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== Approximation to JI ==
[[File:22ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 17-limit intervals approximated in 22edo]]
===Interval mappings===
{{Q-odd-limit intervals|22}}


==Defining features ==
Treating [[Ups and Downs Notation|ups and downs]] as "fused" with sharps and flats, and never appearing separately:


===Septimal vs syntonic comma===
[[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]]
Possibly the most striking characteristic of 22edo to those not used to it is that it does '''not''' temper out the syntonic comma of 81/80, and therefore is not a system of [[meantone]] temperament. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12edo, 19edo, and 31edo do not distinguish, such as the two whole tones 9/8 and 10/9. Indeed, these distinctions are exaggerated in comparison to 5-limit JI and many more accurate temperaments such as [[34edo]], [[41edo]] and [[53edo]].


The diatonic scale it produces is instead derived from [[superpyth]] temperament, which despite having the same melodic structure as meantone's diatonic scale (LLsLLLs or, [[5L 2s]]), has thirds approximating 9/7 and 7/6, rather than 5/4 and 6/5. This means that the septimal comma of 64/63 vanishes, rather than the syntonic comma of 81/80, which is one of the core features of 22et. Superpyth is melodically interesting for having a quasi-equal pentatonic scale (as the large whole tone and subminor third are rather close in size) and a more uneven heptatonic scale, as compared with 12et and other meantone systems: step patterns 4 4 5 4 5 and 4 4 1 4 4 4 1, respectively.
Treating ups and downs as independent of sharps and flats, and sometimes appearing separately:


=== Porcupine comma ===
[[File:Tibia_22edo_ups_and_downs_guide_2.png|alt=Tibia 22edo ups and downs guide 2.png|800x150px|Tibia 22edo ups and downs guide 2.png]]
It additionally tempers out the porcupine comma or maximal diesis of 250/243, which means that 22edo [[support]]s [[porcupine]] temperament. The generator for porcupine is a flat minor whole tone of [[10/9]], two of which is a slightly sharp [[6/5]], and three of which is a slightly flat [[4/3]], implying the existence of an equal-step tetrachord, which is characteristic of porcupine. Porcupine is notable for being the 5-limit temperament lowest in [[badness]] which is ''not'' approximated by the familiar 12-tone equal temperament, and as such represents one excellent point of departure for examining the harmonic properties of 22edo. It forms [[mos scale]]s of 7 and 8, which in 22edo are tuned respectively as 4 3 3 3 3 3 3 and 3 1 3 3 3 3 3 3 (and their respective modes).


===5-limit commas===
A D downmajor scale with mandatory accidentals (no key signature), with minimal accidentals (only when needed to override the key signature), and with independent ups and downs.
Other 5-limit commas 22edo tempers out include the diaschisma, [[2048/2025]] and the magic comma or small diesis, [[3125/3072]]. In a diaschismic system, such as 12et or 22et, the diatonic tritone [[45/32]], which is a major third above a major whole tone representing [[9/8]], is equated to its inverted form, [[64/45]]. That the magic comma is tempered out means that 22et is a magic system, where five major thirds make up a perfect fifth.


===7-limit commas ===
[[File:Tibia_22edo_guide_D_major.png|alt=Tibia 22edo guide D major.png|800x68px|Tibia 22edo guide D major.png]]
In the 7-limit 22edo tempers out certain commas also tempered out by 12et; this relates 12et to 22 in a way different from the way in which meantone systems are akin to it. Both [[50/49]], (jubilee comma), and 64/63, (septimal comma), are tempered out in both systems. Hence because of 50/49 they both equate the two septimal tritones of 7/5 and 10/7, and because of 64/63 they both do not distinguish between a dominant seventh chord and an otonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the [[septimal kleisma]], so that the septimal kleisma augmented triad is a chord of 22et, as it also is of any meantone tuning. A septimal comma not tempered out by 12et which 22et does temper out is 1728/1715, the [[1728/1715|orwell comma]]; and the [[orwell tetrad]] is also a chord of 22et.


