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{{Infobox ET}}
{{Infobox ET}}
{{Wikipedia|Whole tone scale}}
{{Wikipedia|Whole tone scale}}
{{EDO intro|6}}  
{{ED intro}} It is also known as the '''whole tone scale'''.  
 
6edo is also known as the '''whole tone scale'''.  


== Theory ==
== Theory ==
As a subset of [[12edo]], 6edo can be notated on a five-line staff with standard notation. It is the first [[edo]] that is not a [[zeta peak edo|zeta peak]], has lower [[Consistency limits of small EDOs|consistency]] than the one that precedes it, and the highest edo that has no single period mode of symmetry scales other than using the single step as a generator. This means it is relatively poor for its size at creating traditional tonal music, with 5edo and 7edo both having much better representations of the third harmonic, but has still seen more use than most edos other than 12, since it can be played on any 12-tone instrument.
As a subset of [[12edo]], 6edo can be notated on a five-line staff with standard notation. It is the first [[edo]] that is not a [[zeta peak edo|zeta peak]], has lower [[Consistency limits of small EDOs|consistency]] than the one that precedes it, and the highest edo that has no single period mode of symmetry scales other than using the single step as a generator. This means it is relatively poor for its size at creating traditional tonal music, with 5edo and 7edo both having much better representations of the third harmonic, but has still seen more use than most edos other than 12, since it can be played on any 12-tone instrument.


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== Intervals ==
== Intervals ==
{| class="wikitable center-all"
{| class="wikitable center-all"
|+ Intervals of 6edo
|+ style="font-size: 105%;" | Intervals of 6edo
|-
! rowspan="2" | [[Degree]]
! rowspan="2" | [[Degree]]
! rowspan="2" | [[Cent]]s
! rowspan="2" | [[Cent]]s
! rowspan="2" | [[Interval region]]
! rowspan="2" | [[Interval region]]
! colspan="4" | Approximated [[JI]] intervals* ([[error]] in [[¢]])
! colspan="4" | Approximated [[JI]] intervals<ref group="note">{{sg|limit=subset of 12edo, itself treated as a 2.3.5.7.17.19 subgroup}} For example, for 6edo as a 2.5.7.9 subgroup temperament, ignore the "Other" column).</ref>
! rowspan="2" | Audio
! rowspan="2" | Audio
|-
|-
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| 200
| 200
| Major second
| Major second
| [[9/8]] (-3.910)
| [[9/8]] (−3.910)
| [[10/9]] (+17.596)
| [[10/9]] (+17.596)
| [[28/25]] (+3.802)<br>[[8/7]] (-31.174)
| [[28/25]] (+3.802)<br />[[8/7]] (−31.174)
| [[19/17]] (+7.442)<br>[[55/49]] (+0.020)<br>[[64/57]] (-0.532)<br>[[17/15]] (-16.687)
| [[19/17]] (+7.442)<br />[[55/49]] (+0.020)<br />[[64/57]] (−0.532)<br />[[17/15]] (−16.687)
| [[File:piano_1_6edo.mp3]]
| [[File:piano_1_6edo.mp3]]
|-
|-
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| 400
| 400
| Major third
| Major third
| [[81/64]] (-7.820)
| [[81/64]] (−7.820)
| [[5/4]] (+13.686)
| [[5/4]] (+13.686)
| [[63/50]] (-0.108)<br>[[9/7]] (-35.084)
| [[63/50]] (−0.108)<br />[[9/7]] (−35.084)
| [[34/27]] (+0.910)
| [[34/27]] (+0.910)
| [[File:piano_1_3edo.mp3]]
| [[File:piano_1_3edo.mp3]]
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|  
|  
|  
|  
| [[7/5]] (+17.488)<br>[[10/7]] (-17.488)
| [[7/5]] (+17.488)<br />[[10/7]] (−17.488)
| [[24/17]] (+3.000)<br>[[99/70]] (-0.088)<br>[[17/12]] (-3.000)
| [[24/17]] (+3.000)<br />[[99/70]] (−0.088)<br />[[17/12]] (−3.000)
| [[File:piano_1_2edo.mp3]]
| [[File:piano_1_2edo.mp3]]
|-
|-
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| Minor sixth
| Minor sixth
| [[128/81]] (+7.820)
| [[128/81]] (+7.820)
| [[8/5]] (-13.686)
| [[8/5]] (−13.686)
| [[14/9]] (+35.084)<br>[[100/63]] (+0.108)
| [[14/9]] (+35.084)<br />[[100/63]] (+0.108)
| [[27/17]] (-0.910)
| [[27/17]] (−0.910)
| [[File:piano_2_3edo.mp3]]
| [[File:piano_2_3edo.mp3]]
|-
|-
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| Minor seventh
| Minor seventh
| [[16/9]] (+3.910)
| [[16/9]] (+3.910)
| [[9/5]] (-17.596)
| [[9/5]] (−17.596)
| [[7/4]] (+31.174)<br>[[25/14]] (-3.802)
| [[7/4]] (+31.174)<br />[[25/14]] (−3.802)
| [[30/17]] (+16.687)<br>[[57/32]] (+0.532)<br>[[98/55]] (-0.020)<br>[[34/19]] (-7.442)
| [[30/17]] (+16.687)<br />[[57/32]] (+0.532)<br />[[98/55]] (−0.020)<br />[[34/19]] (−7.442)
| [[File:piano_5_6edo.mp3]]
| [[File:piano_5_6edo.mp3]]
|-
|-
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| [[File:piano_1_1edo.mp3]]
| [[File:piano_1_1edo.mp3]]
|}
|}
<nowiki>*</nowiki> based on treating 6edo as a subset of 12edo, itself treated as a 2.3.5.7.17.19 subgroup temperament; other approaches are possible (e.g. for 6edo as a 2.5.7.9 subgroup temperament, ignore the "Other" column).


