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== Intervals ==
== Intervals ==


{| class="wikitable"
{| class="wikitable" style="text-align:center"
! #
! Cents
! Approximate Ratios'''*'''
! colspan="3" | [[Ups_and_Downs_Notation|Ups and Downs Notation]]
! Andrew's <br> Solfege Syllables
|-
|-
! |
| 0
! | Cents
| 0.00
! | Approximate Ratios'''*'''
| [[1/1|1/1]]
! colspan="3" |[[Ups_and_Downs_Notation|Ups and Downs Notation]]
! | Andrew's
Solfege Syllables
|-
| style="text-align:center;" | 0
| style="text-align:center;" | 0.00
| | [[1/1|1/1]]
| perfect unison
| perfect unison
| style="text-align:center;" | P1
| P1
| style="text-align:center;" | D
| D
| | do
| style="text-align:left" | do
|-
|-
| style="text-align:center;" | 1
| 1
| style="text-align:center;" | 29.27
| 29.27
| | [[81/80|81/80]], [[64/63]]
| [[81/80|81/80]], [[64/63]]
| up-unison
| up-unison
| style="text-align:center;" | ^1
| ^1
| style="text-align:center;" | ^D
| ^D
| | di
| di
|-
|-
| style="text-align:center;" | 2
| 2
| style="text-align:center;" | 58.54
| 58.54
| | [[25/24|25/24]], [[28/27|28/27]], [[33/32|33/32]]
| [[25/24|25/24]], [[28/27|28/27]], [[33/32|33/32]]
| double-up unison, downminor 2nd
| double-up unison, downminor 2nd
| style="text-align:center;" | ^^1, vm2
| ^^1, vm2
| style="text-align:center;" | ^^D, vEb
| ^^D, vEb
| | ro
| ro
|-
|-
| style="text-align:center;" | 3
| 3
| style="text-align:center;" | 87.805
| 87.805
| | [[21/20|21/20]], [[22/21|22/21]], [[19/18]], [[20/19]]
| [[21/20|21/20]], [[22/21|22/21]], [[19/18]], [[20/19]]
| down-aug 1sn, minor 2nd
| down-aug 1sn, minor 2nd
| style="text-align:center;" | vA1, m2
| vA1, m2
| style="text-align:center;" | vD#, Eb
| vD#, Eb
| | rih
| rih
|-
|-
| style="text-align:center;" | 4
| 4
| style="text-align:center;" | 117.07
| 117.07
| | [[16/15|16/15]], [[15/14|15/14]], [[14/13]]
| [[16/15|16/15]], [[15/14|15/14]], [[14/13]]
| augmented 1sn, upminor 2nd
| augmented 1sn, upminor 2nd
| style="text-align:center;" | A1, ^m2
| A1, ^m2
| style="text-align:center;" | D#, ^Eb
| D#, ^Eb
| | ra
| ra
|-
|-
| style="text-align:center;" | 5
| 5
| style="text-align:center;" | 146.34
| 146.34
| | [[12/11|12/11]], [[13/12]]
| [[12/11|12/11]], [[13/12]]
| mid 2nd
| mid 2nd
| style="text-align:center;" | ~2
| ~2
| style="text-align:center;" | ^D#, vvE
| ^D#, vvE
| | ru
| ru
|-
|-
| style="text-align:center;" | 6
| 6
| style="text-align:center;" | 175.61
| 175.61
| | [[10/9|10/9]], [[11/10|11/10]], [[21/19]]
| [[10/9|10/9]], [[11/10|11/10]], [[21/19]]
| downmajor 2nd
| downmajor 2nd
| style="text-align:center;" | vM2
| vM2
| style="text-align:center;" | vE
| vE
| | reh
| reh
|-
|-
| style="text-align:center;" | 7
| 7
| style="text-align:center;" | 204.88
| 204.88
| | [[9/8|9/8]]
| [[9/8|9/8]]
| major 2nd
| major 2nd
| style="text-align:center;" | M2
| M2
| style="text-align:center;" | E
