# Music, mathematics and language

## Main Question or Discussion Point

This may be more appropriate for the metaphysics forum, but since this is my first post, I'll give this area a shot.

What is the relationship between music, mathematics and descriptive language?

By descriptive language, I mean any language that describes the world as it really is. Clearly we have different cultural languages, but they all represent the same truths about the world. For example, to say "Romeo loves Juliet" (rlj) is to express, in English, that there is a thing that is a Romeo, and that thing bears the loving relation to another thing, which is called Juliet. This same truth (rlj) can be expressed in any number of languages.

It also seems to be the case that "rlj" can be expressed in mathematics (or some similar offshoot), such as in the function:

L(r, j) = true

(Aside: I do not know how to express the above function in more "numerical" form, perhaps somebody can help. Perhaps it is more of a 3-dimensional equation, such that the entire function is "true" at all the points in a 3-d grid where L, r, and j are all equal)

Now then, is it possible to express a similar truth about the world using music? Certainly we can create a piece of music that expresses the story of Romeo loving Juliet, however that is only one sense (sinn) of the meaning and not the actual meaning (bedeutung) itself.

Is it possible to compose music, such that the composition itself - the arrangement of tones - is a truth-bearing predicate? Note that I am not talking about the notation A,B,C#, etc, but more of the idea of the actual frequencies themselves. Could an arrangement of tones bear truth or falsity?

## Answers and Replies

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chroot
Staff Emeritus
Gold Member
You seem to be rather stuck in the notation of ideas, rather than the ideas themselves.

I can't see how music can be "false" anymore than I can see how the fundemental theorem of calculus can be green.

- Warren

Perhaps a better way to phrase my question is, is there such a thing as a "musical function", such that when you have a function (perhaps by playing a series of tones simultaneously), and you enter an argument (the addition of one or more additional tones), you return some result that can be determined mathematically?

I do not mean for the answer to be something like "Yes, the result will the sound created by the initial set of tones with the addition of the new tone." I question if it is always that simple, or is there certain forms of music such that if you combine multiple tones you get a plotted output like a bell curve. Like, where you play some notes together and it is sounds normal, but then with a certain range of tones, the output sounds dramatically different, and then after you go through that range of tones, the output returns to normal.

chroot
Staff Emeritus
Gold Member
I can't tell if your question is about math or music theory. Either way, it's not philosophy.

- Warren

Pythagorean
Gold Member
Perhaps a better way to phrase my question is, is there such a thing as a "musical function", such that when you have a function (perhaps by playing a series of tones simultaneously), and you enter an argument (the addition of one or more additional tones), you return some result that can be determined mathematically?

I do not mean for the answer to be something like "Yes, the result will the sound created by the initial set of tones with the addition of the new tone." I question if it is always that simple, or is there certain forms of music such that if you combine multiple tones you get a plotted output like a bell curve. Like, where you play some notes together and it is sounds normal, but then with a certain range of tones, the output sounds dramatically different, and then after you go through that range of tones, the output returns to normal.
Erm... The harmonic series? (at the top of the page there's a link to the mathematical version of harmonic series... this links to the musical version.)

If you strike a guitar string, for instance, it rings many different tones. The loudest, fundamental note is the one that musician's refer to it as. Let's say it's an E. So you play a single E note:

But the string also vibrates in halves. This is an E, one octave higher.

It also vibrates a 5th (musically) or in thirds (mathematically) or a B

It also vibrates a 4th (musically) or in quarters (mathematically) or an A

It continues on like this as inverse integers... so we have 1, 1/2, 1/3, 1/4, 1/5, etc.... The string is wiggling in all these "modes" (as a physicist would say).

Amazingly, most pop music you hear follows a chord progression that relies heavily on the 1st, 4th, and 5th - the first four notes of the harmonic series (counting the octave to be the same as the fundamental). So you'd play the E chord for a couple measures, then the A chord.... then the suspenseful B chord... then back to E for resolve.

I think the idea here is that humans enjoy symmetry, and they can detect a sort of musical symmetry in notes and chords.

As for language... I have no clue. Much tougher. The Chinese language relies on about five (i think) different pitches. So you can say the words "Wu Li" in five different way for five different meanings. Some linguists say it's more advanced (and simplistic) than English.

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Here is a breakdown of my theory of music/math/language. Please direct me to any flaws or to where I am misguided.

1. We can describe our world using mathematics. (Assumption)
2. Our world could have turned out differently than it is right now. (Assumption)
3. We can describe those other worlds using mathematics (from 1 & 2)
4. We can create an (albeit very large) "equation" describing our world. (from 1)
5. We can create an "equation" describing those other worlds. (from 3)
6. Our world seems "real" to us. (Assumption)
7. The residents in those worlds also believe that their world is real. (Assumption)
8. Their world is as real to them as our world is to us. (From 6 & 7)
9. The residents can describe our world using math, the same as we can describe theirs (1, 3).
10. Each world perceives itself as real and the other worlds simply as an "equation" (from 6, 8, 9)
11. Therefore, our world is no less of an equation than their world (from 10)
12. Using mathematics, we can describe objects or worlds that may or may not be "real" (from 11)
13. Therefore, just as we consider ourselves "real", despite being simply an equation, we can also create "real" objects like "real" cars, animals, buildings. (from 12).
14. A car created solely from mathematics (that is, existing only in the "mathematical / metaphysical / ethereal" realm) is just as real as any car in our world.
15. Music can be described mathematically, that is, without it having to be played (assumption).
16. Since music is math, we can create extremely large musical "equations". (From 15, 1)
17. Since music is math, we can create objects and worlds using these musical equations (from 16, 12)
18. We then have "real" (or as real as we are) objects that are created solely out of mathematics/music. (From 17)
19. Conclusion. Music is another "language" with which we can describe, and consequently, create (or compose!) real objects or worlds. (Rephrasing of 17 & 18)

Pythagorean
Gold Member
I don't like it

Math Is Hard
Staff Emeritus