=== 11-limit commas===
Alternatively, arrow accidentals from [[Helmholtz–Ellis notation]] can be used instead of independent ups and downs:
In the 11-limit, 22edo tempers out the [[quartisma]], leading to a stack of five 33/32 quartertones being equated with one 7/6 subminor third. This is a trait which, while shared with [[24edo]], is surprisingly ''not'' shared with a number of other relatively small edos such as [[17edo]], [[26edo]] and [[34edo]]. In fact, not even the famous [[53edo]] has this property – although it should be noted that the related [[159edo]] ''does''.


===Other features===
{{Sharpness-sharp3}}
The 164¢ "flat minor whole tone" is a key interval in 22edo, in part because it functions as no less than three different consonant ratios in the [[11-limit]]: 10/9, 11/10, and 12/11. It is thus extremely ambiguous and flexible. The trade-off is that it is very much in the cracks of the 12-equal piano, and so for most 12-equal listeners, it takes some getting used to. Simple translations of 5-limit music into 22edo can sound very different, with a more complex harmonic quality inevitably arising. 22edo does not contain a neutral third but both the 5-limit thirds have a "neutral-like" quality since they are tempered closer together rather than farther apart as in 12edo.


22edo also supports the [[orwell]] temperament, which uses the septimal subminor third as a generator (5 degrees) and forms mos scales with step patterns 3 2 3 2 3 2 3 2 2 and 1 2 2 1 2 2 1 2 2 1 2 2 2. Harmonically, orwell can be tuned more accurately in other temperaments, such as [[31edo]], [[53edo]] and [[84edo]]. But 22edo orwell has a leg-up on the others melodically, as the large and small steps of orwell[9] are easier to distinguish in 22.
Shown below is [[Paul Erlich]]'s "Tibia" in G, with independent ups and downs.


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]], 11 can be notated as every other note of 22.
<gallery mode="slideshow">
File:Tibia in G CORRECTED-1.png|alt=Tibia in G CORRECTED-1.png|Tibia in G (page 1)
File:Tibia in G CORRECTED-2.png|alt=Tibia in G CORRECTED-2.png|Tibia in G (page 2)
</gallery>


