Quindromeda family: Difference between revisions

The '''quindromeda family''' tempers out {{monzo| 56 -28 -5 }}, equating the [[Pythagorean comma]] with a stack of five [[schisma]]s, making it a member of the [[schismic-Pythagorean equivalence continuum]].  

[[Comma list]]: {{monzo| 56 -28 -5 }}

{{Val list|legend=1| 12, 169, 181, 193, 205, 217, 422 }}

=== 2.3.5.17.19 ===

Comma list: 1216/1215, 1445/1444, 6144/6137

Sval mapping: [{{val| 1 2 0 5 4 }}, {{val| 0 -5 28 -11 3 }}]

Gencom: [2 18/17; 1216/1215 1445/1444 6144/6137]

POTE generator: ~18/17 = 99.524

Vals: {{Val list| 12, 169, 181, 193, 205, 422 }}

{{See also| 28ed5 #Regular temperaments }}

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.

{{Val list|legend=1| 12, 217, 229, 446, 675c }}

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

Vals: {{Val list| 12, 205d, 217 }}

Vals: {{Val list| 12f, 205df, 217 }}

Vals: {{Val list| 12f, 205df, 217 }}

Vals: {{Val list| 12f, 205df, 217 }}

Vals: {{Val list| 12, 205d, 217 }}

Vals: {{Val list| 12, 205d, 217 }}

Vals: {{Val list| 12, 205d, 217 }}

=== Quintasandra ===

The name ''quintasandra'' is a play on the words "quintans" and "[[Schismatic family #Garibaldi|cassandra]]". This temperament tempers out 19712/19683 and 41503/41472 in the 2.3.7.11 subgroup as the cassandra temperament, but with the hemimean comma rather than the [[schisma]] tempered out.

Vals: {{Val list| 12e, 217, 446 }}

Vals: {{Val list| 12e, 217, 446, 663c }}

Vals: {{Val list| 12e, 217, 446, 663c }}

Vals: {{Val list| 12e, 217, 446, 663ch }}

=== Quintasandroid ===

Vals: {{Val list| 12, 217e, 229, 470cd, 699cd }}

Vals: {{Val list| 12f, 217ef, 229, 241, 470cd, 711ccd }}

Vals: {{Val list| 12f, 217ef, 229, 241, 470cd }}

Vals: {{Val list| 12f, 217ef, 229, 241, 470cd }}

==== Quintasand ====

Vals: {{Val list| 12, 217e, 229, 446e, 675ceef }}

Vals: {{Val list| 12, 217e, 229, 446e, 675ceef }}

Vals: {{Val list| 12, 217e, 229, 446e, 675ceefh }}

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).

 

{{Val list|legend=1| 12, 169, 181, 193 }}

Vals: {{Val list| 12, 181, 193, 374, 567ce }}

Vals: {{Val list| 12, 181, 193, 374, 567ce, 941bce }}

Vals: {{Val list| 12, 181, 193, 374, 567ce, 941bceg }}

Vals: {{Val list| 12, 181, 193, 374, 567ce, 941bcegh, 1508bccdeegghh }}

Vals: {{Val list| 12f, 169e, 181 }}

Vals: {{Val list| 12f, 169e, 181, 374ff, 555cff }}

Vals: {{Val list| 12f, 169e, 181, 374ff, 555cff }}

Vals: {{Val list| 12f, 181f, 193 }}

Vals: {{Val list| 12f, 181f, 193 }}

Vals: {{Val list| 12f, 181f, 193 }}

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).  

{{Val list|legend=1| 205, 217, 422, 639, 1061 }}

Vals: {{Val list| 205, 217, 422, 639, 1061e }}

Vals: {{Val list| 205, 217, 422, 639, 1061ef }}

Vals: {{Val list| 205, 217, 422, 639, 1061ef }}

Vals: {{Val list| 205, 217, 422, 639h, 1061efh }}

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

{{Val list|legend=1| 12, 398, 410, 422, 832, 1254d, 2086bd }}

Vals: {{Val list| 12, 410, 422 }}

Vals: {{Val list| 12f, 410, 422, 1254df, 1676bdff, 2098bcddff }}

Vals: {{Val list| 12f, 410, 422, 832, 1254df, 1676bdff }}

Vals: {{Val list| 12f, 410, 422, 1254dfhh, 1676bdffhh }}

[[Category:Regular temperament theory]]

[[Category:Temperament family]]