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| | {{Technical data page}} |
| A '''subgroup temperament''' is a regular temperament defined on a [[just intonation subgroup]] that is not a full ''p''-limit group. | | A '''subgroup temperament''' is a regular temperament defined on a [[just intonation subgroup]] that is not a full ''p''-limit group. |
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| For temperaments that omit various prime harmonics, see: | | For temperaments that omit various prime harmonics, see: |
| | * [[No-thirteens subgroup temperaments]] |
| * [[No-elevens subgroup temperaments]] | | * [[No-elevens subgroup temperaments]] |
| * [[No-sevens subgroup temperaments]] | | * [[No-sevens subgroup temperaments]] |
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| = Composite subgroup temperaments = | | = Composite subgroup temperaments = |
| == 2.3.35 subgroup ==
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| === Shaka ===
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| {{See also|Kalismic temperaments}}
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| Two commas that split 2/1 in half, corresponding to convergents to sqrt(2), are the [[1682/1681|''sha''ftesburisma]] [[Square superparticular|S29]]/S41 and the [[9801/9800|''ka''lisma S99]], prompting to temper out {S29, S41, S99}, approximating /29 and /41 [[Primodality|primodal]] chords well.
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| Subgroup: 2.3.35.11.29.41
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| Comma list: 841/840, 1189/1188, 1681/1680
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| {{Mapping|legend=2|2 2 6 5 7 8|0 1 1 -1 1 1|0 0 2 2 1 1}}
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| Optimal tuning (CTE): ~41/29 = 1\2, ~3/2 = 702.031, ~41/24 = 926.693
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| [[Support]]ing [[ET]]s: {{EDOs|22, 26, 36, 48, 70, 96, 106, 118, 140, 154, 176, 188, 224, 272, 294, 342}}
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| Scale: [[Shaka10]]
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| == 2.9.5.7 subgroup == | | == 2.9.5.7 subgroup == |
| See also [[Jubilismic clan #Antikythera|antikythera]] and [[Hemimean clan #Isra|isra]]. | | See also [[Jubilismic clan #Antikythera|antikythera]] and [[Hemimean clan #Isra|isra]]. |
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| === Baldy === | | === Baldy === |
| {{See also|Schismatic family #Garibaldi}} | | {{See also|Schismatic family #Garibaldi}} |
| | {{See also|No-threes subgroup temperaments #Frostburn}} |
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| Baldy results from taking every other generator of the [[garibaldi temperament]]. One of the best extension is 2.9.5.7.13 subgroup with mapping 13/8 to +10 whole tones, as well as the cassandra temperament. | | Baldy results from taking every other generator of the [[garibaldi temperament]]. One of the best extension is 2.9.5.7.13 subgroup with mapping 13/8 to +10 whole tones, as well as the cassandra temperament. |
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| {{Optimal ET sequence|legend=1| 5, 13c, 18, 23, 41, 64, 87, 151 }} | | {{Optimal ET sequence|legend=1| 5, 13c, 18, 23, 41, 64, 87, 151 }} |
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| == 2.15.55 subgroup ==
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| === Spog ===
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| 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).
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| [[Subgroup]]: 2.15.55
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| [[Comma list]]: [[100663296/100656875]]
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| {{Mapping|legend=2| 1 0 5 | 0 5 1 }}
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| [[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.655
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| {{Optimal ET sequence|legend=1|5, 9, 23, 32, 151, 183, 215, 247, 956, 1203, 1450, 3147, 4597 }}
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| ==== 2.15.55.325 ====
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| [[Subgroup]]: 2.15.55.325
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| [[Comma list]]: [[4225/4224]], [[6656/6655]]
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| {{Mapping|legend=2| 1 0 5 6 | 0 5 1 3 }}
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| [[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.647
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| [[Support]]ing [[ET]]s: 5, 9, 13[-15], 14, 23, 32, 37, 41, 50, 55, 64, 73, 78, 87, 96, 101, 105, 119, 128, 151, 183, 206, 311
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| ==== 2.15.189.55.325 ====
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| Related temperament: [[Lehmerismic_temperaments#Lux|lux]]
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| [[Subgroup]]: 2.15.189.55.325
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| [[Comma list]]: [[2080/2079]], [[3025/3024]], [[4096/4095]]
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| {{Mapping|legend=2| 1 0 6 5 6 | 0 5 2 1 3 }}
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| [[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.677
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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
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| ==== 2.15.189.55.325.725 ====
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| [[Subgroup]]: 2.15.189.55.325.725
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| [[Comma list]]: [[1625/1624]], [[2080/2079]], [[3025/3024]], [[4096/4095]]
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| {{Mapping|legend=2| 1 0 6 5 6 -3 | 0 5 2 1 3 16 }}
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| [[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.649
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| [[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
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| ==== 2.15.189.55.325.725.279 ====
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| Here are rational approximations to the intervals of the semiquartal scale.