==Regular temperament properties==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo| 35 -22 }}
|[{{val| 22 35 }}]
|−2.25
|2.25
|4.12
|-
|2.3.5
|250/243, 2048/2025
|[{{val| 22 35 51 }}]
| −0.86
|2.70
|4.94
|-
|2.3.5.7
| 50/49, 64/63, 245/243
|[{{val| 22 35 51 62 }}]
|−1.80
|2.85
|5.23
|-
|2.3.5.7.11
|50/49, 55/54, 64/63, 99/98
| [{{val| 22 35 51 62 76 }}]
|−1.11
|2.90
|5.33
|-
|2.3.5.7.11.17
|50/49, 55/54, 64/63, 85/84, 99/98
|[{{val| 22 35 51 62 76 90 }}]
|−1.09
| 2.65
|4.87
|}
22et is lower in relative error than any previous equal temperaments in the 11-limit. The next equal temperament that does better in this subgroup is [[31edo|31]]. 22et is even more prominent in the 2.3.5.7.11.17 subgroup, and the next equal temperament that does better in this subgroup is [[46edo|46]].
===Uniform maps ===
{{Uniform map|13|21.5|22.5}}
===Commas===
22et [[tempers out]] the following [[commas]]. (Note: This assumes the [[val]] {{val| 22 35 51 62 76 81 }}.)
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
![[Harmonic limit|Prime <br>limit]]
![[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
![[Monzo]]
![[Cents]]
![[Color name]]
!Name
|-
|3
|<abbr title="34359738368/31381059609">(22 digits)</abbr>
|{{monzo| 35 -22 }}
|156.98
|Trisawa
|22-comma
|-
|5
|[[250/243]]
|{{monzo| 1 -5 3 }}
|49.17
|Triyo
|Porcupine comma, maximal diesis
|-
|5
|[[3125/3072]]
|{{monzo| -10 -1 5 }}
|29.61
| Laquinyo
|Magic comma
|-
|5
|[[2048/2025]]
|{{monzo| 11 -4 -2 }}
|19.55
| Sagugu
|Diaschisma
|-
|5
|[[2109375/2097152|(14 digits)]]
|{{monzo| -21 3 7 }}
|10.06
|Lasepyo
|[[Semicomma]]
|-
|5
|<abbr title="4294967296/4271484375">(20 digits)</abbr>
|{{monzo| 32 -7 -9 }}
|9.49
|Sasa-tritrigu
|[[Escapade comma]]
|-
|5
|<abbr title="9010162353515625/9007199254740992">(32 digits)</abbr>
|{{monzo| -53 10 16 }}
|0.57
|Quadla-quadquadyo
|[[Kwazy comma]]
|-
|7
|[[50/49]]
|{{monzo| 1 0 2 -2 }}
|34.98
|Biruyo
|Jubilisma
|-
|7
|[[64/63]]
|{{monzo| 6 -2 0 -1 }}
|27.26
| Ru
|Septimal comma
|-
|7
|[[875/864]]
|{{monzo| -5 -3 3 1 }}
| 21.90
|Zotriyo
|Keema
|-
|7
|[[2430/2401]]
|{{monzo| 1 5 1 -4 }}
|20.79
|Quadru-ayo
|Nuwell comma
|-
|7
|[[245/243]]
|{{monzo| 0 -5 1 2 }}
|14.19
|Zozoyo
|Sensamagic comma
|-
|7
|[[1728/1715]]
|{{monzo| 6 3 -1 -3 }}
|13.07
|Triru-agu
|Orwellisma
|-
|7
|[[225/224]]
|{{monzo| -5 2 2 -1 }}
| 7.71
|Ruyoyo
|Marvel comma
|-
| 7
|[[10976/10935]]
|{{monzo| 5 -7 -1 3 }}
|6.48
|Trizo-agu
| Hemimage comma
