From: torquemada@my-dejanews.com Newsgroups: sci.math Subject: Re: relation between mathematics and music Date: Sat, 19 Sep 1998 00:58:16 GMT In article <19980918180502.23532.00001104@ng127.aol.com>, tangent60@aol.com (Tangent60) wrote: > I really don't think they have any connection. > However, I believe arithmetic and music are connected in various ways. Consistency really isn't your strong point is it? Well I think the quotation by Waldo is relevant here: "A foolish consistency is the hobgoblin of little minds" so don't feel too bad about it. Anyway, back to the subject in hand. There's a chapter on mathematical relationships in musical scales in the book "The Musical Mind : The Cognitive Psychology of Music" by JA Sloboda. It was quite interesting and suggested subtle mathematical similarities between scales used in the West and used in India. Also check out some of the writings by Jackendoff on formal grammars underlying music. The book (and TV programmes) "The Unanswered Question : Six Talks at Harvard " by Bernstein also contains some interesting stuff on the formal grammatical structure of music. There's also the whole subject of the physics of music - harmonics and so on. Any elementary physics text should have an introduction to that. -- _______ _ / o \ / ~ X X ~ \_______/ \ ~ _/EVOLVE!\_ http://travel.to/tanelorn -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/rg_mkgrp.xp Create Your Own Free Member Forum ============================================================================== From: Ted R Shoemaker Newsgroups: aus.mathematics,sci.math Subject: Re: relation between mathematics and music Date: Fri, 18 Sep 1998 21:04:21 -0600 Way back in high school, my geometry text said that Pythagoras' school made a lot of connection between math (particularly ratios of integers) and music (particularly frequency). Some composers (Bach, Haydn, Mozart, and a lot of 20th-century people I don't remember) considered a musical piece to be like a math puzzle, and they composed accordingly. A 20th century composer (Paul Hindemith, if I remember right) came up with a formula for the degree of consonance of a musical chord (i.e. how restful vs stressful it sounds), based on the ratios of the pitches (frequencies) involved. If you allow physics to enter the discussion, we find harmonic overtones, the acoustics of a cathedral or concert hall, the relationship between a waveform (see: Fourier analysis) and the tone, a logarithmic measure of sound called the decibel, how music is managed electronically (e.g. what an equalizer does), etc. Some people would say that by referring to physics, I've crossed the line from music to sound. Maybe they're right. That would depend on the definition of music, but musicians don't agree on what that is. Although I haven't referred you to a particular resource, I hope that the names and topics will help you find something worthwhile. Finally, (or maybe firstly?) both math and music are appreciated in the mind. The more you understand the sense of math, the more you appreciate its beauty. The same is true for music. If you compose your essay on computer, would you mind e-mailing a copy to me? I find the question interesting. Thanks! Ted Shoemaker shoematr@uwec.edu --- Michael Beer wrote: > I'm a Swiss undergraduate student of mathematics temporarily attending > an English language course in Brisbane, Australia. In my next essay due > October 7, I'd like to discuss in some way the relation between > mathematics and music. I'm now looking for ressources (books, web-sites > ...) related to this topic. Could anyone give me any recommendations? > > Thanks. > Michael ============================================================================== Newsgroups: aus.mathematics,sci.math Subject: Re: relation between mathematics and music Date: Fri, 09 Oct 1998 00:26:03 GMT Reply-To: rabbtech@acr.net.au On Thu, 24 Sep 1998 10:22:31 +1200, Ken.Pledger@vuw.ac.nz (Ken Pledger) wrote: >In article <36025794.318D41D8@powerup.com.au>, Michael.Beer@suisse.org wrote: > >> I'm a Swiss undergraduate student of mathematics temporarily attending >> an English language course in Brisbane, Australia. In my next essay due >> October 7, I'd like to discuss in some way the relation between >> mathematics and music. I'm now looking for ressources (books, web-sites >> ...) related to this topic. Could anyone give me any recommendations? >> >> Thanks. >> Michael > > Other people have mentioned the physics of music. There are books on >that subject (including an old but good one by Helmholtz) which you may >find in a library subject catalogue. I find particularly interesting the >frequency ratios occurring in the major and minor scales, and the problem >of tuning an instrument to sound tolerably right in more than one key. > > However, it may be that your question was a psychological one. It's >sometimes claimed that enjoyment of mathematics and enjoyment of music >often (but not always) occur together in the same person. I've certainly >got the impression that music-lovers are more common among mathematicians >than among people in general. But are there any surveys to back this up? >And has anyone produced a serious explanation? That person would need to >be a psychologist who was also well acquainted with both music and >mathematics, and I'm not sure whether such a paragon exists! > > Ken Pledger. Hullo Ken. Yes there is at least one! I just happen to be a physicist/mathematician with an extra degree in psychology and genetics and a devout interest in classical music. I'm sure there is a correlation between maths and music, even though my own brother, an engineer, has absolutely no interest in music at all. Most of the mathematically minded people with whom I have been associated were certainly inclined that way. Maybe the correlation is simply between intelligence, in general, and musical appreciation. Also between intelligence and the complexity of the music that is appreciated. I can't say that I have ever engaged in formal research on this subject but can certainly recognize two aspects of the relationship between maths and music. Firstly, we know that the fundamental mathematical principles behind the physical design of instruments, the frequency ratios of musical scales and the way in which organised sequencing of various chords and keys is used to turns noise into intelligible sound, are pretty well understood and researched. The psychological effects of music, on the other hand, will probably always remain a mystery even though they, too, can usually be descibed in simple mathematic terms. Why, for instance, do major and minor chords create different emotions. Why do note sequences create 'pictures'? Why does western music insist that the last note has to be the fundamental? Why do close frequencies create a dischord? etc. etc? I once programmed my old Amiga computer to churn out endless music, using fairly simple mathematical programs. I understand that other people have gone a lot further and written programs that will compose in the style of Mozart, Bartok or whoever. This is fascinating but purely mathematical stuff. Using my programs, I can experiment with instrument waveforms and with scales that possess any number of semitones (usually, 8 to 24, of equal ratio). I found that many new sound experiences result and that of the chords produced by these scales are meaningful but are unobtainable using our standard 12 semitone scale. I also noted that changing the number of semitones in midstream often gives an intelligent result. I would like to delve into this more closely but haven't yet found a decent version of BASIC that will allow me to do that on the pentium. Do you know of any? I am sure that the future of music will lie in the utilization of entirely new types of scales and in the ingenious sequencing of these as well as of notes and chords. Another question about our appreciation of music - or of any of the arts, for that matter - is its role in evolution. It is hard to see a connection between a liking for certain sequences of sounds and an organism's ability to survive although that could be associated with the fine tuning and efficiency of our hearing system. Other animals don't seem to possess an equivalent mathematical basis for their sound communication systems, although I have occasionally observed some of my wild avarian friends listening quite intently to classical music. This is a very interesting subject, would you not agree?