 (and, indeed, every single instance of this note throughout the entire motet will - if the steps of the gamut are rendered properly as was expected - maintain exactly the same pitch). This is why I have to reject the idea that pitch-stability was not a crucial factor; it must have been if only because correct movement through the steps of the gamut a) would have required it, and b) would have made it inevitable. It is thus the harmony that arises from combined linear movements (all conceived through the steps of the gamut), and not vice versa. Intervalic adjustments to individual lines will, of course, have to occur from time to time to produce a satisfactory harmonic result, but these are all provided via the normal rules of *musica recta* and *musica ficta*. None of these rules, however, caters for such things as "pure thirds" which can, at best, be said to arise not from the apparatus of the gamut but from the individual responses of performers under particular conditions. It is the performers, after all, who will have the final say as to whether the pitch of their performance will be allowed progressively to decline in favour of maintaining purity of thirds, or whether they will obey the requirements of their technical apparatus (the gamut) and maintain relative pitch by attempting to inflect these intervals by something approaching the comma. It is my own view that they would instinctively have done the latter, for I believe that the reason why thirds and sixths (major and minor) were universally classed as *imperfect* consonances was because they were not "pure" but rather *impure*. As such their harmonic function - like that of the dissonances - was to provide yet another tool to highten and emphasize the hierarchical and structural superiority of the perfect consonances towards which they inevitably led, and onto which they inexorably resolved. For those of us (myself included) who were not trained to locate the steps of the gamut (a practice which fell out of use some considerable time ago!), here - for what they are worth - are a few "quick tips" to help singers navigate their way through a motet like the Josquin: a) Octaves, perfect fifths and perfect fourths should always be pure; b) major thirds should *never* be pure, but should be bright and pitched at least as wide as (if not wider than) those familiar to us via equal temperament; c) minor thirds should also *never* be "pure", but should be slightly narrower than those of equal temperament; d) "diatonic" semitones (e.g. e-f, b-c, a-b flat etc.) should be slightly narrower than in equal temperament; e) "chromatic" semitones (e.g. f-f sharp, b flat-b natural) should be slightly wider than equally-tempered ones; f) diminished fifths should never occur as main-beat harmonies between the lowest-sounding voice and any other. Perfection of interval should be achieved by *recta* or *ficta* means (whichever is adjudged to remain more faithful to the integrity of the mode and its "tonal effect" as evinced by the phrase as a whole through its melodic components and their harmonic interplay), and it should not be presumed that either must necessarily be preferred to the other; g) diminished fifths and tritones can be admitted as main-beat harmonies higher up in the texture provided both notes which form this interval also form *independently* an imperfect consonance (3rds and/or 6ths) with the lowest voice AND both move by step to form a consonance on the next main beat (which may be decorated via a suspension). This will obey the principle that intervals should not only be judged "in relation to themselves", but also "in relation to all the other voices". These contingencies cannot ultimately satisfy every conceivable criterion which has come down to us over the years (and I have no doubt that I will be taken to task for some of them in future postings!), but they may at least help to regulate and balance consonance and dissonance in a sensible way that not only preserves pitch-stability, but also yields a result not far removed from what musicians of the time might have wished for. ______________________ Roger Wibberley Head of Studies Music Department Goldsmiths College New Cross London SE14 6NW Tel: 0171 919 7661 Fax: 0171 919 7644 JANET: mua01rw@uk.ac.gold InterNet: mua01rw@gold.ac.uk Web page- http://ludwig.gold.ac.uk/rwibberley/ ______________________ From rjudd@sas.upenn.edu Thu Aug 22 06:06:21 1996 Received: from mail1.sas.upenn.edu (rjudd@MAIL1.SAS.UPENN.EDU [165.123.26.32]) by boethius (8.7.1/8.7.1) with ESMTP id GAA16960 for ; Thu, 22 Aug 1996 06:06:20 -0700 (PDT) Received: (from rjudd@localhost) by mail1.sas.upenn.edu (8.7.5/SAS 8.06) id JAA26670 for mto-talk@boethius.music.ucsb.edu; Thu, 22 Aug 1996 09:05:54 -0400 (EDT) From: rjudd@sas.upenn.edu (Robert F Judd) Posted-Date: Thu, 22 Aug 1996 09:05:54 -0400 (EDT) Message-Id: <199608221305.JAA26670@mail1.sas.upenn.edu> Subject: Re: Wibberley, MTO 2.5 and Tuning (fwd) To: mto-talk@boethius.music.ucsb.edu (MTO -Talk) Date: Thu, 22 Aug 1996 09:05:54 -0400 (EDT) X-Mailer: ELM [version 2.4 PL23-upenn3.1] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: rnkillam@gte.net (Rosemary N. Killam) Subject: Re: Wibberley, MTO 2.5 and Tuning Ref. singing in various tunings--may I suggest that Prof. William Mahrt of Stanford U. be brought into this discussion in some way? He explained some of his pedagogical techniques for teaching varying tunings in his performance practice classes. The top madrigal group (my intonation was not good enough to be selected for this group--I sang "junior varsity madrigals") was trained to sing in different tunings. As I recall, hpschds. with different tunings were kept on stage during performances, to be used if performance practice warranted. Is there anyone lurking on this list who sang varsity madrigals at Stanford and who can provide more detail than I? This topic was covered rather thoroughly on the SMT list this past spring, so perhaps this is