Hemimean clan: Difference between revisions
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== Emka == | == Emka == | ||
[[Emka]] tempers out {{monzo|-50 -8 27}} in the 5-limit. This temperament can be described as 37&50 temperament, which tempers out the hemimean and 84035/82944 (quinzo-ayo). Alternative extension [[Horwell temperaments #Emkay|emkay]] (87&224) tempers out the same 5-limit comma as the emka, but with the horwell (65625/65536) rather than the hemimean tempered out. | [[Emka]] tempers out {{monzo|-50 -8 27}} in the 5-limit. This temperament can be described as 37&50 temperament, which tempers out the hemimean and 84035/82944 (quinzo-ayo). Alternative extension [[Horwell temperaments #Emkay|emkay]] (87&224) tempers out the same 5-limit comma as the emka, but with the horwell (65625/65536) rather than the hemimean tempered out. | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
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== Decipentic == | == Decipentic == | ||
The generator for the ''decipentic'' temperament (43&56) is tenth root of fifth harmonic ([[5/1]], pentave), 5<sup>1/10</sup>, tuned between [[75/64]] and [[20/17]] (close to 27/23). Aside from the hemimean comma, this temperament tempers out the [[Bronzismic temperaments|bronzisma]], 2097152/2083725 (satriru-agugu). [[99edo|99EDO]] is a good tuning for decipentic, with generator 23\99, and MOS of 9, 13, 17, 30, 43 or 56 notes are available. | The generator for the ''decipentic'' temperament (43&56) is tenth root of fifth harmonic ([[5/1]], pentave), 5<sup>1/10</sup>, tuned between [[75/64]] and [[20/17]] (close to 27/23). Aside from the hemimean comma, this temperament tempers out the [[Bronzismic temperaments|bronzisma]], 2097152/2083725 (satriru-agugu). [[99edo|99EDO]] is a good tuning for decipentic, with generator 23\99, and MOS of 9, 13, 17, 30, 43 or 56 notes are available. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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== Mowglic == | == Mowglic == | ||
The ''mowglic'' temperament (19&161) is an extension of the [[Syntonic-enneadecal equivalence continuum|mowgli temperament]] which tempers out the hemimean comma and the secanticornisma (177147/175000, laruquingu) in the 7-limit. | The ''mowglic'' temperament (19&161) is an extension of the [[Syntonic-enneadecal equivalence continuum|mowgli temperament]] which tempers out the hemimean comma and the secanticornisma (177147/175000, laruquingu) in the 7-limit. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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The ''quintagar'' temperament (12&217) tempers out the hemimean comma (3136/3125) and the [[garischisma]] (33554432/33480783) in the 7-limit. In the 2.3.5.7.17.19 subgroup, 256/255 (the difference between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), 361/360 (between 19/18 and 20/19), and 400/399 (between 20/19 and 21/20) are equated together, and 476/475 (between 28/25 and 19/17) is tempered out. Immediate 2.3.5.7.11.17.19 extensions include ''quintoneum'' (12&217, tempering out 441/440), ''quintasandra'' (217&229, equating 385/384 with 400/399), and ''quintasandroid'' (12&229, equating 400/399 with 441/440). Full 19-limit extensions include ''quintoneum'' (12f&217), ''quintoneoid'' (12&217), ''quintasandra'' (217&229), ''quintasandroid'' (12f&229), and ''quintasand'' (12&229). The name ''quintagar'' is so named because the generator is 1/5 of the [[Schismatic family #Garibaldi|garibaldi]] fourth (~4/3, about 497.8 cents) aside from tempering out the garischisma. | The ''quintagar'' temperament (12&217) tempers out the hemimean comma (3136/3125) and the [[garischisma]] (33554432/33480783) in the 7-limit. In the 2.3.5.7.17.19 subgroup, 256/255 (the difference between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), 361/360 (between 19/18 and 20/19), and 400/399 (between 20/19 and 21/20) are equated together, and 476/475 (between 28/25 and 19/17) is tempered out. Immediate 2.3.5.7.11.17.19 extensions include ''quintoneum'' (12&217, tempering out 441/440), ''quintasandra'' (217&229, equating 385/384 with 400/399), and ''quintasandroid'' (12&229, equating 400/399 with 441/440). Full 19-limit extensions include ''quintoneum'' (12f&217), ''quintoneoid'' (12&217), ''quintasandra'' (217&229), ''quintasandroid'' (12f&229), and ''quintasand'' (12&229). The name ''quintagar'' is so named because the generator is 1/5 of the [[Schismatic family #Garibaldi|garibaldi]] fourth (~4/3, about 497.8 cents) aside from tempering out the garischisma. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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Badness: 0.040410 | Badness: 0.040410 | ||
== Undetrita == | |||
The ''undetrita'' temperament (111&118) tempers out the hemimean comma (3136/3125) and [[skeetsma]] (14348907/14336000) in the 7-limit; 3025/3024, 3388/3375, and 8019/8000 in the 11-limit. This temperament is related to [[11edt|11EDT]] tuning, and the name ''undetrita'' is a play on the words "undecimus" (Latin for "eleventh") and "[[tritave]]" (third harmonic). | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 3136/3125, 14348907/14336000 | |||
[[Mapping]]: [{{val|1 0 -2 -8}}, {{val|0 11 30 75}}] | |||
{{Multival|legend=1|11 30 75 22 88 90}} | |||
[[POTE generator]]: ~448/405 = 172.917 | |||
{{Val list|legend=1| 111, 118, 229, 347, 576c }} | |||
[[Badness]]: 0.114188 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 3025/3024, 3136/3125, 8019/8000 | |||
Mapping: [{{val|1 0 -2 -8 0}}, {{val|0 11 30 75 24}}] | |||
POTE generator: ~400/363 = 172.912 | |||
Vals: {{Val list|111, 118, 229, 347 }} | |||
Badness: 0.043883 | |||
== Isra == | == Isra == | ||
Isra results from taking every other generator of [[septimal meantone]]. It is named after the Isrāʾ (''iss-RAH'') night journey in the Qur'an, because it's similar to [[luna]]. | Isra results from taking every other generator of [[septimal meantone]]. It is named after the Isrāʾ (''iss-RAH'') night journey in the Qur'an, because it's similar to [[luna]]. | ||
Subgroup: 2.9.5.7 | Subgroup: 2.9.5.7 | ||