22edo: Difference between revisions

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| ja = 22平均律

}}

In music, '''22 equal temperament''', called '''22-tet''', '''22-edo''', or '''22-et''', is the scale derived by dividing the [[octave]] into 22 equally large steps. Each step represents a frequency ratio of the twenty-second root of 2, or 54.55 [[cent~~|cents~~]]. Because it distinguishes 10/9 and 9/8, it's not meantone.

In music, '''22 equal temperament''', called '''22-tet''', '''22-edo''', or '''22-et''', is the scale derived by dividing the [[octave]] into 22 equally large steps. Each step represents a frequency ratio of the twenty-second root of 2, or 54.55 [[cent]]s. Because it distinguishes 10/9 and 9/8, it's not meantone.

== Theory ==

Line 11:

The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the [[Indian|music theory of India]], Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after [[19edo|19 equal temperament]], and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.

The 22-et system is in fact the third equal division, after 12 and 19, which is capable of approximating the [[5-limit]] to within a TE error of 4 cents/oct. While not an integral or gap edo it at least qualifies as a [[~~The_Riemann_Zeta_Function_and_Tuning~~#Zeta EDO lists|zeta peak]]. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to approximate the [[7-limit|7-]] and [[~~11-limit|~~11-limit]]s to within 3 cents/oct of error. While [[31edo|31 equal temperament]] does much better, 22-et still allows the use of these higher-limit harmonies, and in fact 22 is the smallest equal division to represent the 11-limit [[consistent|consistently]]. Furthermore, 22-et, unlike 12 and [[19edo|19]], is not a [[meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.

The 22-et system is in fact the third equal division, after 12 and 19, which is capable of approximating the [[5-limit]] to within a TE error of 4 cents/oct. While not an integral or gap edo it at least qualifies as a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak]]. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to approximate the [[7-limit|7-]] and [[11-limit]]s to within 3 cents/oct of error. While [[31edo|31 equal temperament]] does much better, 22-et still allows the use of these higher-limit harmonies, and in fact 22 is the smallest equal division to represent the 11-limit [[consistent|consistently]]. Furthermore, 22-et, unlike 12 and [[19edo|19]], is not a [[meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.

22-et can also be treated as adding harmonics 3 and 5 to 11-EDO's 2.7.9.11.15.17 subgroup, making it a (rather accurate) 2.3.5.7.11.17 subgroup temperament. Let us also mind it's approximation of the 31st harmonic is within half a cent, which is fairly accurate. It also approximates some intervals involving the 29th harmonic well, especially 29/24, which is also matched within half a cent. This leaves us with 2.3.5.7.11.17.29.31.

Line 19:

== Properties of 22 equal temperament ==

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 [[~~Regular_Temperaments~~#meantone|meantone]] temperament. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO, 19-EDO, 31-EDO, ... 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]].

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 [[Regular Temperaments#meantone|meantone]] temperament. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO, 19-EDO, 31-EDO, ... 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 22-EDO. 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 12-equal and meantone systems: step patterns 4 4 5 4 5 and 4 4 1 4 4 4 1, respectively.

Line 29:

22-EDO also supports 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 22-equal Orwell has a leg-up on the others melodically, as the large and small steps of Orwell[9] are easier to distinguish in 22.

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 12-et or 22-et, the [[~~diatonic_tritone|~~diatonic tritone]] [[~~45/32|~~45/32]], which is a major third above a [[major_whole_tone|major whole tone]] representing [[~~9/8|~~9/8]], is equated to its inverted form, [[~~64/45|~~64/45]]. That the magic comma is tempered out means that 22-et is a [[Regular_Temperaments#magic|magic]] system, where five major thirds make up a perfect fifth.

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 12-et or 22-et, the [[diatonic tritone]] [[45/32]], which is a major third above a [[major_whole_tone|major whole tone]] representing [[9/8]], is equated to its inverted form, [[64/45]]. That the magic comma is tempered out means that 22-et is a [[Regular_Temperaments#magic|magic]] system, where five major thirds make up a perfect fifth.

