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12edo: Difference between revisions

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== Intervals ==
== Intervals ==
12edo intervals have standard names from classical music theory.
{| class="wikitable center-all"
{| class="wikitable right-1 right-2"
|+ Intervals of 12edo
! Steps
! rowspan="2" | [[Degree]]
! Cents
! rowspan="2" | [[Cent]]s
! Approximate JI Ratios*
! rowspan="2" | [[Interval region]]
! colspan="3" | Interval
! colspan="4" | Approximated [[JI]] intervals* ([[error]] in [[¢]])
!solfege
! rowspan="2" | Audio
! Audio
|-
! [[3-limit]]
! [[5-limit]]
! [[7-limit]]
! Other
|-
| 0
| 0
| Unison (prime)
| 1/1 (just)
|
|
|
| [[File:piano_0_1edo.mp3]]
|-
| 1
| 100
| Minor second
|
| [[25/24]] (+29.328)<br>[[16/15]] (-11.731)
| [[28/27]] (+37.039)<br>[[21/20]] (+15.533)<br>[[15/14]] (-19.443)
| [[18/17]] (+1.045)<br>[[17/16]] (-4.955)
| [[File:piano_1_12edo.mp3]]
|-
| 2
| 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]]
|-
| 3
| 300
| Minor third
| [[32/27]] (+5.865)
| [[6/5]] (-15.641)
| [[7/6]] (+33.129)<br>[[25/21]] (-1.847)
| [[19/16]] (+2.487)
| [[File:piano_1_4edo.mp3]]
|-
| 4
| 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]]
|-
| 5
| 500
| Fourth
| [[4/3]] (+1.955)
|
|
|
| [[File:piano_5_12edo.mp3]]
|-
| 6
| 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]]
|-
| 7
| 700
| Fifth
| [[3/2]] (-1.955)
|
|
|
| [[File:piano_7_12edo.mp3]]
|-
| 8
| 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]]
|-
| 9
| 900
| Major sixth
| [[27/16]] (-5.865)
| [[5/3]] (+15.641)
| [[42/25]] (+1.847)<br>[[12/7]] (-33.129)
| [[32/19]] (-2.487)
| [[File:piano_3_4edo.mp3]]
|-
| 10
| 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]]
|-
| 11
| 1100
| Major seventh
|
| [[15/8]] (+11.731)<br>[[48/25]] (-29.328)
| [[28/15]] (+19.443)<br>[[40/21]] (-15.533)<br>[[27/14]] (-37.039)
| [[32/17]] (+4.955)<br>[[17/9]] (-1.045)
| [[File:piano_11_12edo.mp3]]
|-
| 12
| 1200
| Octave
| [[2/1]] (just)
|
|
|
| [[File:piano_1_1edo.mp3]]
|}
 
<nowiki>*</nowiki> based on treating 12edo as a 2.3.5.7.17.19 subgroup temperament; other approaches are possible.
 
== Notation ==
12edo intervals and notes have standard names from classical music theory. This classical notation system, which was in use before 12edo with other tuning systems based on chains of fifths, is sometimes called the [[chain-of-fifths notation]] or extended Pythagorean notation.
 
