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22edo: Difference between revisions

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Move temperament measures to RTT properties section
Some basic cleanup and thumbnail those very large figures
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| +7
| +7
|-
|-
! colspan="2" | [[nearest edomapping]]
! colspan="2" | [[Nearest edomapping]]
| 22
| 22
| 13
| 13
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| 2
| 2
|-
|-
! colspan="2" | [[fifthspan]]
! colspan="2" | [[Fifthspan]]
| 0
| 0
| +1
| +1
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As 22 is divisible by 11, a 22edo instrument can play any music in [[11edo|11edo]], in the same way that 12edo can play 6edo (the whole tone scale). 11-equal is interesting for sounding melodically very similar to 12-equal (whole steps, half steps and minor thirds in the familiar 1:2:3 ratio), but harmonically very different, in particular because it lacks perfect fifths/fourths and 5-limit major thirds/minor sixths. Similarly, 22edo is melodically similar to 24edo as both contain quarter-tones and minor, neutral, and major seconds; but 22edo offers much better all-around harmonies than 24. In [[Sagittal notation|Sagittal]], 11 can be notated as every other note of 22.
As 22 is divisible by 11, a 22edo instrument can play any music in [[11edo|11edo]], in the same way that 12edo can play 6edo (the whole tone scale). 11-equal is interesting for sounding melodically very similar to 12-equal (whole steps, half steps and minor thirds in the familiar 1:2:3 ratio), but harmonically very different, in particular because it lacks perfect fifths/fourths and 5-limit major thirds/minor sixths. Similarly, 22edo is melodically similar to 24edo as both contain quarter-tones and minor, neutral, and major seconds; but 22edo offers much better all-around harmonies than 24. In [[Sagittal notation|Sagittal]], 11 can be notated as every other note of 22.


