# How does math come into play when composing music?



## level82rat

I've heard some describe Bach's music as being "mathematical" but I struggle to understand the relationship between math and music. Can Bach's music be explained by a system of equations? When would a composer bust out a pencil and paper and start doing math?


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## millionrainbows

Mathematics is a broad area. You can use set theory to analyze any kind of music, using Alan Forte's book Atonal Theory.

Also, symmetry is a mathematical idea, and Bach can be looked at in this way, too; how themes get inverted, turned upside down etc. I think music has a lot in common with geometry.


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## mbhaub

Check out Bartok. He used the Golden Ratio in some of his music, consciously or not:

https://www.cmuse.org/classical-pieces-with-the-golden-ratio/


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## mikeh375

Leibniz....

'Music is the hidden arithmetical exercise of a soul unconscious that it is calculating. If therefore the soul does not notice it calculates, it yet senses the effect of its unconscious reckoning, be this as joy over harmony or oppression over discord.'

We just don't oppress the discord so much these days and for some, the math is not subconscious. Composing is definitely geometric as MR says and it can be algorithmic too.


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## millionrainbows

A good composer for different methods, using geometry & math, is Polish composer Andrzej Panufnik, if you can find anything in the liner notes about his methods. Not much on WIK.


Andrzej Panufnik​​


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## Bwv 1080

Every musician does Mod12 arithmetic


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## millionrainbows

Bwv 1080 said:


> Every musician does Mod12 arithmetic


In normal tonality, not really; if that were true, then chord inversion would be based on quantity, not identity in a tonal hierarchy. Example:

C-E-G, G-E-C, and E-C-G are all C major chords.

If we used modulo 12, these intervals would become quantities, not identities:

C-E-G, (C +M3+m3) when retrograded, becomes (C minus a M3 minus a m3) and results in C-Ab-F, which is an F minor.

Tonality is based on a recursive cycle in which "place" is the determiner, always in relation to a tonic or root note.


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## norman bates

mikeh375 said:


> Leibniz....
> 
> 'Music is the hidden arithmetical exercise of a soul unconscious that it is calculating. If therefore the soul does not notice it calculates, it yet senses the effect of its unconscious reckoning, be this as joy over harmony or oppression over discord.'


I like this quote. I think it's true that if math is a part of music the musician usually uses it in a unconscious way. I think it's the same for architecture, painting, poetry etc. The sense of form and proportion, simmetry (or asimmetry), balance have certainly to do with math but the artist is mostly guided by instinct, even when he's conscious of the mathematical qualities behind his work (even guys like Xenakis).


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## Metromania

norman bates said:


> I like this quote. I think it's true that if math is a part of music the musician usually uses it in a unconscious way. I think it's the same for architecture, painting, poetry etc. The sense of form and proportion, simmetry (or asimmetry), balance have certainly to do with math but the artist is mostly guided by instinct, even when he's conscious of the mathematical qualities behind his work (even guys like Xenakis).


It's too late but I agree with your thoughts


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## catdischawsehole

Metromania said:


> I like this quote. I think it's true that if math is a part of music the musician usually uses it in a unconscious way. I think it's the same for architecture, painting, poetry etc. The sense of form and proportion, simmetry (or asimmetry), balance have certainly to do with math but the artist is mostly guided by instinct, even when he's conscious of the mathematical qualities behind his work (even guys like Xenakis).
> 
> 
> 
> It's too late but I agree with your thoughts
Click to expand...

I can't agree with architecture. It's clearly a math field where you need to know all rules of building your layout. But if we talk about other listed fields - I agree, of course. Math is everywhere, and no one may hide from it. I hated this lesson at school, but then I understood that such knowledge may be so useful for me. So I decided to pass some victorines as here https://quizzes.studymoose.com/flashcards/math/ just for self-education. Must say, I really got some results!


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## Nate Miller

music is an art where the canvas is frequency and time. That is easily expressed mathematically. Fourier analysis of the vibrating systems is one way you could model the sound waves mathematically.

counterpoint is about intervals, which can also be described mathematically as ratios of frequencies

when musicians learn the rules of harmony, the math is still there, but it is abstracted. From a musician's perspective, harmony is about consonance and dissonance, which is a way of talking about the ratios between frequencies without being concerned with the actual mathematical values of the ratios themselves.

one reason Bach is talked about as "mathematical" is because it is from a time before functional harmony and is based on the rules of counterpoint, which is only concerned with the intervals between moving parts. Contrapuntal music just lends itself better to a discussion about the relationship between math and music, so that's why people will say that about Bach


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## Bwv 1080

Nate Miller said:


> music is an art where the canvas is frequency and time. That is easily expressed mathematically. Fourier analysis of the vibrating systems is one way you could model the sound waves mathematically.


Isnt that like saying you could model the transmission of color through visible light in a painting with Schrodinger's Equation? True, but who cares?


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## Nate Miller

Bwv 1080 said:


> Isnt that like saying you could model the transmission of color through visible light in a painting with Schrodinger's Equation? True, but who cares?


yes it is, sort of. The sound waves are happening in time, so that is the real difference. Mathematically, I mean

but then this is why I think its always best to remember what the first four letters of "analysis" really are


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## Phil loves classical

I believe Bach's music described as mathematical (at least any more than others) is pure hyperbole. I think it's much more accurate to say Bach wrote with 'mathematical precision' as some others did, where each note serves a certain purpose or function. Milton Babbitt is more 'mathematical' than any composer I've heard about in terms of source material, and it's not necessarily something that translates tangibly into music. Lindberg's Kraft is supposedly entirely produced by a computer. There is still a human component though in all music composed, even through a computer.


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## bagpipers

Music is made of tones which are frequencies of vibrations like A 4 is 440 hz and a absolute rule of music is double the frequency and you get the octave.
Music is basically math when it comes down to it


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## KlassikerDronning

level82rat said:


> I've heard some describe Bach's music as being "mathematical" but I struggle to understand the relationship between math and music. Can Bach's music be explained by a system of equations? When would a composer bust out a pencil and paper and start doing math?


I was actually just explaining this to someone else. I have been playing piano since I was 7, and then guitar and violin at age 12 for about 15 years now. 
So let me break it down 
Notations in music are by notes and numbers. The notes and measures are divided in timing. There is 4/4 second timing in each measure. The notes are fractions of timing, pitches, and octaves.
Therefor, music is basically a science of sounds and frequencies.
It's called music theory.
Hope this helps.
Dawn I wish I would have seen this question earlier!!!😤


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## BrahmsWasAGreatMelodist

Bwv 1080 said:


> Every musician does Mod12 arithmetic


Not every !


......


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## Roger Knox

How music is not like math:

Music is one of the creative arts
Music is closely related to song and dance
Music is directional and structured in real time
Experientially music is perceived by the human auditory system, cognized by particular neural pathways and areas of the brain, received and produced emotionally and kinesthetically
etc., etc.


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