Newsgroups: rec.music.classical,rec.music. | |-(1) + compose | \-(1) From: Ken@hpsl.demon.co.uk (Ken MOORE) \-(1) Subject: Re: What is "tonality"? Date: Tue Nov 01 16:25:57 EST 1994 In article <1994Oct23.211217.21014@Princeton.EDU> roger@astro.princeton.edu "Roger Lustig" writes: >REad the latter chapters of Helmholtz, where he makes plain that >acoustics and mathematics do *not* explain the history and development >of art. While in very large part I agree with Roger that acoustics and mathematics are a long way from a full explanation of art, perceptual psychology has moved on a little way since Helmholtz. In particular there is growing support for a theory of consonance and dissonance of intervals, both harmonic and melodic. The theory is that dissonance is caused by the beats between the (sine wave) components of the tones. The measure is a weighted sum, the weights being beat frequency dependent (ie very high and very low beat frequencies are not obnoxious). Some experimental support for this was published in the Journal of the Acoustical Society of America in October 1993. The experimenters used synthesised instrumental timbres, including some with non-harmonic overtones. The striking result was that the preferred scales on these extreme pseudo-instruments differed markedly from the normal Western scale. Naive and musically trained subjects showed similar preferences. From this sort of basic result to a mathematical theory of art is a very long way indeed, but that is not to say that the journey is impossible, just that we shall not be making it. Patricia Smith-Churchland (author of `Neurophilosophy') estimates that if present rates of research into the central nervous system are maintained, it will be possible to build a detailed computer model of the brain in about 700 years time! Of course by then there will be a lot more music to be explained. -- Ken MOORE ============================================================================== From: kurtsi@kurtsi.pp.fi (Erkki Kurenniemi) Newsgroups: sci.math Subject: Re: Twelve is special Date: 26 Mar 1995 07:12:31 GMT Twelve is special, what about 8640? ... I don't know but would like to. The funny thing is that its divisors give quite a long stretch of the musical diatonic scale (with a certain catch, a reference is: Thomas D. Rossing, The Science of Sound, Addison-Wesley, 1982, p. 155). In Mathematica, evaluate: d = Divisors[8640] ; Table[d[[i+1]]/d[[i]],{i,15,41}] ============================================================================== From: glipton@abu.isscad.com (Gary Lipton) Newsgroups: sci.math Subject: Re: Music Date: 2 Nov 1995 15:26:26 GMT In article <474orl$bdd@krone.daimi.aau.dk>, Jeppe Stig Nielsen wrote: >I think the word associated with how the octave is divided into a scale is >TEMPERATURE. The word is "temperament". A good reference on these topics is "The Science of Musical Sound" by Johann Sundberg. ============================================================================== Newsgroups: sci.math From: roy@dsbc.icl.co.uk (Roy Lakin) Subject: Re: Music Date: Wed, 1 Nov 1995 17:43:55 GMT ... The "cycle of 53" is more accurate: split the octave into 53 equal divisions. The major scale is approx 9 8 5 9 8 9 5 divisions between successive notes (tones being 8 or 9 and semitones 5). Helmholtz's "Sensation of Tone" describes this more thoroughly. There have been 53-note keyboards invented for this temperament but they never caught on, probably because modulation was so difficult. roy