100edo: Difference between revisions

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== Theory ==

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=== 100bddd and the 22-note scales ===

The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to [[22edo]] for [[pajara]] temperament and for tuning [[Paul Erlich]]'s decatonic scales, as well as diatonic scales (via [[superpyth]] temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60{{c}} which just barely falls within the 60-80 cent range [http://www.anaphoria.com/Secor17puzzle.pdf favored by George Secor] for neomedieval compositions.

The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to [[22edo]] for [[pajara]] temperament and for tuning [[Paul Erlich]]'s decatonic scales, as well as diatonic scales (via [[superpyth]] temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of ~~60¢~~ which just barely falls within the 60-80 cent range [http://www.anaphoria.com/Secor17puzzle.pdf favored by George Secor] for neomedieval compositions.

The 22-note [[modmos]] 5 4 5 4 5 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 could be used to construct a 22-tone piano; this tuning has two chains of fifths (one with 10 notes in it and one with 12), and thus has two "wolf" fifths. Much like meantone, this tuning has "wolf" intervals but in this case they are only twelve cents away from their pure counterparts, and as such they don't sound nearly as bad. They are xenharmonic but not unpleasant and could easily be used in compositions, which makes this tuning akin to well temperaments as well as to meantone. Because most if not all of the "wolves" are still usable (albeit xenharmonic), it might be better to use the term "dog" rather than wolf for these intervals. Dog intervals frequently provide ''closer'' matches to intervals involving the 7th and 11th harmonics. Even if the dog intervals are completely avoided, this modmos still allows for decatonic music in 12 different keys, and diatonic (superpyth) music in 10 different keys, and thus the freedom of modulation and key choice is still comparable to [[12edo]].

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{| class="wikitable"

|-

! Steps of 22-note ~~Modmos~~

! Steps of 22-note MODMOS

! Interval ~~Name~~ (~~Decatonic~~)

! Interval name (decatonic)

! Interval ~~Name~~ (~~Superpyth~~ diatonic)

! Interval name (superpyth diatonic)

