Sycamore family: Difference between revisions

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~~{{Multival|legend=1| 11 6 15 -16 -7 18 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~25/24 = 63.995

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== 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. 94edo) 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. 94edo) 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.

[[Subgroup]]: 2.3.5.7

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~~{{Multival|legend=1| 11 6 34 -16 23 62 }}~~

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 63.741

@@ Line 27: / Line 27: @@
 {{Mapping|legend=1| 1 1 2 2 | 0 11 6 15 }}
-{{Multival|legend=1| 11 6 15 -16 -7 18 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~25/24 = 63.995
@@ Line 63: / Line 61: @@
 == 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. 94edo) or exactly those of Carlos Beta, we get the 19 &amp; 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. 94edo) or exactly those of Carlos Beta, we get the 19 &amp; 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.
 [[Subgroup]]: 2.3.5.7
@@ Line 70: / Line 68: @@
 {{Mapping|legend=1| 1 1 2 1 | 0 11 6 34 }}
-{{Multival|legend=1| 11 6 34 -16 23 62 }}
 [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 63.741