Tour of regular temperaments: Difference between revisions

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== Clans defined by a 2.5.7 (yaza nowa) comma ==
== Clans defined by a 2.5.7 (yaza nowa) comma ==
These are defined by a yaza nowa or 7-limit-no-threes comma. See also [[subgroup temperaments]]. The pergen's multigen (the 2nd term, omitting any fraction) is always a 5-limit-no-threes ratio such as 5/4, 8/5, 25/8, etc.
These are defined by a yaza nowa or 7-limit-no-threes comma. See also [[subgroup temperaments]]. The pergen's multigen (the 2nd term, omitting any fraction) is always a 5-limit-no-threes ratio such as 5/4, 8/5, 25/8, etc.
=== [[Bapbo clan|Bapbo or Rurugu Nowa clan]] (P8, M3/2) ===
This clan tempers out the bapbo comma, [[256/245]]. The genarator is ~8/7 = ~202¢ and two of them equals ~5/4.


=== [[Jubilismic clan|Jubilismic or Biruyo Nowa clan]] (P8/2, M3) ===
=== [[Jubilismic clan|Jubilismic or Biruyo Nowa clan]] (P8/2, M3) ===
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===[[Hemimean clan|Hemimean or Zozoquingu Nowa clan]] (P8, M3/2)===
===[[Hemimean clan|Hemimean or Zozoquingu Nowa clan]] (P8, M3/2)===
This clan tempers out the hemimean comma, {{Monzo|6 0 -5 2}} = 3136/3125. The generator is ~28/25 = ~194¢. Two generators equals the nowa major 3rd = ~5/4, three of them equals ~7/5, and five of them equals ~7/4.
This clan tempers out the hemimean comma, {{Monzo|6 0 -5 2}} = 3136/3125. The generator is ~28/25 = ~194¢. Two generators equals the nowa major 3rd = ~5/4, three of them equals ~7/5, and five of them equals ~7/4.
===[[Quince clan|Quince or Lasepzo-agugu Nowa clan]] (P8, m6/7)===
This clan tempers out the quince, {{Monzo|-15 0 -2 7}} = 823543/819200. The trizo-agu generator is ~343/320 = ~116¢. Two generators equals ~8/7, five generators equals ~7/5, and seven generators equals the nowa minor 6th ~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 Quinzo-atriyo Nowa clan]] (P8, M3/5)===
===[[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 rurugu generator is ~256/245 = ~77¢. Three generators equals ~8/7 and five of them equals the nowa major 3rd = ~5/4.
This clan tempers out the [[rainy comma]], {{Monzo|-21 0 3 5}} = 2100875/2097152. The rurugu generator is ~256/245 = ~77¢. Three generators equals ~8/7 and five of them equals the nowa major 3rd = ~5/4.
===[[Quince clan|Quince or Lasepzo-agugu Nowa clan]] (P8, m6/7)===
This clan tempers out the quince, {{Monzo|-15 0 -2 7}} = 823543/819200. The trizo-agu generator is ~343/320 = ~116¢. Two generators equals ~8/7, five generators equals ~7/5, and seven generators equals the nowa minor 6th ~8/5. An obvious 5-limit interpretation of the generator is 16/15, leading to the [[miracle]] temperament, which is in the gamelismic clan.


== Clans defined by a 3.5.7 (yaza noca) comma ==
== Clans defined by a 3.5.7 (yaza noca) comma ==