/sci/ - Science & Math

[Anonymous No.12053068]

>Music has """"""mathematical"""""" properties
What the fuck does this even mean?

[Anonymous No.12053071]

>>12053068
Spatial and temporal symmetries and patterns

[Anonymous No.12053073]

>>12053068
sounds are just waveforms.

[Anonymous No.12053076]

>>12053068
Most people who say this have no idea what they are talking about. Music can follow certain structures which involve interesting patterns, and there are certain basic physical symmetries underlying how tonal sounds are made, how they form keys and how harmonics are produced, but beyond that it's all very vague and largely intuitive.

[Anonymous No.12053092]

>>12053068
240hz is an octave above 120hz
different intervals are expressed in ratios
etc.

[Anonymous No.12053205]

>>12053068
The Harmonic Series is a phenomenon that interacts with music all over the world. Every sound that could be described as a pitch has a harmonic series. Essentially, the fundamental pitch, aka the note an instrument is playing, has a series of harmonics which are multiples of that frequency.

For example, a 100hz note also has harmonics extending to 200hz, 300hz, 400hz, etc. n*x

There is an exponential property to the way our ears experience these harmonics. Every harmonic that is n*2^x (n=fundamental pitch) is heard as an octave higher, for each increment of x. Every harmonic n*3*2^x is heard as a fifth, again rising in octsves. N*2*4^x is covered by n*2^x. Therefore every odd number dictate a new interval. 5*2^x describes thirds, 7*2^x describes "harmonic sevenths." Halway between the natural 7 and flat seven. And so on. All these interval names (octave, fifth, third, seventh) are music theory intervals, has nothing to do with the matemagic terms.

The volume profile of all these harmonics is what determines a particular timbre of sound.

Also, the pentatonic scale, the most universal collection of notes (at varying intonations) is based on the harmonic series. Odd harmonics 2^x through 9*2^x

[Anonymous No.12053207]

>>12053068
harmonic series, beats/chorus effect, cross modulation and octaves

[Anonymous No.12053221]

>>12053205
>>12053092
>>12053207
Most people know that intervals and harmonics are based on mathematical ratios (and that simpler ratios tend to be perceived as more consonant than less simple ones).

But I guess the question is other than that, in what ways is music mathematical? In some sense music is nothing but math (you can analyze rhythm in terms of ratios in the same way, etc.), but on the other hand, beyond basic multiplication and division of integers, what math is involved? Are there are other fields of math that are involved? Fourier transforms for analyzing frequencies is all I can think of right now, and that's not necessarily something you need to ever consider since your ear and brain does something similar for you automatically.

[Anonymous No.12053232]

>>12053221
Well the hatmonic series contains the pentatonic scale which is present in cultures all over the world, from led zeppelin to Japanese Koto music.

[Anonymous No.12053246]

Fourier transforms are wider than music, nothing special about music in maths.

[Anonymous No.12053266]

>>12053221
>other than that, in what ways is music mathematical?

Nothing really. You're right.

[Anonymous No.12053281]

>>12053068
The distance between a and a# is the 12th root of 2 times the hz of a

[Anonymous No.12053291]

>>12053221
>ourier transforms for analyzing frequencies is all I can think of right now, and that's not necessarily something you need to ever consider since your ear and brain does something similar for you automatically.
absolutely necessary is you want to do/make digital stuff. How do you think pitch-shifting works?
Sound synthesis and DSP are where the real math is. Listening is something any brainlet could do.

[Anonymous No.12053455]

https://phys.org/news/2008-04-music-geometry.html#:~:text=Mathematics-,The%20new%20shape%20of%20music%3A%20Music,its%20own%20geometry%2C%20researchers%20find&text=The%20connection%20between%20music%20and,be%20described%20using%20simple%20ratios.

[Anonymous No.12053464]

Well people don't usually mean this when they say music involves maths but it is interesting how mathematical truths influence which temperaments can be chosen.
With temperament I basically mean the set of pitches you choose to include in your music, so you could say a temperament is a set [math] T \subset \mathbb{R}_+ [/math] which is countable and has at most 0 as an accumulation point.
These are the frequencies you include.
Now you can write down some preferable properties. Simple ratios of frequencies sound harmonic, so we say that [math] T [/math] contains the interval [math] q \in \mathbb{R} [/math] if [math] x \ in T \Rightarrow qx, q^{-1}x \in T[/math], i.e. the set is closed under multiplication with q and its inverse.
What we call just intonation is the smallest temperament [math] T [/math] which contains 1 and contains the imtervals 16/15, 9/8, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 16/9, 15/8, 2.
If you were to plot this set it would look nontrivial.
A further property that would be nice would for our temperament to look the same when setting a different pitch to be 1. We say [math] T [/math] is equal, if [math] qT = q^{-1}T = T[/math] for every interval [math] q \ in \mathbb{R} [/math] which [math] T [/math] includes.
An unfortunate truth is that the just temperament is not equal. For example (2/3)^12 is almost (1/2)^7, meaning that the temperament (2/3)^12 T would include a pitch very close to 1.
The solution musicians found is that the intervals listed above are quite close to [math] 2^{\frac{n}{12}} [/math]. By choosing [math] T [/math] as the smallest temperament which includes [math] 2^{\frac{1}{12}}[/math] we get an equal temperament that almost includes our intervals.

[Anonymous No.12053511]

>>12053221
The technical side of music is math but the theoretical side is also math but more like you have sets of pitches that all relate to each other in different ways. Any chromatic/diatonic composition can be described in essentially mathematical functions. I'm not sure of the math terms but it's groups, patterns, series, etc. The most basic way of putting it is a song needs to be composed of chords which relate to each other as well as a key which is like the 'background' upon which chords, scales, and roots (the main note of a key) exist. But you can also break the rules, but whatever notes you play will make the sound those notes make. The entire system of actually feeling music is arranged in precise diagrams and circles and musicians have to do mental music math to transpose and compose

Tldr circle of fifths