# Near-Equal Temperament



## andonoff

I have developed a new method for acoustic tuning to improve the harmony of Equal Temperament. The research is based on just intervals and it is still theoretical. The kernel of my theory is the stack of just interval 7 perfect fifths (7 * 3/2) and 1 major third (5/4). The result is perfect fourth and it's ratio (1.3348388671875) is close more than enough the Equal Temperament. The mathematical precision is till 5th digit after the decimal point, the error is 0.00128 cents. JND is usually between 2-5 cents depending on professional experience. I'm suggesting a method to get equally tempered tones with unconditional accuracy. Repeating same stack 11 times gives a final error 11 * 0.00128 = 0.01408 cents. This is over 200 times better than any known tuning process. The full article and procedures how to achieve it is on following website. I would be grateful share with me your thoughts.

https://nearequaltemperament.com/


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## BabyGiraffe

This does not improve anything, because the problem in 12 ET is is that it has poor major and minor thirds/sixths.
12 ET= almost ideal P4/P5
19 ET =almost ideal min3rd/maj 6th
31 ET =almost ideal maj3rd/min 6th
All these are flawed system, you want a system that distributes the syntonic comma (so, diatonic music works can work without wolves) between the harmonic intervals and any chord inversion should sounds OK.
Selection of 12 notes (chain of 11 P4 or P5) from 43 equal (1/5 comma meantone) or 55 equal (1/6 comma meantone) is a good solution and these were supposedly used back in the day (check Barbour: "Tuning and temperament" from 1951, there is a public domain scan online)
43 equal harmonic intervals in cents:
306.976744 m3
390.697674 M3
502.325581 P4
697.674419 P5
809.302326 m6
893.023256 M6

55 equal
305.454545
392.727273
501.818182
698.181818
807.272727
894.545455


What you suggeste is not really better than 12 ET (which is ideal for rock music = power chords, not for classical music).


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## parlando

As one who has tuned pianos and for years with perfect pitch listened to pianos being carefully tuned, it seems to me that using this system would require an electronic adjunct that might need an oscilloscope to achieve accuracy. I’m sorry I didn’t go to the linked site above. Perhaps something like that is mentioned. But my own feeling is that the ears are the best test. Good tuning is not a quicky. Like love, tuning is in the soul of the tuner. Nice idea though. Still, when out in the urban boondocks with rubber dampers, a correct wrench, and lots of time, something approaching perfection is possible. There will always be certain compromises, just as dissonances will exist — perhaps to be resolved (like a lover’s quarrel) with a soothing chord or in a slow cadenza.


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## Opisthokont

I'm not sure here - remember that instruments in the real world already have pitch variation for many different physical reasons. It's unclear to me that the methods that orchestra or piano technicians use to tune actually need fixing to begin with. I think that you would need actual musicians and piano technicians to do side by side testing - see if it actually is faster or better in the real world.

I'm also wary in general of claims to 'improve' equal temperment music, it's not clear to me that we actually like to hear things perfectly tuned to JI intervals. I'm quite fond of dissonance. Aren't there studies showing that people prefer certain intervals sharper of flatter than JI? Regardless, it's not clear to me that improving the scientific consonance of an interval is the same thing as improving harmony. In fact, in some cases, especially in atonal harmony, I would argue that it does the opposite!


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