|-
|7
|[[6144/6125]]
|{{monzo| 11 1 -3 -2 }}
|5.36
|Saruru-atrigu
|Porwell comma
|-
|7
|[[65625/65536]]
|{{monzo| -16 1 5 1 }}
|2.35
|Lazoquinyo
|Horwell comma
|-
|7
|<abbr title="420175/419904">(12 digits)</abbr>
|{{monzo| -6 -8 2 5 }}
|1.12
|Quinzo-ayoyo
|[[Wizma]]
|-
|11
|[[99/98]]
|{{monzo| -1 2 0 -2 1 }}
|17.58
| Loruru
|Mothwellsma
|-
|11
|[[100/99]]
|{{monzo| 2 -2 2 0 -1 }}
|17.40
|Luyoyo
|Ptolemisma
|-
|11
|[[121/120]]
|{{monzo| -3 -1 -1 0 2 }}
|14.37
|Lologu
|Biyatisma
|-
|11
|[[176/175]]
|{{monzo| 4 0 -2 -1 1 }}
|9.86
|Lorugugu
|Valinorsma
|-
|11
|[[896/891]]
|{{monzo| 7 -4 0 1 -1 }}
|9.69
|Saluzo
|Pentacircle comma
|-
|11
|[[65536/65219]]
|{{monzo| 16 0 0 -2 -3 }}
|8.39
|Satrilu-aruru
|Orgonisma
|-
| 11
|[[385/384]]
|{{monzo| -7 -1 1 1 1 }}
|4.50
|Lozoyo
|Keenanisma
|-
|11
|[[540/539]]
|{{monzo| 2 3 1 -2 -1 }}
|3.21
|Lururuyo
|Swetisma
|-
|11
|[[4000/3993]]
|{{monzo| 5 -1 3 0 -3 }}
|3.03
|Triluyo
|Wizardharry comma
|-
|11
|[[9801/9800]]
|{{monzo| -3 4 -2 -2 2 }}
|0.18
|Bilorugu
| Kalisma
|-
|13
|[[65/64]]
|{{monzo| -6 0 1 0 0 1 }}
|26.84
|Thoyo
|Wilsorma
|-
|13
|[[78/77]]
|{{monzo| 1 1 0 -1 -1 1 }}
|22.34
|Tholuru
|Negustma
|-
|13
|[[91/90]]
|{{monzo| -1 -2 -1 1 0 1 }}
| 19.13
| Thozogu
| Superleap comma, biome comma
|-
|13
|[[31213/31104]]
|{{monzo| -7 -5 0 4 0 1 }}
|6.06
|Thoquadzo
|Praveensma
|-
|31
|[[125/124]]
|{{monzo| -2 0 3 0 0 0 0 0 0 0 -1 }}
| 13.91
| Thiwutriyo
|Twizzler comma
|}
<references />
===Rank-2 temperaments===
*[[List of 22et rank two temperaments by badness]]
*[[List of 22et rank two temperaments by complexity]]
*[[List of edo-distinct 22et rank two temperaments]]
{| class="wikitable center-1 center-2"
|-
!Periods <br> per octave
!Generator
!Temperaments
|-
|1
|1\22
|[[Sensamagic clan #Sensa|Sensa]]<br>[[Chromo]]<br>[[Ceratitid]]
|-
| 1
| 3\22
|[[Porcupine]]
|-
|1
| 5\22
|[[Orwell]] (22) / blair (22) / winston (22f)
|-
|1
|7\22
|[[Magic]] / telepathy
|-
|1
| 9\22
|[[Superpyth]] / [[suprapyth]]
|-
|2
|1\22
|[[Shrutar]] / hemipaj<br>[[Comic]]
|-
|2
| 2\22
|[[Srutal]] / [[pajara]] / pajarous
|-
|2
|3\22
|[[Hedgehog]] / [[echidna]]
|-
|2
|4\22
|[[Astrology]]<br>[[Antikythera]]<br>[[Wizard]]
|-
|2
|5\22
|[[Doublewide]] / fleetwood
|-
|11
|1\22
|[[Undeka]]<br>[[Hendecatonic]]
|}
==Scales==
''See [[22edo modes]]''.
==Tetrachords ==
''See [[22edo tetrachords]].''
==Notation==
===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.
Line 850: Line 483:


