Quindromeda family: Difference between revisions

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== Quindromeda ==

The name ''quindromeda'' comes from "quintans" (Latin for "one fifth") and "[[Wikipedia:Andromeda|Andromeda]]", because the generator is 1/5 of the [[Schismatic family #Garibaldi|andromeda]] fourth (~4/3, about 497.6 cents).

Subgroup: 2.3.5

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=== 2.3.5.17.19 ===

The quindromeda temperament works well for the 2.3.5.17.19 subgroup, tempering out the password comma ([[1216/1215]]), aureusma ([[1445/1444]]), and 6144/6137. An obvious 17-limit interpretation of the generator is ~[[18/17]], equating three 18/17s with [[19/16]], five 18/17s with [[4/3]], and twenty-eight 18/17s with the [[5/1|fifth harmonic]].

Subgroup: 2.3.5.17.19

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The ''quintagar'' temperament (12&217) tempers out the hemimean comma (3136/3125) and the [[garischisma]] (33554432/33480783) in the 7-limit. In the 2.3.5.7.17.19 subgroup, 256/255 (the difference between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), 361/360 (between 19/18 and 20/19), and 400/399 (between 20/19 and 21/20) are equated together, and 476/475 (between 28/25 and 19/17) is tempered out. Immediate 2.3.5.7.11.17.19 extensions include ''quintoneum'' (12&217, tempering out 441/440), ''quintasandra'' (217&229, equating 385/384 with 400/399), and ''quintasandroid'' (12&229, equating 400/399 with 441/440). Full 19-limit extensions include ''quintoneum'' (12f&217), ''quintoneoid'' (12&217), ''quintasandra'' (217&229), ''quintasandroid'' (12f&229), and ''quintasand'' (12&229). The name ''quintagar'' is so named because the generator is 1/5 of the [[Schismatic family #Garibaldi|garibaldi]] fourth (~4/3, about 497.8 cents) aside from tempering out the garischisma.

Subgroup: 2.3.5.7

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=== Quintoneum ===

The name ''quintoneum'' is a play on the words "quintans" ~~(Latin for "one fifth")~~ and "[[Hemimage temperaments #Cotoneum|cotoneum]]".

The name ''quintoneum'' is a play on the words "quintans" and "[[Hemimage temperaments #Cotoneum|cotoneum]]".

Subgroup: 2.3.5.7.11

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== Quintakwai ==

The ''quintakwai'' temperament (12&193) tempers out the hemifamity comma (5120/5103) and the compass comma (9765625/9680832, quinruyoyo) in the 7-limit; 1375/1372 and 4375/4356 in the 11-limit. In the 2.3.5.7.17.19 subgroup, 225/224 (the difference between 15/14 and 16/15), 256/255 (between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), and 361/360 (between 19/18 and 20/19) are equated together, and 400/399 (between 20/19 and 21/20) is tempered out. The name ''quintakwai'' is so named because the generator is 1/5 of the [[Mirkwai clan #Kwai|kwai]] fourth (~4/3, about 497.4 cents).

Subgroup: 2.3.5.7

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== Quindro ==

The ''quindro'' temperament (205&217) is an extension of the ~~[[28ed5 #Regular temperaments|~~''quindromeda'' temperament]] which tempers out the ragisma (4375/4374), the vishdel comma (5632/5625), and the ibnsinma (2080/2079).

The ''quindro'' temperament (205&217) is an extension of the ''quindromeda'' temperament which tempers out the ragisma (4375/4374), the vishdel comma (5632/5625), and the ibnsinma (2080/2079).

Subgroup: 2.3.5.7

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== Semiquindromeda ==

The ''semiquindromeda'' temperament (410&422) is an extension of the ~~[[28ed5 #Regular temperaments|~~''quindromeda'' temperament]] with a half-octave period.

The ''semiquindromeda'' temperament (410&422) is an extension of the ''quindromeda'' temperament with a half-octave period.