== Notation ==
== Notation ==
{| class="wikitable center-all"
{| class="wikitable center-all"
|+ Notation of 6edo
|+ style="font-size: 105%;" | Notation of 6edo
|-
! rowspan="2" | [[Degree]]
! rowspan="2" | [[Degree]]
! rowspan="2" | [[Cent]]s
! rowspan="2" | [[Cent]]s
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| 1
| 1
| 200
| 200
| '''Major second (M2)'''<br>Diminished third (d3)
| '''Major second (M2)'''<br />Diminished third (d3)
| '''E'''<br>Fb
| '''E'''<br />Fb
|-
|-
| 2
| 2
| 400
| 400
| Major third (M3)<br>Diminished fourth (d4)
| Major third (M3)<br />Diminished fourth (d4)
| F#<br>Gb
| F#<br />Gb
|-
|-
| 3
| 3
| 600
| 600
| Augmented fourth (A4)<br>Diminished fifth (d5)
| Augmented fourth (A4)<br />Diminished fifth (d5)
| G#<br>Ab
| G#<br />Ab
|-
|-
| 4
| 4
| 800
| 800
| Augmented fifth (A5)<br>Minor sixth (m6)
| Augmented fifth (A5)<br />Minor sixth (m6)
| A#<br>Bb
| A#<br />Bb
|-
|-
| 5
| 5
| 1000
| 1000
| Augmented sixth (A6)<br>'''Minor seventh (m7)'''
| Augmented sixth (A6)<br />'''Minor seventh (m7)'''
| B#<br>'''C'''
| B#<br />'''C'''
|-
|-
| 6
| 6
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* mixed [[sagittal notation]] is identical to standard notation, but pure sagittal notation exchanges sharps (#) and flats (b) for sagittal sharp ([[File:Sagittal sharp.png]]) and sagittal flat ([[File:Sagittal flat.png]]) respectively.
* mixed [[sagittal notation]] is identical to standard notation, but pure sagittal notation exchanges sharps (#) and flats (b) for sagittal sharp ([[File:Sagittal sharp.png]]) and sagittal flat ([[File:Sagittal flat.png]]) respectively.