[[File:22edo Sagittal.png|800px]]
[[File:22edo Sagittal.png|800px]]
===Ups and Downs Notation===
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]]
Treating ups and downs as independent of sharps and flats, and sometimes appearing separately:
[[File:Tibia_22edo_ups_and_downs_guide_2.png|alt=Tibia 22edo ups and downs guide 2.png|800x150px|Tibia 22edo ups and downs guide 2.png]]
A D downmajor scale with mandatory accidentals (no key signature), with minimal accidentals (only when needed to override the key signature), and with independent ups and downs.
[[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}}
Shown below is [[Paul Erlich]]'s "Tibia" in G, with independent ups and downs.
<gallery mode="slideshow">
File:Tibia in G CORRECTED-1.png|alt=Tibia in G CORRECTED-1.png|Tibia in G (page 1)
File:Tibia in G CORRECTED-2.png|alt=Tibia in G CORRECTED-2.png|Tibia in G (page 2)
</gallery>


===Comparison of 22edo notation systems===
===Comparison of 22edo notation systems===
Line 1,351: Line 959:
|D
|D
|}
|}
== Approximation to JI ==
[[File:22ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 17-limit intervals approximated in 22edo]]
===Interval mappings===
{{Q-odd-limit intervals|22}}
==Defining features ==
===Septimal vs syntonic comma===
Possibly the most striking characteristic of 22edo to those not used to it is that it does '''not''' temper out the syntonic comma of 81/80, and therefore is not a system of [[meantone]] temperament. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12edo, 19edo, and 31edo do not distinguish, such as the two whole tones 9/8 and 10/9. Indeed, these distinctions are exaggerated in comparison to 5-limit JI and many more accurate temperaments such as [[34edo]], [[41edo]] and [[53edo]].
The diatonic scale it produces is instead derived from [[superpyth]] temperament, which despite having the same melodic structure as meantone's diatonic scale (LLsLLLs or, [[5L 2s]]), has thirds approximating 9/7 and 7/6, rather than 5/4 and 6/5. This means that the septimal comma of 64/63 vanishes, rather than the syntonic comma of 81/80, which is one of the core features of 22et. Superpyth is melodically interesting for having a quasi-equal pentatonic scale (as the large whole tone and subminor third are rather close in size) and a more uneven heptatonic scale, as compared with 12et and other meantone systems: step patterns 4 4 5 4 5 and 4 4 1 4 4 4 1, respectively.
=== Porcupine comma ===
It additionally tempers out the porcupine comma or maximal diesis of 250/243, which means that 22edo [[support]]s [[porcupine]] temperament. The generator for porcupine is a flat minor whole tone of [[10/9]], two of which is a slightly sharp [[6/5]], and three of which is a slightly flat [[4/3]], implying the existence of an equal-step tetrachord, which is characteristic of porcupine. Porcupine is notable for being the 5-limit temperament lowest in [[badness]] which is ''not'' approximated by the familiar 12-tone equal temperament, and as such represents one excellent point of departure for examining the harmonic properties of 22edo. It forms [[mos scale]]s of 7 and 8, which in 22edo are tuned respectively as 4 3 3 3 3 3 3 and 3 1 3 3 3 3 3 3 (and their respective modes).
===5-limit commas===
Other 5-limit commas 22edo tempers out include the diaschisma, [[2048/2025]] and the magic comma or small diesis, [[3125/3072]]. In a diaschismic system, such as 12et or 22et, the diatonic tritone [[45/32]], which is a major third above a major whole tone representing [[9/8]], is equated to its inverted form, [[64/45]]. That the magic comma is tempered out means that 22et is a magic system, where five major thirds make up a perfect fifth.