Subgroup: 2.3.5.7

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 == Quindromeda ==
+The name ''quindromeda'' comes from "quintans" (Latin for "one fifth") and "[[Wikipedia:Andromeda|Andromeda]]", because the generator is 1/5 of the [[Schismatic family #Garibaldi|andromeda]] fourth (~4/3, about 497.6 cents).
 Subgroup: 2.3.5
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 === 2.3.5.17.19 ===
+The quindromeda temperament works well for the 2.3.5.17.19 subgroup, tempering out the password comma ([[1216/1215]]), aureusma ([[1445/1444]]), and 6144/6137. An obvious 17-limit interpretation of the generator is ~[[18/17]], equating three 18/17s with [[19/16]], five 18/17s with [[4/3]], and twenty-eight 18/17s with the [[5/1|fifth harmonic]].
 Subgroup: 2.3.5.17.19
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 The ''quintagar'' temperament (12&amp;217) tempers out the hemimean comma (3136/3125) and the [[garischisma]] (33554432/33480783) in the 7-limit. In the 2.3.5.7.17.19 subgroup, 256/255 (the difference between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), 361/360 (between 19/18 and 20/19), and 400/399 (between 20/19 and 21/20) are equated together, and 476/475 (between 28/25 and 19/17) is tempered out. Immediate 2.3.5.7.11.17.19 extensions include ''quintoneum'' (12&amp;217, tempering out 441/440), ''quintasandra'' (217&amp;229, equating 385/384 with 400/399), and ''quintasandroid'' (12&amp;229, equating 400/399 with 441/440). Full 19-limit extensions include ''quintoneum'' (12f&amp;217), ''quintoneoid'' (12&amp;217), ''quintasandra'' (217&amp;229), ''quintasandroid'' (12f&amp;229), and ''quintasand'' (12&amp;229). The name ''quintagar'' is so named because the generator is 1/5 of the [[Schismatic family #Garibaldi|garibaldi]] fourth (~4/3, about 497.8 cents) aside from tempering out the garischisma.
 Subgroup: 2.3.5.7
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 === Quintoneum ===
-The name ''quintoneum'' is a play on the words "quintans" (Latin for "one fifth") and "[[Hemimage temperaments #Cotoneum|cotoneum]]".
+The name ''quintoneum'' is a play on the words "quintans" and "[[Hemimage temperaments #Cotoneum|cotoneum]]".
 Subgroup: 2.3.5.7.11
@@ Line 289: / Line 292: @@
 == Quintakwai ==
 The ''quintakwai'' temperament (12&amp;193) tempers out the hemifamity comma (5120/5103) and the compass comma (9765625/9680832, quinruyoyo) in the 7-limit; 1375/1372 and 4375/4356 in the 11-limit. In the 2.3.5.7.17.19 subgroup, 225/224 (the difference between 15/14 and 16/15), 256/255 (between 16/15 and 17/16), 289/288 (between 17/16 and 18/17), 324/323 (between 18/17 and 19/18), and 361/360 (between 19/18 and 20/19) are equated together, and 400/399 (between 20/19 and 21/20) is tempered out. The name ''quintakwai'' is so named because the generator is 1/5 of the [[Mirkwai clan #Kwai|kwai]] fourth (~4/3, about 497.4 cents).
 Subgroup: 2.3.5.7
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 == Quindro ==
-The ''quindro'' temperament (205&amp;217) is an extension of the [[28ed5 #Regular temperaments|''quindromeda'' temperament]] which tempers out the ragisma (4375/4374), the vishdel comma (5632/5625), and the ibnsinma (2080/2079).
+The ''quindro'' temperament (205&amp;217) is an extension of the ''quindromeda'' temperament which tempers out the ragisma (4375/4374), the vishdel comma (5632/5625), and the ibnsinma (2080/2079).
 Subgroup: 2.3.5.7
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 == Semiquindromeda ==
-The ''semiquindromeda'' temperament (410&amp;422) is an extension of the [[28ed5 #Regular temperaments|''quindromeda'' temperament]] with a half-octave period.
+The ''semiquindromeda'' temperament (410&amp;422) is an extension of the ''quindromeda'' temperament with a half-octave period.
 Subgroup: 2.3.5.7