Fractional-octave temperaments: Difference between revisions
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Vanilla regular temperament theory does not distinguish periods and generators, so it treats divisions of periods (for example, what [[hemiennealimmal]] is to [[ennealimmal]]) as [[extension]]s of a temperament with a subset period, just like how it treats divisions of generators. However, fractional-octave temperaments and scales are sometimes sought for being able to treat each equal division as an entity in its own right, so a composer might find hemiennealimmal to be a drastically different system to ennealimmal in line with [[18edo]] being very different from [[9edo]]. | Vanilla regular temperament theory does not distinguish periods and generators, so it treats divisions of periods (for example, what [[hemiennealimmal]] is to [[ennealimmal]]) as [[extension]]s of a temperament with a subset period, just like how it treats divisions of generators. However, fractional-octave temperaments and scales are sometimes sought for being able to treat each equal division as an entity in its own right, so a composer might find hemiennealimmal to be a drastically different system to ennealimmal in line with [[18edo]] being very different from [[9edo]]. | ||
Besides, on this wiki, temperament collection pages are used to collect temperaments that temper out a common comma. For example, the [[landscape microtemperaments]] list features temperaments which all temper out the [[landscape comma]], as they are all related by that. A fractional-octave temperament user might consider that it contains wildly different temperaments due to the fact that edo multiples of 3 themselves are different. For example, magnesium (12), and zinc (30), are both landscape systems due to being multiples of 3, but 30edo is drastically different from 12edo in terms of composition, and therefore such temperaments are not alike at all. | Besides, on this wiki, temperament collection pages are used to collect temperaments that temper out a common comma. For example, the [[landscape microtemperaments]] are the most prominent example of this phenomenon, as the list features temperaments which all temper out the [[landscape comma]], as they are all related by that. A fractional-octave temperament user might consider that it contains wildly different temperaments due to the fact that edo multiples of 3 themselves are different. For example, magnesium (12), and zinc (30), are both landscape systems due to being multiples of 3, but 30edo is drastically different from 12edo in terms of composition, and therefore such temperaments are not alike at all. | ||
== Octave-splitting comma == | == Octave-splitting comma == | ||
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| [[100th-octave temperaments|100]] | | [[100th-octave temperaments|100]] | ||
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* C = compton family | * C = compton family | ||
* CC = countercomp family | * CC = countercomp family | ||
* M = mercator family equated with 53rd-octave temperaments until otherwise documented, also contains 106th-octave temperaments | * M = mercator family equated with 53rd-octave temperaments until otherwise documented, also contains 106th-octave temperaments | ||
=== 101 and up === | |||
[[111th-octave temperaments|111]], [[118th-octave temperaments|118]], [[159th-octave temperaments|159]], [[400th-octave temperaments|400]], [[665th-octave temperaments|665]] | |||
== Temperaments discussed elsewhere == | == Temperaments discussed elsewhere == | ||
Other temperaments discussed as a part of a commatic family, or otherwise in temperament lists unrelated to fractional-octave theory include: | |||
* 1\5 period temperaments | * 1\5 period temperaments | ||
** [[Quintile family|Quintile temperaments]] | ** [[Quintile family|Quintile temperaments]] | ||
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** [[Cloudy comma #Temperaments|Cloudy temperaments]] | ** [[Cloudy comma #Temperaments|Cloudy temperaments]] | ||
** [[Blackwood family]] | ** [[Blackwood family]] | ||
* [[Ragismic microtemperaments #Octoid|Octoid]], [[Schismatic family #Octant|octant]] (1\8 period) | * [[Ragismic microtemperaments #Octoid|Octoid]], [[Schismatic family #Octant|octant]] (1\8 period) | ||
* [[Septiennealimmal clan|Septiennealimmal temperaments]] (1\9 period) | * [[Septiennealimmal clan|Septiennealimmal temperaments]] (1\9 period) | ||
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** [[Marvel temperaments #Enneaportent|Enneaportent]] | ** [[Marvel temperaments #Enneaportent|Enneaportent]] | ||
** [[Kleismic family #Novemkleismic|Novemkleismic]] | ** [[Kleismic family #Novemkleismic|Novemkleismic]] | ||
* [[Porwell temperaments #Hendecatonic|Hendecatonic]] (1\11 period) | * [[Porwell temperaments #Hendecatonic|Hendecatonic]] (1\11 period) | ||
* [[Compton family|Compton]], [[Very high accuracy temperaments #Atomic|atomic]] (1\12 period) | * [[Compton family|Compton]], [[Very high accuracy temperaments #Atomic|atomic]] (1\12 period) | ||