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== Notation ==
== Notation ==
=== Ups and downs notation ===
=== Stein–Zimmermann–Gould notation ===
Since a sharp raises by three steps, 22edo is a good candidate for [[Stein–Zimmermann–Gould notation]], using sharps and flats with arrows similar to 29edo:
{{Sharpness-sharp3-szg}}
 
If arrows are taken to have their own layer of enharmonic spellings, then in some cases certain notes may be best spelled with double arrows.
 
=== Kite's ups and downs notation ===
Spoken as up, downsharp, sharp, upsharp, etc. Note that downsharp can be respelled as dup (double-up), and upflat as dud.
Spoken as up, downsharp, sharp, upsharp, etc. Note that downsharp can be respelled as dup (double-up), and upflat as dud.
{{sharpness-sharp3a}}
{{sharpness-sharp3a}}


Standard Pythagorean [[chain-of-fifths notation]] can be used alongside ups (^) and downs (v), where a single up or down alters the pitch of a note by 1 EDOstep (1\22). Note that E♭ and D♯ are different notes and that E♭ is significantly lower in pitch than D♯.
Standard Pythagorean [[chain-of-fifths notation]] can be used alongside ups (^) and downs (v), where a single up or down alters the pitch of a note by 1 edostep (1\22). Note that E♭ and D♯ are different notes and that E♭ is significantly lower in pitch than D♯.