redundant? Best, Rosemary Killam, UNTCOM, rnkillam@gte.net From rjudd@sas.upenn.edu Mon Aug 26 11:29:32 1996 Received: from mail1.sas.upenn.edu (rjudd@MAIL1.SAS.UPENN.EDU [165.123.26.32]) by boethius (8.7.1/8.7.1) with ESMTP id LAA17392 for ; Mon, 26 Aug 1996 11:29:30 -0700 (PDT) Received: (from rjudd@localhost) by mail1.sas.upenn.edu (8.7.5/SAS 8.06) id OAA00608 for mto-talk@boethius.music.ucsb.edu; Mon, 26 Aug 1996 14:29:03 -0400 (EDT) From: rjudd@sas.upenn.edu (Robert F Judd) Posted-Date: Mon, 26 Aug 1996 14:29:03 -0400 (EDT) Message-Id: <199608261829.OAA00608@mail1.sas.upenn.edu> Subject: Wibberley, MTO 2.5 (fwd) To: mto-talk@boethius.music.ucsb.edu (MTO -Talk) Date: Mon, 26 Aug 1996 14:29:02 -0400 (EDT) X-Mailer: ELM [version 2.4 PL23-upenn3.1] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: meeus@musi.ucl.ac.be (Nicolas Meeus) Subject: Wibberley, MTO 2.5 What I had in mind, when I mentioned the problem of just intonation in the context of Josquin's Ave Maria, was that the singers would have performed the necessary pitch adjustments during the dissonances. Roger Wibberley suggests that they may have sung impure thirds, more or less resembling Pythagorean ones. Discussing this will lead us away from the problem of modality which, I believe, is the interesting one, but the discussion may have some interest of its own. Roger writes : "just intonation can never have had any real *practical* application in vocal music". Right, but I would be tempted to say exactly the same of the Pythagorean intonation, so many medieval and Renaissance theorists notwithstanding. A distinction must be made, I believe, between theoretical descriptions of pitch systems, such as the Pythagorean or Zarlino's, and their practical realization in singing or on instruments. That the medieval theory described whole-tone steps corresponding to the ratio of 9/8 and that it made a distinction between major and minor semitones does not necessarily entail that they were sung or played that way. One possible way of defining a consonant interval may be to say that it has a strong "definition" -- that is, that the difference between a pure and an impure intonation is striking. Helmholtz' *Sensations of Tone* has a good illustration of this (fig. 60 in Ellis' translation), showing that the octave not only is the most consonant of intervals, but also that the slightest deviation from its pure intonation causes the highest possible level of dissonance. The reproducibility of an interval depends on this kind of definition. A pure major third is reproducible, a Pythagorean one may not be. Modern singers may develop an ability to sing in equal or some other temperament, but that is the result of recent standardizations and hardly could apply in the first half of the 16th century. Therefore, while I agree with Robert that octaves, fifths and fourths were sung pure (or as pure as possible), I doubt that thirds *never* were pure, as he suggests. I think they were sung pure as often as possible or convenient, depending on the extent to which pitch stability at short and long term was considered important. (Even today, choirs tend to lower in pitch, even although they strongly believe in the importance of a pitch standard.) I trust that some thirds (major or minor) were sung purer than others, depending on the context and, among others, on the dissonance level at any moment. But Robert is right, of course, that whenever the thirds were made impure, the major ones were larger, the minor ones narrower than pure. The earliest descriptions of keyboard tunings date from the late 14th-century or the early 15th-century (Baudecetus [Baudenet de Reims] quoted by Arnault of Zwolle, Georgio Anselmi of Parma, etc.). All are Pythagorean in principle. However, as Mark Lindley shew, many tune several or all the black keys as flats, even although they certainly were used as sharps. The reason is that a Pythagorean diminished fourth, such as D-G flat, is a very close approximation to a pure major third and thus easily stands for D-F sharp. (498*8-1200*3=384, 2 cents less than the pure third of 386 cents; the difference is what the Ancients called a schisma.) With this system, the *recta* notes were tuned in Pythagorean tuning, the *ficta* ones in just intonation. It was an elegant way to reconcile a practice based on pure consonance with a faithfully Pythagorean theory. This also is the closest we may get to knowing actual practices of the time with respect to intonation. (I will be away for a week and won't answer E-mail before 2 September.) Nicolas Meeus Universite de Paris Sorbonne Universite Catholique de Louvain a Louvain-la-Neuve meeus@musi.ucl.ac.be From rjudd@sas.upenn.edu Mon Aug 26 11:31:41 1996 Received: from mail1.sas.upenn.edu (rjudd@MAIL1.SAS.UPENN.EDU [165.123.26.32]) by boethius (8.7.1/8.7.1) with ESMTP id LAA17598 for ; Mon, 26 Aug 1996 11:31:41 -0700 (PDT) Received: (from rjudd@localhost) by mail1.sas.upenn.edu (8.7.5/SAS 8.06) id OAA00974 for mto-talk@boethius.music.ucsb.edu; Mon, 26 Aug 1996 14:31:16 -0400 (EDT) From: rjudd@sas.upenn.edu (Robert F Judd) Posted-Date: Mon, 26 Aug 1996 14:31:16 -0400 (EDT) Message-Id: <199608261831.OAA00974@mail1.sas.upenn.edu> Subject: Re: Wibberley, MTO 2.5 (fwd) To: mto-talk@boethius.music.ucsb.edu (MTO -Talk) Date: Mon, 26 Aug 1996 14:31:16 -0400 (EDT) X-Mailer: ELM [version 2.4 PL23-upenn3.1] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Sender: rnkillam@gte.net (Rosemary N. Killam) Subject: Re: Wibberley, MTO 2.5 I'm over my head here, but why is it important to consider the area a modulation rather than a passage written deliberately out of mode? I was just rereading Lester's *Between Modes and Keys--* last night and he seems to have a very different take on Glareanus' meaning of mode? Could you possibly expand on similarities and differences between your and Lester's treatment of Glareanus? I'd appreciate anyone else's ideas on this, as well? Thanks, Rosemary, UNT-COM rnkillam@gte.net