Quindromeda family: Difference between revisions
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The '''quindromeda family''' tempers out {{monzo| 56 -28 -5 }}, equating the [[Pythagorean comma]] with a stack of five [[schisma]]s, making it a member of the [[ | {{Technical data page}} | ||
The '''quindromeda family''' tempers out {{monzo| 56 -28 -5 }}, equating the [[Pythagorean comma]] with a stack of five [[schisma]]s, making it a member of the [[schismic–Pythagorean equivalence continuum]]. | |||
== Quindromeda == | == Quindromeda == | ||
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=== Subgroup temperament === | === Subgroup temperament === | ||
The quindromeda temperament works well for the 2.3.5.17.19 subgroup, tempering out the | The quindromeda temperament works well for the 2.3.5.17.19 subgroup, tempering out the [[1216/1215|password comma]] (1216/1215), [[1445/1444|aureusma]] (1445/1444), and [[6144/6137|langwisma]] (6144/6137). An obvious 17-limit interpretation of the generator is ~[[18/17]], equating three 18/17s with [[19/16]], five 18/17s with [[4/3]], and twenty-eight 18/17s with the [[5/1|fifth harmonic]]. | ||
==== 2.3.5.17 ==== | ==== 2.3.5.17 ==== | ||
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[[Tp tuning #T2 tuning|RMS error]]: 0.0813 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.0813 cents | ||
Badness: 0.007140 | [[Badness]]: 0.007140 | ||
== Quintagar == | == Quintagar == | ||
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), ''quinsandra'' (217&229, equating 385/384 with 400/399), and ''quinsandric'' (12&229, equating 400/399 with 441/440). Full 19-limit extensions include ''quintoneum'' (12f&217), ''quintoneoid'' (12&217), ''quinsandra'' (217&229), ''quinsandric'' (12f&229), and ''quinsandro'' (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). | The ''quintagar'' temperament (12&217) tempers out the [[3136/3125|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]]), ''quinsandra'' (217&229, equating [[385/384]] with 400/399), and ''quinsandric'' (12&229, equating 400/399 with 441/440). Full 19-limit extensions include ''quintoneum'' (12f&217), ''quintoneoid'' (12&217), ''quinsandra'' (217&229), ''quinsandric'' (12f&229), and ''quinsandro'' (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). | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Mapping]]: [{{val| 1 2 0 -3 }}, {{val| 0 -5 28 70 }}] | [[Mapping]]: [{{val| 1 2 0 -3 }}, {{val| 0 -5 28 70 }}] | ||
[[POTE generator]]: ~200/189 = 99.555 | [[POTE generator]]: ~200/189 = 99.555 | ||
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== Quintakwai == | == Quintakwai == | ||
The ''quintakwai'' temperament (12&193) tempers out the hemifamity comma (5120/5103) and the compass comma (9765625/9680832 | The ''quintakwai'' temperament (12&193) tempers out the [[5120/5103|hemifamity comma]] (5120/5103) and the compass comma (9765625/9680832) in the 7-limit; 1375/1372 and 4375/4356 in the 11-limit. In the 2.3.5.7.17.19 subgroup, [[225/224]] (the difference between 15/14 and 16/15), 256/255 (between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), and 361/360 (between 19/18 and 20/19) are equated together, and 400/399 (between 20/19 and 21/20) is tempered out. The name ''quintakwai'' is so named because the generator is 1/5 of the [[Mirkwai clan #Kwai|kwai]] fourth (~4/3, about 497.4 cents). | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Mapping]]: [{{val| 1 2 0 -2 }}, {{val| 0 -5 28 58 }}] | [[Mapping]]: [{{val| 1 2 0 -2 }}, {{val| 0 -5 28 58 }}] | ||
[[POTE generator]]: ~625/588 = 99.483 | [[POTE generator]]: ~625/588 = 99.483 | ||
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== Quindro == | == Quindro == | ||
The ''quindro'' temperament (205&217) is an extension of the ''quindromeda'' temperament which tempers out the ragisma (4375/4374), the vishdel comma (5632/5625), and the ibnsinma (2080/2079). | The ''quindro'' temperament (205&217) is an extension of the ''quindromeda'' temperament which tempers out the [[4375/4374|ragisma]] (4375/4374), the [[5632/5625|vishdel comma]] (5632/5625), and the [[2080/2079|ibnsinma]] (2080/2079). | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Mapping]]: [{{val| 1 2 0 15 }}, {{val| 0 -5 28 -147 }}] | [[Mapping]]: [{{val| 1 2 0 15 }}, {{val| 0 -5 28 -147 }}] | ||
[[POTE generator]]: ~4428675/4194304 = 99.529 | [[POTE generator]]: ~4428675/4194304 = 99.529 | ||
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[[Mapping]]: [{{val|1 2 0 6}}, {{val|0 -10 56 -77}}] | [[Mapping]]: [{{val|1 2 0 6}}, {{val|0 -10 56 -77}}] | ||
[[POTE generator]]: ~36/35 = 49.756 | [[POTE generator]]: ~36/35 = 49.756 | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Quindromeda family| ]] <!-- main article --> | [[Category:Quindromeda family| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] |