{| class="wikitable right-1 right-2 center-3 center-4"
{| class="wikitable right-1 right-2 center-3 center-4"
|+ style="font-size: 105%;" | Notation of 22edo
|+ style="font-size: 105%;" | Notation of 22edo
|-
|-
! rowspan="2" | [[Degree]]
! rowspan="2" | [[Degree|#]]
! rowspan="2" | [[Cent]]s
! rowspan="2" | [[Cent]]s
! colspan="2" | [[Ups and downs notation|Ups and downs notation]]
! colspan="2" | [[Kite's ups and downs notation]]
|-
|-
! [[5L 2s|Diatonic Interval Names]]
! [[5L 2s|Diatonic interval names]]
! Note Names
! Note names
|-
|-
| 0
| 0
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| 1
| 1
| 54.5
| 54.5
| Minor second (m2)<br />Up unison (^1)
| Minor second (m2)<br>Up unison (^1)
| Eb<br />^D
| Eb<br>^D
|-
|-
| 2
| 2
| 109.1
| 109.1
| Upminor second (^m2)<br />Downaugmented unison (vA1)<br />Diminished third (d3)
| Upminor second (^m2)<br>Downaugmented unison (vA1)<br>Diminished third (d3)
| ^Eb<br />vD#<br />Fb
| ^Eb<br>vD#<br>Fb
|-
|-
| 3
| 3
| 163.6
| 163.6
| Downmajor second (vM2)<br />Augmented unison (A1)
| Downmajor second (vM2)<br>Augmented unison (A1)
| vE<br />D#
| vE<br>D#
|-
|-
| 4
| 4
| 218.2
| 218.2
| '''Major second (M2)'''<br />Upaugmented unison (^A1)<br />Downminor third (vm3)
| '''Major second (M2)'''<br>Upaugmented unison (^A1)<br>Downminor third (vm3)
| '''E'''<br />^D#<br />vF
| '''E'''<br>^D#<br />vF
|-
|-
| 5
| 5
| 272.7
| 272.7
| Upmajor second (^M2)<br />'''Minor third (m3)'''
| Upmajor second (^M2)<br>'''Minor third (m3)'''
| ^E<br />'''F'''
| ^E<br>'''F'''
|-
|-
| 6
| 6
| 327.3
| 327.3
| '''Upminor third (^m3)'''<br />Diminished fourth (d4)
| '''Upminor third (^m3)'''<br>Diminished fourth (d4)
| '''^F'''<br />Gb
| '''^F'''<br>Gb
|-
|-
| 7
| 7
| 381.8
| 381.8
| '''Downmajor third (vM3)'''<br />Augmented second (A2)<br />Updiminished fourth (^d4)
| '''Downmajor third (vM3)'''<br>Augmented second (A2)<br>Updiminished fourth (^d4)
| '''vF#'''<br />E#<br />^Gb
| '''vF#'''<br>E#<br>^Gb
|-
|-
| 8
| 8
| 436.4
| 436.4
| '''Major third (M3)'''<br />Upaugmented second (^A2)<br />Down fourth (v4)
| '''Major third (M3)'''<br>Upaugmented second (^A2)<br>Down fourth (v4)
| '''F#'''<br />^E#<br />vG
| '''F#'''<br>^E#<br>vG
|-
|-
| 9
| 9
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| 10
| 10
| 545.5
| 545.5
| Up fourth (^4)<br />Diminished fifth (d5)
| Up fourth (^4)<br>Diminished fifth (d5)
| ^G<br />Ab
| ^G<br>Ab
|-
|-
| 11
| 11
| 600.0
| 600.0
| Downaugmented fourth (vA4)<br />Updiminished fifth (^d5)
| Downaugmented fourth (vA4)<br>Updiminished fifth (^d5)
| vG#<br />^Ab
| vG#<br>^Ab
|-
|-
| 12
| 12
| 654.5
| 654.5
| Augmented fourth (A4)<br />Down fifth (v5)
| Augmented fourth (A4)<br>Down fifth (v5)
| G#<br />vA
| G#<br>vA
|-
|-
| 13
| 13
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| 14
| 14
| 763.6
| 763.6
| Up fifth (^5)<br />Minor sixth (m6)
| Up fifth (^5)<br>Minor sixth (m6)
| ^A<br />Bb
| ^A<br>Bb
|-
|-
| 15
| 15
| 818.2
| 818.2
| Downaugmented fifth (vA5)<br />Upminor sixth (^m6)
| Downaugmented fifth (vA5)<br>Upminor sixth (^m6)
| vA#<br />^Bb
| vA#<br>^Bb
|-
|-
| 16
| 16
| 872.7
| 872.7
| Augmented fifth (A5)<br />'''Downmajor sixth (vM6)'''
| Augmented fifth (A5)<br>'''Downmajor sixth (vM6)'''
| A#<br />'''vB'''
| A#<br>'''vB'''
|-
|-
| 17
| 17
| 927.3
| 927.3
| '''Major sixth (M6)'''<br />Upaugmented fifth (^A5)<br />Downminor seventh (vm7)
| '''Major sixth (M6)'''<br>Upaugmented fifth (^A5)<br>Downminor seventh (vm7)
| '''B'''<br />^A#<br />vC
| '''B'''<br>^A#<br />vC
|-
|-
| 18
| 18
| 981.8
| 981.8
| '''Minor seventh (m7)'''<br />Upmajor sixth (^M6)<br />Downdiminished octave (vd8)
| '''Minor seventh (m7)'''<br>Upmajor sixth (^M6)<br>Downdiminished octave (vd8)
| '''C'''<br />^B<br />vDb
| '''C'''<br>^B<br>vDb
|-
|-
| 19
| 19
| 1036.4
| 1036.4
| '''Upminor seventh (^m7)'''<br />Diminished octave (d8)
| '''Upminor seventh (^m7)'''<br>Diminished octave (d8)
| '''^C'''<br />Db
| '''^C'''<br>Db
|-
|-
| 20
| 20
| 1090.9
| 1090.9
| Downmajor seventh (vM7)<br />Updiminished octave (^d8)<br />Augmented sixth (A6)
| Downmajor seventh (vM7)<br>Updiminished octave (^d8)<br>Augmented sixth (A6)
| vC#<br />^Db<br />B#
| vC#<br>^Db<br>B#
|-
|-
| 21
| 21
| 1145.5
| 1145.5
| Major seventh (M7)<br />Down octave (v8)
| Major seventh (M7)<br>Down octave (v8)
| C#<br />vD
| C#<br>vD
|-
|-
| 22
| 22
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|}
|}


Treating [[Ups and downs notation|ups and downs]] as "fused" with sharps and flats, and never appearing separately:
Treating ups and downs as "fused" with sharps and flats, and never appearing separately:


[[File:Tibia_22edo_ups_and_downs_guide_1.png|alt=Tibia 22edo ups and downs guide 1.png|800x147px|Tibia 22edo ups and downs guide 1.png]]
[[File:Tibia_22edo_ups_and_downs_guide_1.png|alt=Tibia 22edo ups and downs guide 1.png|800x147px|Tibia 22edo ups and downs guide 1.png]]
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[[File:Tibia_22edo_guide_D_major.png|alt=Tibia 22edo guide D major.png|800x68px|Tibia 22edo guide D major.png]]
[[File:Tibia_22edo_guide_D_major.png|alt=Tibia 22edo guide D major.png|800x68px|Tibia 22edo guide D major.png]]
Alternatively, arrow accidentals from [[Helmholtz–Ellis notation]] can be used instead of independent ups and downs:
{{Sharpness-sharp3}}
If arrows are taken to have their own layer of enharmonic spellings, then in some cases certain notes may be best spelled with double arrows.


