39edt: Difference between revisions

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If octaves are inserted, 39edt is related to the {{nowrap|49f & 172f}} temperament in the full 13-limit, known as [[Sensamagic clan#Triboh|triboh]], tempering out 245/243, 275/273, 847/845 and 1575/1573, which has mapping [{{val|1 0 0 0 0 0}}, {{val|0 39 57 69 85 91}}]. This has a POTE generator which is an approximate 77/75 of 48.822 cents. 39edt is the ninth [[The Riemann zeta function and tuning#Removing primes|no-twos zeta peak edt]].

When treated as an octave-repeating tuning with the sharp octave of 25 steps (about 1219 cents), and the other primes chosen by their best octave-reduced mappings, it functions as a tuning of [[mavila]] temperament, analogous to [[25edo]]'s mavila.

Mavila is one of the few places where octave-stretching makes sense, due to how flat the fifth and often the major third are; this fifth of 683 cents is much more recognizable as a perfect fifth of 3/2 than the 672-cent tuning with just octaves.

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 If octaves are inserted, 39edt is related to the {{nowrap|49f &amp; 172f}} temperament in the full 13-limit, known as [[Sensamagic clan#Triboh|triboh]], tempering out 245/243, 275/273, 847/845 and 1575/1573, which has mapping [{{val|1 0 0 0 0 0}}, {{val|0 39 57 69 85 91}}]. This has a POTE generator which is an approximate 77/75 of 48.822 cents. 39edt is the ninth [[The Riemann zeta function and tuning#Removing primes|no-twos zeta peak edt]].
+When treated as an octave-repeating tuning with the sharp octave of 25 steps (about 1219 cents), and the other primes chosen by their best octave-reduced mappings, it functions as a tuning of [[mavila]] temperament, analogous to [[25edo]]'s mavila.
+Mavila is one of the few places where octave-stretching makes sense, due to how flat the fifth and often the major third are; this fifth of 683 cents is much more recognizable as a perfect fifth of 3/2 than the 672-cent tuning with just octaves.
 {{Harmonics in equal|39|3|1|intervals=prime|columns=12}}