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.

== Sycamore ==

Subgroup: 2.3.5

[[Comma list]]: 48828125/47775744

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[[Badness]]: 0.209966

== 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.

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[[Badness]]: 0.062018

=== 11-limit ===

Subgroup: 2.3.5.7.11

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Badness: 0.055940

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

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Badness: 0.034295

== 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. 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 … }}.

Subgroup: 2.3.5.7

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[[Badness]]: 0.069748

=== 11-limit ===

Subgroup: 2.3.5.7.11

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Badness: 0.056874

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

@@ Line 3: / Line 3: @@
 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 ==
+Subgroup: 2.3.5
 [[Comma list]]: 48828125/47775744
@@ Line 14: / Line 16: @@
 [[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&amp;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.
@@ Line 31: / Line 33: @@
 [[Badness]]: 0.062018
-=== 11-limit  ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 44: / Line 46: @@
 Badness: 0.055940
-=== 13-limit  ===
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 57: / Line 59: @@
 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&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. The wedgie starts {{multival| 11 6 34 -29 … }}.
 Subgroup: 2.3.5.7
@@ Line 74: / Line 76: @@
 [[Badness]]: 0.069748
-=== 11-limit  ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 87: / Line 89: @@
 Badness: 0.056874
-=== 13-limit  ===
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13