Fractional-octave temperaments: Difference between revisions
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A particularly strong offender of this is the [[landscape microtemperaments]] list, which features temperaments which are all supersets of 3edo, but from a composer's perspective 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. | A particularly strong offender of this is the [[landscape microtemperaments]] list, which features temperaments which are all supersets of 3edo, but from a composer's perspective 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 == | |||
An '''octave-splitting comma''' is a rational [[interval]] which induces a fractional-octave temperament. If tempering out the comma leads to splitting the [[octave]] into ''N'' equal parts (''N'' > 1), the comma is an octave-splitting comma which induces an ''N''th-octave temperament. This terminology was developed by [[Xenllium]]. | |||
=== Examples === | |||
Below is a list of octave-splitting commas for common temperaments: | |||
{| class="wikitable" | |||
|- | |||
! Comma !! Associated <br>temperament !! Harmonic <br>limit !! Splitting <br>order | |||
|- | |||
| [[256/243]] || [[Limmic temperaments|Blackwood]] || 3 || 5 | |||
|- | |||
| [[2187/2048]] || [[Apotome family|Whitewood]] || 3 || 7 | |||
|- | |||
| [[531441/524288]] || [[Compton family|Compton]] || 3 || 12 | |||
|- | |||
| [[2048/2025]] || [[Diaschismic family|Diaschismic]] || 5 || 2 | |||
|- | |||
| [[128/125]] || [[Augmented family|Augmented]] || 5 || 3 | |||
|- | |||
| [[648/625]] || [[Diminished family|Diminished]] || 5 || 4 | |||
|- | |||
| [[50/49]] || [[Jubilismic clan|Jubilismic]] || 7 || 2 | |||
|- | |||
| [[250047/250000]] || [[Landscape microtemperaments|Landscape]] || 7 || 3 | |||
|- | |||
| [[9801/9800]] || [[Kalismic temperaments|Kalismic]] || 11 || 2 | |||
|- | |||
| [[289/288]] || [[Semitonismic]] || 17 || 2 | |||
|} | |||
== Individual pages of temperaments by subtending equal division == | == Individual pages of temperaments by subtending equal division == | ||
=== 2 to 100 === | === 2 to 100 === | ||
{| class="wikitable center-all" | |||
{| class="wikitable" | |||
|+ | |+ | ||
| | | | ||
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|- | |- | ||
| [[11th-octave temperaments|11]] | | [[11th-octave temperaments|11]] | ||
| [[12th-octave temperaments|12]] | | [[12th-octave temperaments|12]]/[[Compton family|C]] | ||
| [[13th-octave temperaments|13]] | | [[13th-octave temperaments|13]] | ||
| [[14th-octave temperaments|14]] | | [[14th-octave temperaments|14]] | ||
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| [[40th-octave temperaments|40]] | | [[40th-octave temperaments|40]] | ||
|- | |- | ||
| [[41st-octave temperaments|41]] / [[Countercomp family| | | [[41st-octave temperaments|41]]/[[Countercomp family|CC]] | ||
| [[42nd-octave temperaments|42]] | | [[42nd-octave temperaments|42]] | ||
| [[43rd-octave temperaments|43]] | | [[43rd-octave temperaments|43]] | ||
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| [[51st-octave temperaments|51]] | | [[51st-octave temperaments|51]] | ||
| [[52nd-octave temperaments|52]] | | [[52nd-octave temperaments|52]] | ||
| [[53rd-octave temperaments|53]] / [[Mercator family|M]] | | [[53rd-octave temperaments|53]]/[[Mercator family|M]] | ||
| [[54th-octave temperaments|54]] | | [[54th-octave temperaments|54]] | ||
| [[55th-octave temperaments|55]] | | [[55th-octave temperaments|55]] | ||
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[[111th-octave temperaments|111]], [[118th-octave temperaments|118]], [[159th-octave temperaments|159]], [[400th-octave temperaments|400]], [[665th-octave temperaments|665]] | [[111th-octave temperaments|111]], [[118th-octave temperaments|118]], [[159th-octave temperaments|159]], [[400th-octave temperaments|400]], [[665th-octave temperaments|665]] | ||
* C = compton family | |||
C = | * CC = countercomp family | ||
* M = mercator family equated with 53rd-octave temperaments until otherwise documented, also contains 106th-octave temperaments | |||
M = | |||
== Temperaments discussed elsewhere == | == Temperaments discussed elsewhere == | ||
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** [[Landscape microtemperaments|Landscape temperaments]] | ** [[Landscape microtemperaments|Landscape temperaments]] | ||
