Tour of regular temperaments: Difference between revisions
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corrected the color names: Quinzotriyo --> Quinzo-atriyo (because 5-exponent is 3 not 15) and Trisaseprugu --> Trisa-seprugu (consistent hyphen use makes searches easier) |
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This clan tempers out the quince, {{Monzo|-15 0 -2 7}} = 823543/819200. The generator is ~343/320 = ~116¢. Two generators equals ~8/7 (a M2), and seven generators equals ~8/5. An obvious 5-limit interpretation of the generator is 16/15, leading to the [[miracle]] temperament, which is in the gamelismic clan. | This clan tempers out the quince, {{Monzo|-15 0 -2 7}} = 823543/819200. The generator is ~343/320 = ~116¢. Two generators equals ~8/7 (a M2), and seven generators equals ~8/5. An obvious 5-limit interpretation of the generator is 16/15, leading to the [[miracle]] temperament, which is in the gamelismic clan. | ||
===[[Rainy clan|Rainy or | ===[[Rainy clan|Rainy or Quinzo-atriyo Nowa clan]] (P8, M3/5)=== | ||
This clan tempers out the [[rainy comma]], {{Monzo|-21 0 3 5}} = 2100875/2097152. The generator is ~256/245 = ~77¢. Three generators equals ~8/7 and five of them equals ~5/4. | This clan tempers out the [[rainy comma]], {{Monzo|-21 0 3 5}} = 2100875/2097152. The generator is ~256/245 = ~77¢. Three generators equals ~8/7 and five of them equals ~5/4. | ||
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Hewuermera rank-two temperaments temper out the ''hewuermera'' comma (named by [[User:Xenllium|Xenllium]]), {{Monzo|16 2 -1 -6}} = 589824/588245. | Hewuermera rank-two temperaments temper out the ''hewuermera'' comma (named by [[User:Xenllium|Xenllium]]), {{Monzo|16 2 -1 -6}} = 589824/588245. | ||
===[[Akjaysmic temperaments|Akjaysmic or | ===[[Akjaysmic temperaments|Akjaysmic or Trisa-seprugu temperaments]]=== | ||
Akjaysmic rank-two temperaments temper out the akjaysma, {{Monzo|47 -7 -7 -7}}. These have a period of 1/7 octave, and five periods equals ~105/64. Unlike the Whitewood or Lawa family, ~3/2 is not equated with four-sevenths of an octave, resulting in small intervals. | Akjaysmic rank-two temperaments temper out the akjaysma, {{Monzo|47 -7 -7 -7}}. These have a period of 1/7 octave, and five periods equals ~105/64. Unlike the Whitewood or Lawa family, ~3/2 is not equated with four-sevenths of an octave, resulting in small intervals. | ||