Subgroup temperaments: Difference between revisions

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=== Spog ===

This temperament produces [[Slendro_clan#Superpelog|superpelog]]-like [[5L 4s|semiquartal]] scales while being more accurate ([[Subgroup temperaments#2.15.189.55.325.279|see]] rational approximations to their intervals).

This temperament produces [[Slendro_clan#Superpelog|superpelog]]-like [[5L 4s|semiquartal]] scales while being more accurate ([[Subgroup temperaments#2.15.189.55.325.725.279|see]] rational approximations to their intervals).

[[Subgroup]]: 2.15.55

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[[Support]]ing [[ET]]s: 5, 9, 14, 23, 32, 37, 41, 50, 55, 64, 73, 78, 87, 96, 101, 105, 119, 128, 151, 183, 206, 311

==== 2.15.189.55.325.279 ====

==== 2.15.189.55.325.725 ====

[[Subgroup]]: 2.15.189.55.325.725

[[Comma list]]: [[1625/1624]], [[2080/2079]], [[3025/3024]], [[4096/4095]]

[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.649

[[Support]]ing [[ET]]s: 9[-725], 14[+725], 23, 32, 41[-725], 55, 73[-725], 87, 105[-725], 119, 142[+725], 151, 183, 206[+725], 311

==== 2.15.189.55.325.725.279 ====

Here are rational approximations to the intervals of the semiquartal scale.

[[Modal_UDP_notation#Generalizing_to_arbitrary_MOS_scales:_bright_and_dark_generators_.28chroma-positive_and_chroma-negative.29|Chroma-positive]]: 12/11, 25/21, 33/26, 18/13, 65/44 ~ 96/65, 50/31, 55/32, 15/8.

[[Modal_UDP_notation#Generalizing_to_arbitrary_MOS_scales:_bright_and_dark_generators_.28chroma-positive_and_chroma-negative.29|Chroma-positive]]: 12/11, 25/21, 33/26, 18/13, 65/44 ~ 96/65, 50/31 ~ 29/18, 55/32, 15/8.

Chroma-negative: 16/15, 64/55, 31/25, 65/48 ~ 88/65, 13/9, 52/33, 42/25, 11/6.

Chroma-negative: 16/15, 64/55, 31/25 ~ 36/29, 65/48 ~ 88/65, 13/9, 52/33, 42/25, 11/6.

[[Subgroup]]: 2.15.189.55.325.279

[[Subgroup]]: 2.15.189.55.325.725.279

[[Comma list]]: [[2016/2015]], [[2080/2079]], [[3025/3024]], [[4096/4095]]

[[Comma list]]: [[1625/1624]], [[2016/2015]], [[2080/2079]], [[3025/3024]], [[4096/4095]]

[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.~~666~~

[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.638

[[Support]]ing [[ET]]s: 5, 9, 14, 23, 32~~, 37~~, 41~~, 50~~, 55~~, 64~~, 73~~, 78~~, 87~~, 96, 101~~, 105, 119~~, 128~~, 151, 183, 206, 311

[[Support]]ing [[ET]]s: 9[-725], 14[+725], 23, 32, 41[-725], 55, 73[-725], 87, 105[-725], 119, 151, 183, 206[+725], 311

== 4.3.5 subgroup ==

@@ Line 218: / Line 218: @@
 === Spog ===
-This temperament produces [[Slendro_clan#Superpelog|superpelog]]-like [[5L 4s|semiquartal]] scales while being more accurate ([[Subgroup temperaments#2.15.189.55.325.279|see]] rational approximations to their intervals).
+This temperament produces [[Slendro_clan#Superpelog|superpelog]]-like [[5L 4s|semiquartal]] scales while being more accurate ([[Subgroup temperaments#2.15.189.55.325.725.279|see]] rational approximations to their intervals).
 [[Subgroup]]: 2.15.55
@@ Line 254: / Line 254: @@
 [[Support]]ing [[ET]]s: 5, 9, 14, 23, 32, 37, 41, 50, 55, 64, 73, 78, 87, 96, 101, 105, 119, 128, 151, 183, 206, 311
-==== 2.15.189.55.325.279 ====
+==== 2.15.189.55.325.725 ====
+[[Subgroup]]: 2.15.189.55.325.725
+[[Comma list]]: [[1625/1624]], [[2080/2079]], [[3025/3024]], [[4096/4095]]
+{{Mapping|legend=2| 1 0 6 5 6 -3 | 0 5 2 1 3 16 }}
+[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.649
+[[Support]]ing [[ET]]s: 9[-725], 14[+725], 23, 32, 41[-725], 55, 73[-725], 87, 105[-725], 119,  142[+725], 151, 183, 206[+725], 311
+==== 2.15.189.55.325.725.279 ====
 Here are rational approximations to the intervals of the semiquartal scale.
-[[Modal_UDP_notation#Generalizing_to_arbitrary_MOS_scales:_bright_and_dark_generators_.28chroma-positive_and_chroma-negative.29|Chroma-positive]]: 12/11, 25/21, 33/26, 18/13, 65/44 ~ 96/65, 50/31, 55/32, 15/8.
+[[Modal_UDP_notation#Generalizing_to_arbitrary_MOS_scales:_bright_and_dark_generators_.28chroma-positive_and_chroma-negative.29|Chroma-positive]]: 12/11, 25/21, 33/26, 18/13, 65/44 ~ 96/65, 50/31 ~ 29/18, 55/32, 15/8.
-Chroma-negative: 16/15, 64/55, 31/25, 65/48 ~ 88/65, 13/9, 52/33, 42/25, 11/6.
+Chroma-negative: 16/15, 64/55, 31/25 ~ 36/29, 65/48 ~ 88/65, 13/9, 52/33, 42/25, 11/6.
-[[Subgroup]]: 2.15.189.55.325.279
+[[Subgroup]]: 2.15.189.55.325.725.279
-[[Comma list]]: [[2016/2015]], [[2080/2079]], [[3025/3024]], [[4096/4095]]
+[[Comma list]]: [[1625/1624]], [[2016/2015]], [[2080/2079]], [[3025/3024]], [[4096/4095]]
-{{Mapping|legend=2| 1 0 6 5 6 5 | 0 5 2 1 3 4 }}
+{{Mapping|legend=2| 1 0 6 5 6 -3 5 | 0 5 2 1 3 16 4 }}
-[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.666
+[[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.638
-[[Support]]ing [[ET]]s: 5, 9, 14, 23, 32, 37, 41, 50, 55, 64, 73, 78, 87, 96, 101, 105, 119, 128, 151, 183, 206, 311
+[[Support]]ing [[ET]]s: 9[-725], 14[+725], 23, 32, 41[-725], 55, 73[-725], 87, 105[-725], 119, 151, 183, 206[+725], 311
 == 4.3.5 subgroup ==