! Pure ~~Interval Size~~ [~~Multiplicity~~] Difference from 22edo

! Pure interval size [multiplicity] Difference from 22edo

! Dog ~~Interval Size~~ [~~Multiplicity~~] Difference from 22edo

! Dog interval size [multiplicity] Difference from 22edo

|-

| 1

| Diminished 2nd10

| Minor second

| ~~60¢~~ [12] 5.~~4545¢~~

| 60{{c}} [12] 5.4545{{c}}

| ~~48¢~~ [10] -6.~~5455¢~~

| 48{{c}} [10] −6.5455{{c}}

|-

| 2

| Minor 2nd10

| Augmented seventh

| ~~108¢~~ [20] -1.~~091¢~~

| 108{{c}} [20] −1.091{{c}}

| ~~120¢~~ [2] 10.~~909¢~~

| 120{{c}} [2] 10.909{{c}}

|-

| 3

| Major 2nd10

| Augmented unison

| ''~~168¢~~ [14]'' 4.~~364¢~~

| ''168{{c}} [14]'' 4.364{{c}}

| ''~~156¢~~ [8]'' -7.~~636¢~~

| ''156{{c}} [8]'' −7.636{{c}}

|-

| 4

| Minor 3rd10

| Major second

| ~~216¢~~ [18] -2.~~182¢~~

| 216{{c}} [18] −2.182{{c}}

| ~~228¢~~ [4] 9.~~818¢~~

| 228{{c}} [4] 9.818{{c}}

|-

| 5

| Major 3rd10

| Minor third

| ~~276¢~~ [16] 3.~~273¢~~

| 276{{c}} [16] 3.273{{c}}

| ~~264¢~~ [6] -8.~~727¢~~

| 264{{c}} [6] −8.727{{c}}

|-

| 6

| Minor 4th10

| Diminished fourth

| ''~~324¢~~ [16]'' -3.~~273¢~~

| ''324{{c}} [16]'' −3.273{{c}}

| ''~~336¢~~ [6]'' 8.~~727¢~~

| ''336{{c}} [6]'' 8.727{{c}}

|-

| 7

| Major 4th10

| Augmented second

| ~~384¢~~ [18] 2.~~182¢~~

| 384{{c}} [18] 2.182{{c}}

| ~~372¢~~ [4] -9.~~818¢~~

| 372{{c}} [4] −9.818{{c}}

|-

| 8

| Augmented 4th10 Diminished 5th10

| Major third

| ~~432¢~~ [14] -4.~~364¢~~

| 432{{c}} [14] −4.364{{c}}

| ~~444¢~~ [8] 7.~~636¢~~

| 444{{c}} [8] 7.636{{c}}

|-

| 9

| Perfect 5th10

| Perfect fourth

| ~~492¢~~ [20] 1.~~091¢~~

| 492{{c}} [20] 1.091{{c}}

| ~~480¢~~ [2] ~~-10~~.~~909¢~~

| 480{{c}} [2] −10.909{{c}}

|-

| 10

| Augmented 5th10 Diminished 6th10

| Diminished fifth

| ~~540¢~~ [12] -5.~~4545¢~~

| 540{{c}} [12] −5.4545{{c}}

| ~~552¢~~ [10] 6.~~5455¢~~

| 552{{c}} [10] 6.5455{{c}}

|-

| 11

| Perfect 6th10

| Augmented third Diminished sixth

| ~~600¢~~ [20]

| 600{{c}} [20]