| E
| | re
| re
|-
|-
| style="text-align:center;" | 8
| 8
| style="text-align:center;" | 234.15
| 234.15
| | [[8/7|8/7]], [[15/13]]
| [[8/7|8/7]], [[15/13]]
| upmajor 2nd
| upmajor 2nd
| style="text-align:center;" | ^M2
| ^M2
| style="text-align:center;" | ^E
| ^E
| | ri
| ri
|-
|-
| style="text-align:center;" | 9
| 9
| style="text-align:center;" | 263.415
| 263.415
| | [[7/6|7/6]], [[22/19]]
| [[7/6|7/6]], [[22/19]]
| downminor 3rd
| downminor 3rd
| style="text-align:center;" | vm3
| vm3
| style="text-align:center;" | vF
| vF
| | ma
| ma
|-
|-
| style="text-align:center;" | 10
| 10
| style="text-align:center;" | 292.68
| 292.68
| | [[32/27|32/27]], [[13/11]], [[19/16]]
| [[32/27|32/27]], [[13/11]], [[19/16]]
| minor 3rd
| minor 3rd
| style="text-align:center;" | m3
| m3
| style="text-align:center;" | F
| F
| | meh
| meh
|-
|-
| style="text-align:center;" | 11
| 11
| style="text-align:center;" | 321.95
| 321.95
| | [[6/5|6/5]]
| [[6/5|6/5]]
| upminor 3rd
| upminor 3rd
| style="text-align:center;" | ^m3
| ^m3
| style="text-align:center;" | ^F
| ^F
| | me
| me
|-
|-
| style="text-align:center;" | 12
| 12
| style="text-align:center;" | 351.22
| 351.22
| | [[11/9|11/9]], [[27/22|27/22]], [[16/13]]
| [[11/9|11/9]], [[27/22|27/22]], [[16/13]]
| mid 3rd
| mid 3rd
| style="text-align:center;" | ~3
| ~3
| style="text-align:center;" | ^^F, vGb
| ^^F, vGb
| | mu
| mu
|-
|-
| style="text-align:center;" | 13
| 13
| style="text-align:center;" | 380.49
| 380.49
| | [[5/4|5/4]], [[26/21]]
| [[5/4|5/4]], [[26/21]]
| downmajor 3rd
| downmajor 3rd
| style="text-align:center;" | vM3
| vM3
| style="text-align:center;" | vF#, Gb
| vF#, Gb
| | mi
| mi
|-
|-
| style="text-align:center;" | 14
| 14
| style="text-align:center;" | 409.76
| 409.76
| | [[81/64]], [[14/11|14/11]], [[24/19]], [[19/15]]
| [[81/64]], [[14/11|14/11]], [[24/19]], [[19/15]]
| major 3rd
| major 3rd
| style="text-align:center;" | M3
| M3
| style="text-align:center;" | F#, ^Gb
| F#, ^Gb
| | maa
| maa
|-
|-
| style="text-align:center;" | 15
| 15
| style="text-align:center;" | 439.02
| 439.02
| | [[9/7|9/7,]] [[32/25|32/25]]
| [[9/7|9/7,]] [[32/25|32/25]]
| upmajor 3rd
| upmajor 3rd
| style="text-align:center;" | ^M3
| ^M3
| style="text-align:center;" | ^F#, vvG
| ^F#, vvG
| | mo
| mo
|-
|-
| style="text-align:center;" | 16
| 16
| style="text-align:center;" | 468.29
| 468.29
| | [[21/16|21/16]], [[13/10]]
| [[21/16|21/16]], [[13/10]]
| down-4th
| down-4th
| style="text-align:center;" | v4
| v4
| style="text-align:center;" | vG
| vG
| | fe
| fe
|-
|-
| style="text-align:center;" | 17
| 17
| style="text-align:center;" | 497.56
| 497.56
| | [[4/3|4/3]]
| [[4/3|4/3]]
| perfect 4th
| perfect 4th
| style="text-align:center;" | P4
| P4
| style="text-align:center;" | G
| G
| | fa
| fa
|-
|-
| style="text-align:center;" | 18
| 18
| style="text-align:center;" | 526.83
