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*[[Greeley8]]
*[[Greeley8]]
*[[Greeley15]]
*[[Greeley15]]
 
Since 100edo has a step of 12 cents, it also allows one to use its MOS scales as circulating temperaments.
=100bddd and the 22-note scales=
{| class="wikitable"
|+Circulating temperaments in 100edo
! Tones
!Pattern
! L:s
|-
|5
|[[5edo]]
|equal
|-
| 6
|[[4L 2s]]
|17:16
|-
|7
|[[2L 5s]]
|15:14
|-
|8
|[[4L 4s]]
|13:12
|-
|9
|[[1L 8s]]
|12:11
|-
| 10
|[[10edo]]
|equal
|-
|11
|[[1L 10s]]
|10:9
|-
|12
|[[4L 8s]]
|9:8
|-
|13
|[[9L 4s]]
| rowspan="2" |8:7
|-
|14
|[[2L 12s]]
|-
|15
|[[10L 5s]]
| rowspan="2" |7:6
|-
|16
| 4L 12s
|-
| 17
|[[15L 2s]]
| rowspan="3" |6:5
|-
|18
| 10L 8s
|-
|19
|[[5L 14s]]
|-
|20
|[[20edo]]
|equal
|-
|21
|16L 5s
| rowspan="4" |5:4
|-
| 22
|12L 10s
|-
|23
|8L 15s
|-
|24
|4L 20s
|-
|25
|[[25edo]]
|equal
|-
|26
|22L 4s
| rowspan="8" |4:3
|-
|27
|19L 8s
|-
| 28
|16L 12s
|-
|29
|13L 16s
|-
|30
|10L 20s
|-
|31
|7L 24s
|-
| 32
|4L 28s
|-
|33
|1L 32s
|-
|34
|32L 2s
| rowspan="16" | 3:2
|-
|35
|30L 5s
|-
|36
|28L 8s
|-
|37
|26L 11s
|-
|38
| 24L 14s
|-
|39
| 22L 17s
|-
|40
| 20L 20s
|-
|41
|18L 23s
|-
|42
|16L 26s
|-
| 43
| 14L 29s
|-
| 44
|12L 32s
|-
| 45
|10L 35s
|-
|46
|8L 38s
|-
|47
|6L 41s
|-
|48
|4L 44s
|-
|49
|2L 47s
|-
|50
|[[50edo]]
| equal
|-
| 51
|49L 2s
| rowspan="29" |2:1
|-
|52
|48L 4s
|-
|53
|47L 6s
|-
|54
|46L 8s
|-
| 55
| 45L 10s
|-
|56
|44L 12s
|-
| 57
| 43L 14s
|-
|58
|42L 16s
|-
|59
|41L 18s
|-
|60
|40L 20s
|-
|61
|39L 22s
|-
| 62
|38L 24s
|-
|63
|37L 26s
|-
|64
|36L 28s
|-
| 65
|35L 30s
|-
| 66
|34L 32s
|-
|67
|33L 34s
|-
|68
|32L 36s
|-
|69
|31L 38s
|-
|70
|30L 40s
|-
|71
|29L 42s
|-
|72
|28L 44s
|-
|73
|27L 46s
|-
|74
|26L 48s
|-
|75
|25L 50s
|-
|76
| 24L 52s
|-
|77
| 23L 54s
|-
|78
|22L 56s
|-
|79
|21L 58s
|}
= 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|22EDO]] for [[Diaschismic family|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 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|22EDO]] for [[Diaschismic family|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.
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{| class="wikitable"
{| 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]
| |Pure interval size [multiplicity]
| | Dog interval size [multiplicity]
| |Dog interval size [multiplicity]
|-
|-
| | 1
| |1
| | Diminished 2nd<span style="vertical-align: sub;">10</span>
| |Diminished 2nd<span style="vertical-align: sub;">10</span>
| | Minor second
| |Minor second
| | 60¢ [12]
| |60¢ [12]
| | 48¢ [10]
| |48¢ [10]
|-
|-
| | 2
| | 2
| | Minor 2nd<span style="vertical-align: sub;">10</span>
| |Minor 2nd<span style="vertical-align: sub;">10</span>
| | Augmented seventh
| |Augmented seventh
| | 108¢ [20]
| |108¢ [20]
| | 120¢ [2]
| |120¢ [2]
|-
|-
| | 3
| |3
| | Major 2nd<span style="vertical-align: sub;">10</span>
| |Major 2nd<span style="vertical-align: sub;">10</span>
| | Augmented unison
| |Augmented unison
| | ''168¢ [14]''
| |''168¢ [14]''
| | ''156<span style="line-height: 1.5;">¢ [8]</span>''
| |''156<span style="line-height: 1.5;">¢ [8]</span>''
|-
|-
| | 4
| |4
| | Minor 3rd<span style="vertical-align: sub;">10</span>
| |Minor 3rd<span style="vertical-align: sub;">10</span>
| | Major second
| |Major second
| | 216¢ [18]
| | 216¢ [18]
| | 228¢ [4]
| |228¢ [4]
|-
|-
| | 5
| |5
| | Major 3rd<span style="vertical-align: sub;">10</span>
| |Major 3rd<span style="vertical-align: sub;">10</span>
| | Minor third
| |Minor third
| | 276¢ [16]
| |276¢ [16]
| | 264¢ [6]
| |264¢ [6]
|-
|-
| | 6
| |6
| | Minor 4th<span style="vertical-align: sub;">10</span>
| |Minor 4th<span style="vertical-align: sub;">10</span>
| |Diminished fourth
| |Diminished fourth
| | ''324¢ [16]''
| |''324¢ [16]''
| | ''336¢ [6]''
| |''336¢ [6]''
|-
|-
| | 7
| |7
| | Major 4th<span style="vertical-align: sub;">10</span>
| |Major 4th<span style="vertical-align: sub;">10</span>
| | Augmented second
| |Augmented second
| | 384¢ [18]
| |384¢ [18]
| | 372¢ [4]
| |372¢ [4]
|-
|-
| | 8
| |8
| | Augmented 4th<span style="vertical-align: sub;">10</span>
| |Augmented 4th<span style="vertical-align: sub;">10</span>