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| Sharp: 12/11, 25/21, 33/26, 18/13, 31/21 ~ 65/44 ~ 96/65, 50/31 ~ 29/18, 55/32, 15/8.
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| Flat: 16/15, 64/55, 31/25 ~ 36/29, 42/31 ~ 65/48 ~ 88/65, 13/9, 52/33, 42/25, 11/6.
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| [[Subgroup]]: 2.15.189.55.325.725.279
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| [[Comma list]]: [[1625/1624]], [[2016/2015]], [[2080/2079]], [[3025/3024]], [[4096/4095]]
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| {{Mapping|legend=2| 1 0 6 5 6 -3 5 | 0 5 2 1 3 16 4 }}
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| [[Optimal tuning]] (subgroup [[CTE]]): ~55/32 = 937.638
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| [[Support]]ing [[ET]]s: 9[-725], 14[+725], 23, 32, 41[-725], 55, 73[-725], 87, 105[-725], 119, 151, 183, 206[+725], 311
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| == 4.3.5 subgroup == | | == 4.3.5 subgroup == |
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| [[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents | | [[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents |
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| ==== Semidim ==== | | ==== Ammon ==== |
| {{See also| Chromatic pairs #Semidim }} | | {{See also| Chromatic pairs #Ammon }} |
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| Semidim can be described as the {{nowrap| 8 & 29 }} temperament in the 2.5/3.7/3.11/3.13/3 subgroup. It extends [[tridec]], and is related to [[ammonite]]. It is generated by a semidiminished fourth, hence the name.
| | Ammon can be described as the {{nowrap| 8 & 29 }} temperament in the 2.5/3.7/3.11/3.13/3 subgroup. It extends [[tridec]], and is related to [[ammonite]]. It is generated by a semidiminished fourth, hence the old name ''semidim'', which has been rejected since 2025 to avoid confusion with another temperament of the same name. |
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| [[Subgroup]]: 2.5/3.7/3.11/3.13/3 | | [[Subgroup]]: 2.5/3.7/3.11/3.13/3 |
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| {{See also | Chromatic pairs #Laz }} | | {{See also | Chromatic pairs #Laz }} |
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| Laz is related to [[georgian]] as well as to [[winston]]. | | Laz is related to [[avalokita]] as well as to [[winston]]. |
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| [[Subgroup]]: 2.5.7/3.11/3.13/3 | | [[Subgroup]]: 2.5.7/3.11/3.13/3 |
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| [[Tp tuning #T2 tuning|RMS error]]: 1.074 cents | | [[Tp tuning #T2 tuning|RMS error]]: 1.074 cents |
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| == 2.….15/11… subgroups ==
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| === Poggers ===
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| Related temperaments: [[Stearnsmic_clan#Pogo|pogo]], [[Stearnsmic_clan#Supers|supers]]
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| [[Subgroup]]: 2.9.7.15/11.13
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| [[Comma list]]: [[540/539]], [[1716/1715]], [[2080/2079]]
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| {{Mapping|legend=2| 1 1 1 -1 -1 | 0 6 5 4 13 }}
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| [[Optimal tuning]] (subgroup [[CTE]]): ~9/7 = 433.888
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| [[Support]]ing [[ET]]s: 8[+9, +7, +13], 11, 14[-13], 19[+9, +7, ++13], 25[-13], 36, 47, 58, 61[-13], 69[+13], 80[+13], 83, 91[+9, +7, +13], 105
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| == 2.….7/5… subgroups == | | == 2.….7/5… subgroups == |
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| <!-- main article --> | | <!-- main article --> |
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| [[Category:Temperament collections]][[Category:Subgroup]] | | [[Category:Temperament collections]] |
| | [[Category:Pages with mostly numerical content]][[Category:Subgroup]] |