| 526.83
| | [[15/11|15/11]], [[27/20|27/20]], [[19/14]]
| [[15/11|15/11]], [[27/20|27/20]], [[19/14]]
| up-4th
| up-4th
| style="text-align:center;" | ^4
| ^4
| style="text-align:center;" | ^G
| ^G
| | fih
| fih
|-
|-
| style="text-align:center;" | 19
| 19
| style="text-align:center;" | 556.1
| 556.1
| | [[11/8|11/8]], [[18/13]], [[26/19]]
| [[11/8|11/8]], [[18/13]], [[26/19]]
| mid-4th
| mid-4th
| style="text-align:center;" | ~4
| ~4
| style="text-align:center;" | ^^G, vAb
| ^^G, vAb
| | fu
| fu
|-
|-
| style="text-align:center;" | 20
| 20
| style="text-align:center;" | 585.37
| 585.37
| | [[7/5|7/5]]
| [[7/5|7/5]]
| downaug 4th, dim 5th
| downaug 4th, dim 5th
| style="text-align:center;" | vA4, d5
| vA4, d5
| style="text-align:center;" | vG#, Ab
| vG#, Ab
| | fi
| fi
|-
|-
| style="text-align:center;" | 21
| 21
| style="text-align:center;" | 614.63
| 614.63
| | [[10/7|10/7]]
| [[10/7|10/7]]
| aug 4th, updim 5th
| aug 4th, updim 5th
| style="text-align:center;" | A4, ^d5
| A4, ^d5
| style="text-align:center;" | G#, ^Ab
| G#, ^Ab
| | se
| se
|-
|-
| style="text-align:center;" | 22
| 22
| style="text-align:center;" | 643.90
| 643.90
| | [[16/11|16/11]], [[13/9]], [[19/13]]
| [[16/11|16/11]], [[13/9]], [[19/13]]
| mid-5th
| mid-5th
| style="text-align:center;" | ~5
| ~5
| style="text-align:center;" | vvA
| vvA
| | su
| su
|-
|-
| style="text-align:center;" | 23
| 23
| style="text-align:center;" | 673.17
| 673.17
| | [[22/15|22/15]], [[40/27|40/27]], [[28/19]]
| [[22/15|22/15]], [[40/27|40/27]], [[28/19]]
| down-5th
| down-5th
| style="text-align:center;" | v5
| v5
| style="text-align:center;" | vA
| vA
| | sih
| sih
|-
|-
| style="text-align:center;" | 24
| 24
| style="text-align:center;" | 702.44
| 702.44
| | [[3/2|3/2]]
| [[3/2|3/2]]
| perfect 5th
| perfect 5th
| style="text-align:center;" | P5
| P5
| style="text-align:center;" | A
| A
| | sol
| sol
|-
|-
| style="text-align:center;" | 25
| 25
| style="text-align:center;" | 731.71
| 731.71
| | [[32/21|32/21]], [[20/13]]
| [[32/21|32/21]], [[20/13]]
| up-5th
| up-5th
| style="text-align:center;" | ^5
| ^5
| style="text-align:center;" | ^A
| ^A
| | si
| si
|-
|-
| style="text-align:center;" | 26
| 26
| style="text-align:center;" | 760.98
| 760.98
| | [[14/9|14/9]], [[25/16|25/16]]
| [[14/9|14/9]], [[25/16|25/16]]
| downminor 6th
| downminor 6th
| style="text-align:center;" | vm6
| vm6
| style="text-align:center;" | ^^A, vBb
| ^^A, vBb
| | lo
| lo
|-
|-
| style="text-align:center;" | 27
| 27
| style="text-align:center;" | 790.24
| 790.24
| | [[128/81|128/81]], [[11/7|11/7]], [[19/12]], [[30/19]]
| [[128/81|128/81]], [[11/7|11/7]], [[19/12]], [[30/19]]
| minor 6th
| minor 6th
| style="text-align:center;" | m6
| m6
| style="text-align:center;" | vA#, Bb
| vA#, Bb
| | leh
| leh
|-
|-
| style="text-align:center;" | 28
| 28
| style="text-align:center;" | 819.51
