71zpi: Difference between revisions

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== Theory ==

'''71zpi''' marks the most prominent [[zeta peak index]] in the [[vicinity]] of [[20edo]]. While [[70zpi]] is the nearest peak to [[20edo]] and closely competes with 71zpi in terms of strength, 71zpi remains superior across all measures of strength. 71zpi may also be viewed as a tritave compression of [[32edt]], a [[~~The_Riemann_zeta_function_and_tuning~~#Removing_primes|no-2s zeta peak EDT]] (consistent in the [[Odd_limit#Nonoctave_equaves|no-2s 19-integer-limit]]), but with less extreme stretch than [[71zpi#Record on the Riemann zeta function with prime 2 removed|the no-2s peak]] at 59.271105 cents.

'''71zpi''' marks the most prominent [[zeta peak index]] in the [[vicinity]] of [[20edo]]. While [[70zpi]] is the nearest peak to [[20edo]] and closely competes with 71zpi in terms of strength, 71zpi remains superior across all measures of strength. 71zpi may also be viewed as a tritave compression of [[32edt]], a [[Riemann zeta function#Removing_primes|no-2s zeta peak EDT]] (consistent in the [[Odd_limit#Nonoctave_equaves|no-2s 19-integer-limit]]), but with less extreme stretch than [[71zpi#Record on the Riemann zeta function with prime 2 removed|the no-2s peak]] at 59.271105 cents.

71zpi features a good 3:5:9:11:14:15:16:19:25:26:33 chord, which differs a lot from the harmonic characteristics of [[20edo]].

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 == Theory ==
-'''71zpi''' marks the most prominent [[zeta peak index]] in the [[vicinity]] of [[20edo]]. While [[70zpi]] is the nearest peak to [[20edo]] and closely competes with 71zpi in terms of strength, 71zpi remains superior across all measures of strength. 71zpi may also be viewed as a tritave compression of [[32edt]], a [[The_Riemann_zeta_function_and_tuning#Removing_primes|no-2s zeta peak EDT]] (consistent in the [[Odd_limit#Nonoctave_equaves|no-2s 19-integer-limit]]), but with less extreme stretch than [[71zpi#Record on the Riemann zeta function with prime 2 removed|the no-2s peak]] at 59.271105 cents.
+'''71zpi''' marks the most prominent [[zeta peak index]] in the [[vicinity]] of [[20edo]]. While [[70zpi]] is the nearest peak to [[20edo]] and closely competes with 71zpi in terms of strength, 71zpi remains superior across all measures of strength. 71zpi may also be viewed as a tritave compression of [[32edt]], a [[Riemann zeta function#Removing_primes|no-2s zeta peak EDT]] (consistent in the [[Odd_limit#Nonoctave_equaves|no-2s 19-integer-limit]]), but with less extreme stretch than [[71zpi#Record on the Riemann zeta function with prime 2 removed|the no-2s peak]] at 59.271105 cents.
 zpi features a good 3:5:9:11:14:15:16:19:25:26:33 chord, which differs a lot from the harmonic characteristics of [[20edo]].