Near-Equal Temperament

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Near-Equal Temperament

Post by 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/
andonoff
Posts: 2 Joined: Wed Aug 04, 2021 2:01 pm

Re: Near-Equal Temperament

Post by Folderol »

I had a look at this hoping to try it out in practice, but the ratios you show would need a lot of massage to get them anything like Scala compatible.
Can you present these either as integer pairs such as:
196/185
422/375
etc.
or as cents:
0076.049000
0193.156860
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Re: Near-Equal Temperament

Post by andonoff »

The stack I'm offering might be considered as an overhead. Working with small ratios like 3/2 and 5/4 make more sense. They are easy to catch without mistake. Others like 196/185, 422/375, no idea what to do with them in terms of acoustics.
andonoff
Posts: 2 Joined: Wed Aug 04, 2021 2:01 pm
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