== Notation ==
== Intervals ==
 
{| class="wikitable center-all right-2 left-3"
{| class="wikitable center-all right-2"
|-
|-
! Degree
! Degree
Line 106: Line 105:
| 0.000
| 0.000
| [[1/1]]
| [[1/1]]
|perfect unison
| perfect unison
|P1
| P1
|D
| D
|-
|-
| 1
| 1
| 54.545
| 54.545
| [[36/35]], [[34/33]], [[33/32]], [[32/31]]
| [[36/35]], [[34/33]], [[33/32]], [[32/31]]
|minor 2nd
| minor 2nd
|m2
| m2
|Eb
| Eb
|-
|-
| 2
| 2
| 109.091
| 109.091
| [[18/17]], [[17/16]], [[16/15]], [[15/14]]
| [[18/17]], [[17/16]], [[16/15]], [[15/14]]
|upminor 2nd
| upminor 2nd
|^m2
| ^m2
|^Eb
| ^Eb
|-
|-
| 3
| 3
| 163.636
| 163.636
| [[12/11]], [[11/10]], [[10/9]]
| [[12/11]], [[11/10]], [[10/9]]
|downmajor 2nd
| downmajor 2nd
|vM2
| vM2
|vE
| vE
|-
|-
| 4
| 4
| 218.182
| 218.182
| [[9/8]], [[17/15]], [[8/7]]
| [[9/8]], [[17/15]], [[8/7]]
|major 2nd
| major 2nd
|M2
| M2
|E
| E
|-
|-
| 5
| 5
| 272.737
| 272.737
| [[20/17]], [[7/6]]
| [[20/17]], [[7/6]]
|minor 3rd
| minor 3rd
|m3
| m3
|F
| F
|-
|-
| 6
| 6
| 327.273
| 327.273
| [[6/5]], [[17/14]], [[11/9]]
| [[6/5]], [[17/14]], [[11/9]]
|upminor 3rd
| upminor 3rd
|^m3
| ^m3
|^F
| ^F
|-
|-
| 7
| 7
| 381.818
| 381.818
| [[5/4]], [[96/77]]
| [[5/4]], [[96/77]]
|downmajor 3rd
| downmajor 3rd
|vM3
| vM3
|vF#
| vF#
|-
|-
| 8
| 8
| 436.364
| 436.364
| [[14/11]], [[9/7]], [[22/17]]
| [[14/11]], [[9/7]], [[22/17]]
|major 3rd
| major 3rd
|M3
| M3
|F#
| F#
|-
|-
| 9
| 9
| 490.909
| 490.909
| [[4/3]]
| [[4/3]]
|perfect fourth
| perfect fourth
|P4
| P4
|G
| G
|-
|-
| 10
| 10
| 545.455
| 545.455
| [[15/11]], [[11/8]]
| [[15/11]], [[11/8]]
|up-4th, dim 5th
| up-4th, dim 5th
|^4, d5
| ^4, d5
|^G, Ab
| ^G, Ab
|-
|-
| 11
| 11
| 600.000
| 600.000
| [[7/5]], [[24/17]], [[17/12]], [[10/7]]
| [[7/5]], [[24/17]], [[17/12]], [[10/7]]
|downaug 4th, updim 5th
| downaug 4th, updim 5th
|vA4, ^d5
| vA4, ^d5
|vG#, ^Ab
| vG#, ^Ab
|-
|-
| 12
| 12
| 654.545
| 654.545
| [[16/11]], [[22/15]]
| [[16/11]], [[22/15]]
|aug 4th, down-5th
| aug 4th, down-5th
|A4, v5
| A4, v5
|G#, vA
| G#, vA
|-
|-
| 13
| 13
| 709.091
| 709.091
| [[3/2]]
| [[3/2]]
|perfect 5th
| perfect 5th
|P5
| P5
|A
| A
|-
|-
| 14
| 14
| 763.636
| 763.636
| [[17/11]], [[14/9]], [[11/7]]
| [[17/11]], [[14/9]], [[11/7]]
|minor 6th
| minor 6th
|m6
| m6
|Bb
| Bb
|-
|-
| 15
| 15
| 818.182
| 818.182
| [[8/5]], [[77/48]]
| [[8/5]], [[77/48]]
|upminor 6th
| upminor 6th
|^m6
| ^m6
|^Bb
| ^Bb
|-
|-
| 16
| 16
| 872.727
| 872.727
| [[18/11]], [[28/17]], [[5/3]]
| [[18/11]], [[28/17]], [[5/3]]
|downmajor 6th
| downmajor 6th
|vM6
| vM6
|vB
| vB
|-
|-
| 17
| 17
| 927.273
| 927.273
| [[17/10]], [[12/7]]
| [[17/10]], [[12/7]]
|major 6th
| major 6th
|M6
| M6
|B
| B
|-
|-
| 18
| 18
| 981.818
| 981.818
| [[7/4]], [[30/17]], [[16/9]]
| [[7/4]], [[30/17]], [[16/9]]
|minor 7th
| minor 7th
|m7
| m7
|C
| C
|-
|-
| 19
| 19
| 1036.364
| 1036.364
| [[9/5]], [[11/6]], [[20/11]]
| [[9/5]], [[11/6]], [[20/11]]
|upminor 7th
| upminor 7th
|^m7
| ^m7
|^C
| ^C
|-
|-
| 20
| 20
| 1090.909
| 1090.909
| [[28/15]], [[15/8]], [[32/17]], [[17/9]]
| [[28/15]], [[15/8]], [[32/17]], [[17/9]]
|downmajor 7th
| downmajor 7th
|vM7
| vM7
|vC#
| vC#
|-
|-
| 21
| 21
| 1145.455
| 1145.455
| [[31/16]], [[64/33]], [[33/17]], [[35/18]]
| [[31/16]], [[64/33]], [[33/17]], [[35/18]]
|major 7th
| major 7th
|M7
| M7
|C#
| C#
|-
|-
| 22
| 22
| 1200.000
| 1200.000
| [[2/1]]
| [[2/1]]
|perfect octave
| perfect octave
|P8
| P8
|D
| D
|}
|}


<nowiki>*</nowiki> some simpler ratios, ordered by increasing size, based on treating 22-edo as a 2.3.5.7.11.17 subgroup temperament; other approaches are possible.
<nowiki>*</nowiki> some simpler ratios, ordered by increasing size, based on treating 22-edo as a 2.3.5.7.11.17 subgroup temperament; other approaches are possible.


== Notations ==
=== Superpyth/Porcupine Notation, Porcupine Notation and Pentatonic Notation ===
=== Superpyth/Porcupine Notation, Porcupine Notation and Pentatonic 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.