Shown below is [[Paul Erlich]]'s "Tibia" in G, with independent ups and downs.
Shown below is [[Paul Erlich]]'s "Tibia" in G, with independent ups and downs.
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=== Sagittal notation ===
=== Sagittal notation ===
This notation uses the same sagittal sequence as EDOs [[15edo#Sagittal notation|15]] and [[29edo#Sagittal notation|29]], is a subset of the notations for EDOs [[44edo#Sagittal notation|44]] and [[66edo#Sagittal notation|66]], and is a superset of the notation for [[11edo#Sagittal notation|11-EDO]].
This notation uses the same sagittal sequence as edos [[15edo #Sagittal notation|15]] and [[29edo #Sagittal notation|29]], is a subset of the notations for edos [[44edo #Sagittal notation|44]] and [[66edo #Sagittal notation|66]], and is a superset of the notation for [[11edo #Sagittal notation|11edo]].


==== Evo flavor ====
==== Evo flavor ====
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[[File:22edo Sagittal.png|800px]]
[[File:22edo Sagittal.png|800px]]


=== Superpyth/Porcupine notation ===
=== Superpyth/porcupine notation ===
Superpyth/Porcupine notation is a system arising from both superpyth and porcupine temperament. It categorizes each 22edo interval as major and minor of one or both of those temperaments. s indicates superpyth and p indicates porcupine. Because p now represents porcupine and not perfect, P in perfect intervals is no longer used in this system. Instead the number is used without P and is read as either just the number or "Natural". Example: P5 becomes 5 or N5 = Perfect fifth becomes Natural fifth.
Superpyth/porcupine notation is a system arising from both superpyth and porcupine temperament. It categorizes each 22edo interval as major and minor of one or both of those temperaments. s indicates superpyth and p indicates porcupine. Because p now represents porcupine and not perfect, P in perfect intervals is no longer used in this system. Instead the number is used without P and is read as either just the number or "Natural". Example: P5 becomes 5 or N5 = Perfect fifth becomes Natural fifth.