| ~~588¢~~ [1] ~~-12¢~~ ~~612¢~~ [1] ~~12¢~~

| 588{{c}} [1] −12{{c}} 612{{c}} [1] 12{{c}}

|-

| 12

| Augmented 6th10 Diminished 7th10

| Augmented fourth

| ~~660¢~~ [12] 6.~~5455¢~~

| 660{{c}} [12] 6.5455{{c}}

| ~~648¢~~ [10] -5.~~4545¢~~

| 648{{c}} [10] −5.4545{{c}}

|-

| 13

| Perfect 7th10

| Perfect fifth

| ~~708¢~~ [20] -1.~~091¢~~

| 708{{c}} [20] −1.091{{c}}

| ~~720¢~~ [2] 10.~~909¢~~

| 720{{c}} [2] 10.909{{c}}

|-

| 14

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Diminished 8th10

| Minor sixth

| ~~768¢~~ [14] 4.~~364¢~~

| 768{{c}} [14] 4.364{{c}}

| ~~756¢~~ [8] -7.~~636¢~~

| 756{{c}} [8] −7.636{{c}}

|-

| 15

| Minor 8th10

| Diminished seventh

| ~~816¢~~ [18] -2.~~182¢~~

| 816{{c}} [18] −2.182{{c}}

| ~~828¢~~ [4] 9.~~818¢~~

| 828{{c}} [4] 9.818{{c}}

|-

| 16

| Major 8th10

| Augmented fifth

| ''~~876¢~~ [16]'' 3.~~273¢~~

| ''876{{c}} [16]'' 3.273{{c}}

| ''~~864¢~~ [6]'' -8.~~727¢~~

| ''864{{c}} [6]'' −8.727{{c}}

|-

| 17

| Minor 9th10

| Major sixth

| ~~924¢~~ [16] -3.~~273¢~~

| 924{{c}} [16] −3.273{{c}}

| ~~936¢~~ [6] 8.~~727¢~~

| 936{{c}} [6] 8.727{{c}}

|-

| 18

| Major 9th10

| Minor seventh

| ~~984¢~~ [18] 2.~~182¢~~

| 984{{c}} [18] 2.182{{c}}

| ~~972¢~~ [4] -9.~~818¢~~

| 972{{c}} [4] −9.818{{c}}

|-

| 19

| Minor 10th10

| Diminished octave

| ''~~1032¢~~ [14]'' -4.~~364¢~~

| ''1032{{c}} [14]'' −4.364{{c}}

| ''~~1044¢~~ [8]'' 7.~~636¢~~

| ''1044{{c}} [8]'' 7.636{{c}}

|-

| 20

| Major 10th10

| Diminished second

| ~~1092¢~~ [20] 1.~~091¢~~

| 1092{{c}} [20] 1.091{{c}}

| ~~1080¢~~ [2] ~~-10~~.~~909¢~~

| 1080{{c}} [2] −10.909{{c}}

|-

| 21

| Augmented 10th10 Diminished 11th10

| Major seventh

| ~~1140¢~~ [12] -5.~~4545¢~~

| 1140{{c}} [12] −5.4545{{c}}

| ~~1152¢~~ [10] 6.~~5455¢~~

| 1152{{c}} [10] 6.5455{{c}}

|-

| 22

| 11th10

| Octave

| ~~1200¢~~ [22]

| 1200{{c}} [22]

| N/A

|}

Alternatively, the unmodified, symmetrical [[2mos]] scale 5 4 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 5 4 5 could be used instead. This scale is very similar to the modified version except that it lacks dog tritones; every 6th10 is exactly 600 ~~cents~~. Because it repeats every half-octave, this scale could be used to construct straight-fretted guitars as long as they are {{w|Augmented-fourths tuning|tuned in tritones}}. This makes guitar construction much easier compared to other non-equally-tempered scales. The modmos would allow ''almost'' all the frets to be straight if the tritones tuning is used; only every eleventh fret would need to be curved. While the 2mos is simpler, the modmos very closely approximates the [[Indian]] sruti system.

Alternatively, the unmodified, symmetrical [[2mos]] scale 5 4 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 5 4 5 could be used instead. This scale is very similar to the modified version except that it lacks dog tritones; every 6th10 is exactly 600{{c}}. Because it repeats every half-octave, this scale could be used to construct straight-fretted guitars as long as they are {{w|Augmented-fourths tuning|tuned in tritones}}. This makes guitar construction much easier compared to other non-equally-tempered scales. The modmos would allow ''almost'' all the frets to be straight if the tritones tuning is used; only every eleventh fret would need to be curved. While the 2mos is simpler, the modmos very closely approximates the [[Indian]] sruti system.

Other, "gentle" alternatives to 22edo for pajara include [[78edo|78ddd]] and [[56edo|56d]]. The resulting 22-note scales have large and small steps in ratios of 4:3 or 3:2, respectively, and the rest of the spectrum of 22 & [[34edo|34d]] temperaments is also usable. On the other hand, the "rough" alternatives to 22edo for pajara include [[58edo|58d]] and [[46edo|46d]]. The resulting 22-note scales have large and small steps in ratios of 4:1 or 3:1, respectively, and the rest of the spectrum of 12 & [[34edo|34d]] temperaments up to 58d is also usable.

Other, "gentle" alternatives to 22edo for pajara include [[78edo|78ddd]] and [[56edo|56d]]. The resulting 22-note scales have large and small steps in ratios of 4:3 or 3:2, respectively, and the rest of the spectrum of {{nowrap|22 & [[34edo|34d]]}} temperaments is also usable. On the other hand, the "rough" alternatives to 22edo for pajara include [[58edo|58d]] and [[46edo|46d]]. The resulting 22-note scales have large and small steps in ratios of 4:1 or 3:1, respectively, and the rest of the spectrum of {{nowrap|12 & [[34edo|34d]]}} temperaments up to 58d is also usable.

