Ragismic microtemperaments: Difference between revisions
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If 1/9 of an octave is too small of a period for you, you could try generator-period pairs of [3, 5], [5/3, 3], [6/5, 4/3], [4/3, 8/5] or [10/9, 4/3] (for example). In particular, people fond of the idea of "tritaves" as analogous to octaves might consider the 28 or 43 note MOS with generator an approximate 5/3 within 3; for instance as given by 451/970 of a "tritave". Tetrads have a low enough complexity that (for example) there are nine 1-3/2-7/4-5/2 tetrads in the 28 notes to the tritave MOS, which is equivalent in average step size to a 17 2/3 to the octave MOS. | If 1/9 of an octave is too small of a period for you, you could try generator-period pairs of [3, 5], [5/3, 3], [6/5, 4/3], [4/3, 8/5] or [10/9, 4/3] (for example). In particular, people fond of the idea of "tritaves" as analogous to octaves might consider the 28 or 43 note MOS with generator an approximate 5/3 within 3; for instance as given by 451/970 of a "tritave". Tetrads have a low enough complexity that (for example) there are nine 1-3/2-7/4-5/2 tetrads in the 28 notes to the tritave MOS, which is equivalent in average step size to a 17 2/3 to the octave MOS. | ||
Ennealimmal extensions discussed elsewhere include [[Compton family #Omicronbeta|omicronbeta]], [[Tritrizo clan #Undecentic|undecentic]], [[Tritrizo clan #Schisennealimmal|schisennealimmal]], and [[Tritrizo clan #Lunennealimmal|lunennealimmal]]. | |||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Tuning ranges]]: | [[Tuning ranges]]: | ||
* [[ | * 7-odd-limit [[diamond monotone]]: ~36/35 = [26.667, 66.667] (1\45 to 1\18) | ||
* [[ | * 9-odd-limit diamond monotone: ~36/35 = [44.444, 53.333] (1\27 to 2\45) | ||
* | * 7- and 9-odd-limit [[diamond tradeoff]]: ~36/35 = [48.920, 49.179] | ||
* 7- and 9-odd-limit diamond monotone and tradeoff: ~36/35 = [48.920, 49.179] | |||
{{Val list|legend=1| 27, 45, 72, 99, 171, 441, 612 }} | {{Val list|legend=1| 27, 45, 72, 99, 171, 441, 612 }} | ||
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=== 11-limit === | === 11-limit === | ||
The ennealimmal temperament can be described as 99e&270 temperament, which tempers out 5632/5625 (vishdel comma) and 19712/19683 (symbiotic comma). | The ennealimmal temperament can be described as 99e&270 temperament, which tempers out 5632/5625 (vishdel comma) and 19712/19683 (symbiotic comma). | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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=== Ennealimmia === | === Ennealimmia === | ||
Ennealimmal temperament has various extensions to the 11-limit. Tempering out 131072/130977 (salururu comma) leads to the ''ennealimmia'' temperament (171&270). | Ennealimmal temperament has various extensions to the 11-limit. Tempering out 131072/130977 (salururu comma) leads to the ''ennealimmia'' temperament (171&270). | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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=== Ennealimnic === | === Ennealimnic === | ||
Ennealimnic temperament (72&171) equates 11/9 with 27/22, 49/40, and 60/49 as a neutral third interval. | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Tuning ranges: | Tuning ranges: | ||
* | * 11-odd-limit diamond monotone: ~36/35 = [44.444, 53.333] (1\27 to 2\45) | ||
* | * 11-odd-limit diamond tradeoff: ~36/35 = [48.920, 52.592] | ||
* | * 11-odd-limit diamond monotone and tradeoff: ~36/35 = [48.920, 52.592] | ||
Vals: {{Val list| 72, 171, 243 }} | Vals: {{Val list| 72, 171, 243 }} | ||
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Tuning ranges: | Tuning ranges: | ||
* | * 13- and 15-odd-limit diamond monotone: ~36/35 = [48.485, 50.000] (4\99 to 3\72) | ||
* | * 13- and 15-odd-limit diamond tradeoff: ~36/35 = [48.825, 52.592] | ||
* | * 13- and 15-odd-limit diamond monotone and tradeoff: ~36/35 = [48.825, 50.000] | ||
Vals: {{Val list| 72, 171, 243 }} | Vals: {{Val list| 72, 171, 243 }} | ||
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Tuning ranges: | Tuning ranges: | ||
* | * 17-odd-limit diamond monotone: ~36/35 = [48.485, 50.000] (4\99 to 3\72) | ||
* | * 17-odd-limit diamond tradeoff: ~36/35 = [46.363, 52.592] | ||
* | * 17-odd-limit diamond monotone and tradeoff: ~36/35 = [48.485, 50.000] | ||
Vals: {{Val list| 72, 171, 243 }} | Vals: {{Val list| 72, 171, 243 }} | ||
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=== Hemiennealimmal === | === Hemiennealimmal === | ||
Hemiennealimmal (72&198) has a period of 1/18 octave and tempers out the four smallest superparticular commas of the 11-limit JI, 2401/2400, 3025/3024, 4375/4374, and 9801/9800. Tempering out [[9801/9800]] leads an octave split into two equal parts. | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Tuning ranges: | Tuning ranges: | ||
* | * 11-odd-limit diamond monotone: ~99/98 = [13.333, 22.222] (1\90 to 1\54) | ||
* | * 11-odd-limit diamond tradeoff: ~99/98 = [17.304, 17.985] | ||
* | * 11-odd-limit diamond monotone and tradeoff: ~99/98 = [17.304, 17.985] | ||
Vals: {{Val list| 72, 198, 270, 342, 612, 954, 1566 }} | Vals: {{Val list| 72, 198, 270, 342, 612, 954, 1566 }} | ||
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Tuning ranges: | Tuning ranges: | ||
* | * 13-odd-limit diamond monotone: ~99/98 = [16.667, 22.222] (1\72 to 1\54) | ||
* | * 15-odd-limit diamond monotone: ~99/98 = [16.667, 19.048] (1\72 to 2\126) | ||
* | * 13-odd-limit diamond tradeoff: ~99/98 = [17.304, 18.309] | ||
* 15-odd-limit diamond tradeoff: ~99/98 = [17.304, 18.926] | |||
* 13-odd-limit diamond monotone and tradeoff: ~99/98 = [17.304, 18.309] | |||
* 15-odd-limit diamond monotone and tradeoff: ~99/98 = [17.304, 18.926] | |||
Vals: {{Val list| 72, 198, 270 }} | Vals: {{Val list| 72, 198, 270 }} | ||