Circular temperament: Difference between revisions

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A circular temperament is a temperament that equates some number of a given prime harmonic to the number of octaves that is closest in numerical value, by tempering out a comma of less than 600c, thus closing the circle of that interval (hence the name). The most widespread circular temperament is that of the 12edo circle of fifths, called [[compton]] temperament, and each EDO has a circular temperament for any given prime greater than 2.
{{Distinguish|circulating temperament}}


Names in bold are placeholder names assigned by Vector Graphics. Please add the correct name of the temperament if it is available.
A '''circular temperament'''{{idiosyncratic}} is a [[regular temperament|temperament]] that equates some number of a given [[prime harmonic]] to the number of [[octave]]s that is closest in numerical value, by [[tempering out]] a [[comma]] of less than 600c, thus closing the circle of that interval (hence the name). The most widespread circular temperament is that of the 12edo circle of fifths, called [[compton]] temperament, and each [[edo]] has a circular temperament for any given prime greater than 2.


Names in bold are placeholder names assigned by [[User:VectorGraphics|Vector Graphics]]. Please add the correct name of the temperament if it is available.


The circular temperaments include the comptonesque temperaments, which are the column labeled 3.
The circular temperaments include the comptonesque temperaments, which are the column labeled 3.
{| class="wikitable"
 
{| class="wikitable center-1"
|+
|+
!EDO
! Edo
![[Comptonesque|3]]
! [[Comptonesque|3]]
!5
! 5
!7
! 7
|-
|-
|1
| 1
|bixby
| [[bixby]]
|'''archon'''
| [[Very low accuracy temperaments#Archon|archon]]
|'''corvus'''
| '''corvus'''
|-
|-
|2
| 2
|antitonic
| antitonic
|'''xalie'''
| '''xalie'''
|'''venti'''
| (corvus)**
|-
|-
|3
| 3
|alteraugment
| alteraugment
|augmented
| augmented
|'''azazel'''
| '''azazel'''
|-
|-
|4
| 4
|(antitonic)
| (antitonic)
|'''thao'''
| '''thao'''
|'''gregario'''
| '''gregario'''
|-
|-
|5
| 5
|blackwood
| blackwood
|'''aledai'''
| '''aledai'''
|cloudy
| cloudy
|-
|-
|6
| 6
|(alteraugment)
| (alteraugment)
|(augmented)
| (augmented)
|'''kobold'''
| '''kobold'''
|-
|-
|7
| 7
|whitewood
| whitewood
|'''eryam'''
| '''eryam'''
|'''sobaka'''
| '''sobaka'''
|-
|-
|8
| 8
|'''alphard'''
| '''alphard'''
|'''issimi'''
| '''issimi'''
|(gregario)
| (gregario)
|-
|-
|9
| 9
|tervenna
| [[tervenna]]
|(augmented)
| (augmented)
|'''argentine'''
| '''argentine'''
|-
|-
|10
| 10
|(blackwood)
| (blackwood)
|'''rumekogan'''
| '''rumekogan'''
|(cloudy)
| (cloudy)
|-
|-
|11
| 11
|'''yarzon'''
| '''yarzon'''
|'''glazia'''
| '''glazia'''
|'''abaddon'''
| '''abaddon'''
|-
|-
|12
| 12
|compton
| compton
|(augmented)
| (augmented)
|(kobold)
| (kobold)
|-
|-
|13
| 13
|'''adarion'''
| '''adarion'''
|'''pextum'''
| '''pextum'''
|[[dilemmic]]*
| [[dilemmic]] (requiem)*
|-
|-
|14
| 14
|(whitewood)
| (whitewood)
|'''kaoad*'''
| '''kaoad'''
|'''requiem'''
| '''alteki'''
|-
|-
|15
| 15
|(blackwood)
| (blackwood)
|(augmented)
| (augmented)
|(cloudy)
| (cloudy)
|-
|-
|16
| 16
|ntiscifer
| [[ntiscifer]]
|'''celeth'''
| '''celeth'''
|'''tabaraxi'''
| '''tabaraxi'''
|-
|-
|17
| 17
|gothic
| gothic
|'''roklot'''
| '''roklot'''
|'''azura'''
| '''azura'''
|-
|-
|18
| 18
|'''haidomanz'''
| '''haidomanz'''
|(augmented)
| (augmented)
|'''succoria'''
| '''succoria'''
|-
|-
|19
| 19
|graywood
| graywood
|'''vitenle'''
| '''vitenle'''
|'''skaire'''
| '''skaire'''
|}
|}
<nowiki>*</nowiki>this is literally just barely its own thing
<nowiki>*</nowiki>yes this means that [[96889010407/68719476736]] is now called the ''dilemma''. this can be called requiem temperament if taken together with the temperament of [[137438953472/96889010407]], or the tsuchi temperament.


<nowiki>**</nowiki>Corvus and Venti are basically the same thing


<nowiki>*</nowiki>yes this means that [[96889010407/68719476736]] is now called the ''dilemma''.
[[Category:Regular temperament theory]]
[[Category:Terms]]

Latest revision as of 22:43, 17 June 2025

Not to be confused with circulating temperament.

A circular temperament[idiosyncratic term] is a temperament that equates some number of a given prime harmonic to the number of octaves that is closest in numerical value, by tempering out a comma of less than 600c, thus closing the circle of that interval (hence the name). The most widespread circular temperament is that of the 12edo circle of fifths, called compton temperament, and each edo has a circular temperament for any given prime greater than 2.

Names in bold are placeholder names assigned by Vector Graphics. Please add the correct name of the temperament if it is available.

The circular temperaments include the comptonesque temperaments, which are the column labeled 3.

Edo 3 5 7
1 bixby archon corvus
2 antitonic xalie (corvus)**
3 alteraugment augmented azazel
4 (antitonic) thao gregario
5 blackwood aledai cloudy
6 (alteraugment) (augmented) kobold
7 whitewood eryam sobaka
8 alphard issimi (gregario)
9 tervenna (augmented) argentine
10 (blackwood) rumekogan (cloudy)
11 yarzon glazia abaddon
12 compton (augmented) (kobold)
13 adarion pextum dilemmic (requiem)*
14 (whitewood) kaoad alteki
15 (blackwood) (augmented) (cloudy)
16 ntiscifer celeth tabaraxi
17 gothic roklot azura
18 haidomanz (augmented) succoria
19 graywood vitenle skaire

*yes this means that 96889010407/68719476736 is now called the dilemma. this can be called requiem temperament if taken together with the temperament of 137438953472/96889010407, or the tsuchi temperament.

**Corvus and Venti are basically the same thing

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