== Video ==

<youtube>shcrw2vtmJU</youtube>

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|100}}
+{{ED intro}}
 == Theory ==
@@ Line 21: / Line 21: @@
 === 100bddd and the 22-note scales ===
+The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to [[22edo]] for [[pajara]] temperament and for tuning [[Paul Erlich]]'s decatonic scales, as well as diatonic scales (via [[superpyth]] temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60{{c}} which just barely falls within the 60-80 cent range [http://www.anaphoria.com/Secor17puzzle.pdf favored by George Secor] for neomedieval compositions.
-The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to [[22edo]] for [[pajara]] temperament and for tuning [[Paul Erlich]]'s decatonic scales, as well as diatonic scales (via [[superpyth]] temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60¢ which just barely falls within the 60-80 cent range [http://www.anaphoria.com/Secor17puzzle.pdf favored by George Secor] for neomedieval compositions.
 The 22-note [[modmos]] 5 4 5 4 5 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 could be used to construct a 22-tone piano; this tuning has two chains of fifths (one with 10 notes in it and one with 12), and thus has two "wolf" fifths. Much like meantone, this tuning has "wolf" intervals but in this case they are only twelve cents away from their pure counterparts, and as such they don't sound nearly as bad. They are xenharmonic but not unpleasant and could easily be used in compositions, which makes this tuning akin to well temperaments as well as to meantone. Because most if not all of the "wolves" are still usable (albeit xenharmonic), it might be better to use the term "dog" rather than wolf for these intervals. Dog intervals frequently provide ''closer'' matches to intervals involving the 7th and 11th harmonics. Even if the dog intervals are completely avoided, this modmos still allows for decatonic music in 12 different keys, and diatonic (superpyth) music in 10 different keys, and thus the freedom of modulation and key choice is still comparable to [[12edo]].
@@ Line 28: / Line 27: @@
 {| class="wikitable"
 |-
-! Steps of 22-note Modmos
+! Steps of 22-note MODMOS
-! Interval Name (Decatonic)
+! Interval name (decatonic)
-! Interval Name (Superpyth diatonic)
+! Interval name (superpyth diatonic)
-! Pure Interval Size [Multiplicity] <br /> Difference from 22edo
+! Pure interval size [multiplicity]<br />Difference from 22edo
-! Dog Interval Size [Multiplicity] <br /> Difference from 22edo
+! Dog interval size [multiplicity]<br />Difference from 22edo
 |-
 | 1
 | Diminished 2nd<sub>10</sub>
 | Minor second
-| 60¢ [12] <br />5.4545¢
+| 60{{c}} [12] <br />5.4545{{c}}
-| 48¢ [10] <br />-6.5455¢
+| 48{{c}} [10] <br />−6.5455{{c}}
 |-
 | 2
 | Minor 2nd<sub>10</sub>
 | Augmented seventh
-| 108¢ [20] <br />-1.091¢
+| 108{{c}} [20] <br />−1.091{{c}}
-| 120¢ [2] <br />10.909¢
+| 120{{c}} [2] <br />10.909{{c}}
 |-
 | 3
 | Major 2nd<sub>10</sub>
 | Augmented unison
-| ''168¢ [14]'' <br />4.364¢
+| ''168{{c}} [14]'' <br />4.364{{c}}
-| ''156¢ [8]'' <br />-7.636¢
+| ''156{{c}} [8]'' <br />−7.636{{c}}
