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are there mathemathics related to music and piano?

Anonymous Thu 27 Aug 08:41:28 2020 No.12053662 View Reply Original Report

Quoted By: >>12055067 >>12056045

looking for mathemathica related to music and piano and instruments...

like maybe sounding several notes or chords together is equal to a certain interval or something?

Anonymous

Anonymous Thu 27 Aug 2020 08:46:47 No.12053665 Report

Quoted By: >>12053668 >>12053688 >>12055067 >>12055344

music is math
see pythagorus who finessed western tuning
some of our greatest music is some of our greatest mathematical formulas

Anonymous

Anonymous Thu 27 Aug 2020 08:48:55 No.12053668 Report

Quoted By:

>>12053665
good articulation by leonard bernstein: https://youtu.be/3TlQryUBz3E

Anonymous

Anonymous Thu 27 Aug 2020 09:06:24 No.12053688 Report

Quoted By: >>12054650 >>12056117

>>12053665
cool. are there math for music to play a certain songs in different scales and modes? or playing it in the same scale and modes but with different intervals and different chords?

Anonymous

Anonymous Thu 27 Aug 2020 16:21:59 No.12054650 Report

Quoted By:

>>12053688
If a chord progression is written in Roman numerals, you can play it in any key. Likewise, a chord progression written with note names can be converted to Roman numeral notation and then rewritten in any key

Anonymous

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Anonymous Thu 27 Aug 2020 17:15:31 No.12054868 Report

Quoted By:

Anonymous

Anonymous Thu 27 Aug 2020 17:22:28 No.12054885 Report

Quoted By:

Th is isn’t what you’re looking for but it is what u want
https://youtu.be/xGoR0mqLXTY
https://youtu.be/xGoR0mqLXTY
He’s wrong about 1 very simple fact though the rest is spot on

Anonymous

Anonymous Thu 27 Aug 2020 18:29:45 No.12055067 Report

Quoted By: >>12055075 >>12055972

>>12053665
>see pythagorus who finessed western tuning
?????????????

"Western tuning" wasn't invented until the 18th century.
>>12053662
Acoustics are of course a fundamental science i the study of music, but it is equal parts cutural conditioning given how Western listeners generally prefer our tuning systems despite it being technically "out of tune": Helmholtz' "On The Sensation of Tone" is a good starting point as any, I am also partial to Harry Partch's "Genesis of a Music" for a musicological overview, albeit he is heavily biased.

Anonymous

Anonymous Thu 27 Aug 2020 18:32:24 No.12055075 Report

Quoted By: >>12055093

>>12055067
Look up Pythagorean tuning, the tuning you're talking about is equal temperament I think

Anonymous

Anonymous Thu 27 Aug 2020 18:38:20 No.12055093 Report

Quoted By: >>12055157 >>12055992

>>12055075
Some form of equal temperament IS western tuning. Pythagorean tuning all but disappeared during the renaissance, only reemerging in certain modern composers, like Harry Partch or in HIP early music practictioners.

Anonymous

Anonymous Thu 27 Aug 2020 18:54:20 No.12055157 Report

Quoted By:

>>12055093
Of course, but equal temperament is an 'improved' version of Pythagorean tuning. Mostly the same, but modified so any key can be played.

Anyway I think we're just talking about semantics.

Anonymous

Anonymous Thu 27 Aug 2020 19:02:40 No.12055195 Report

Quoted By:

12th root of 2

Anonymous

Anonymous Thu 27 Aug 2020 19:41:59 No.12055344 Report

Quoted By: >>12055967

>>12053665
>HURR EVERYTHING IS MATH
>MUH PYTHAGORAS JESUS

Shut the fuck up, schizo.

Anonymous

Anonymous Thu 27 Aug 2020 22:58:11 No.12055967 Report

Quoted By:

>>12055344
Yea... you’re definitely the schizo here. Nurse! Get this fucker back in bed!

Anonymous

Anonymous Thu 27 Aug 2020 23:01:03 No.12055972 Report

Quoted By: >>12055978

>>12055067
It all stems from Pythagoreans they discovered the foundations of music theory

Anonymous

Anonymous Thu 27 Aug 2020 23:03:49 No.12055978 Report

Quoted By: >>12055993 >>12055996

>>12055972
wrong

Anonymous

Anonymous Thu 27 Aug 2020 23:09:15 No.12055992 Report

Quoted By:

>>12055093
>Pythagorean tuning all but disappeared during the renaissance
I'm pretty sure non-fretted instruments and the human voice naturally gravitate to pythagorean tuning for melodies, and just harmony for intervals and chords. Then there's well temperaments for fixed note instruments that allowed different keys and chords to take on a different character, but made certain things unplayable. Equal temperament really grew in popularity in the mid-19th century and played a role in the era of romanticism and chromaticism.

