Schismatic family: Difference between revisions
Intro to each temp (1/) |
Intro to each temp (2/2) |
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* [[WE]]: ~2 = 1200.0749{{c}}, ~3/2 = 701.7797{{c}} | * [[WE]]: ~2 = 1200.0749{{c}}, ~3/2 = 701.7797{{c}} | ||
: [[error map]]: {{val| +0.075 -0.100 -0.027 }} | : [[error map]]: {{val| +0.075 -0.100 -0.027 }} | ||
* [[CWE]]: ~2 = 1200.0000{{c | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7308{{c}} | ||
: error map: {{val| 0.000 -0.224 -0.160 }} | : error map: {{val| 0.000 -0.224 -0.160 }} | ||
| Line 70: | Line 70: | ||
* [[WE]]: ~2 = 1200.1233{{c}}, ~3/2 = 702.1573{{c}} | * [[WE]]: ~2 = 1200.1233{{c}}, ~3/2 = 702.1573{{c}} | ||
: [[error map]]: {{val| +0.123 +0.326 -2.709 +2.328 }} | : [[error map]]: {{val| +0.123 +0.326 -2.709 +2.328 }} | ||
* [[CWE]]: ~2 = 1200.0000{{c | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0774{{c}} | ||
: error map: {{val| 0.000 +0.122 -2.933 +2.090 }} | : error map: {{val| 0.000 +0.122 -2.933 +2.090 }} | ||
| Line 90: | Line 90: | ||
=== Cassandra === | === Cassandra === | ||
Cassandra is one of the best extensions of garibaldi to the 11- and 13-limit as well as the 2.3.5.7.11.13.19 subgroup, though it comes with a higher complexity. | Cassandra is one of the best extensions of garibaldi to the 11- and 13-limit as well as the 2.3.5.7.11.13.19 subgroup, even though it comes with a much higher complexity. | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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== Tsaharuk == | == Tsaharuk == | ||
{{Main| Tsaharuk }} | {{Main| Tsaharuk }} | ||
Tsaharuk tempers out 420175/419904, the [[wizma]], and may be described as the {{nowrap| 77 & 94 }} temperament. It is generated by a slightly flat neutral second of [[~]][[13/12]], five of which make the [[3/2|perfect fifth]], so its [[ploidacot]] is pentacot. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Quanharuk == | == Quanharuk == | ||
Quanharuk tempers out 16875/16807, the [[mirkwai]] comma, and may be described as the {{nowrap| 41 & 183 }} temperament. The generator is a slightly flat major third of [[~]][[56/45]], five of which make the [[3/1|3rd]] [[harmonic]], so the [[ploidacot]] of this temperament is alpha-pentacot. [[224edo]] makes for a recommendable tuning. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Quintilipyth == | == Quintilipyth == | ||
Quintilipyth (formerly ''quintilischis'') slices the [[4/3|perfect fourth]] into five semitones and tempers out the [[compass comma]] (9765625/9680832) in the [[7-limit]]. It may be described as the {{nowrap| 12 & 253 }} temperament, and its [[ploidacot]] is omega-pentacot. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Quintaschis == | == Quintaschis == | ||
Quintaschis slices the [[4/3|perfect fourth]] into five semitones and tempers out 49009212/48828125 in the [[7-limit]]. It may be described as the {{nowrap| 12 & 289 }} temperament, and its [[ploidacot]] is omega-pentacot. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Sextilifourths == | == Sextilifourths == | ||
Sextilifourths (also known as ''sextilischis'', formerly ''sextilififths'') slices the [[4/3|perfect fourth]] into six small semitones, which serves as both [[21/20]] and [[22/21]]. It may be described as {{nowrap| 130 & 159 }}, and its [[ploidacot]] is omega-hexacot. [[289edo]] gives a highly recommendable tuning. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Octant == | == Octant == | ||
Octant may be described as the {{nowrap| 224 & 248 }} temperament. It has a period of 1/8 octave, and its [[ploidacot]] is octaploid monocot. In this temperament, [[12/11]], [[35/27]], and [[99/70]] are mapped to 1\8, 3\8, and 4\8 respectively. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Nonant == | == Nonant == | ||
Nonant tempers out the [[septimal ennealimma]] ({{monzo| -11 -9 0 9 }}) and may be described as the {{nowrap| 36 & 171 }} temperament. It has a period of 1/9 octave, and its [[ploidacot]] is enneaploid monocot. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Septant == | == Septant == | ||
Septant notably tempers out the [[akjaysma]] ({{monzo| 47 -7 -7 -7 }}) and may be described as the {{nowrap| 224 & 301 }} temperament. It has a period of 1/7 octave, and its [[ploidacot]] is heptaploid monocot. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Septiquarschis == | == Septiquarschis == | ||
Septiquarschis tempers out [[829440/823543]] (mynaslender comma) and [[67108864/66706983]] (septiness comma), and may be described as the {{nowrap| 89 & 94 }} temperament. It splits septimal minor seventh ([[7/4]]) into four generators. Note that in the data below, the generator is the [[octave complement]] so that seven of them minus five octaves make a [[3/2|perfect fifth]]; its [[ploidacot]] is thus epsilon-heptacot. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Tridecafifths == | == Tridecafifths == | ||
Tridecafifths divides the | Tridecafifths may be described as the {{nowrap| 89 & 200 }} temperament. It divides the [[3/2|perfect fifth]] into thirteen quartertones, so its [[ploidacot]] is 13-cot. [[289edo]] gives a highly recommendable tuning. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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: ''See also: [[No-elevens subgroup temperaments #Garibaldia]] and [[No-elevens subgroup temperaments #Pontia|#Pontia]]'' | : ''See also: [[No-elevens subgroup temperaments #Garibaldia]] and [[No-elevens subgroup temperaments #Pontia|#Pontia]]'' | ||
The [[S-expression]]-based comma list of this temperament is {[[1216/1215|S16/S18]], [[361/360|S19]] , ([[513/512|S15/S20]])}. | The [[S-expression]]-based comma list of this temperament is {[[1216/1215|S16/S18]], [[361/360|S19]], ([[513/512|S15/S20]])}. Note that despite prime [[19/1|19]] being optimized by a flatter fifth, the fifth in optimal tunings of nestoria is generally not flatter than the fifth in optimal schismic due to its optimization considering intervals like [[19/10]] and [[19/15]]. | ||
[[Subgroup]]: 2.3.5.19 | [[Subgroup]]: 2.3.5.19 | ||