 |-
 | 4
 | Minor 3rd<sub>10</sub>
 | Major second
-| 216¢ [18] <br />-2.182¢
+| 216{{c}} [18] <br />−2.182{{c}}
-| 228¢ [4] <br />9.818¢
+| 228{{c}} [4] <br />9.818{{c}}
 |-
 | 5
 | Major 3rd<sub>10</sub>
 | Minor third
-| 276¢ [16] <br />3.273¢
+| 276{{c}} [16] <br />3.273{{c}}
-| 264¢ [6] <br />-8.727¢
+| 264{{c}} [6] <br />−8.727{{c}}
 |-
 | 6
 | Minor 4th<sub>10</sub>
 | Diminished fourth
-| ''324¢ [16]''<br />-3.273¢
+| ''324{{c}} [16]''<br />−3.273{{c}}
-| ''336¢ [6]''<br />8.727¢
+| ''336{{c}} [6]''<br />8.727{{c}}
 |-
 | 7
 | Major 4th<sub>10</sub>
 | Augmented second
-| 384¢ [18] <br />2.182¢
+| 384{{c}} [18] <br />2.182{{c}}
-| 372¢ [4] <br />-9.818¢
+| 372{{c}} [4] <br />−9.818{{c}}
 |-
 | 8
 | Augmented 4th<sub>10</sub> <br> Diminished 5th<sub>10</sub>
 | Major third
-| 432¢ [14] <br />-4.364¢
+| 432{{c}} [14] <br />−4.364{{c}}
-| 444¢ [8] <br />7.636¢
+| 444{{c}} [8] <br />7.636{{c}}
 |-
 | 9
 | Perfect 5th<sub>10</sub>
 | Perfect fourth
-| 492¢ [20] <br />1.091¢
+| 492{{c}} [20] <br />1.091{{c}}
-| 480¢ [2] <br />-10.909¢
+| 480{{c}} [2] <br />−10.909{{c}}
 |-
 | 10
 | Augmented 5th<sub>10</sub> <br> Diminished 6th<sub>10</sub>
 | Diminished fifth
-| 540¢ [12] <br />-5.4545¢
+| 540{{c}} [12] <br />−5.4545{{c}}
-| 552¢ [10] <br />6.5455¢
+| 552{{c}} [10] <br />6.5455{{c}}
 |-
 | 11
 | Perfect 6th<sub>10</sub>
 | Augmented third <br> Diminished sixth
-| 600¢ [20]
+| 600{{c}} [20]
-| 588¢ [1] <br>-12¢ <br> 612¢ [1] <br>12¢
+| 588{{c}} [1] <br>−12{{c}} <br> 612{{c}} [1] <br>12{{c}}
 |-
 | 12
 | Augmented 6th<sub>10</sub> <br> Diminished 7th<sub>10</sub>
 | Augmented fourth
-| 660¢ [12] <br />6.5455¢
+| 660{{c}} [12] <br />6.5455{{c}}
-| 648¢ [10] <br />-5.4545¢
+| 648{{c}} [10] <br />−5.4545{{c}}
 |-
 | 13
 | Perfect 7th<sub>10</sub>
 | Perfect fifth
-| 708¢ [20] <br />-1.091¢
+| 708{{c}} [20] <br />−1.091{{c}}
-| 720¢ [2] <br />10.909¢
+| 720{{c}} [2] <br />10.909{{c}}
 |-
 | 14
@@ Line 117: / Line 116: @@
 Diminished 8th<sub>10</sub>
 | Minor sixth
-| 768¢ [14] <br />4.364¢
+| 768{{c}} [14] <br />4.364{{c}}
-| 756¢ [8] <br />-7.636¢
+| 756{{c}} [8] <br />−7.636{{c}}
 |-
 | 15
 | Minor 8th<sub>10</sub>
 | Diminished seventh
-| 816¢ [18] <br />-2.182¢
+| 816{{c}} [18] <br />−2.182{{c}}
-| 828¢ [4] <br />9.818¢
+| 828{{c}} [4] <br />9.818{{c}}
 |-
 | 16
 | Major 8th<sub>10</sub>
 | Augmented fifth
-| ''876¢ [16]''<br />3.273¢
+| ''876{{c}} [16]''<br />3.273{{c}}
-| ''864¢ [6]''<br />-8.727¢
+| ''864{{c}} [6]''<br />−8.727{{c}}
 |-
 | 17
 | Minor 9th<sub>10</sub>
 | Major sixth
-| 924¢ [16] <br />-3.273¢
+| 924{{c}} [16] <br />−3.273{{c}}
-| 936¢ [6] <br />8.727¢
+| 936{{c}} [6] <br />8.727{{c}}
 |-
 | 18
 | Major 9th<sub>10</sub>
 | Minor seventh
-| 984¢ [18] <br />2.182¢
+| 984{{c}} [18] <br />2.182{{c}}
-| 972¢ [4] <br />-9.818¢
+| 972{{c}} [4] <br />−9.818{{c}}
 |-
 | 19
 | Minor 10th<sub>10</sub>
 | Diminished octave
-| ''1032¢ [14]''<br />-4.364¢
+| ''1032{{c}} [14]''<br />−4.364{{c}}
-| ''1044¢ [8]''<br />7.636¢
+| ''1044{{c}} [8]''<br />7.636{{c}}
 |-
 | 20
 | Major 10th<sub>10</sub>
 | Diminished second
-| 1092¢ [20] <br />1.091¢