=== Porcupine notation ===
=== Porcupine notation ===
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! [[Degree]]
! [[Degree]]
! [[Cent]]s
! [[Cent]]s
! colspan="2" | Superpyth/Porcupine
! colspan="2" | Superpyth/porcupine
! colspan="3" | Porcupine (Onyx)
! colspan="3" | Porcupine (Onyx)
! colspan="3" |Porcupine (Zarlino)
! colspan="3" | Porcupine (Zarlino)
! colspan="3" | Pentatonic
! colspan="3" | Pentatonic
! colspan="3" | Decatonic
! colspan="3" | Decatonic
! colspan="3" | [[Ups and downs notation|Ups and Downs]]
! colspan="3" | [[Ups and downs notation|Ups and downs]]
! colspan="3" | [[SKULO interval names]]
! colspan="3" | [[SKULO interval names]]
|-
|-
| 0
| 0
| 0
| 0
| Natural Unison
| Natural unison
| 1
| 1
| perfect unison
| perfect unison
| P1
| P1
| D
| D
|perfect unison
| perfect unison
|P1
| P1
|C
| C
| perfect unison
| perfect unison
| P1
| P1
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| A1
| A1
| D#
| D#
|augmented unison
| augmented unison
|A1
| A1
|C#
| C#
| aug unison
| aug unison
| A1
| A1
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| d2
| d2
| Eb
| Eb
|minor second
| minor second
|m2
| m2
|Db
| Db
| double-aug unison,<br />double-dim sub3rd
| double-aug unison,<br>double-dim sub3rd
| AA1,<br />dds3
| AA1,<br>dds3
| Dx,<br />Fb<span style="vertical-align: super;">3</span>
| Dx,<br>Fb<span style="vertical-align: super;">3</span>
| natural 2nd
| natural 2nd
| N2
| N2
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| P2
| P2
| E
| E
|narrow major second
| narrow major second
|nM2
| nM2
|D
| D
| dim sub3rd
| dim sub3rd
| ds3
| ds3
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| 4
| 4
| 218
| 218
| (s/p) Major second
| (s/p) major second
| M2
| M2
| aug 2nd
| aug 2nd
| A2
| A2
| E#
| E#
|wide major second
| wide major second
|WM2
| WM2
|D#
| D#
| minor sub3rd
| minor sub3rd
| ms3
| ms3
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| d3
| d3
| Fb
| Fb
|wolf third
| wolf third
|w3
| w3
|Ebb
| Ebb
| major sub3rd
| major sub3rd
| Ms3
| Ms3
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| m3
| m3
| F
| F
|minor third
| minor third
|m3
| m3
|Eb
| Eb
| aug sub3rd
| aug sub3rd
| As3
| As3
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| 7
| 7
| 382
| 382
| p-Major third
| p-major third
| pM3
| pM3
| major 3rd
| major 3rd
| M3
| M3
| F#
| F#
|major third
| major third
|M3
| M3
|E
| E
| double-aug sub3rd,<br />double-dim 4thoid
| double-aug sub3rd,<br>double-dim 4thoid
| AAs3,<br />dd4d
| AAs3,<br>dd4d
| Fx,<br />Gbb
| Fx,<br>Gbb
| natural 4th
| natural 4th
| N4
| N4
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| 8
| 8
| 436
| 436
| s-Major third
| s-major third
| sM3
| sM3
| aug 3rd, dim 4th
| aug 3rd, dim 4th
| A3, d4
| A3, d4
| Fx, Gb
| Fx, Gb
|augmented third
| augmented third
|A3
| A3
|E#
| E#
| dim 4thoid
| dim 4thoid
| d4d
| d4d
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| 9
| 9
| 491
| 491
| Natural Fourth
| Natural fourth
| 4, N4
| 4, N4
| minor 4th
| minor 4th
| m4
| m4
| G
| G
|perfect fourth
| perfect fourth
|P4
| P4
|F
| F
| perfect 4thoid
| perfect 4thoid
| P4d
| P4d
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| 10
| 10
| 545
| 545
| p-Major fourth, s-dim fifth
| p-major fourth, s-dim fifth
| pM4, sd5
| pM4, sd5
| major 4th
| major 4th
| M4
| M4
| G#
| G#
|wolf fourth
| wolf fourth
|w4
| w4
|F#
| F#
| aug 4thoid
| aug 4thoid
| A4d
| A4d
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| 11
| 11
| 600
| 600
| p-Augmented Fourth,<br />p-diminished Fifth,<br />Half-Octave
| p-augmented fourth,<br>p-diminished fifth,<br>half-octave
| A4, HO
| A4, HO
| aug 4th, <br />dim 5th
| aug 4th, <br>dim 5th
| A4, d5
| A4, d5
| Gx, <br />Abb
| Gx, <br>Abb
|augmented fourth, diminished fifth
