Path: utzoo!utgpu!jarvis.csri.toronto.edu!clyde.concordia.ca!uunet!tut.cis.ohio-state.edu!zaphod.mps.ohio-state.edu!usc!chaph.usc.edu!nunki.usc.edu!alves From: alves@nunki.usc.edu (William Alves) Newsgroups: comp.music Subject: Re: Perfect/Well Tempered Message-ID: <7433@chaph.usc.edu> Date: 16 Jan 90 20:07:22 GMT References: <136000003@peg> <1758@rex.cs.tulane.edu> <7267@chaph.usc.edu> <434@iconsys.UUCP> Sender: news@chaph.usc.edu Organization: University of Southern California, Los Angeles, CA Lines: 57 In article jv@mh.nl (Johan Vromans) writes: >In article <434@iconsys.UUCP> tom@iconsys.UUCP (Tom Kimpton) writes: >> I was wondering if any electronic >> music instruments have options to play "perfect" scales. >Yes, modern synthesizers can be made to play in perfect scales. >Which brings me to a question which has been in my mind for long: >If a piece is playes in a perfect scale, say c major, and is then >played in perfect scale d major, does it sound different? Yes, it will >sound higher. But does it feel different? >Alternative question: if a piece in (tempered) c-major sounds (feels) >different when played in d-major, it this because of the minor >differences in pitches due to the tempered scale? First of all, what is a "perfect" scale? Tuning systems since ancient times have faced two competing goals: to have small, whole number ratios in the commonly used intervals to increase the consonance, and to be able to play in more than one key center. They are not mutually compatible; one or the other has to be compromised. For example, to take your c/d major question: let's say the A is tuned to a frequency exactly 3/2 times D (a "perfect" or Pythagorean fifth) to aid in consonance in the tonic triad of D. Then let's assume that D is 3/2 above G (for the G triad), and that G is 3/2 above C (for the C triad in C major). This would make the D 9/8 from C and the A 27/16 from C. Now 27/16 isn't exactly a low number ratio, which may be okay if you're playing in D, but in C you'll probably want it to be 5/3 so that the A minor triad will be consonant. This is a simple example, but it demonstrates that tuning systems with small whole-number ratios ("just" intonation) do not lend themselves to modulation. Likewise, equal-temperament has much more dissonant sounding intervals. The history of tuning systems in Europe is entirely bound up in various solutions to this fundamental problem. The nature of the compromise at which you arrive has to do with the nature of your music. To Schoenberg, equal temperament is the "perfect" tuning system, because it makes all intervals equal. Personally, I prefer just systems (when they are practical) in my own music. Different keys in just systems have quite different sounds because a "minor sixth" for example, may actually be three or four different intervals de- pending on what key it is in. The same is true to more or less of a degree in all non-equal tuning systems. This could definitely have an effect on mood and compositional usage. As I have written before, I think supposed changes in "mood" when transposing in equal temperament are mostly due to changes in timbre in different registers of the instruments. Some electronic instruments which have tunable scales include: Yamaha DX-7II, TX802, TX81Z Ensoniq Mirage, EPS (with special software) Akai S-900, S-950, S-1000 (with a lot of work) Synclavier II and probably several others. (This was discussed in rec.music.synth a few weeks ago). Bill Alves USC School of Music / Center for Scholarly Technology