* 1\4 period temperaments | * 1\4 period temperaments | ||
** [[ | ** [[Diminished family|Diminished temperaments]] | ||
** [[Undim family|Undim temperaments]] | ** [[Undim family|Undim temperaments]] | ||
* 1\5 period temperaments | * 1\5 period temperaments | ||
** [[ | ** [[Quintile family|Quintile temperaments]] | ||
** [[Quintosec family|Quintosec temperaments]] | ** [[Quintosec family|Quintosec temperaments]] | ||
** [[Trisedodge family|Trisedodge temperaments]] | ** [[Trisedodge family|Trisedodge temperaments]] | ||
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** [[Stearnsmic clan #Stearnscape|Stearnscape]] | ** [[Stearnsmic clan #Stearnscape|Stearnscape]] | ||
* [[Akjaysma|Akjaysmic temperaments]] (1\7 period) | * [[Akjaysma|Akjaysmic temperaments]] (1\7 period) | ||
**[[Ragismic microtemperaments #Brahmagupta|Brahmagupta]] | ** [[Ragismic microtemperaments #Brahmagupta|Brahmagupta]] | ||
** [[Schismatic family #Septant|Septant]] | ** [[Schismatic family #Septant|Septant]] | ||
** [[ | ** [[Whitewood family #Whitewood|Whitewood temperaments]] | ||
** [[Keemic temperaments #Sevond|Sevond]] | ** [[Keemic temperaments #Sevond|Sevond]] | ||
** [[Mistismic temperaments #Neutron|Neutron]] | ** [[Mistismic temperaments #Neutron|Neutron]] | ||
* [[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) | ||
** [[Ragismic microtemperaments #Ennealimmal|Ennealimmal]] | ** [[Ragismic microtemperaments #Ennealimmal|Ennealimmal]] | ||
** [[Augmented family #Niner|Niner]] | ** [[Augmented family #Niner|Niner]] | ||
| Line 185: | Line 214: | ||
** [[Cloudy clan #Decic|Decic]] | ** [[Cloudy clan #Decic|Decic]] | ||
** [[Stearnsmic clan #Decistearn|Decistearn]] | ** [[Stearnsmic clan #Decistearn|Decistearn]] | ||
** [[ | ** [[Quintile family #Decile|Decile]] | ||
** [[Vishnuzmic family #Decavish|Decavish]] | ** [[Vishnuzmic family #Decavish|Decavish]] | ||
** [[Metric microtemperaments #Decimetra|Decimetra]] | ** [[Metric microtemperaments #Decimetra|Decimetra]] | ||
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* [[Ragismic microtemperaments #Octoid|Hexadecoid]], [[Jubilismic clan #Sedecic|sedecic]] (1\16 period) | * [[Ragismic microtemperaments #Octoid|Hexadecoid]], [[Jubilismic clan #Sedecic|sedecic]] (1\16 period) | ||
* [[Ragismic microtemperaments #Chlorine|Chlorine]] (1\17 period) | * [[Ragismic microtemperaments #Chlorine|Chlorine]] (1\17 period) | ||
* [[ | * [[Septiennealimmal clan #Ennealimmal|Hemiennealimmal]] (1\18 period) | ||
* [[Ragismic microtemperaments #Enneadecal|Enneadecal]], [[Meantone family #Meanmag|meanmag]] (1\19 period) | * [[Ragismic microtemperaments #Enneadecal|Enneadecal]], [[Meantone family #Meanmag|meanmag]] (1\19 period) | ||
* [[Hemimage temperaments #Degrees|Degrees]] (1\20 period) | * [[Hemimage temperaments #Degrees|Degrees]] (1\20 period) | ||
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* [[Porwell temperaments #Icositritonic|Icositritonic]] (1\23 period) | * [[Porwell temperaments #Icositritonic|Icositritonic]] (1\23 period) | ||
* [[Compton family #Hours|Hours]], [[chromium]] (1\24 period) | * [[Compton family #Hours|Hours]], [[chromium]] (1\24 period) | ||
* [[ | * [[Septiennealimmal clan #Ennealimmal|Trinealimmal]], [[Tritrizo clan #Cobalt|cobalt]] (1\27 period) | ||
* [[Horwell temperaments #Oquatonic|Oquatonic]] (1\28 period) | * [[Horwell temperaments #Oquatonic|Oquatonic]] (1\28 period) | ||
* [[Hemifamity temperaments #Mystery|Mystery]], [[Copper comma|copper]] (1\29 period) | * [[Hemifamity temperaments #Mystery|Mystery]], [[Copper comma|copper]] (1\29 period) | ||
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* [[Parkleiness temperaments #Octogintic|Octogintic]] (1\80 period) | * [[Parkleiness temperaments #Octogintic|Octogintic]] (1\80 period) | ||
* [[Stearnsmic clan #Garistearn|Garistearn]] (1\94 period) | * [[Stearnsmic clan #Garistearn|Garistearn]] (1\94 period) | ||
* [[ | * [[Septiennealimmal clan #Undecentic|Undecentic]] (1\99 period) | ||
* [[ | * [[Septiennealimmal clan #Schisennealimmal|Schisennealimmal]] (1\171 period) | ||
* [[ | * [[Septiennealimmal clan #Lunennealimmal|Lunennealimmal]] (1\441 period) | ||
== See also == | == See also == | ||
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[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||