<span style="vertical-align: sub;">Diminished </span>5th<span style="vertical-align: sub;">10</span>
<span style="vertical-align: sub;">Diminished </span>5th<span style="vertical-align: sub;">10</span>
| | Major third
| |Major third
| | 432¢ [14]
| |432¢ [14]
| | 444¢ [8]
| |444¢ [8]
|-
|-
| | 9
| |9
| | Perfect 5th<span style="vertical-align: sub;">10</span>
| |Perfect 5th<span style="vertical-align: sub;">10</span>
| | Perfect fourth
| |Perfect fourth
| | 492¢ [20]
| |492¢ [20]
| | 480¢ [2]
| |480¢ [2]
|-
|-
| | 10
| |10
| | Augmented 5th<span style="vertical-align: sub;">10</span>
| |Augmented 5th<span style="vertical-align: sub;">10</span>


Diminished 6th<span style="vertical-align: sub;">10</span>
Diminished 6th<span style="vertical-align: sub;">10</span>
| | Diminished fifth
| | Diminished fifth
| | 540¢ [12]
| |540¢ [12]
| | 552¢ [10]
| |552¢ [10]
|-
|-
| | 11
| |11
| | Perfect 6th<span style="vertical-align: sub;">10</span>
| |Perfect 6th<span style="vertical-align: sub;">10</span>
| | Augmented third
| |Augmented third


Diminished sixth
Diminished sixth
| | 600¢ [20]
| |600¢ [20]
| | 588¢ [1]
| |588¢ [1]


612¢ [1]
612¢ [1]
|-
|-
| | 12
| |12
| | Augmented 6th<span style="vertical-align: sub;">10</span>
| |Augmented 6th<span style="vertical-align: sub;">10</span>