| 819.51
| | [[8/5|8/5]], [[21/13]]
| [[8/5|8/5]], [[21/13]]
| upminor 6th
| upminor 6th
| style="text-align:center;" | ^m6
| ^m6
| style="text-align:center;" | A#, ^Bb
| A#, ^Bb
| | le
| le
|-
|-
| style="text-align:center;" | 29
| 29
| style="text-align:center;" | 848.78
| 848.78
| | [[18/11|18/11]], [[44/27|44/27]], [[13/8]]
| [[18/11|18/11]], [[44/27|44/27]], [[13/8]]
| mid 6th
| mid 6th
| style="text-align:center;" | ~6
| ~6
| style="text-align:center;" | ^A#, vvB
| ^A#, vvB
| | lu
| lu
|-
|-
| style="text-align:center;" | 30
| 30
| style="text-align:center;" | 878.05
| 878.05
| | [[5/3|5/3]]
| [[5/3|5/3]]
| downmajor 6th
| downmajor 6th
| style="text-align:center;" | vM6
| vM6
| style="text-align:center;" | vB
| vB
| | la
| la
|-
|-
| style="text-align:center;" | 31
| 31
| style="text-align:center;" | 907.32
| 907.32
| | [[27/16|27/16]], [[22/13]], [[32/19]]
| [[27/16|27/16]], [[22/13]], [[32/19]]
| major 6th
| major 6th
| style="text-align:center;" | M6
| M6
| style="text-align:center;" | B
| B
| | laa
| laa
|-
|-
| style="text-align:center;" | 32
| 32
| style="text-align:center;" | 936.59
| 936.59
| | [[12/7|12/7]], [[19/11]]
| [[12/7|12/7]], [[19/11]]
| upmajor 6th
| upmajor 6th
| style="text-align:center;" | ^M6
| ^M6
| style="text-align:center;" | ^B
| ^B
| | li
| li
|-
|-
| style="text-align:center;" | 33
| 33
| style="text-align:center;" | 965.85
| 965.85
| | [[7/4|7/4]], [[26/15]]
| [[7/4|7/4]], [[26/15]]
| downminor 7th
| downminor 7th
| style="text-align:center;" | vm7
| vm7
| style="text-align:center;" | vC
| vC
| | ta
| ta
|-
|-
| style="text-align:center;" | 34
| 34
| style="text-align:center;" | 995.12
| 995.12
| | [[16/9|16/9]]
| [[16/9|16/9]]
| minor 7th
| minor 7th
| style="text-align:center;" | m7
| m7
| style="text-align:center;" | C
| C
| | teh
| teh
|-
|-
| style="text-align:center;" | 35
| 35
| style="text-align:center;" | 1024.39
| 1024.39
| | [[9/5|9/5]], [[20/11|20/11]], [[38/21]]
| [[9/5|9/5]], [[20/11|20/11]], [[38/21]]
| upminor 7th
| upminor 7th
| style="text-align:center;" | ^m7
| ^m7
| style="text-align:center;" | ^C
| ^C
| | te
| te
|-
|-
| style="text-align:center;" | 36
| 36
| style="text-align:center;" | 1053.66
| 1053.66
| | [[11/6|11/6]], [[24/13]]
| [[11/6|11/6]], [[24/13]]
| mid 7th
| mid 7th
| style="text-align:center;" | ~7
| ~7
| style="text-align:center;" | ^^C, vDb
| ^^C, vDb
| | tu
| tu
|-
|-
| style="text-align:center;" | 37
| 37
| style="text-align:center;" | 1082.93
| 1082.93
| | [[15/8|15/8]], [[28/15]], [[13/7]]
| [[15/8|15/8]], [[28/15]], [[13/7]]
| downmajor 7th
| downmajor 7th
| style="text-align:center;" | vM7
| vM7
| style="text-align:center;" | vC#, Db
| vC#, Db
| | ti
| ti
|-
|-
| style="text-align:center;" | 38
| 38
| style="text-align:center;" | 1112.195
| 1112.195
| | [[40/21|40/21]], [[21/11|21/11]], [[36/19]], [[19/10]]
