Clavier tuning optimization: Difference between revisions

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{{Project
{{Project
|Name=An equally tempered 12-key scale for clavier instruments that is optimized for more usable intervals and an overall groovy sound.
|Name=Optimized temperaments for clavier instruments
|Skills=Music,
|Skills=Music,
|Status=Active
|Status=Active
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The minor adjusments of the syntonic comma resulted in a slightly stretched octave to accentuate the 3rd and 5th harmonics and to avoid the 7th and up. The 7th can be clearly heard in less mainstream music like jazz and blues and is often referred to as "the blue note". Wind instruments easily accomodate higher harmonics because without tuning they play notes from the harmonic series. Other instruments like claviers are not as accomodating, e.g. most piano's are not tuned to play the blue note.
The minor adjusments of the syntonic comma resulted in a slightly stretched octave to accentuate the 3rd and 5th harmonics and to avoid the 7th and up. The 7th can be clearly heard in less mainstream music like jazz and blues and is often referred to as "the blue note". Wind instruments easily accomodate higher harmonics because without tuning they play notes from the harmonic series. Other instruments like claviers are not as accomodating, e.g. most piano's are not tuned to play the blue note.


This article presents a tuning scale based on the microtonal 28/27 ratio, originating from a 19-keyed piano. The scale uses this ratio to create distances of two (E-F, B-C) or three (C-D, D-E, F-G, G-A, A-B) quarter tones, rather than the usual semitones. The 3 quartertone intervals leave room for the black keys to be used for the 18/17 interval relative to the key before it. C#/Db is a pure 18/17 tone, D#/Eb becomes (28/27)^3 * (18/17). Note how the factor 9 is present in both 27 and 18, creating optimal consonance despite using the high prime number 17.


Octaves are very slightly narrowed using this scale, but are closer to an actual 1:2 ratio. All other just ratio's like C:G = 2:3 and C:F = 3:4 are very well maintained. The C and following A are closer together, so the scale as a whole is tuned to A-438.
(More bla to be added)


The calculated frequencies for a five octave keyboard:
Bla about finding a better compromise between harmony and equal temperament, after which I present to you:


C2 66.09554941
Update: After having a master pianist play around with the samples, I didn't hear the sound I wanted. I realized I overlooked some equations and started again. The sound is now getting much closer to what I was looking for.
69.98352291
73.71485550
78.05102347
82.21249341
88.41508208
93.61596926
98.60732012
104.40775071
109.97449023
116.44357789
122.65203523
C3 131.90561814
139.66477215
147.11132090
155.76492802
164.06989364
176.44828068
186.82759130
196.78873431
208.36454221
219.47397732
232.38421128
244.77431032
C4 263.24150795
278.72630253
293.58723683
310.85707429
327.43113462
352.13444382
372.84823463
392.72749636
415.82911379
A4 438.00000000
463.76470588
488.49138851
C5 525.34602001
556.24872707
585.90640814
620.37149097
653.44802476
702.74794433
744.08605870
783.75871940
829.86217348
874.10818514
925.52631368
974.87287915
C6 1048.42295919
1110.09489797
1169.28216228
1238.06346595
1304.07366897
1402.46057130
1484.95825196
1564.13221872
1656.13999629
1744.44091172
1847.05508300
1945.53507565
C7 2092.31755736


Note that this is a work in progress. Samples for a 61-key clavier are available at [https://space.nurdspace.nl/~cu64/samples.zip]  
 
Mathematical equations for each key will be made available.
 
 
Note that this is a work in progress. Samples for up to 61 keys are available here:
[https://space.nurdspace.nl/~cu64/Claviertuningv1.2.zip] (Last updated 12-6-2019)
 
Details included in readme file.

Revision as of 14:51, 12 June 2019

Optimized temperaments for clavier instruments
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Skills Music
Status Active
Niche Music
Purpose Use in other project
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Music is all about patterns. From rhythmic patterns to melodies built from harmonic intervals, mathematics are everywhere. This article illustrates a possible tuning scale which is, like all tuning scales, built around prime numbers.

The goal is to better tune any clavier to create better sounding intervals. Current standard tuning methods revolve around the 81/80 ratio, also known as the syntonic comma. The origin lies with Pythagorean scales, which contained only the 2nd and 3rd harmonics. Musicians found that slightly adjusting some intervals created a much more consonant sound with more usable intervals.

The minor adjusments of the syntonic comma resulted in a slightly stretched octave to accentuate the 3rd and 5th harmonics and to avoid the 7th and up. The 7th can be clearly heard in less mainstream music like jazz and blues and is often referred to as "the blue note". Wind instruments easily accomodate higher harmonics because without tuning they play notes from the harmonic series. Other instruments like claviers are not as accomodating, e.g. most piano's are not tuned to play the blue note.


(More bla to be added)

Bla about finding a better compromise between harmony and equal temperament, after which I present to you:

Update: After having a master pianist play around with the samples, I didn't hear the sound I wanted. I realized I overlooked some equations and started again. The sound is now getting much closer to what I was looking for.



Note that this is a work in progress. Samples for up to 61 keys are available here: [1] (Last updated 12-6-2019)

Details included in readme file.