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User:Overthink/41edo well temperament: Difference between revisions

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Prime 5 is closest to the root on the circle of fifths; being only 8 fifths down due to 41edo tempering out the [[schisma]]. We build our well temperament down the chain of fifths to reach a more accurate prime 5, using slightly flat fifths of 701.792[[{{c}}]], or 1/12 schisma flat of just. We continue this chain of schismic fifths down until we reach -12 fifths, or an exact [[81/80]]. We then stack down 12 [[parapyth]] fifths of 704.002{{c}} to obtain accurate approximations of harmonics 7, 11, and 13. Finally, the remaining fifths are all 1/12-schisma flat, giving a total of 29 schismic fifths and 12 parapyth fifths.
Prime 5 is closest to the root on the circle of fifths; being only 8 fifths down due to 41edo tempering out the [[schisma]]. We build our well temperament down the chain of fifths to reach a more accurate prime 5, using slightly flat fifths of 701.792[[{{c}}]], or 1/12 schisma flat of just. We continue this chain of schismic fifths down until we reach -12 fifths, or an exact [[160/81]]. We then stack down 12 [[parapyth]] fifths of 704.002{{c}} to obtain accurate approximations of harmonics 7, 11, and 13. Finally, the remaining fifths are all 1/12-schisma flat, giving a total of 29 schismic fifths and 12 parapyth fifths.
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