Sycamore family: Difference between revisions
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Another possible tuning uses a generator which is a pure 3/2 divided into 11 parts, and this makes the generator chain of sycamore exactly the same as [[Carlos Beta]]. In fact, Carlos Beta is characterized by Carlos as taking five steps to reach 6/5 and six to reach 5/4, which means it tempers out the sycamore comma. It can be described as the generator chain of sycamore, or sycamore can be called Carlos Beta with octaves. | Another possible tuning uses a generator which is a pure 3/2 divided into 11 parts, and this makes the generator chain of sycamore exactly the same as [[Carlos Beta]]. In fact, Carlos Beta is characterized by Carlos as taking five steps to reach 6/5 and six to reach 5/4, which means it tempers out the sycamore comma. It can be described as the generator chain of sycamore, or sycamore can be called Carlos Beta with octaves. | ||
= Sycamore = | == Sycamore == | ||
[[Comma list]]: 48828125/47775744 | [[Comma list]]: 48828125/47775744 | ||
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[[Badness]]: 0.209966 | [[Badness]]: 0.209966 | ||
= Septimal sycamore = | == Septimal sycamore == | ||
The second element of the [[Normal lists #Normal interval list|normal comma list]] for septimal sycamore is [[875/864]], the keema, and it also tempers out [[686/675]], the senga, and [[3136/3125]], hemimean. It may also be called the 19&56 temperament. This may also be used as the name for the temperament obtained by adding [[100/99]] to sycamore's commas, giving unidecimal sycamore, where 10 generator steps reaches 16/11, 11 reach 3/2, and 15 give 7/4, adding a considerable dose of 11-limit harmonies to the 19-note MOS. [[75edo|75EDO]] is an excellent tuning for 7-limit sycamore, and [[56edo|56EDO]] for the 11-limit version. | The second element of the [[Normal lists #Normal interval list|normal comma list]] for septimal sycamore is [[875/864]], the keema, and it also tempers out [[686/675]], the senga, and [[3136/3125]], hemimean. It may also be called the 19&56 temperament. This may also be used as the name for the temperament obtained by adding [[100/99]] to sycamore's commas, giving unidecimal sycamore, where 10 generator steps reaches 16/11, 11 reach 3/2, and 15 give 7/4, adding a considerable dose of 11-limit harmonies to the 19-note MOS. [[75edo|75EDO]] is an excellent tuning for 7-limit sycamore, and [[56edo|56EDO]] for the 11-limit version. | ||
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[[Badness]]: 0.062018 | [[Badness]]: 0.062018 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.055940 | Badness: 0.055940 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.034295 | Badness: 0.034295 | ||
= Betic = | == Betic == | ||
Septimal sycamore sharpens the fifth from where it stands in the 5-limit, and lowers accuracy in order to reach 7-limit harmonies. If we retain tunings approximately (e.g. 94et) or exactly those of Carlos Beta, we get the 19&94 temperament, betic, for the 7-limit. This adds [[225/224]] to the sycamore comma. The Carlos Beta tuning, with pure fifths, is a good tuning choice, but 94 or 113 equal are as well. Betic extends to the 11-limit upon addition of [[385/384]] or [[540/539]] to the list of commas, which means it supports both 7 and 11-limit marvel. The wedgie starts {{multival| 11 6 34 -29 … }}. | Septimal sycamore sharpens the fifth from where it stands in the 5-limit, and lowers accuracy in order to reach 7-limit harmonies. If we retain tunings approximately (e.g. 94et) or exactly those of Carlos Beta, we get the 19&94 temperament, betic, for the 7-limit. This adds [[225/224]] to the sycamore comma. The Carlos Beta tuning, with pure fifths, is a good tuning choice, but 94 or 113 equal are as well. Betic extends to the 11-limit upon addition of [[385/384]] or [[540/539]] to the list of commas, which means it supports both 7 and 11-limit marvel. The wedgie starts {{multival| 11 6 34 -29 … }}. | ||
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[[Badness]]: 0.069748 | [[Badness]]: 0.069748 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 87: | Line 87: | ||
Badness: 0.056874 | Badness: 0.056874 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||