source file: m1415.txt Date: Thu, 14 May 1998 16:33:41 -0400 Subject: ET vs JI From: monz@juno.com (Joseph L Monzo) Carl Lumma wrote: > I've always viewed these "commas" as making modulation > more interesting. But many disagree. Partch's chapter in > Genesis of a Music is really great about this point (the one > with the letter from Fox-Strangeways). Boy that chapter > is really a thrill! > Basically, what I got from this chapter is that modulation is > best defined simply as switching the 1/1, and that common > tones, while playing, of all things, perhaps the most important > role in the use of modulation, are not necessary in its definition > or execution. And perhaps, that a theory of modulation may > be constructed where tones separated by a comma can still be > considered "common"! I've written about this same passage in my book. Partch describes three ways of modulating, assuming two chords which possess a "common tone": 1) Making the "common tone" consonant with the first chord and dissonant with the second. 2) Making the "common tone" dissonant with the first chord and consonant with the second. 3) Making the "common tone" actually two different tones which are close by in frequency (differing by said "comma") and which are each consonant with their respective chords. His conclusion, with which I agree, is that all three methods can be used to effect a modulation in just-intonation, giving a richness and subtlety of expression which is _utterly non-existent_ when utilizing the 12-Eq scale to present the same musical passage. I have some interesting observations of my own in this regard, involving not full-fledged modulation, but rather short-term tonicization: 1) I have tried sequencing Mozart's 40th Symphony in several different versions, using ratios that were 5-limit, 7-Limit and 19-Limit. 5-Limit sounded best, 7- and 19- were both OK, but when tonicization was effected by a common-tone related by 7, it didn't sound right. It sounded to me like the tonality veered off into a weird key that was microtonally "off". This argued against the applicability of 7 in Mozart's music. 2) In my own "Incidental music to 'Invisible Haircut'", I use tonicizations which have 19 as a factor in the common-tone. This piece has a jazz/ blues flavor, and I find that the 19-limit tonicizations work well (they certainly provide a richness that the bland 12-Eq version lacks completely). This may, however, be because 19/16 is so close to the 12-equal "minor 3rd" that the _interval of modulation_ is not so strange to my ears. I'll grant that it's possible that, had I used it in the tonicization, 7 may have sounded just as strange in this piece as in Mozart. 3) I sequenced some of Satie's "Sarabande No. 1" in just-intonation, and found that tonicizations involving 7 sounded "off" here too, tending to corroborate what I said in #2. My original point was that no matter how well any equal temperament represents whatever ratios, there's no substitute for the richness and subtlety of expression which is possible when using ratios themselves. Numbers can be compared in all sorts of different patterns and combinations, and when these numbers represent _easy-to-hear_ musical relationships, the variety of musical relationships is correspondingly expansive. I'll grant that equal temperaments are easy to hear in melodic terms, but, aside from the ratios they imply well or badly, they don't have much significance from a _harmonic_ standpoint. Part of the problem I have with 12-Eq serial music is that I just can't hear many of the supposed relationships in the music that have been pointed out by theorists. I will admit the possibility that things that are happening in music that are numerically related but are not consciously audible may still have some kind of effect on our nervous system, but at our present state of theoretical knowledge, I think it's best if we deal in terms of what can demonstrably be _heard_. I think a large part of the reason Schoenberg stuck with the 12-Eq scale was because he realized intuitively that within the vastly expanded resources of his implied 13-Limit, were he to work in just-intonation, the number-play involved could quickly become a bottomless pit from which his musical inspiration would never again emerge into the light of day. Then again, I also think he wanted to make use of the ambiguities made possible by a comparison of so many close ratios on the one hand and their nearby 12-Eq equivalents on the other. My whole idea of primes having distinct qualities is useful compositionally when, for example, using a precisely-tuned 81/64 "Pythagorean major 3rd" or 9/7 "septimal major 3rd" instead of the usual 5/4 "just major 3rd", or when sliding around between them, as good blues singers do, to create a specific effect that 5/4 just doesn't give. I refuse to accept an equal-temperament because it makes modulation "easy" or (excuse me while I laugh) "possible". Part of the reason JI composers use JI is because, within a restricted JI scale, modulation to a new key brings a whole new set of intervallic relationships into play, giving each key its own distinct "flavor", far more pronounced in their differences than anything a well-temperament can do. The only reasons I can see for accepting any equal-temperament is that it is easier to play on most instruments, and, as I stated in another post to this issue, the study of the interplay between JI and ET in the same piece is becoming more and more interesting to me. Joseph L. Monzo monz@juno.com _____________________________________________________________________ You don't need to buy Internet access to use free Internet e-mail. Get completely free e-mail from Juno at http://www.juno.com Or call Juno at (800) 654-JUNO [654-5866]