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Tour of regular temperaments: Difference between revisions

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Corrected the noca pergens so that the multigens are all 5-limit-no-twos ratios, analogous to 2.3.5 and 2.3.5.7 pergens using only 3-limit multigens. Fixed some typos in Procyon and Metric color names.
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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]].
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]].


===[[Sensamagic clan|Sensamagic or Zozoyo Noca clan]] (P12, M3)===
=== [[Arcturus clan|Arcturus or Rutribiyo Noca clan]] (P12, M6) ===
This 3.5.7 clan tempers out the sensamagic comma {{Monzo|0 -5 1 2}} = 245/243. The M3 generator is ~9/7, and two generators equals ~5/3.
This 3.5.7 clan tempers out the Arcturus comma {{Monzo|0 -7 6 -1}} = 15625/15309. The generator is a noca M6 = ~5/3, and six generators equals ~21/1.


===[[Gariboh clan|Gariboh or Triru-Aquinyo Noca clan]] (P12, m3)===
===[[Sensamagic clan|Sensamagic or Zozoyo Noca clan]] (P12, M6/2)===
This 3.5.7 clan tempers out the gariboh comma {{Monzo|0 -2 5 -3}} = 3125/3087. The m3 generator is ~25/21, and three generators equals ~5/3.
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 a noca major 6th = ~5/3.


===[[Mirkwai clan|Mirkwai or Quinru-aquadyo Noca clan]] (P12, cM7/4)===
===[[Gariboh clan|Gariboh or Triru-aquinyo Noca clan]] (P12, M6/3)===
This 3.5.7 clan tempers out the mirkwai comma, {{Monzo|0 3 4 -5}} = 16875/16807. The generator is ~7/5, and four generators equals a compound major 7th = ~27/7.
This 3.5.7 clan tempers out the gariboh comma {{Monzo|0 -2 5 -3}} = 3125/3087. The generator is ~25/21, two generators equals ~7/5, and three generators equals a noca major 6th = ~5/3.


===[[Arcturus clan|Arcturus or Rutribiyo Noca clan]] (P12, M6)===
===[[Mirkwai clan|Mirkwai or Quinru-aquadyo Noca clan]] (P12, cm7/5)===
This 3.5.7 clan tempers out the Arcturus comma {{Monzo|0 -7 6 -1}} = 15625/15309. The M6 generator is ~5/3, and six generators equals ~21/1.
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 a noca compound minor 7th = ~27/5. In a noca pergen, "compound" means increased by 3/1 not 2/1.


===[[Procyon clan|Procyon or Sasepz-Atrigu Noca clan]] (P12, (~7/5)/4)===
===[[Procyon clan|Procyon or Sasepzo-atrigu Noca clan]] (P12, m7/7)===
This 3.5.7 clan tempers out the Procyon comma {{Monzo|0 -8 -3 7}} = 823543/820125. The generator is ~49/45, and four generators equals ~7/5.
This 3.5.7 clan tempers out the Procyon comma {{Monzo|0 -8 -3 7}} = 823543/820125. The generator is ~49/45, three generators equals ~9/7, four equals ~7/5, and seven equals a noca minor seventh = ~9/5.


== Rank-two temperaments defined by a 2.3.5.7 (yaza) comma ==
== Rank-two temperaments defined by a 2.3.5.7 (yaza) comma ==
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Mint rank-two temperaments temper out the septimal quarter-tone 36/35, equating 7/6 with 6/5, and 5/4 with 9/7.
Mint rank-two temperaments temper out the septimal quarter-tone 36/35, equating 7/6 with 6/5, and 5/4 with 9/7.


===[[Septisemi temperaments|Septisemi or Zogu temperaments]] (P8, P5, ^1)===
===[[Septisemi temperaments|Septisemi or Zogu temperaments]]===
These are very low complexity temperaments tempering out the minor septimal semitone, [[21/20]] and hence equating 5/3 with 7/4.
These are very low complexity temperaments tempering out the minor septimal semitone, [[21/20]] and hence equating 5/3 with 7/4.


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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.


===[[Metric microtemperaments|Metric or Latritu-asepyo temperaments]]===
===[[Metric microtemperaments|Metric or Latriru-asepyo temperaments]]===
Metric rank-two temperaments temper out the meter comma, {{Monzo|-11 2 7 -3}} = 703125/702464.
Metric rank-two temperaments temper out the meter comma, {{Monzo|-11 2 7 -3}} = 703125/702464.


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===[[Stearnsmic family|Stearnsmic or Latribiru family]] (P8/2, P4/3, ^1)===
===[[Stearnsmic family|Stearnsmic or Latribiru family]] (P8/2, P4/3, ^1)===
Stearnsmic temperaments temper out the stearnsma, {{Monzo|1 10 0 -6}} = 118098/117649. In the pergen, P8/2 is 343/243 and P4/3 is ~54/49.
Stearnsmic temperaments temper out the stearnsma, {{Monzo|1 10 0 -6}} = 118098/117649. In the pergen, P8/2 is ~343/243 and P4/3 is ~54/49.


== Families defined by a 2.3.5.7 (yaza) comma ==
== Families defined by a 2.3.5.7 (yaza) comma ==
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