===7-limit commas ===
In the 7-limit 22edo tempers out certain commas also tempered out by 12et; this relates 12et to 22 in a way different from the way in which meantone systems are akin to it. Both [[50/49]], (jubilee comma), and 64/63, (septimal comma), are tempered out in both systems. Hence because of 50/49 they both equate the two septimal tritones of 7/5 and 10/7, and because of 64/63 they both do not distinguish between a dominant seventh chord and an otonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the [[septimal kleisma]], so that the septimal kleisma augmented triad is a chord of 22et, as it also is of any meantone tuning. A septimal comma not tempered out by 12et which 22et does temper out is 1728/1715, the [[1728/1715|orwell comma]]; and the [[orwell tetrad]] is also a chord of 22et.
=== 11-limit commas===
In the 11-limit, 22edo tempers out the [[quartisma]], leading to a stack of five 33/32 quartertones being equated with one 7/6 subminor third. This is a trait which, while shared with [[24edo]], is surprisingly ''not'' shared with a number of other relatively small edos such as [[17edo]], [[26edo]] and [[34edo]]. In fact, not even the famous [[53edo]] has this property – although it should be noted that the related [[159edo]] ''does''.
===Other features===
The 164¢ "flat minor whole tone" is a key interval in 22edo, in part because it functions as no less than three different consonant ratios in the [[11-limit]]: 10/9, 11/10, and 12/11. It is thus extremely ambiguous and flexible. The trade-off is that it is very much in the cracks of the 12-equal piano, and so for most 12-equal listeners, it takes some getting used to. Simple translations of 5-limit music into 22edo can sound very different, with a more complex harmonic quality inevitably arising. 22edo does not contain a neutral third but both the 5-limit thirds have a "neutral-like" quality since they are tempered closer together rather than farther apart as in 12edo.
22edo also supports the [[orwell]] temperament, which uses the septimal subminor third as a generator (5 degrees) and forms mos scales with step patterns 3 2 3 2 3 2 3 2 2 and 1 2 2 1 2 2 1 2 2 1 2 2 2. Harmonically, orwell can be tuned more accurately in other temperaments, such as [[31edo]], [[53edo]] and [[84edo]]. But 22edo orwell has a leg-up on the others melodically, as the large and small steps of orwell[9] are easier to distinguish in 22.
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]], 11 can be notated as every other note of 22.
==Regular temperament properties==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo| 35 -22 }}
|[{{val| 22 35 }}]
|−2.25
|2.25
|4.12
|-
|2.3.5
|250/243, 2048/2025
|[{{val| 22 35 51 }}]
| −0.86
|2.70
|4.94
|-
|2.3.5.7
| 50/49, 64/63, 245/243
|[{{val| 22 35 51 62 }}]
|−1.80
|2.85
|5.23
|-
|2.3.5.7.11
|50/49, 55/54, 64/63, 99/98
| [{{val| 22 35 51 62 76 }}]
|−1.11
|2.90
|5.33
|-
|2.3.5.7.11.17
|50/49, 55/54, 64/63, 85/84, 99/98
|[{{val| 22 35 51 62 76 90 }}]
|−1.09
| 2.65
|4.87
|}
22et is lower in relative error than any previous equal temperaments in the 11-limit. The next equal temperament that does better in this subgroup is [[31edo|31]]. 22et is even more prominent in the 2.3.5.7.11.17 subgroup, and the next equal temperament that does better in this subgroup is [[46edo|46]].
===Uniform maps ===
{{Uniform map|13|21.5|22.5}}
===Commas===
22et [[tempers out]] the following [[commas]]. (Note: This assumes the [[val]] {{val| 22 35 51 62 76 81 }}.)
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
![[Harmonic limit|Prime <br>limit]]
![[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
![[Monzo]]
![[Cents]]
![[Color name]]