| augmented fourth, diminished fifth
|A4, d5
| A4, d5
|F##, Gbb
| F##, Gbb
| double-aug 4thoid,<br />double-dim 5thoid
| double-aug 4thoid,<br>double-dim 5thoid
| AA4d, <br />dd5d
| AA4d, <br>dd5d
| Gx, <br />Abb
| Gx, <br>Abb
| natural 6th
| natural 6th
| N6
| N6
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| vA4, ^d5
| vA4, ^d5
| vG#, ^Ab
| vG#, ^Ab
| comma-narrow augmented 4th<br />comma-wide diminished 5th
| comma-narrow augmented 4th<br>comma-wide diminished 5th
| kA4<br />Kd5
| kA4<br>Kd5
| kG#, KAb
| kG#, KAb
|-
|-
| 12
| 12
| 655
| 655
| p-minor Fifth, s-aug Fourth
| p-minor fifth, s-aug fourth
| pm5, sA4
| pm5, sA4
| minor 5th
| minor 5th
| m5
| m5
| Ab
| Ab
|wolf fifth
| wolf fifth
|w5
| w5
|Gb
| Gb
| dim 5thoid
| dim 5thoid
| d5d
| d5d
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| 13
| 13
| 709
| 709
| Natural Fifth
| Natural fifth
| 5, N5
| 5, N5
| major 5th
| major 5th
| M5
| M5
| A
| A
|perfect fifth
| perfect fifth
|P5
| P5
|G
| G
| perfect 5thoid
| perfect 5thoid
| P5d
| P5d
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| A5, d6
| A5, d6
| A#, Bbb
| A#, Bbb
|diminished sixth
| diminished sixth
|d6
| d6
|Abb
| Abb
| aug 5thoid
| aug 5thoid
| A5d
| A5d
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| m6
| m6
| Bb
| Bb
|minor sixth
| minor sixth
|m6
| m6
|Ab
| Ab
| double-aug 5thoid,<br />double-dim sub7th
| double-aug 5thoid,<br>double-dim sub7th
| AA5d,<br />dds7
| AA5d,<br>dds7
| Ax,<br />Cb<span style="vertical-align: super;">3</span>
| Ax,<br>Cb<span style="vertical-align: super;">3</span>
| flat 8th
| flat 8th
| f8
| f8
Line 918: Line 918:
| 16
| 16
| 873
| 873
| p-Major sixth
| p-major sixth
| pM6
| pM6
| major 6th
| major 6th
| M6
| M6
| B
| B
|major sixth
| major sixth
|M6
| M6
|A
| A
| dim sub7th
| dim sub7th
| ds7
| ds7
Line 941: Line 941:
| 17
| 17
| 927
| 927
| s-Major sixth
| s-major sixth
| sM6
| sM6
| aug 6th
| aug 6th
| A6
| A6
| B#
| B#
|wolf sixth
| wolf sixth
|w6
| w6
|A#
| A#
| minor sub7th
| minor sub7th
| ms7
| ms7
Line 969: Line 969:
| d7
| d7
| Cb
| Cb
|narrow minor seventh
| narrow minor seventh
|nm7
| nm7
|Bbb
| Bbb
| major sub7th
| major sub7th
| Ms7
| Ms7
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| 19
| 19
| 1036
| 1036
| p-Major seventh
| p-major seventh
| pM7
| pM7
| perfect 7th
| perfect 7th
| P7
| P7
| C
| C
|wide minor seventh
| wide minor seventh
|Wm7
| Wm7
|Bb
| Bb
| aug sub7th
| aug sub7th
| As7
| As7
Line 1,010: Line 1,010:
| 20
| 20
| 1091
| 1091
| p-Augmented seventh
| p-augmented seventh
| pA7
| pA7
| aug 7th
| aug 7th
| A7
| A7
| C#
| C#
|major seventh
| major seventh
|M7
| M7
|B
| B
| double-aug sub7th,<br />double-dim octave
| double-aug sub7th,<br>double-dim octave
| AAs7,<br />dd8
| AAs7,<br>dd8
| Cx,<br />Dbb
| Cx,<br>Dbb
| natural 10th
| natural 10th
| N10
| N10
Line 1,033: Line 1,033:
| 21
| 21
| 1145
| 1145
| s-Major seventh
| s-major seventh
| sM7
| sM7
| dim 8ve
| dim 8ve
| d8
| d8
| Db
| Db
|diminished octave
| diminished octave
|d8
| d8
|Cb
| Cb
| dim octave
| dim octave
| d8
| d8
Line 1,061: Line 1,061:
| P8
| P8
| D
| D
|perfect octave
| perfect octave
|P8
| P8
|C
| C
| perfect octave
| perfect octave
| P8
| P8
Line 1,547: Line 1,547:


== Instruments ==
== Instruments ==
== Scordatura piano ==
Although it does not allow for much in the way of modulation, it is possible to make some music using a piano tuned to a 12 note subset of 22edo, as shown by [[Juhani Nuorvala]]'s [https://www.youtube.com/watch?v=raRiTvogBBA ''Improvisations on a piano tuned to 22edo''] (2026).
=== Keyboards ===
=== Keyboards ===
[[File:22-tone halberstadt layout.png|alt=|frameless]]
[[File:22-tone halberstadt layout.png|alt=|frameless]]
Retrieved from "https://en.xen.wiki/w/22edo"