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.


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 66,0955494142999
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.
70,4678514975879
73,7148554967589
78,5911840712824
82,2124934138525
88,4150820801927
94,2638487671923
98,6073201150427
105,130315914109
109,974490228391
117,249438345096
122,652035233127
C3 131,905618138233
140,63133740517
147,111320904866
156,842916157004
164,069893639365
176,448280676629
188,120551987352
196,788734309473
209,806551705855
219,473977318577
233,99245150876
244,774310323497
C4 263,241507947355
280,655258249839
293,58723682672
313,008394507975
327,431134624812
352,134443821473
375,428571428571
392,727496355684
418,706904435299
A4 438
466,97424001238
488,491388507849
C5 525,346020013928
560,098306939574
585,906408136244
624,66483940139
653,448024762836
702,747944326561
749,235587265204
783,758719395246
835,605324983272
874,10818514274
931,931519282263
974,872879147151
C6 1048,42295919255
1117,77743054902
1169,2821622819
1246,63161893066
1304,07366897386
1402,46057129699
1495,23506718891
1564,13221872232
1667,60149341721
1744,44091172039
1859,83782876058
1945,53507565341
C7 2092,31755735565




Note that this is a work in progress. Samples for a 61-key clavier are available at [https://space.nurdspace.nl/~cu64/samplesv10.zip] (Last updated to v1.0 as of 18-3-2019)
 
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 13:51, 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.