| [[40/21|40/21]], [[21/11|21/11]], [[36/19]], [[19/10]]
| major 7th
| major 7th
| style="text-align:center;" | M7
| M7
| style="text-align:center;" | C#, ^Db
| C#, ^Db
| | taa
| taa
|-
|-
| style="text-align:center;" | 39
| 39
| style="text-align:center;" | 1141.46
| 1141.46
| | [[48/25|48/25]], [[27/14|27/14]], [[64/33|64/33]]
| [[48/25|48/25]], [[27/14|27/14]], [[64/33|64/33]]
| upmajor 7th
| upmajor 7th
| style="text-align:center;" | ^M7
| ^M7
| style="text-align:center;" | C#^, vvD
| C#^, vvD
| | to
| to
|-
|-
| style="text-align:center;" | 40
| 40
| style="text-align:center;" | 1170.73
| 1170.73
| | [[160/81|160/81]], [[63/32]]
| [[160/81|160/81]], [[63/32]]
| dim 8ve
| dim 8ve
| style="text-align:center;" | v8
| v8
| style="text-align:center;" | vD
| vD
| | da
| da
|-
|-
| style="text-align:center;" | 41
| 41
| style="text-align:center;" | 1200
| 1200
| | 2/1
| 2/1
| perfect 8ve
| perfect 8ve
| style="text-align:center;" | P8
| P8
| style="text-align:center;" | D
| D
| | do
| do
|}
|}
<nowiki>*</nowiki> Based on treating 41-edo as a 2.3.5.7.11.13.19 subgroup temperament; other approaches are possible.  
<nowiki>*</nowiki> Based on treating 41-edo as a 2.3.5.7.11.13.19 subgroup temperament; other approaches are possible.  
Line 363: Line 361:
Combining ups and downs notation with [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors:
Combining ups and downs notation with [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors:


{| class="wikitable"
{| class="wikitable" style="text-align:center"
! quality
! [[Kite's color notation|color]]
! monzo format
! examples
|-
|-
! | quality
| downminor
! | [[Kite's color notation|color]]
| zo
! | monzo format
| (a, b, 0, 1)
! | examples
| 7/6, 7/4
|-
|-
| style="text-align:center;" | downminor
| minor
| style="text-align:center;" | zo
| fourthward wa
| style="text-align:center;" | (a, b, 0, 1)
| (a, b) with b &lt; -1
| style="text-align:center;" | 7/6, 7/4
| 32/27, 16/9
|-
|-
| style="text-align:center;" | minor
| upminor
| style="text-align:center;" | fourthward wa
| gu
| style="text-align:center;" | (a, b) with b &lt; -1
| (a, b, -1)
| style="text-align:center;" | 32/27, 16/9
| 6/5, 9/5
|-
|-
| style="text-align:center;" | upminor
| mid
| style="text-align:center;" | gu
| ilo
| style="text-align:center;" | (a, b, -1)
| (a, b, 0, 0, 1)
| style="text-align:center;" | 6/5, 9/5
| 11/9, 11/6
|-
|-
| style="text-align:center;" | mid
| "
| style="text-align:center;" | ilo
| lu
| style="text-align:center;" | (a, b, 0, 0, 1)
| (a, b, 0, 0, -1)
| style="text-align:center;" | 11/9, 11/6
| 12/11, 18/11
|-
|-
| style="text-align:center;" | "
| downmajor
| style="text-align:center;" | lu
| yo
| style="text-align:center;" | (a, b, 0, 0, -1)
| (a, b, 1)
| style="text-align:center;" | 12/11, 18/11
| 5/4, 5/3
|-
|-
| style="text-align:center;" | downmajor
| major