In the 7-limit 22edo tempers out certain commas also tempered out by 12-et; this relates 12 equal to 22 in a way different from the way in which meantone systems are akin to it. Both [[50/49]], (the [[jubilee comma]]), and [[64/63]], (the [[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 22-et, as it also is of any meantone tuning. A septimal comma not tempered out by 12-et which 22-et does temper out is 1728/1715, the [[orwell comma]]; and the [[orwell tetrad]] is also a chord of 22-et.

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In the 11-limit, 22edo tempers out [[Quartisma|117440512/117406179]], 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''.

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 ==

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{| class="wikitable center-all"

|-

! | [[Kite's color notation|color of the 3rd]]

! [[Kite's color notation|color of the 3rd]]

! | JI chord

! JI chord

! | notes as edosteps

! notes as edosteps

! | notes of C chord

! notes of C chord

! | written name

! written name

! | spoken name

! spoken name

|-

| zo

Line 837:

|-

! rowspan="2" |Error

![[TE error|absolute]] (¢)

! [[TE error|absolute]] (¢)

| 2.25

| 2.70

Line 844:

| 2.65

|-

![[TE simple badness|relative]] (%)

! [[TE simple badness|relative]] (%)

| 4.12

| 4.94

Line 864:

{| class="wikitable"

|-

! | Periods

! Periods <br> per octave

! Period

per octave

! Generator

! | Period

! Temperaments

! | Generator

! | Temperaments

|-

| | 1

| 1

| | 22\22

| 22\22

| | 1\22

| 1\22

| | [[~~Sensamagic_clan~~#Sensa|Sensa]]/chromo/ceratitid

| [[Sensamagic clan#Sensa|Sensa]]/chromo/ceratitid

|-

| | 1

| 1

| | 22\22

| 22\22

| | 3\22

| 3\22

| | [[~~Porcupine|~~Porcupine]]

| [[Porcupine]]

|-

| | 1

| 1

| | 22\22

| 22\22

| | 5\22

| 5\22

| | [[~~Orwell|~~Orwell]]/blair/orson

| [[Orwell]]/blair/orson

|-

| | 1

| 1

| | 22\22

| 22\22

| | 7\22

| 7\22

| | [[~~Magic|~~Magic]]/telepathy

| [[Magic]]/telepathy

|-

| | 1

| 1

| | 22\22

| 22\22

| | 9\22

| 9\22

| | [[~~Superpyth|~~Superpyth]]/[[Suprapyth~~|suprapyth~~]]

| [[Superpyth]]/[[Suprapyth]]

|-

| | 2

| 2

| | 11\22

| 11\22

| | 1\22

| 1\22

| | [[~~Shrutar|~~Shrutar]]/hemipaj/comic

| [[Shrutar]]/hemipaj/comic

|-

| | 2

| 2

| | 11\22

| 11\22

| | 2\22

| 2\22

| | [[~~Srutal|~~Srutal]]/[[~~pajara|~~pajara]]/pajarous

| [[Srutal]]/[[pajara]]/pajarous

|-

| | 2

| 2

| | 11\22

| 11\22

| | 3\22

| 3\22

| | [[~~Porcupine_family~~#Hedgehog|Hedgehog]]/[[~~Echidna|~~echidna]]

| [[Porcupine family#Hedgehog|Hedgehog]]/[[echidna]]

|-

| | 2

| 2

| | 11\22

| 11\22

| | 4\22

| 4\22

| [[Astrology]]/[[wizard]]/[[antikythera]]

|-

| | 2

| 2

| | 11\22

| 11\22

| | 5\22

| 5\22

| | [[~~Doublewide|~~Doublewide]]/fleetwood

| [[Doublewide]]/fleetwood

|-

| | 11

| 11

| | 2\22

| 2\22

| | 1\22

| 1\22

| | [[~~Hendecatonic|~~Hendecatonic]]/undeka

| [[Hendecatonic]]/undeka

|}

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=== [[MOS scales]] ===

See also [[22edo Modes]], [[22edo tetrachords~~|22edo Tetrachords~~]].

See also [[22edo Modes]], [[22edo tetrachords]].