+| 1092{{c}} [20] <br />1.091{{c}}
-| 1080¢ [2] <br />-10.909¢
+| 1080{{c}} [2] <br />−10.909{{c}}
 |-
 | 21
 | Augmented 10th<sub>10</sub> <br> Diminished 11th<sub>10</sub>
 | Major seventh
-| 1140¢ [12] <br />-5.4545¢
+| 1140{{c}} [12] <br />−5.4545{{c}}
-| 1152¢ [10] <br />6.5455¢
+| 1152{{c}} [10] <br />6.5455{{c}}
 |-
 | 22
 | 11th<sub>10</sub>
 | Octave
-| 1200¢ [22]
+| 1200{{c}} [22]
 | N/A
 |}
-Alternatively, the unmodified, symmetrical [[2mos]] scale 5 4 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 5 4 5 could be used instead. This scale is very similar to the modified version except that it lacks dog tritones; every 6th<sub>10</sub> is exactly 600 cents. Because it repeats every half-octave, this scale could be used to construct straight-fretted guitars as long as they are {{w|Augmented-fourths tuning|tuned in tritones}}. This makes guitar construction much easier compared to other non-equally-tempered scales. The modmos would allow ''almost'' all the frets to be straight if the tritones tuning is used; only every eleventh fret would need to be curved. While the 2mos is simpler, the modmos very closely approximates the [[Indian]] sruti system.
+Alternatively, the unmodified, symmetrical [[2mos]] scale 5 4 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 5 4 5 could be used instead. This scale is very similar to the modified version except that it lacks dog tritones; every 6th<sub>10</sub> is exactly 600{{c}}. Because it repeats every half-octave, this scale could be used to construct straight-fretted guitars as long as they are {{w|Augmented-fourths tuning|tuned in tritones}}. This makes guitar construction much easier compared to other non-equally-tempered scales. The modmos would allow ''almost'' all the frets to be straight if the tritones tuning is used; only every eleventh fret would need to be curved. While the 2mos is simpler, the modmos very closely approximates the [[Indian]] sruti system.
-Other, "gentle" alternatives to 22edo for pajara include [[78edo|78ddd]] and [[56edo|56d]]. The resulting 22-note scales have large and small steps in ratios of 4:3 or 3:2, respectively, and the rest of the spectrum of 22 & [[34edo|34d]] temperaments is also usable. On the other hand, the "rough" alternatives to 22edo for pajara include [[58edo|58d]] and [[46edo|46d]]. The resulting 22-note scales have large and small steps in ratios of 4:1 or 3:1, respectively, and the rest of the spectrum of 12 & [[34edo|34d]] temperaments up to 58d is also usable.
+Other, "gentle" alternatives to 22edo for pajara include [[78edo|78ddd]] and [[56edo|56d]]. The resulting 22-note scales have large and small steps in ratios of 4:3 or 3:2, respectively, and the rest of the spectrum of {{nowrap|22 &amp; [[34edo|34d]]}} temperaments is also usable. On the other hand, the "rough" alternatives to 22edo for pajara include [[58edo|58d]] and [[46edo|46d]]. The resulting 22-note scales have large and small steps in ratios of 4:1 or 3:1, respectively, and the rest of the spectrum of {{nowrap|12 &amp; [[34edo|34d]]}} temperaments up to 58d is also usable.
 == Video ==
 <youtube>shcrw2vtmJU</youtube>