39edt: Difference between revisions
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It is a strong no-twos 13-limit system, a fact first noted by [[Paul Erlich]], and like [[26edt]] and [[52edt]], it is a multiple of 13edt and so contains the Bohlen-Pierce scale. It is [[contorted]] in the 7-limit, tempering out the same BP commas 245/243 and 3125/3087 as 13edt. In the 11-limit it tempers out 1331/1323 and in the 13-limit 275/273, 847/845 and 1575/1573. It is related to the 49f&172f temperament 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]]. | It is a strong no-twos 13-limit system, a fact first noted by [[Paul Erlich]], and like [[26edt]] and [[52edt]], it is a multiple of 13edt and so contains the Bohlen-Pierce scale. It is [[contorted]] in the 7-limit, tempering out the same BP commas 245/243 and 3125/3087 as 13edt. In the 11-limit it tempers out 1331/1323 and in the 13-limit 275/273, 847/845 and 1575/1573. It is related to the 49f&172f temperament 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]]. | ||
==Harmonics== | == Harmonics == | ||
{{Harmonics in equal|39|3|1|intervals=prime}} | {{Harmonics in equal|39|3|1|intervals=prime}} | ||
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! [[Hekt]]s | ! [[Hekt]]s | ||
! [[4L 5s (3/1-equivalent)|Enneatonic]] degree | ! [[4L 5s (3/1-equivalent)|Enneatonic]] degree | ||
! Corresponding | ! Corresponding<br />3.5.7.11.13 subgroup<br />intervals | ||
3.5.7.11.13 subgroup <br> | ! [[Lambda ups and downs notation|Lambda]] <br />(sLsLsLsLs,<br />J = 1/1) | ||
intervals | ! Mintaka[7]<br />(E macro-Phrygian) | ||
! [[Lambda ups and downs notation|Lambda]] | |||
(sLsLsLsLs, <br> | |||
J = 1/1) | |||
! Mintaka[7] | |||
(E macro-Phrygian) | |||
|- | |- | ||
| 0 | | 0 | ||