Another possible notation uses the porcupine generator to generate the notation as well. The 2nd and 7th are perfect, and the 4th and 5th are imperfect like the 3rd and 6th. This is the only way to use a heptatonic notation without additional accidentals. The keyboard runs D * * E * * F * * G * * * A * * B * * C * * D. The natural notes represent a chain of 2nds ABCDEFG.
Another possible notation uses the porcupine generator to generate the notation as well. The 2nd and 7th are perfect, and the 4th and 5th are imperfect like the 3rd and 6th. This is the only way to use a heptatonic notation without additional accidentals. The keyboard runs D * * E * * F * * G * * * A * * B * * C * * D. The natural notes represent a chain of 2nds ABCDEFG.
Line 1,252: Line 1,252:


=== Ups and Downs Notation ===
=== Ups and Downs Notation ===
[[File:Tibia_in_G_for_the_book-1.png|alt=Tibia in G for the book-1.png|thumb|Tibia in G (page 1)]]
[[File:Tibia_in_G_for_the_book-2.png|alt=Tibia in G for the book-2.png|thumb|Tibia in G (page 2)]]


Treating [[Ups_and_Downs_Notation|ups and downs]] as "fused" with sharps and flats, and never appearing separately:
Treating [[Ups and Downs Notation|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]]
Line 1,265: Line 1,267:
[[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]]


Paul Erlich's "Tibia" in G, with independent ups and downs:
Shown at right is [[Paul Erlich]]'s "Tibia" in G, with independent ups and downs.  
 
[[File:Tibia_in_G_for_the_book-1.png|alt=Tibia in G for the book-1.png|800x956px|Tibia in G for the book-1.png]]
 
[[File:Tibia_in_G_for_the_book-2.png|alt=Tibia in G for the book-2.png|800x889px|Tibia in G for the book-2.png]]
 
==Internal links==
<ul><li>[[William_Lynch's_Thoughts_on_Septimal_Harmony_and_22_EDO|William Lynch's Thoughts on Septimal Harmony and 22 EDO]]</li></ul>
 
==External links==
<ul><li>[http://lumma.org/tuning/erlich/erlich-decatonic.pdf Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament'']</li><li>[http://porcupinemusic.weebly.com/ "Porcupine Music" - Website Focused on the Development of 22 EDO music]</li></ul>


==References==
== Internal links ==
*Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]
* [[William_Lynch's_Thoughts_on_Septimal_Harmony_and_22_EDO|William Lynch's Thoughts on Septimal Harmony and 22 EDO]]


*Bosanquet, R.H.M. [http://www.webcitation.org/5kjJcrhEx ''On the Hindoo division of the octave, with additions to the theory of higher orders''], Proceedings of the Royal Society of London vol. 26, 1879, pp. 272-284. Reproduced in Tagore, Sourindro Mohun, ''Hindu Music from Various Authors'', Chowkhamba Sanskrit Series, Varanasi, India, 1965
== External links ==
* [http://lumma.org/tuning/erlich/erlich-decatonic.pdf Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament'']
* [http://porcupinemusic.weebly.com/ "Porcupine Music" - Website Focused on the Development of 22 EDO music]


==Music==
== References ==
# Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]
# Bosanquet, R.H.M. [http://www.webcitation.org/5kjJcrhEx ''On the Hindoo division of the octave, with additions to the theory of higher orders''], Proceedings of the Royal Society of London vol. 26, 1879, pp. 272-284. Reproduced in Tagore, Sourindro Mohun, ''Hindu Music from Various Authors'', Chowkhamba Sanskrit Series, Varanasi, India, 1965


== Music ==
* [https://soundcloud.com/overtoneshock/dose-of-familiarityode-to-microtonality-22-edo-studio-version Stephen Weigel · Dose Of Familiarity/Ode to Microtonality]
* [https://soundcloud.com/overtoneshock/dose-of-familiarityode-to-microtonality-22-edo-studio-version Stephen Weigel · Dose Of Familiarity/Ode to Microtonality]
* [https://soundcloud.com/metaclown/couples-therapy Couples' Therapy] by metaclown
* [https://soundcloud.com/metaclown/couples-therapy Couples' Therapy] by metaclown
Line 1,335: Line 1,332:
* [https://youtu.be/XS6wxEtttU8 "Unreachable Island"] (from his 2020 album "Realism")
* [https://youtu.be/XS6wxEtttU8 "Unreachable Island"] (from his 2020 album "Realism")
* [https://youtu.be/U5BZ2KncKs8 "Hysteria"] (from his 2017 album "Neutral Paradise")
* [https://youtu.be/U5BZ2KncKs8 "Hysteria"] (from his 2017 album "Neutral Paradise")
=== By Johann alias Circular17 ===
=== By Johann alias Circular17 ===
* [https://d.tube/v/circular17/QmWDXi7hgSwZF9kRUUXUkCjEz8BMepoxehM9mRhUecTubQ Good devil]
* [https://d.tube/v/circular17/QmWDXi7hgSwZF9kRUUXUkCjEz8BMepoxehM9mRhUecTubQ Good devil]
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