Anonymous

Anonymous Thu 27 Aug 2020 23:09:26 No.12055993 Report

Quoted By: >>12055996 >>12055998

>>12055978
I love you

Anonymous

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Anonymous Thu 27 Aug 2020 23:10:55 No.12055996 Report

Quoted By:

>>12055978
>>12055993
dumb fucks

Anonymous

Anonymous Thu 27 Aug 2020 23:11:40 No.12055998 Report

Quoted By:

>>12055993
why do you insult me anon

Anonymous

Anonymous Thu 27 Aug 2020 23:39:43 No.12056045 Report

Quoted By: >>12056048

>>12053662
(1/2)
You can express music theory and simple Harmony (chord progressions) through group theory by the group $\mathbb{Z}_{12}$ (integers modulo 12) representing every pitch. Then the musical intervals are represented as $a-b \in \mathbb{Z}_{12}$ for $a, b \in \mathbb{Z}_{12}$ and the sequences which the generators of the group produce it are: the chromatic ascending and descending scale, the cycle of fifths and the cycle of fours. (Since you like piano, Bach's WTC are actually preludes and fugues on the sequence of the generator $<1>=\{1,2,\dots ,11, 0\}$ ) You can then study various transformations on this group, for example the three accidentals ( $\sharp, \flat$ ,) are automorphisms on $\mathbb{Z}_{12}$ . Taking it one step further, you can represent chords as elements $(\Delta, \sigma)$ in some space $\Gamma$ which is isomorphic as a group to:
$(\Gamma, \cdot) \cong (\mathbb{Z}_{12}\times \mathbb{Z}_2 ,\cdot )$

where the $\mathbb{Z}_2 \cong \{ + , -\}$ part keeps track of the information about the chord being major or minor. Eg $\Delta = (2, - )$ is a D minor triad (0 is C). Then you one can see that transformations on the group $\Gamma$ have also interesting properties and are called Uniform Triadic Transformations which can actually express chord progressions. If you're interested you should also read the work of J.Hook and D.Lewin.

Anonymous

Anonymous Thu 27 Aug 2020 23:42:22 No.12056048 Report

Quoted By: >>12056052

>>12056045
Now there are also other takes on the subject, Tymoczko gave a try at continuous groups using the fact that the human ear has logarithmis perception of sound with its frequency and did music on the n-dimensional torus $\mathbb{T}^n$ where every point represents a pitch class (using the orbit space $\mathbb{R}/\mathbb{Z}_{12}$ ): $\mathbb{T}^n \cong \mathbb{S}^1\times \dots \times \mathbb{S}^1 \cong ( \mathbb{R}/\mathbb{Z}_{12})\times \dots \times (\mathbb{R}/\mathbb{Z}_{12})$ (you can work out the math). Also Iannis Xenakis open the field of stochastic music theory which is fascinating.

Anonymous

Anonymous Thu 27 Aug 2020 23:43:25 No.12056052 Report

Quoted By:

>>12056048
(2/2)*

Anonymous

Anonymous Fri 28 Aug 2020 00:10:35 No.12056117 Report

Quoted By: >>12057067

>>12053688
If you look at the harmonic series (in this case of the the note C): [C, G, C, E, G, Bb...]

In the key of C, G is the dominant degree of the scale. The dominant has a feeling of pull towards the tonic C. But, in the series, you also see the order of CEGBb, a C7 chord, the dominant 7th of F major. So the crucial pivots of western harmony are laid bare in the overtone series. The tonic (C), the dominant (G) and the subdominant (F). Hence the prolific I-IV-V (C-F-G) progression.

Anonymous

Anonymous Fri 28 Aug 2020 08:34:12 No.12057067 Report

Quoted By:

>>12056117
ah sorry this is frustating

i just wanna play some or a few things that goes along well with the melody...
variety of chords going in variety scale styles and genres...

often itinvolves just choosing "which" chords to go with the melody and make it as good as a pro pianists...something to sound awesome and fun.

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