|
|
| Line 554: |
Line 554: |
| ** 7-tone pelog: 6 8 12 8 5 14 7 | | ** 7-tone pelog: 6 8 12 8 5 14 7 |
| ** 5-tone slendro: 12 12 12 12 12 | | ** 5-tone slendro: 12 12 12 12 12 |
|
| |
| == Nearby equal-step tunings ==
| |
| There are a few other useful [[equal-step tuning]]s which occur close to 60edo in step size:
| |
|
| |
| ; 207ed11, 168ed7
| |
|
| |
| The tunings [[207ed11]] and [[168ed7]] are almost identical. Each is 60edo but with slightly ''stretched'' octaves.
| |
|
| |
| Each induces relatively large improvement to [[5/1]], [[7/1]] and [[11/1]] at the cost of worsening of [[2/1]] and [[3/1]]. Each also causes the [[patent val]] to flip for [[11/1]] and [[13/1]].
| |
| {{Harmonics in equal|207|11|1|intervals=prime|columns=11|collapsed=1}}
| |
| {{Harmonics in equal|168|7|1|intervals=prime|columns=11|collapsed=1}}
| |
|
| |
| ; 139ed5
| |
|
| |
| The tuning [[139ed5]] is 60edo but with slightly ''stretched'' octaves.
| |
|
| |
| It induces relatively large improvement to 5/1, 7/1 and 11/1 at the cost of worsening of 2/1 and 13/1. It also causes the patent val for 11/1 to flip from 208 steps to 207 steps.
| |
| {{Harmonics in equal|139|5|1|intervals=prime|columns=11|collapsed=1}}
| |
|
| |
| ; 301zpi
| |
|
| |
| The tuning [[301zpi]], the 301st [[zeta peak index]], is 60edo but with slightly ''stretched'' octaves.
| |
|
| |
| It induces relatively large improvement to 3/1, 5/1, 7/1, 11/1 and 17/1 at the cost of worsening of 2/1 and 13/1. It also causes the patent val for 11/1 to flip from 208 steps to 207 steps.
| |
|
| |
| Like 60edo, 301zpi is distinctly consistent up to the [[integer limit|10-integer-limit]].
| |
| {{Harmonics in equal|1|38083|37645|intervals=prime|columns=11|title=Approximation of prime harmonics in 301zpi|collapsed=1}}
| |
|
| |
| ; 60edo
| |
| {{Harmonics in equal|60|2|1|intervals=prime|columns=11|collapsed=1}}
| |
|
| |
| ; 255ed19
| |
|
| |
| The tuning [[255ed19]] is 60edo but with slightly ''compressed'' octaves.
| |
|
| |
| It induces a relatively large improvement to 11/1, at the cost of worsening of every smaller prime. It also causes the patent val for 7/1 to flip from 168 steps to 169.
| |
| {{Harmonics in equal|255|19|1|intervals=prime|columns=11|collapsed=1}}
| |
|
| |
| ; 208ed11
| |
|
| |
| The tuning [[208ed11]] is 60edo but with slightly ''compressed'' octaves.
| |
|
| |
| It induces a relatively large improvement to 7/1 and 11/1, at the cost of worsening of 2/1, 3/1 and 5/1. It also causes the patent val to flip for 5/1, 7/1 and 17/1.
| |
| {{Harmonics in equal|208|11|1|intervals=prime|columns=11|collapsed=1}}
| |
|
| |
| ; 272ed23
| |
|
| |
| The tuning [[272ed23]] is 60edo but with slightly ''compressed'' octaves.
| |
|
| |
| It induces a relatively large improvement to 7/1 and 11/1, at the cost of worsening of 2/1, 3/1 and 5/1. It also causes the patent val to flip for 5/1, 7/1, 13/1 and 17/1.
| |
|
| |
| These characteristics, particularly the flipped 5/1 and 13/1, are preferred over pure-octaves 60edo for [[catnip]] temperament specifically. They change catnip's [[wart]]s from 60cf to i272dg (later letters in the alphabet are better). Given this, 272ed23 can be thought of as a 60edo clone tailor-made for catnip.
| |
| {{Harmonics in equal|272|23|1|intervals=prime|columns=11|collapsed=1}}
| |
|
| |
|
| == Instruments == | | == Instruments == |