!Name
|-
|3
|<abbr title="34359738368/31381059609">(22 digits)</abbr>
|{{monzo| 35 -22 }}
|156.98
|Trisawa
|22-comma
|-
|5
|[[250/243]]
|{{monzo| 1 -5 3 }}
|49.17
|Triyo
|Porcupine comma, maximal diesis
|-
|5
|[[3125/3072]]
|{{monzo| -10 -1 5 }}
|29.61
| Laquinyo
|Magic comma
|-
|5
|[[2048/2025]]
|{{monzo| 11 -4 -2 }}
|19.55
| Sagugu
|Diaschisma
|-
|5
|[[2109375/2097152|(14 digits)]]
|{{monzo| -21 3 7 }}
|10.06
|Lasepyo
|[[Semicomma]]
|-
|5
|<abbr title="4294967296/4271484375">(20 digits)</abbr>
|{{monzo| 32 -7 -9 }}
|9.49
|Sasa-tritrigu
|[[Escapade comma]]
|-
|5
|<abbr title="9010162353515625/9007199254740992">(32 digits)</abbr>
|{{monzo| -53 10 16 }}
|0.57
|Quadla-quadquadyo
|[[Kwazy comma]]
|-
|7
|[[50/49]]
|{{monzo| 1 0 2 -2 }}
|34.98
|Biruyo
|Jubilisma
|-
|7
|[[64/63]]
|{{monzo| 6 -2 0 -1 }}
|27.26
| Ru
|Septimal comma
|-
|7
|[[875/864]]
|{{monzo| -5 -3 3 1 }}
| 21.90
|Zotriyo
|Keema
|-
|7
|[[2430/2401]]
|{{monzo| 1 5 1 -4 }}
|20.79
|Quadru-ayo
|Nuwell comma
|-
|7
|[[245/243]]
|{{monzo| 0 -5 1 2 }}
|14.19
|Zozoyo
|Sensamagic comma
|-
|7
|[[1728/1715]]
|{{monzo| 6 3 -1 -3 }}
|13.07
|Triru-agu
|Orwellisma
|-
|7
|[[225/224]]
|{{monzo| -5 2 2 -1 }}
| 7.71
|Ruyoyo
|Marvel comma
|-
| 7
|[[10976/10935]]
|{{monzo| 5 -7 -1 3 }}
|6.48
|Trizo-agu
| Hemimage comma
|-
|7
|[[6144/6125]]
|{{monzo| 11 1 -3 -2 }}
|5.36
|Saruru-atrigu
|Porwell comma
|-
|7
|[[65625/65536]]
|{{monzo| -16 1 5 1 }}
|2.35
|Lazoquinyo
|Horwell comma
|-
|7
|<abbr title="420175/419904">(12 digits)</abbr>
|{{monzo| -6 -8 2 5 }}
|1.12
|Quinzo-ayoyo
|[[Wizma]]
|-
|11
|[[99/98]]
|{{monzo| -1 2 0 -2 1 }}
|17.58
| Loruru
|Mothwellsma
|-
|11
|[[100/99]]
|{{monzo| 2 -2 2 0 -1 }}
|17.40
|Luyoyo
|Ptolemisma
|-
|11
|[[121/120]]
|{{monzo| -3 -1 -1 0 2 }}
|14.37
|Lologu
|Biyatisma
|-
|11
|[[176/175]]
|{{monzo| 4 0 -2 -1 1 }}
|9.86
|Lorugugu
|Valinorsma
|-
|11
|[[896/891]]
|{{monzo| 7 -4 0 1 -1 }}
|9.69
|Saluzo
|Pentacircle comma
|-
|11
|[[65536/65219]]
|{{monzo| 16 0 0 -2 -3 }}
|8.39
|Satrilu-aruru
|Orgonisma
|-
| 11
|[[385/384]]
|{{monzo| -7 -1 1 1 1 }}
|4.50
|Lozoyo
|Keenanisma
|-
|11
|[[540/539]]
|{{monzo| 2 3 1 -2 -1 }}
|3.21
|Lururuyo
|Swetisma
|-
|11
|[[4000/3993]]
|{{monzo| 5 -1 3 0 -3 }}
|3.03
|Triluyo
|Wizardharry comma
|-
|11
|[[9801/9800]]
|{{monzo| -3 4 -2 -2 2 }}
|0.18
|Bilorugu
| Kalisma
|-
|13
|[[65/64]]
|{{monzo| -6 0 1 0 0 1 }}
|26.84
|Thoyo
|Wilsorma
|-
|13
|[[78/77]]
|{{monzo| 1 1 0 -1 -1 1 }}
|22.34
|Tholuru
|Negustma
|-
|13
|[[91/90]]
|{{monzo| -1 -2 -1 1 0 1 }}
| 19.13
| Thozogu
| Superleap comma, biome comma
|-
|13
|[[31213/31104]]
|{{monzo| -7 -5 0 4 0 1 }}
|6.06
|Thoquadzo
|Praveensma
|-
|31
|[[125/124]]
|{{monzo| -2 0 3 0 0 0 0 0 0 0 -1 }}
| 13.91
| Thiwutriyo
|Twizzler comma
|}
<references />
===Rank-2 temperaments===
*[[List of 22et rank two temperaments by badness]]
*[[List of 22et rank two temperaments by complexity]]
*[[List of edo-distinct 22et rank two temperaments]]
{| class="wikitable center-1 center-2"
|-
!Periods <br> per octave
!Generator
!Temperaments
|-
|1
|1\22
|[[Sensamagic clan #Sensa|Sensa]]<br>[[Chromo]]<br>[[Ceratitid]]
|-
| 1
| 3\22
|[[Porcupine]]
|-
|1
| 5\22
|[[Orwell]] (22) / blair (22) / winston (22f)
|-
|1
|7\22
|[[Magic]] / telepathy
|-
|1
| 9\22
|[[Superpyth]] / [[suprapyth]]
|-
|2
|1\22
|[[Shrutar]] / hemipaj<br>[[Comic]]
|-
|2
| 2\22
|[[Srutal]] / [[pajara]] / pajarous
|-
|2
|3\22
|[[Hedgehog]] / [[echidna]]
|-
|2
|4\22
|[[Astrology]]<br>[[Antikythera]]<br>[[Wizard]]
|-
|2
|5\22
|[[Doublewide]] / fleetwood
|-
|11
|1\22
|[[Undeka]]<br>[[Hendecatonic]]
|}
==Scales==
''See [[22edo modes]]''.
==Tetrachords ==
''See [[22edo tetrachords]].''


==Chord names==
==Chord names==
Retrieved from "https://en.xen.wiki/w/22edo"