| style="text-align:center;" | yo
| fifthward wa
| style="text-align:center;" | (a, b, 1)
| (a, b) with b &gt; 1
| style="text-align:center;" | 5/4, 5/3
| 9/8, 27/16
|-
|-
| style="text-align:center;" | major
| upmajor
| style="text-align:center;" | fifthward wa
| ru
| style="text-align:center;" | (a, b) with b &gt; 1
| (a, b, 0, -1)
| style="text-align:center;" | 9/8, 27/16
| 9/7, 12/7
|-
| style="text-align:center;" | upmajor
| style="text-align:center;" | ru
| style="text-align:center;" | (a, b, 0, -1)
| style="text-align:center;" | 9/7, 12/7
|}
|}


Line 415: Line 412:
All 41edo chords can be named using ups and downs. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are. Here are the zo, gu, ilo, yo and ru triads:
All 41edo chords can be named using ups and downs. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are. Here are the zo, gu, ilo, yo and ru triads:


{| class="wikitable"
{| class="wikitable" style="text-align:center"
! [[Kite's color notation|color of the 3rd]]
! JI chord
! notes as edosteps
! notes of C chord
! written name
! spoken name
|-
|-
! | [[Kite's color notation|color of the 3rd]]
| zo
! | JI chord
| 6:7:9
! | notes as edosteps
| 0-9-24
! | notes of C chord
| C vEb G
! | written name
| Cvm
! | spoken name
| C downminor
|-
|-
| style="text-align:center;" | zo
| gu
| style="text-align:center;" | 6:7:9
| 10:12:15
| style="text-align:center;" | 0-9-24
| 0-11-24
| style="text-align:center;" | C vEb G
| C ^Eb G
| style="text-align:center;" | Cvm
| C^m
| style="text-align:center;" | C downminor
| C upminor
|-
|-
| style="text-align:center;" | gu
| ilo
| style="text-align:center;" | 10:12:15
| 18:22:27
| style="text-align:center;" | 0-11-24
| 0-12-24
| style="text-align:center;" | C ^Eb G
| C vvE G
| style="text-align:center;" | C^m
| C~
| style="text-align:center;" | C upminor
| C mid
|-
|-
| style="text-align:center;" | ilo
| yo
| style="text-align:center;" | 18:22:27
| 4:5:6
| style="text-align:center;" | 0-12-24
| 0-13-24
| style="text-align:center;" | C vvE G
| C vE G
| style="text-align:center;" | C~
| Cv
| style="text-align:center;" | C mid
| C downmajor or C down
|-
|-
| style="text-align:center;" | yo
| ru
| style="text-align:center;" | 4:5:6
| 14:18:21
| style="text-align:center;" | 0-13-24
| 0-15-24
| style="text-align:center;" | C vE G
| C ^E G
| style="text-align:center;" | Cv
| C^
| style="text-align:center;" | C downmajor or C down
| C upmajor or C up
|-
| style="text-align:center;" | ru
| style="text-align:center;" | 14:18:21
| style="text-align:center;" | 0-15-24
| style="text-align:center;" | C ^E G
| style="text-align:center;" | C^
| style="text-align:center;" | C upmajor or C up
|}
|}
0-10-20 = D F Ab = Ddim = D dim
0-10-20 = D F Ab = Ddim = D dim


Line 498: Line 495:


{| class="wikitable" style="text-align:center;"
{| class="wikitable" style="text-align:center;"
! |
!  
