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Is music mathematical !!!!!!

Topic started by Kumar (@ ext-3054.rational.com) on Wed Jul 11 20:51:05 EDT 2001.
All times in EST +10:30 for IST.

Now I dont know if I am making any sense in this question... but just thought about this while reading about the 'got milk' thread.. where the discussion is about music going into a cycle..

Music is harmonics. I read somewhere music and
math are the only two universal things. R there
theories behind music.. do they follow rules
which r universal.. can they be mapped to math..

Continuing with my babble.. can they be extra
polated and can we predict the future of music..
can we put the changes in music to a statistical
trend.. ??? on.. and on..

:-)

(ps: if u want to blame me for talking something
which even i dont understand, its all because
of my influence of seeing AI.. makes one think
'out of the box' :-))))) )

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Responses:

• Old responses
  
• From: O_IS_G (@ 193.188.97.152) on: Tue Feb 26 03:26:44 EST 2002
  
  I suggest Prof.Sambhamurthy's books on South Indian music.His linking of Pythogoras and Devagandhari raga will certainly interest core mathematicians.He relates Pi to 7 swaras and the 22 shrutis.
  
  Venkatamahi, to me ,must be a equally good mathematician.
  
  
• From: MS (@ 129.252.26.165) on: Tue Feb 26 10:15:03 EST 2002
  
  Swamji:
  
  Pretty much :-) It seems like I appear completely defeated when it comes to talking about midi. I shall keep mu mouth shut about it since I still cannot express properly what I want to.
  
  
• From: O_IS_G (@ 193.188.97.152) on: Tue Feb 26 10:24:02 EST 2002
  
  I heard that a dancer by name Bavani Suresh has published a book on "Music & Mathematics".I could not get a copy.Any inputs?
  
  
• From: hihi:-) (@ 128.111.113.76) on: Tue Feb 26 14:17:24 EST 2002
  
  aruL: I guess I did not word it properly. yes - all music is wave and waves are math :-)MS: a slight clarification. music being mathematical doesn't have
  anything to do with sound being "waves". music is pattern identification/recognition. what i meant by this is: there is a relationship between the notes we use in any
  music; knowingly or unknowingly we decipher these relationships - and hence a pattern emerges - when we hear what we call music; when we are unable to unravel
  these relationships we call it noise (pl. note that noise is not something necessarily without pattern; it's rather our inability to decipher these patterns that make them
  noise!). a good analogy is: when we "see" a ravi varma painting we "understand" what is meant by it - we understand the patterns; but, most of us will be baffled by
  most modern painting and we just end up making fun of them calling them kOzhi kiRukkal, blah blah blah... . swamiji: i think, whatever one does in a computer could
  be represented as a mathematical operation. that way, MS is correct :-)
  
  
• From: MS (@ 129.252.25.204) on: Tue Feb 26 15:08:07 EST 2002
  
  I do understand that there is a relation between the notes/octaves and am familiar with the frequency scales too. I understand simple concepts like tempo etc..but I am wondering if there is a particular way of expressing harmony rules mathematically. For example - the rules behind chord making and bass that follows the lead.
  
  Or in simple words is there a proven formula which gives you the way chords must be formed ? Or are they just a set of axioms laid down by people of past ?
  
  Because, as I understand math, the results of it are NOT subjective (ok..dont come with quantum theory :-) ). But if music is purely based on perception how can that be termed mathematical ?Is there a way we can delineate between "bad" music and "good" music mathematically ?
  
