Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!uwm.edu!gem.mps.ohio-state.edu!usc!merlin.usc.edu!aludra.usc.edu!alves From: alves@aludra.usc.edu (William Alves) Newsgroups: comp.music Subject: Re: New tunings Keywords: Intonation systems, octaves, tuning systems Message-ID: <6460@merlin.usc.edu> Date: 14 Nov 89 03:31:58 GMT References: <3068@husc6.harvard.edu> <6335@merlin.usc.edu> <3113@husc6.harvard.edu> Sender: news@merlin.usc.edu Reply-To: alves@aludra.usc.edu (Bill Alves) Organization: University of Southern California, Los Angeles, CA Lines: 122 In article <3113@husc6.harvard.edu> elkies@brauer.UUCP (Noam Elkies) writes: > >Of course you can easily retune the fundamentals of any number of existing >instruments to your favorite New Tuning. But this still leaves two >problems: First, the Pythagorean overtone structure would remain, whereas >you'd probably prefer to redo the entire harmonic series as well; that's where >you'd spend all this time constructing new instruments. [I realize that >I may be here implicitly invoking a controversial assumption about the >relation between the harmonic series and Western tuning---see below.(*)] Aha! Is there or should there be a connection between tuning systems and the harmonic series? As, I think, a previous posting of mine demonstrated, it is the 12-tone equal temperament system which bears little relationship to the intervals found in the harmonic series. That is why the lovely the ratio be- tween the fifth and fourth harmonics (5/4) has been tempered practically be- yond recognition to the modern major third for the sake of rendering all the keys equally useful (or equally out of tune, as Lou Harrison has said). Instead, it is JUST INTONATION which seeks to preserve the intervals found in the harmonic series for the sake of improved consonance (and at the expense of rendering some keys less "useful"). Virtually every non-percussion instrument as well as most mallet instruments have harmonic spectra (after the first few milliseconds of the attack on some). An exception to this that has been brought up is the piano, where the inharmonicity resulting from the stiffness of the strings necessitates stretched and compressed octaves. Here, admittedly, the question becomes more complex, and I'm not entirely satisfied by the "conso- nance formulas" in such acoustics texts as Dick Moore's that take into account the relative ratios of some of the partials, and not just the fundamentals. However, consider this: if the fundamentals have a low number integral ratio, so too will the lower-order harmonics. >Second, while the instrumentalist will then easily play the notes in >your score, (s)he will need a lot of coaching to play them musically; >I see no reason why musical intuition developed over years in the context >of Western tuning must directly transfer to your new tuning system. If you're talking about a fixed pitch instrument, such as a retuned piano, I don't think it would necessarily require extra training at all. It has been my experience that musicians who have a sense of the important issues of musicality (phrasing, dynamics, etc.) are not "thrown off" by having a 5/4 result from two keys which would normally give them a major third. It is somewhat more difficult if you're talking about continuous pitch instru- ments, such as unfretted strings, but because they have to learn to play in tune, not because of a cognitive dissonance [:-)] which goes against "musical intuition developed over years." >But the various systems that were used were all within a few cents of >each other and of equal temperament, and thus mutually compatible for >many purposes; furthermore, as several posters have noted, the differences >are academic except for rigidly pre-tuned instruments (mostly keyboards >and fretted strings). I'm sorry, but I don't think that's true at all. I will admit that the dif- ferences between the various "good" temperaments towards the end of the 18th century and equal temperament could be considered "academic" or "within a few cents." But that is not at all true before that period. The differences be- tween Pythagorean tuning, mean-tone temperaments, just tunings, and equal temperament are quite apparent and not simply "a few cents" off. For the de- tails see the reference I mentioned before "Tunings and Temperaments: A His- torical Survey" by J. Murray Barbour (even though it's awfully prejudiced to equal temperament). > >Why, then, did generations of composers struggle between a theory that >proclaimed the fourth a "perfect" consonance and the third an "imperfect" >one, and their ears that told them otherwise? Well, first of all, up until about 1200 many theorists called the fourth a con- sonance and the third a dissonance. As the thirds became more popular with composers, theorists begrudgingly labelled them imperfect consonances. The problem here was that if one used Pythagorean tuning (standard at that time because it was Boethius' fave) then the thirds are complex ratios (major third, or ditone, = 81/64 and minor third, or semiditone = 32/27 or 19/16). It was Walter Odington, I believe, who was the first to suggest that they were ac- tually consonances because of their proximity to 5/4 and 6/5 respectively. The fourth was considered a dissonance because they always measured intervals from the bottom voice up. If one used a fourth and a fifth up from the bottom voice, the dissonance would, of course, be the result of the second in the upper voices. And if one uses it in two-part writing, the dominant is in the bottom voice when the tonic is in the top, creating not a "dissonance" but a unstable sonority in the harmonic scheme. > >So, out of honest curiosity, I ask: why do you create tuning systems? > That's a big question, and I can only answer for myself. First of all, I work in just tuning systems, not microtonal or other tempered systems. I do so partly because of the increased consonance, but also from the enormously in- creased pallette that results from the inclusion of such intervals as 7/4, 11/8, or 7/6. The difference in clarity and sonority is striking and beautiful. Such chords as a 5/7/11, which when played on the corresponding keys in equal temperament would be jarringly dissonant, are actually quite consonant, not as consonant as a 4/5/6 (major chord), but somewhere in the middle of that vast spectrum. >(*) Something I've been wondering about intermittently, and reminded >of by your mention of gamelan music: Gamelan music is dominated by >instruments with an overtone series very different from the familiar >overtone series that dominates most Western music. It also uses >very different tunings, tunings which unlike their Western counterpart >developed (I assume) without knowledge of overtones. Thus it could >make an interesting test case for the perennial debate about the >naturalness of a system of tonality based on the overtone series. >Has any significant research been done into the relation or lack >thereof between gamelan tunings and gamelan overtones? > Funny you should ask, Noam, because I just happen to have done a number of spectral analyses on gamelan instruments. First of all, most of these are not at all "very different" from Western instruments in their spectra. As I said before, apart from their attacks, these instruments exhibit the same harmonic frequencies as most other instruments. Exceptions are: 1) The hanging gongs. In these instruments the harmonics have been (presumably) intentionally com- pressed by the flange, giving them the beats that characterize them as well as the stretched and compressed octaves in the other instruments. 2) Drums. 3) The bonang and other kettle-gongs (kempul, ketuk) have some inharmonic par- tials, but they also exhibit very strong harmonics, like the other instruments. However, I don't think such a study will necessarily shed any light on the relationship between the tuning system and the spectra, because there is no standard gamelan tuning system. Every set of instruments is tuned to itself and no other. See Mantle Hood's "Pelog and Slendro Redefined" in Selected Reports (in Ethnomusicology) 1#1. Bill Alves USC School of Music / Center for Scholarly Technology