Schismatic family: Difference between revisions
→Term: +intro to note its utility |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| Line 562: | Line 562: | ||
=== Helenoid === | === Helenoid === | ||
The helenoid temperament (53 & 118) is closely related to the helenus temperament, but with the ragisma rather than the [[225/224|marvel comma]] tempered out. | The helenoid temperament ({{nowrap|53 & 118}}) is closely related to the helenus temperament, but with the ragisma rather than the [[225/224|marvel comma]] tempered out. | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 654: | Line 654: | ||
=== Ponta === | === Ponta === | ||
The ponta temperament (53 & 171) tempers out the [[540/539|swetisma]] and the ragisma. | The ponta temperament ({{nowrap|53 & 171}}) tempers out the [[540/539|swetisma]] and the ragisma. | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 707: | Line 707: | ||
=== Pontic === | === Pontic === | ||
The pontic temperament (118 & 171) tempers out the [[441/440|werckisma]] and the ragisma. | The pontic temperament ({{nowrap|118 & 171}}) tempers out the [[441/440|werckisma]] and the ragisma. | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 786: | Line 786: | ||
=== Bipont === | === Bipont === | ||
The bipont temperament (118 & 224) has a period of half octave and tempers out the [[3025/3024|lehmerisma (3025/3024)]] and the [[9801/9800|kalisma (9801/9800)]]. | The bipont temperament ({{nowrap|118 & 224}}) has a period of half octave and tempers out the [[3025/3024|lehmerisma (3025/3024)]] and the [[9801/9800|kalisma (9801/9800)]]. | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,280: | Line 1,280: | ||
== Squirrel == | == Squirrel == | ||
The squirrel temperament (29 & 36) has a ~11/10 generator, three of which give the fourth (~4/3), and thirteen of which give 7/4 with octave reduction. | The squirrel temperament ({{nowrap|29 & 36}}) has a ~11/10 generator, three of which give the fourth (~4/3), and thirteen of which give 7/4 with octave reduction. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 1,323: | Line 1,323: | ||
== Tertiaschis == | == Tertiaschis == | ||
The tertiaschis temperament (94 & 159) has a ~11/10 generator, sharing the same 2.3.5.11 subgroup with [[#Squirrel]], but tempers out 1071785/1062882 for prime 7. | The tertiaschis temperament ({{nowrap|94 & 159}}) has a ~11/10 generator, sharing the same 2.3.5.11 subgroup with [[#Squirrel]], but tempers out 1071785/1062882 for prime 7. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 1,379: | Line 1,379: | ||
== Countertertiaschis == | == Countertertiaschis == | ||
The countertertiaschis temperament (159 & 224) has a ~11/10 generator, sharing the same 2.3.5.11 subgroup with [[#Squirrel]], but tempers out 244140625/243045684 for prime 7. | The countertertiaschis temperament ({{nowrap|159 & 224}}) has a ~11/10 generator, sharing the same 2.3.5.11 subgroup with [[#Squirrel]], but tempers out 244140625/243045684 for prime 7. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 1,422: | Line 1,422: | ||
{{See also| Stearnsmic clan #Pogo }} | {{See also| Stearnsmic clan #Pogo }} | ||
The pogo temperament (94 & 130) splits the period in two to address the difference between [[#Tertiaschis]] and [[#Countertertiaschis]]. The schismic tempering of the fifth is just about right for tempering out the stearnsma. | The pogo temperament ({{nowrap|94 & 130}}) splits the period in two to address the difference between [[#Tertiaschis]] and [[#Countertertiaschis]]. The schismic tempering of the fifth is just about right for tempering out the stearnsma. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 1,467: | Line 1,467: | ||
== Term == | == Term == | ||
Term tempers out the [[landscape comma]], mapping ~63/50 to the 1/3-octave period. It can be described as 12 & 171, and is the unique temperament that equates a syntonic~Pythagorean comma with a stack of three [[marvel comma]]s. A [[septimal comma]] is then found as a stack of four marvel commas. In some 7-limit adaptive-tuning practice, the marvel comma corresponds to a melodic unit called a [[kleisma]], with three kleismas making a comma, so this temperament may be useful for modeling that. [[171edo]] makes for an excellent tuning. | Term tempers out the [[landscape comma]], mapping ~63/50 to the 1/3-octave period. It can be described as {{nowrap|12 & 171}}, and is the unique temperament that equates a syntonic~Pythagorean comma with a stack of three [[marvel comma]]s. A [[septimal comma]] is then found as a stack of four marvel commas. In some 7-limit adaptive-tuning practice, the marvel comma corresponds to a melodic unit called a [[kleisma]], with three kleismas making a comma, so this temperament may be useful for modeling that. [[171edo]] makes for an excellent tuning. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 1,490: | Line 1,490: | ||