  Is it getting a li'l crazy in here ? :-)
  
  
• From: UV (@ 134.113.200.23) on: Tue Feb 26 15:23:36 EST 2002
  
  Well nice topic and good discussion
  HiHi/Arulacaran
  you can give more inputs on this esp with Carnatic music
  as we know that there are 72melakartha ragams the base structures for scales from which various scales involved based on permutation and combination as kartha ragam and janya ragams
  example madhyamavathi(parentraga) and andolika(derived from madhyamavathi)
  And there is a popular song on this also 'Ezghu Swaranagalkul ethanai padal' :)
  
  Swamiji can explain about flat and sharp notes and how it works on Western side and structures
  
  And someone also can talk about Kalapramanam/rhtym pattern as melody & rthym has to go hand in hand
  UV
  
  
• From: hihi:-) (@ 128.111.113.76) on: Tue Feb 26 15:39:28 EST 2002
  
  But if music is purely based on perception how can that be termed mathematical? MS: mATTikkiniyA :-))) perception is mathematical! i dont want to go in to that now (but if you are interested send me an email). there are some excellent works done in music perception and how people distinguish between "good" music and "bad" music (it all depends on the environment one grows up in :-) ). i will try to dig up some references and post them here. till then ... peace :-)
  
  
• From: bhoomii (@ 172.162.204.15) on: Tue Feb 26 19:02:28 EST 2002
  
  Well, Madyamavathi is itself a Janya Raga, The good song Ezhu Swarangalukkul is a ragamalika starting on the raga Pantuvaralai. Lot of janya Ragas are there in Indian Classical Music. Well so many scales are there also. But whereas in Western or European How many are there pl can anybody explain. I am not so fluent in western music.
  
  
• From: MS (@ 129.252.25.204) on: Wed Feb 27 01:05:36 EST 2002
  
  aruL:
  
  fyi, yes I will be interested in it for sure. But IMO, this is the place u shd put them since I feel the context will be more apt and bound to have more inputs from other users.
  
  
• From: Kupps (@ 156.153.255.134) on: Wed Feb 27 01:11:06 EST 2002
  
  yes MS, i second you...
  
  arul please post those views here...
  
  
• From: vazipokan (@ 208.51.40.107) on: Wed Feb 27 09:00:47 EST 2002
  
  hihi,
  can you tell us one thing,
  what do we gain by knowing music being mathematical or not ?
  from today can we call ramanujam as a composer? or IR as a mathemagician? (some might start calling him so from now on who knows :)
  
  if you manage to answer all above without slipping
  next tell me
  How do equate a raga alapanai to math?
  (i know you might say each note has a duration so it is number hence it becomes a math. i am sure you can do better than this answer)
  
  please explain without slipping (nazuval).
  
  
  Roundtable :math physics and economics gurus meet.
  
  Mathematican : Any thing in the world boils down to math
  Physics guy : Any thing in the world boils down to matter
  Economics kizam: Let us assume music starts from ne instead of Sa, hence from here we go towards a theory to measure musical statisfaction if sa had been ne and ne had been sa. Does the satisfaction multiply or it is just additive. so music might have math principles in its structure but liking music is just perception which is economics, math liking is not natural often people are being forced to like it, while music is not so.
  
  clap clap clap!
  
  
• From: WhyNot (@ 203.24.100.132) on: Wed Feb 27 10:24:32 EST 2002
  
  I think maths can be used to model short instantaneous pieces of music effectively, as maths can be used to model even the most random and unpredictable events. But from the way i see it, digitisation or numerical methods wud be more effective than analytical methods, for effective and more simplistic modeling (and it makes more sense too), especially when applied for the purpose of programming it. This may also help remove the confusion for some on how maths can be applied for music or other random sequences.
  
  Now the whole idea of programming music or modeling music, doesn't mean music is hence mathematical. Even the most random events like weather changes and population fluctuations can be mathematically modelled. Hence hihi:-) has a point in dismissing all these gabra about midi/analog etc.
  
  However, producing music is an effect of vibration, whether it is the vibration of a string, the surface of a drum or the air column in a flute. And vibration analysis, while it requires more than pure mathematics, relies heavily on several mathematical principles.
  
  Therefore hihi, I wudn't dismiss the fundamental wave nature of sound as evidence of the mathematical nature of music. And in proving your point that the difference between music and noise lies in our own ability to detect a pattern, you have come closer to stating that hence music or noise are jus sequences of sound, when considered independent of human recognition. (One man's Music is another man's Noise). Therefore, if you want to talk about absolutes, music (or noise) is sound and sound is made up of waves, which can be studied by vibration analysis, putting its mathematical nature to good use.
  
