6edo: Difference between revisions

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 == Intervals ==
-{| class="wikitable right-1 right-2"
+{| class="wikitable center-all"
-! Steps
+|+ Intervals of 6edo
-! Cents
+! rowspan="2" | [[Degree]]
-! colspan="3" | Interval
+! rowspan="2" | [[Cent]]s
-! Approximate JI Ratios*
+! rowspan="2" | [[Interval region]]
+! colspan="4" | Approximated [[JI]] intervals* ([[error]] in [[¢]])
+! rowspan="2" | Audio
+|-
+! [[3-limit]]
+! [[5-limit]]
+! [[7-limit]]
+! Other
+|-
+| 0
+| 0
+| Unison (prime)
+| 1/1 (just)
+|
+|
+|
+| [[File:piano_0_1edo.mp3]]
+|-
+| 1
+| 200
+| Major second
+| [[9/8]] (-3.910)
+| [[10/9]] (+17.596)
+| [[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)
+| [[File:piano_1_6edo.mp3]]
+|-
+| 2
+| 400
+| Major third
+| [[81/64]] (-7.820)
+| [[5/4]] (+13.686)
+| [[63/50]] (-0.108)<br>[[9/7]] (-35.084)
+| [[34/27]] (+0.910)
+| [[File:piano_1_3edo.mp3]]
+|-
+| 3
+| 600
+| Tritone
+|
+|
+| [[7/5]] (+17.488)<br>[[10/7]] (-17.488)
+| [[24/17]] (+3.000)<br>[[99/70]] (-0.088)<br>[[17/12]] (-3.000)
+| [[File:piano_1_2edo.mp3]]
+|-
+| 4
+| 800
+| Minor sixth
+| [[128/81]] (+7.820)
+| [[8/5]] (-13.686)
+| [[14/9]] (+35.084)<br>[[100/63]] (+0.108)
+| [[27/17]] (-0.910)
+| [[File:piano_2_3edo.mp3]]
+|-
+| 5
+| 1000
+| Minor seventh
+| [[16/9]] (+3.910)
+| [[9/5]] (-17.596)
+| [[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)
+| [[File:piano_5_6edo.mp3]]
+|-
+| 6
+| 1200
+| Octave
+| [[2/1]] (just)
+|
+|
+|
+| [[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 ==
+{| class="wikitable center-all"
+|+ Notation of 6edo
+! rowspan="2" | [[Degree]]
+! rowspan="2" | [[Cent]]s
+! colspan="2" | [[12edo]] [[subset notation]]
+|-
+! [[5L 2s|Diatonic]] interval names
+! Note names (on D)
+|-
+| 0
+| 0
+| '''Perfect unison (P1)'''
+| '''D'''
+|-
+| 1
+| 200
+| '''Major second (M2)'''<br>Diminished third (d3)
+| '''E'''<br>Fb
+|-
+| 2
+| 400
+| Major third (M3)<br>Diminished fourth (d4)
+| F#<br>Gb
+|-
+| 3
+| 600
+| Augmented fourth (A4)<br>Diminished fifth (d5)
+| G#<br>Ab
+|-
+| 4
+| 800
+| Augmented fifth (A5)<br>Minor sixth (m6)
+| A#<br>Bb
+|-
+| 5
+| 1000
+| Augmented sixth (A6)<br>'''Minor seventh (m7)'''
+| B#<br>'''C'''
+|-
+| 6
+| 1200
+| '''Perfect octave (P8)'''
+| '''D'''
+|}
+In 6edo:
+* [[ups and downs notation]] is identical to standard notation;
+* 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.
+== Solfege ==
+{| class="wikitable center-all"
+|+ Solfege of 6edo
+! [[Degree]]
+! [[Cents]]
+! 12edo subset<br>standard [[solfege]]<br>(movable do)
+! 12edo subset<br>[[uniform solfege]]<br>(2-3 vowels)
 |-
 | 0
 | 0
-| unison
+| Do
-| P1
+| Da
-| D
-| [[1/1]]
 |-
 | 1
 | 200
-| major 2nd
+| Re
-| M2
+| Ra
-| E
-| [[8/7]], [[9/8]], [[10/9]]
 |-
 | 2
 | 400
-| major 3rd
+| Mi
-| M3
+| Ma (M3)<br>Fo (d4)
-| F#
-| [[5/4]], [[9/7]]
 |-
 | 3
 | 600
-| aug 4th, dim 5th
+| Fi (A4)<br>Se (d5)
-| A4, d5
+| Pa (A4)<br>Sha (d5)
-| G#, Ab
-| [[7/5]], [[10/7]]
 |-
 | 4
 | 800
-| minor 6th
+| Si (A5)<br>Le (m6)
-| m6
+| Su (A5)<br>Fla (m6)
-| Bb
-| [[8/5]], [[14/9]]
 |-
 | 5
 | 1000
-| minor 7th
+| Li (A6)<br>Te (m7)
-| m7
+| Lu (A6)<br>Tha (m7)
-| C
-| [[7/4]], [[9/5]], [[16/9]]
 |-
 | 6
 | 1200
-| perfect 8ve
+| Do
-| P8
+| Da
-| D
-| [[2/1]]
 |}
-<nowiki>*</nowiki> based on treating 6edo as a 2.5.7.9 subgroup temperament; other approaches are possible.
 == Regular temperament properties ==