=== Terminal === | === Terminal === | ||
The terminal temperament (12 & 159) tempers out 441/440 and 4375/4356. In this temperament, 44/35 and 63/50 are represented as one period of 1/3 octave. | The terminal temperament ({{nowrap|12 & 159}}) tempers out 441/440 and 4375/4356. In this temperament, 44/35 and 63/50 are represented as one period of 1/3 octave. | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,570: | Line 1,570: | ||
=== Semiterm === | === Semiterm === | ||
The semiterm temperament (12 & 342) has a period of 1/6 octave and tempers out [[9801/9800]] (kalisma) and 151263/151250 (odiheim comma). | The semiterm temperament ({{nowrap|12 & 342}}) has a period of 1/6 octave and tempers out [[9801/9800]] (kalisma) and 151263/151250 (odiheim comma). | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,850: | Line 1,850: | ||
== Quintilipyth == | == Quintilipyth == | ||
The quintilipyth temperament (12 & 253, formerly ''quintilischis'') slices the pythagorean fourth ([[4/3]]) into five semitones and tempers out the compass comma (9765625/9680832) in the 7-limit. | The quintilipyth temperament ({{nowrap|12 & 253}}, formerly ''quintilischis'') slices the pythagorean fourth ([[4/3]]) into five semitones and tempers out the compass comma (9765625/9680832) in the 7-limit. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 1,919: | Line 1,919: | ||
== Quintaschis == | == Quintaschis == | ||
The quintaschis temperament (12 & 289) slices the fourth (4/3) into five semitones and tempers out 49009212/48828125 in the 7-limit. | The quintaschis temperament ({{nowrap|12 & 289}}) slices the fourth (4/3) into five semitones and tempers out 49009212/48828125 in the 7-limit. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 2,079: | Line 2,079: | ||
== Sextilififths == | == Sextilififths == | ||
The sextilififths (130 & 159, also known as ''sextilischis'') slices the fourth (4/3) into six small semitones, which serves as both 21/20 and 22/21. | The sextilififths ({{nowrap|130 & 159}}, also known as ''sextilischis'') slices the fourth (4/3) into six small semitones, which serves as both 21/20 and 22/21. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 2,124: | Line 2,124: | ||
== Septiquarschis == | == Septiquarschis == | ||
The septiquarschis temperament (89 & 94) splits septimal minor seventh ([[7/4]]) into four generators and tempers out 829440/823543 (mynaslender comma) and 67108864/66706983 (septiness comma). | The septiquarschis temperament ({{nowrap|89 & 94}}) splits septimal minor seventh ([[7/4]]) into four generators and tempers out 829440/823543 (mynaslender comma) and 67108864/66706983 (septiness comma). | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 2,255: | Line 2,255: | ||
== Quadrant == | == Quadrant == | ||
The ''quadrant'' temperament (12 & 224) has a period of quarter octave and tempers out the [[dimcomp comma]], 390625/388962. In this temperament, 25/21 is mapped into quarter octave. | The ''quadrant'' temperament ({{nowrap|12 & 224}}) has a period of quarter octave and tempers out the [[dimcomp comma]], 390625/388962. In this temperament, 25/21 is mapped into quarter octave. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 2,300: | Line 2,300: | ||
== Septant == | == Septant == | ||
The ''septant'' temperament (224 & 301) has a period of 1/7 octave and tempers out the [[akjaysma]], {{monzo| 47 -7 -7 -7 }}. | The ''septant'' temperament ({{nowrap|224 & 301}}) has a period of 1/7 octave and tempers out the [[akjaysma]], {{monzo| 47 -7 -7 -7 }}. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 2,345: | Line 2,345: | ||
== Octant == | == Octant == | ||
The octant temperament (224 & 472) has a period of 1/8 octave. In this temperament, 12/11, 35/27, and 99/70 are mapped into 1\8, 3\8, and 4\8 respectively. | The octant temperament ({{nowrap|224 & 472}}) has a period of 1/8 octave. In this temperament, 12/11, 35/27, and 99/70 are mapped into 1\8, 3\8, and 4\8 respectively. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 2,390: | Line 2,390: | ||
== Nonant == | == Nonant == | ||
The ''nonant'' temperament (36 & 135) has a period of 1/9 octave and tempers out the [[septimal ennealimma]], {{monzo| -11 -9 0 9 }}. | The ''nonant'' temperament ({{nowrap|36 & 135}}) has a period of 1/9 octave and tempers out the [[septimal ennealimma]], {{monzo| -11 -9 0 9 }}. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||