Tour of regular temperaments: Difference between revisions

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

These are defined by a yaza noca or 7-limit-no-twos comma. Any no-twos comma is a ratio of odd numbers. If no other commas are tempered out, It is a non-octave tuning, with a period of a perfect 12th or tritave, 3/1 (or some fraction of that). See also [[subgroup temperaments]]. The pergen's multigen (the 2nd term, omitting any fraction) is always a 5-limit-no-twos ratio such as 5/3, 9/5, 25/9, etc.

These are defined by a yaza noca or 7-limit-no-twos comma. Any no-twos comma is a ratio of odd numbers. If no other commas are tempered out, It is a non-octave tuning, with a period of a perfect 12th or tritave, 3/1 (or some fraction of that). See also [[subgroup temperaments]]. The pergen's multigen (the 2nd term, omitting any fraction) is always a 5-limit-no-twos ratio such as 5/3, 9/5, 25/9, etc. In a noca subgroup, "compound" means increased by 3/1 not 2/1.

=== [[Arcturus clan|Arcturus or Rutribiyo Noca clan]] (P12, M6) ===

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===[[Sensamagic clan|Sensamagic or Zozoyo Noca clan]] (P12, M6/2)===

This 3.5.7 clan tempers out the sensamagic comma {{Monzo|0 -5 1 2}} = 245/243. The generator is ~9/7, and two generators equals the noca major 6th = ~5/3.

===[[Betelgeuse clan|Betelgeuse or Satritrizo-agugu Noca clan]] (P12, c<sup>3</sup>M6) ===

This 3.5.7 clan tempers out the Betelgeuse comma {{Monzo|0 -13 -2 9}} = 40353607/39858075. The generator is ~3645/2401, two generators equals ~7/3, and nine generators equals the noca triple-compound major 6th = ~45/1.

===[[Gariboh clan|Gariboh or Triru-aquinyo Noca clan]] (P12, M6/3)===

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===[[Mirkwai clan|Mirkwai or Quinru-aquadyo Noca clan]] (P12, cm7/5)===

This 3.5.7 clan tempers out the mirkwai comma, {{Monzo|0 3 4 -5}} = 16875/16807. The generator is ~7/5, four generators equals ~27/7, and five generators equals the noca compound minor 7th = ~27/5~~. In a noca subgroup, "compound" means increased by 3/1 not 2/1~~.

This 3.5.7 clan tempers out the mirkwai comma, {{Monzo|0 3 4 -5}} = 16875/16807. The generator is ~7/5, four generators equals ~27/7, and five generators equals the noca compound minor 7th = ~27/5.

===[[Procyon clan|Procyon or Sasepzo-atrigu Noca clan]] (P12, m7/7)===

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 == Clans defined by a 3.5.7 (yaza noca) comma ==
-These are defined by a yaza noca or 7-limit-no-twos comma. Any no-twos comma is a ratio of odd numbers. If no other commas are tempered out, It is a non-octave tuning, with a period of a perfect 12th or tritave, 3/1 (or some fraction of that). See also [[subgroup temperaments]]. The pergen's multigen (the 2nd term, omitting any fraction) is always a 5-limit-no-twos ratio such as 5/3, 9/5, 25/9, etc.
+These are defined by a yaza noca or 7-limit-no-twos comma. Any no-twos comma is a ratio of odd numbers. If no other commas are tempered out, It is a non-octave tuning, with a period of a perfect 12th or tritave, 3/1 (or some fraction of that). See also [[subgroup temperaments]]. The pergen's multigen (the 2nd term, omitting any fraction) is always a 5-limit-no-twos ratio such as 5/3, 9/5, 25/9, etc. In a noca subgroup, "compound" means increased by 3/1 not 2/1.
 === [[Arcturus clan|Arcturus or Rutribiyo Noca clan]] (P12, M6) ===
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 ===[[Sensamagic clan|Sensamagic or Zozoyo Noca clan]] (P12, M6/2)===
 This 3.5.7 clan tempers out the sensamagic comma {{Monzo|0 -5 1 2}} = 245/243. The generator is ~9/7, and two generators equals the noca major 6th = ~5/3.
+===[[Betelgeuse clan|Betelgeuse or Satritrizo-agugu Noca clan]] (P12, c<sup>3</sup>M6) ===
+This 3.5.7 clan tempers out the Betelgeuse comma {{Monzo|0 -13 -2 9}} = 40353607/39858075. The generator is ~3645/2401, two generators equals ~7/3, and nine generators equals the noca triple-compound major 6th = ~45/1.
 ===[[Gariboh clan|Gariboh or Triru-aquinyo Noca clan]] (P12, M6/3)===
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 ===[[Mirkwai clan|Mirkwai or Quinru-aquadyo Noca clan]] (P12, cm7/5)===
-This 3.5.7 clan tempers out the mirkwai comma, {{Monzo|0 3 4 -5}} = 16875/16807. The generator is ~7/5, four generators equals ~27/7, and five generators equals the noca compound minor 7th = ~27/5. In a noca subgroup, "compound" means increased by 3/1 not 2/1.
+This 3.5.7 clan tempers out the mirkwai comma, {{Monzo|0 3 4 -5}} = 16875/16807. The generator is ~7/5, four generators equals ~27/7, and five generators equals the noca compound minor 7th = ~27/5.
 ===[[Procyon clan|Procyon or Sasepzo-atrigu Noca clan]] (P12, m7/7)===