Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!cs.utexas.edu!usc!brutus.cs.uiuc.edu!psuvax1!husc6!brauer!elkies From: elkies@brauer.harvard.edu (Noam Elkies) Newsgroups: comp.music Subject: Re: New tunings [was Re: Eliminating the octave] Keywords: Intonation systems, octaves, tuning systems Message-ID: <3113@husc6.harvard.edu> Date: 10 Nov 89 04:08:40 GMT References: <3068@husc6.harvard.edu> <6335@merlin.usc.edu> Sender: news@husc6.harvard.edu Reply-To: elkies@brauer.UUCP (Noam Elkies) Organization: Harvard Math Department Lines: 98 In article <6335@merlin.usc.edu> alves@aludra.usc.edu (Bill Alves) writes: :In article <3068@husc6.harvard.edu> [I wrote:] :> [...] Smileys aside, my point was that if you :>embark on a radically new tuning (as opposed to a subtle tweaking of a pre- :>existing one) you'll have to create an entire musical system practically from :>scratch, and there's a lot more to that than simply setting down a list of :>frequencies. New instruments, too; existing instruments, after all, evolved to :>best complement existing tuning systems. : :I think this exaggerates the effort required to invent and successfully use a :new tuning system. [...] I rather think most practitioners underestimate this effort. Of course here we could both be right... :Here are some of the most common solutions: :[...] :2) Retune an existing instrument. I've seen composers retune harpsichords, but : certainly pianos and harps (without using the pedals) could be too. I've : even seen one percussionist who altered the tuning on his vibraphone by : tightly winding thick wire on one end of each of the bars. : :3) Use continuous pitch instruments in conjunction with specially tuned ones. : [...] : :4) It is also possible to write for all continuous pitch instruments (such as : a string quartet) and ask them to play in the cracks, [...] 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.(*)] 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. [And it's by no means certain that your instrumentalist does much more than play the notes in the music (s)he was brought up with, either! :-( ] :I also take exception to the implication that equal temperament is the result :of hundreds of years of "evolution" towards the most "perfect" tuning system. :(Certainly Murray Barbour's book has done a lot towards perpetuating this :myth). I do not believe this, and have not read Barbour's book. :Equal temperament has been known about for a very long time. Composers :simply haven't wanted to use it until the last 100 to 200 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). :A corollary to this misconception seems to be that it is simply impossible :(or at least inadvisable to attempt) to create an artistically effective :tuning system, when 12-tone equal temperament has taken the "heroic efforts" :of hundreds of composers and theorists hundreds of years to perfect. Since I disavow the premise, this cannot be a corollary. I would put it differently, anyway: it's not the tuning system that evolved, but composition within an essentially constant tuning. :Ridiculous. While the science of tuning is certainly not easy to grasp, I :don't think it's any harder than the 16th century counterpoint that under- :graduates traditionally suffer through. [...] 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? At any rate I hope that the exponents of New Tunings are aiming higher than the equivalent of exercises in species counterpoint... :My goodness! You don't think we'd go out and create tuning systems :WILLY-NILLY? No, and presumably also not just because you can. But this process of elimination isn't getting me very far. So, out of honest curiosity, I ask: why do you create tuning systems? (*) 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? --Noam D. Elkies (elkies@zariski.harvard.edu) Department of Mathematics, Harvard University