  I know of a mechanical engineering undergraduate who undertook as his final year project, the modal analysis of Marimba bars. Being a professional choir singer, he put his musical knowledge to good use in conjunction with vibration analysis techniques for his project. A very practical example of mathematics being used in music. Of course I'm assuming here that in allowing for the use of maths for this purpose, it is an evidence that music is hence of a mathematical nature, if that's what the topic is stating. Because we are not just programming or digitising music, but we are actually studying or analysing its maths.
  
  Hence I guess in a very fundamental way, music is pretty much mathematical, without having to really go too much into the philosophies behind it. btw, the point of this guy's project was to come up with a practical method for tuning Marimba bars. (MS, you may have a point there when u talked about replacing instruments, if you go from the vibration viewpoint).
  
  As for 'predicting', I guess one can predict what kind of music (the pitch or frequency, loudness or amplitude, etc) can be produced by a particular set of equipment (but of course), configured or arranged in a certain manner, using maths. Otherwise, I dont know what exactly it is you'd want to 'predict' here? What exactly is the 'future of music' anyway?
  
  That's my view on this matter. But i believe this topic is greater than individual inputs. Like the 3 blind men who felt an elephant (heard tat story?), I think each of us are coming up with our own singular views on the topic. I dont think we are necessarily contradicting each other or telling the full story, but probably helping to build up a bigger and better picture of the whole thing.
  
  
• From: Krishnamurthy (@ 198.102.112.18) on: Wed Feb 27 14:02:38 EST 2002
  
  Theres two different things discussed. One is music, another is the elements of music -which is sound (hence we talk of waves, instrument's tonal aspect etc). While we all agree that there can be no music without sound, it doesn't stop there.
  On sound: Mathematical analysis of a sound wave for example is used in synthesizers. Waves are modeled, and manipulated in so many ways - and this is what the whole range of analog synths do. It is an interesting read on analog synths history and where it is now.
  In addition to its use in synths, this aspect of music is used to improve not only the tone of a natural instrument, but also its acoustics. The kind of sound u hear from an instrument today should be better fine tuned than what it would have been sometime back.
  
  On Music: Music is not just how sound is produced, but on a certain level a perception of intervals (distance between two notes) and how it is laid out over a cycle (rythm). There is a high degree of mathematics involved here. An analysis of intervals show some "pattern" or symmetry - something which our brains perceive without involving too much of numbers.
  Having said that, music also has a structure. Theres many techniques a composer uses which he knows will work in a particular situation. Repetition, retrograde, transposition and many more. This analyis at some point can also be studied with mathematics.
  
  Afterall mathematics is a tool to explain something. This tool may be effective in some situations, and sometimes not. A mathematician will derive most pleasure by playing with numbers on music, while an average listener will quantify music on emotions it produces. In either case a pleasure is derived at some point - through emotions or numbers. A child derives pleasure from music not on the above two, but on the rythmn and plain "interval jumps" that makes it want to dance. This is an answer to someone that asked "what do we gain...". The gain is pleasure. If you gain nothing, its simply useless to you.
  
  MS: I am surprised you asked the question on MIDI, because i thought u sequenced. It has nothing to do with mathematics - except that it is a digital "instruction". MIDI is just a set of instructions that tell the computer what note to play for how long (duration) and how strong (velocity). The sound itself is stored as a table of actual waves (wavetable) in the computers sound card, or in a synth where an instruction (note press, or midi event) is processed depending on synth. Now you can handle that instruction in any manner u wish!! Suppose you have a strobe light (like the "flashing" light used in discotheques), and that which has a midi interface. You make make the light flash different colors for different durations with the same MIDI instruction!! In a laser light show, the same MIDI instruction can drive those devices that produces light that "dance" to music.
  If u knew these before, please ignore.
  
  
• From: hihi:-) (@ 128.111.113.76) on: Wed Feb 27 15:11:38 EST 2002
  
  swamiji explained it perfect. thanks krishnamurthy.
  
  

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