===Sagittal notation===
=== Sagittal notation ===
This notation is a subset of the notations for EDOs [[12edo#Sagittal notation|12]], [[18edo#Sagittal notation|18]], [[24edo#Sagittal notation|24]], [[36edo#Sagittal notation|36]], [[48edo#Sagittal notation|48]], [[60edo#Sagittal notation|60]], [[72edo#Sagittal notation|72]], and [[84edo#Sagittal notation|84]].
This notation is a subset of the notations for EDOs [[12edo#Sagittal notation|12]], [[18edo#Sagittal notation|18]], [[24edo#Sagittal notation|24]], [[36edo#Sagittal notation|36]], [[48edo#Sagittal notation|48]], [[60edo#Sagittal notation|60]], [[72edo#Sagittal notation|72]], and [[84edo#Sagittal notation|84]].
====Evo flavor====


==== Evo flavor ====
<imagemap>
<imagemap>
File:6-EDO_Evo_Sagittal.svg
File:6-EDO_Evo_Sagittal.svg
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Because it includes no Sagittal symbols, this Evo Sagittal notation is also a conventional notation.
Because it includes no Sagittal symbols, this Evo Sagittal notation is also a conventional notation.


====Revo flavor====
==== Revo flavor ====
 
<imagemap>
<imagemap>
File:6-EDO_Revo_Sagittal.svg
File:6-EDO_Revo_Sagittal.svg
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== Solfege ==
== Solfege ==
{| class="wikitable center-all"
{| class="wikitable center-all"
|+ Solfege of 6edo
|+ style="font-size: 105%;" | Solfege of 6edo
|-
! [[Degree]]
! [[Degree]]
! [[Cents]]
! [[Cents]]
! 12edo subset<br>standard [[solfege]]<br>(movable do)
! 12edo subset<br />standard [[solfege]]<br />(movable do)
! 12edo subset<br>[[uniform solfege]]<br>(2-3 vowels)
! 12edo subset<br />[[uniform solfege]]<br />(2–3 vowels)
|-
|-
| 0
| 0
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| 400
| 400
| Mi
| Mi
| Ma (M3)<br>Fo (d4)
| Ma (M3)<br />Fo (d4)
|-
|-
| 3
| 3
| 600
| 600
| Fi (A4)<br>Se (d5)
| Fi (A4)<br />Se (d5)
| Pa (A4)<br>Sha (d5)
| Pa (A4)<br />Sha (d5)
|-
|-
| 4
| 4
| 800
| 800
| Si (A5)<br>Le (m6)
| Si (A5)<br />Le (m6)
| Su (A5)<br>Fla (m6)
| Su (A5)<br />Fla (m6)
|-
|-
| 5
| 5
| 1000
| 1000
| Li (A6)<br>Te (m7)
| Li (A6)<br />Te (m7)
| Lu (A6)<br>Tha (m7)
| Lu (A6)<br />Tha (m7)
|-
|-
| 6
| 6
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{| class="commatable wikitable center-1 center-2 right-4 center-5"
{| class="commatable wikitable center-1 center-2 right-4 center-5"
|-
|-
! [[Harmonic limit|Prime<br>limit]]
! [[Harmonic limit|Prime<br />limit]]
! [[Ratio]]<ref group="note">Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Monzo]]
! [[Cent]]s
! [[Cent]]s
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| Tridecimal neutral second
| Tridecimal neutral second
|}
|}
<references group="note"/>


== Music ==
== Music ==
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; [[Chris Vaisvil]]
; [[Chris Vaisvil]]
* ''The Good Boundless'' (2011) – [https://www.chrisvaisvil.com/the-good-boundless/ blog] | [https://web.archive.org/web/20230530111053/http://micro.soonlabel.com/6edo/the-good-boundless-03.mp3 play]
* ''The Good Boundless'' (2011) – [https://www.chrisvaisvil.com/the-good-boundless/ blog] | [https://web.archive.org/web/20230530111053/http://micro.soonlabel.com/6edo/the-good-boundless-03.mp3 play]
== Notes ==
<references group="note" />


[[Category:6-tone scales]]
[[Category:6-tone scales]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Macrotonal]]
[[Category:Macrotonal]]
Retrieved from "https://en.xen.wiki/w/6edo"