{| class="wikitable center-all"
|+ Notation of 12edo
! rowspan="2" | [[Degree]]
! rowspan="2" | [[Cent]]s
! colspan="2" | [[Chain-of-fifths notation|Standard notation]]
|-
! [[5L 2s|Diatonic]] interval names
! Note names (on D)
|-
|-
| 0
| 0
| 0
| 0
| [[1/1]]
| '''Perfect unison (P1)'''
| unison
| '''D'''
| P1
| D
|Do
|[[File:piano_0_1edo.mp3]]
|-
|-
| 1
| 1
| 100
| 100
| [[15/14]], [[16/15]], [[17/16]], [[18/17]], [[21/20]], [[25/24]], [[28/27]]
| Augmented unison (A1)<br>Minor second (m2)
| aug 1sn, minor 2nd
| D#<br>Eb
| A1, m2
| D#, Eb
|Di / Ra
|[[File:piano_1_12edo.mp3]]
|-
|-
| 2
| 2
| 200
| 200
| [[8/7]], [[9/8]], [[10/9]], [[17/15]], [[19/17]], [[55/49]], [[64/57]]
| '''Major second (M2)'''<br>Diminished third (d3)
| major 2nd
| '''E'''<br>Fb
| M2
| E
|Re
|[[File:piano_1_6edo.mp3]]
|-
|-
| 3
| 3
| 300
| 300
| [[7/6]], [[6/5]], [[32/27]], [[19/16]], [[25/21]]
| Augmented second (A2)<br>'''Minor third (m3)'''
| minor 3rd
| E#<br>'''F'''
| m3
| F
|Ri / Me
|[[File:piano_1_4edo.mp3]]
|-
|-
| 4
| 4
| 400
| 400
| [[5/4]], [[9/7]], [[81/64]], [[63/50]], [[34/27]]
| Major third (M3)<br>Diminished fourth (d4)
| major 3rd
| F#<br>Gb
| M3
| F#
|Mi
|[[File:piano_1_3edo.mp3]]
|-
|-
| 5
| 5
| 500
| 500
| [[4/3]]
| '''Perfect fourth (P4)'''
| perfect 4th
| '''G'''
| P4
| G
|Fa
|[[File:piano_5_12edo.mp3]]
|-
|-
| 6
| 6
| 600
| 600
| [[7/5]], [[10/7]], [[17/12]], [[24/17]], [[99/70]]
| Augmented fourth (A4)<br>Diminished fifth (d5)
| aug 4th, dim 5th
| G#<br>Ab
| A4, d5
| G#, Ab
|Fi / Se
|[[File:piano_1_2edo.mp3]]
|-
|-
| 7
| 7
| 700
| 700
| [[3/2]]
| '''Perfect fifth (P5)'''
| perfect 5th
| P5
| A
| A
|So
|[[File:piano_7_12edo.mp3]]
|-
|-
| 8
| 8
| 800
| 800
| [[8/5]], [[14/9]], [[27/17]]
| Augmented fifth (A5)<br>Minor sixth (m6)
| minor 6th
| A#<br>Bb
| m6
|-
| Bb
| 9
|Si / Le
| 900
|[[File:piano_2_3edo.mp3]]
| '''Major sixth (M6)'''<br>Diminished seventh (d7)
| '''B'''<br>Cb
|-
| 10
| 1000
| Augmented sixth (A6)<br>'''Minor seventh (m7)'''
| B#<br>'''C'''
|-
| 11
| 1100
| Major seventh (M7)<br>Diminished octave (d8)
| C#<br>Db
|-
| 12
| 1200
| '''Perfect octave (P8)'''
| '''D'''
|}
 
In 12edo:
* [[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 12edo
! [[Degree]]
! [[Cents]]
! Standard [[solfege]]<br>(movable do)
! [[Uniform solfege]]<br>(2-3 vowels)
|-
| 0
| 0
| '''Do'''
| '''Da'''
|-
| 1
| 100
| Di (A1)<br>Ra (m2)
| Du (A1)<br>Fra (m2)
|-
| 2
| 200
| '''Re'''
| '''Ra'''
|-
| 3
| 300
| Ri (A2)<br>'''Me''' (m3)
| Ru (A2)<br>'''Na''' (m3)
|-
| 4
| 400
| Mi
| Ma (M3)<br>Fo (d4)
|-
| 5
| 500
| Fa
| Mu (A3)<br>Fa (P4)
|-
| 6
| 600
| Fi (A4)<br>Se (d5)
| Pa (A4)<br>Sha (d5)
|-
| 7
| 700
| '''So'''
| Sa
|-
| 8
| 800
| Si (A5)<br>Le (m6)
| Su (A5)<br>Fla (m6)
|-
|-
| 9
| 9
| 900
| 900
| [[5/3]], [[12/7]], [[32/19]]
| '''La'''
| major 6th
| La (M6)<br>Tho (d7)
| M6
| B
|La
|[[File:piano_3_4edo.mp3]]
|-
|-
| 10
| 10
| 1000
| 1000
| [[7/4]], [[9/5]], [[16/9]], [[25/14]]
| Li (A6)<br>'''Te''' (m7)
| minor 7th
| Lu (A6)<br>Tha (m7)
| m7
| C
|Li / Te
|[[File:piano_5_6edo.mp3]]
|-
|-
| 11
| 11
| 1100
| 1100
| [[15/8]], [[17/9]], [[28/15]], [[40/21]], [[48/25]], [[27/14]]
| Ti
| major 7th
| Ta (M7)<br>Do (d8)
| M7
| C#
|Ti
|[[File:piano_11_12edo.mp3]]
|-
|-
| 12
| 12
| 1200
| 1200
| [[2/1]]
| '''Do'''
| perfect 8ve
| '''Da'''
| P8
| D
|Do
|[[File:piano_1_1edo.mp3]]
|}
|}
<nowiki>*</nowiki> based on treating 12edo as a 2.3.5.7.17.19 subgroup temperament; other approaches are possible.


== JI approximation ==
== JI approximation ==
Retrieved from "https://en.xen.wiki/w/12edo"