Diminished 7th<span style="vertical-align: sub;">10</span>
Diminished 7th<span style="vertical-align: sub;">10</span>
| | Augmented fourth
| |Augmented fourth
| | 660¢ [12]
| |660¢ [12]
| | 648¢ [10]
| |648¢ [10]
|-
|-
| | 13
| |13
| | Perfect 7th<span style="vertical-align: sub;">10</span>
| |Perfect 7th<span style="vertical-align: sub;">10</span>
| | Perfect fifth
| |Perfect fifth
| | 708¢ [20]
| |708¢ [20]
| | 720¢ [2]
| |720¢ [2]
|-
|-
| | 14
| |14
| | Augmented 7th<span style="vertical-align: sub;">10</span>
| |Augmented 7th<span style="vertical-align: sub;">10</span>


Diminished 8th<span style="vertical-align: sub;">10</span>
Diminished 8th<span style="vertical-align: sub;">10</span>
| | Minor sixth
| |Minor sixth
| | 768¢ [14]
| |768¢ [14]
| | 756¢ [8]
| |756¢ [8]
|-
|-
| | 15
| |15
| | Minor 8th<span style="vertical-align: sub;">10</span>
| |Minor 8th<span style="vertical-align: sub;">10</span>
| | Diminished seventh
| | Diminished seventh
| | 816¢ [18]
| |816¢ [18]
| | 828¢ [4]
| |828¢ [4]
|-
|-
| | 16
| |16
| | Major 8th<span style="vertical-align: sub;">10</span>
| |Major 8th<span style="vertical-align: sub;">10</span>
| | Augmented fifth
| |Augmented fifth
| | ''876¢ [16]''
| |''876¢ [16]''
| | ''864¢ [6]''
| |''864¢ [6]''
|-
|-
| | 17
| | 17
| | Minor 9th<span style="vertical-align: sub;">10</span>
| |Minor 9th<span style="vertical-align: sub;">10</span>
| | Major sixth
| |Major sixth
| | 924¢ [16]
| |924¢ [16]
| | 936¢ [6]
| |936¢ [6]
|-
|-
| | 18
| |18
| | Major 9th<span style="vertical-align: sub;">10</span>
| |Major 9th<span style="vertical-align: sub;">10</span>
| | Minor seventh
| |Minor seventh
| | 984¢ [18]
| |984¢ [18]
| | 972¢ [4]
| |972¢ [4]
|-
|-
| | 19
| |19
| | Minor 10th<span style="vertical-align: sub;">10</span>
| | Minor 10th<span style="vertical-align: sub;">10</span>
| | Diminished octave
| |Diminished octave
| | ''1032¢ [14]''
| |''1032¢ [14]''
| | ''1044¢ [8]''
| |''1044¢ [8]''
|-
|-
| | 20
| |20
| | Major 10th<span style="vertical-align: sub;">10</span>
| | Major 10th<span style="vertical-align: sub;">10</span>
| | Diminished second
| |Diminished second
| | 1092¢ [20]
| |1092¢ [20]
| | 1080¢ [2]
| |1080¢ [2]
|-
|-
| | 21
| |21
| | Augmented 10th<span style="vertical-align: sub;">10</span>
| |Augmented 10th<span style="vertical-align: sub;">10</span>


Diminished 11th<span style="vertical-align: sub;">10</span>
Diminished 11th<span style="vertical-align: sub;">10</span>
| | Major seventh
| |Major seventh
| | 1140¢ [12]
| |1140¢ [12]
| | 1152¢ [10]
| |1152¢ [10]
|-
|-
| | 22
| |22
| | 11th<span style="vertical-align: sub;">10</span>
| |11th<span style="vertical-align: sub;">10</span>
| | Octave
| |Octave
| | 1200¢ [22]
| |1200¢ [22]
| | N/A
| |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<span style="vertical-align: sub;">10 </span>is exactly 600 cents. Because it repeats every half-octave, this scale could be used to construct straight-fretted guitars as long as they [https://en.wikipedia.org/wiki/Augmented-fourths_tuning are 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<span style="vertical-align: sub;">10 </span>is exactly 600 cents. Because it repeats every half-octave, this scale could be used to construct straight-fretted guitars as long as they [[wikipedia:Augmented-fourths_tuning|are 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 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.
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