Porcupine[7] - 3334333

@@ Line 5: / Line 5: @@
 | ja = 22平均律
 }}
-In music, '''22 equal temperament''', called '''22-tet''', '''22-edo''', or '''22-et''', is the scale derived by dividing the [[octave]] into 22 equally large steps. Each step represents a frequency ratio of the twenty-second root of 2, or 54.55 [[cent|cents]]. Because it distinguishes 10/9 and 9/8, it's not meantone.
+In music, '''22 equal temperament''', called '''22-tet''', '''22-edo''', or '''22-et''', is the scale derived by dividing the [[octave]] into 22 equally large steps. Each step represents a frequency ratio of the twenty-second root of 2, or 54.55 [[cent]]s. Because it distinguishes 10/9 and 9/8, it's not meantone.
 == Theory ==
@@ Line 11: / Line 11: @@
 The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the [[Indian|music theory of India]], Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after [[19edo|19 equal temperament]], and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.
-The 22-et system is in fact the third equal division, after 12 and 19, which is capable of approximating the [[5-limit]] to within a TE error of 4 cents/oct. While not an integral or gap edo it at least qualifies as a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak]]. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to approximate the [[7-limit|7-]] and [[11-limit|11-limit]]s to within 3 cents/oct of error. While [[31edo|31 equal temperament]] does much better, 22-et still allows the use of these higher-limit harmonies, and in fact 22 is the smallest equal division to represent the 11-limit [[consistent|consistently]]. Furthermore, 22-et, unlike 12 and [[19edo|19]], is not a [[meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.
+The 22-et system is in fact the third equal division, after 12 and 19, which is capable of approximating the [[5-limit]] to within a TE error of 4 cents/oct. While not an integral or gap edo it at least qualifies as a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak]]. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to approximate the [[7-limit|7-]] and [[11-limit]]s to within 3 cents/oct of error. While [[31edo|31 equal temperament]] does much better, 22-et still allows the use of these higher-limit harmonies, and in fact 22 is the smallest equal division to represent the 11-limit [[consistent|consistently]]. Furthermore, 22-et, unlike 12 and [[19edo|19]], is not a [[meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.
 -et can also be treated as adding harmonics 3 and 5 to 11-EDO's 2.7.9.11.15.17 subgroup, making it a (rather accurate) 2.3.5.7.11.17 subgroup temperament. Let us also mind it's approximation of the 31st harmonic is within half a cent, which is fairly accurate. It also approximates some intervals involving the 29th harmonic well, especially 29/24, which is also matched within half a cent. This leaves us with 2.3.5.7.11.17.29.31.
@@ Line 19: / Line 19: @@
 == Properties of 22 equal temperament ==
-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 [[Regular_Temperaments#meantone|meantone]] temperament. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO, 19-EDO, 31-EDO, ... 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]].
+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 [[Regular Temperaments#meantone|meantone]] temperament. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO, 19-EDO, 31-EDO, ... 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 22-EDO. 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 12-equal and meantone systems: step patterns 4 4 5 4 5 and 4 4 1 4 4 4 1, respectively.
@@ Line 29: / Line 29: @@
 -EDO also supports 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 22-equal Orwell has a leg-up on the others melodically, as the large and small steps of Orwell[9] are easier to distinguish in 22.
