Hemimean clan: Difference between revisions

Line 500:

Badness: 0.029741

== ~~Quintoneum~~ ==

== Quintagar ==

The ''~~quintoneum~~'' 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 ''~~quintoneum~~'' is so named because the generator is 1/5 of the [[~~Hemimage temperaments~~ #~~Cotoneum~~|~~cotoneum~~]] fourth (~4/3, about 497.7 cents).

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

Line 519:

[[Badness]]: 0.142897

=== ~~11-limit~~ ===

=== Quintoneum ===

Subgroup: 2.3.5.7.11

@@ Line 500: / Line 500: @@
 Badness: 0.029741
-== Quintoneum ==
+== Quintagar ==
 {{See also| 28ed5 #28ed5 as a generator }}
-The ''quintoneum'' 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 ''quintoneum'' is so named because the generator is 1/5 of the [[Hemimage temperaments #Cotoneum|cotoneum]] fourth (~4/3, about 497.7 cents).
+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
@@ Line 519: / Line 519: @@
 [[Badness]]: 0.142897
-=== 11-limit ===
+=== Quintoneum ===
 Subgroup: 2.3.5.7.11