-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 12-et or 22-et, the [[diatonic_tritone|diatonic tritone]] [[45/32|45/32]], which is a major third above a [[major_whole_tone|major whole tone]] representing [[9/8|9/8]], is equated to its inverted form, [[64/45|64/45]]. That the magic comma is tempered out means that 22-et is a [[Regular_Temperaments#magic|magic]] system, where five major thirds make up a perfect fifth.
+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 12-et or 22-et, the [[diatonic tritone]] [[45/32]], which is a major third above a [[major_whole_tone|major whole tone]] representing [[9/8]], is equated to its inverted form, [[64/45]]. That the magic comma is tempered out means that 22-et is a [[Regular_Temperaments#magic|magic]] system, where five major thirds make up a perfect fifth.
 In the 7-limit 22edo tempers out certain commas also tempered out by 12-et; this relates 12 equal to 22 in a way different from the way in which meantone systems are akin to it. Both [[50/49]], (the [[jubilee comma]]), and [[64/63]], (the [[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 22-et, as it also is of any meantone tuning. A septimal comma not tempered out by 12-et which 22-et does temper out is 1728/1715, the [[orwell comma]]; and the [[orwell tetrad]] is also a chord of 22-et.
@@ Line 35: / Line 35: @@
 In the 11-limit, 22edo tempers out [[Quartisma|117440512/117406179]], 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''.
-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 ==
@@ Line 518: / Line 518: @@
 {| class="wikitable center-all"
 |-
-! | [[Kite's color notation|color of the 3rd]]
+! [[Kite's color notation|color of the 3rd]]
-! | JI chord
+! JI chord
-! | notes as edosteps
+! notes as edosteps
-! | notes of C chord
+! notes of C chord
-! | written name
+! written name
-! | spoken name
+! spoken name
 |-
 | zo
@@ Line 837: / Line 837: @@
 |-
 ! rowspan="2" |Error
-![[TE error|absolute]] (¢)
+! [[TE error|absolute]] (¢)
 | 2.25
 | 2.70
@@ Line 844: / Line 844: @@
 | 2.65
 |-
-![[TE simple badness|relative]] (%)
+! [[TE simple badness|relative]] (%)
 | 4.12
 | 4.94
@@ Line 864: / Line 864: @@
 {| class="wikitable"
 |-
-! | Periods
+! Periods <br> per octave
+! Period
-per octave
+! Generator
-! | Period
+! Temperaments
-! | Generator
-! | Temperaments
 |-
-| | 1
+| 1
-| | 22\22
+| 22\22
-| | 1\22
+| 1\22
-| | [[Sensamagic_clan#Sensa|Sensa]]/chromo/ceratitid
+| [[Sensamagic clan#Sensa|Sensa]]/chromo/ceratitid
 |-
-| | 1
+| 1
-| | 22\22
+| 22\22
-| | 3\22
+| 3\22
-| | [[Porcupine|Porcupine]]
+| [[Porcupine]]
 |-
-| | 1
+| 1
-| | 22\22
+| 22\22
-| | 5\22
+| 5\22
-| | [[Orwell|Orwell]]/blair/orson
+| [[Orwell]]/blair/orson
 |-
-| | 1
+| 1
-| | 22\22
+| 22\22
-| | 7\22
+| 7\22
-| | [[Magic|Magic]]/telepathy
+| [[Magic]]/telepathy
 |-
-| | 1
+| 1
-| | 22\22
+| 22\22
-| | 9\22
+| 9\22
-| | [[Superpyth|Superpyth]]/[[Suprapyth|suprapyth]]
+| [[Superpyth]]/[[Suprapyth]]
 |-
-| | 2
+| 2
-| | 11\22
+| 11\22
-| | 1\22
+| 1\22
-| | [[Shrutar|Shrutar]]/hemipaj/comic
+| [[Shrutar]]/hemipaj/comic
 |-
-| | 2
+| 2
-| | 11\22
+| 11\22
-| | 2\22
+| 2\22
-| | [[Srutal|Srutal]]/[[pajara|pajara]]/pajarous
+| [[Srutal]]/[[pajara]]/pajarous
 |-
-| | 2
+| 2
-| | 11\22
+| 11\22
-| | 3\22
+| 3\22
-| | [[Porcupine_family#Hedgehog|Hedgehog]]/[[Echidna|echidna]]
+| [[Porcupine family#Hedgehog|Hedgehog]]/[[echidna]]
 |-
-| | 2
+| 2
-| | 11\22
+| 11\22
-| | 4\22
+| 4\22
-| | [[Astrology|Astrology]]/[[wizard|wizard]]/[[antikythera|antikythera]]
+| [[Astrology]]/[[wizard]]/[[antikythera]]
 |-
-| | 2
+| 2
-| | 11\22
+| 11\22
-| | 5\22
+| 5\22
-| | [[Doublewide|Doublewide]]/fleetwood
+| [[Doublewide]]/fleetwood
 |-
-| | 11
+| 11
-| | 2\22
+| 2\22
-| | 1\22
+| 1\22
-| | [[Hendecatonic|Hendecatonic]]/undeka
+| [[Hendecatonic]]/undeka
 |}
@@ Line 931: / Line 929: @@
 === [[MOS scales]] ===
-See also [[22edo Modes]], [[22edo tetrachords|22edo Tetrachords]].
+See also [[22edo Modes]], [[22edo tetrachords]].
 Porcupine[7] - 3334333