! |prime 2
! prime 2
! |prime 3
! prime 3
! |prime 5
! prime 5
! |prime 7
! prime 7
! |prime 11
! prime 11
! |prime 13
! prime 13
! |prime 17
! prime 17
! |prime 19
! prime 19
|-
|-
! |error
! error
| 0.0¢
| 0.0¢
| +0.48¢
| +0.48¢
Line 518: Line 515:
| -4.8¢
| -4.8¢
|-
|-
! |[[fifthspan]]
! [[fifthspan]]
| 0
| 0
| +1
| +1
Line 528: Line 525:
| -3
| -3
|}
|}
The following table shows how [[Just-24|some prominent just intervals]] are represented in 41edo (ordered by absolute error).
The following table shows how [[Just-24|some prominent just intervals]] are represented in 41edo (ordered by absolute error).
{| class="wikitable"
 
{| class="wikitable" style="text-align:center"
! Interval, complement
! Error (abs., in [[cent|cents]])
|-
|-
| | '''Interval, complement'''
| '''[[4/3|4/3]], [[3/2|3/2]]'''
| | '''Error (abs., in [[cent|cents]])'''
| '''0.484'''
|-
|-
| style="text-align:center;" | '''[[4/3|4/3]], [[3/2|3/2]]'''
| [[9/8|9/8]], [[16/9|16/9]]
| style="text-align:center;" | '''0.484'''
| 0.968
|-
|-
| style="text-align:center;" | [[9/8|9/8]], [[16/9|16/9]]
| [[15/14|15/14]], [[28/15|28/15]]
| style="text-align:center;" | 0.968
| 2.370
|-
|-
| style="text-align:center;" | [[15/14|15/14]], [[28/15|28/15]]
| [[7/5|7/5]], [[10/7|10/7]]
| style="text-align:center;" | 2.370
| 2.854
|-
|-
| style="text-align:center;" | [[7/5|7/5]], [[10/7|10/7]]
| '''[[8/7|8/7]], [[7/4|7/4]]'''
| style="text-align:center;" | 2.854
| '''2.972'''
|-
|-
| style="text-align:center;" | '''[[8/7|8/7]], [[7/4|7/4]]'''
| [[7/6|7/6]], [[12/7|12/7]]
| style="text-align:center;" | '''2.972'''
| 3.456
|-
|-
| style="text-align:center;" | [[7/6|7/6]], [[12/7|12/7]]
| [[13/11|13/11]], [[22/13|22/13]]
| style="text-align:center;" | 3.456
| 3.473
|-
|-
| style="text-align:center;" | [[13/11|13/11]], [[22/13|22/13]]
| [[11/9|11/9]], [[18/11|18/11]]
| style="text-align:center;" | 3.473
| 3.812
|-
|-
| style="text-align:center;" | [[11/9|11/9]], [[18/11|18/11]]
| [[9/7|9/7]], [[14/9|14/9]]
| style="text-align:center;" | 3.812
| 3.940
|-
|-
| style="text-align:center;" | [[9/7|9/7]], [[14/9|14/9]]
| [[12/11|12/11]], [[11/6|11/6]]
| style="text-align:center;" | 3.940
| 4.296
|-
|-
| style="text-align:center;" | [[12/11|12/11]], [[11/6|11/6]]
| '''[[11/8|11/8]], [[16/11|16/11]]'''
| style="text-align:center;" | 4.296
| '''4.780'''
|-
|-
| style="text-align:center;" | '''[[11/8|11/8]], [[16/11|16/11]]'''
| [[16/15|16/15]], [[15/8|15/8]]
| style="text-align:center;" | '''4.780'''
| 5.342
|-
|-
| style="text-align:center;" | [[16/15|16/15]], [[15/8|15/8]]
| '''[[5/4|5/4]], [[8/5|8/5]]'''
| style="text-align:center;" | 5.342
| '''5.826'''
|-
|-
| style="text-align:center;" | '''[[5/4|5/4]], [[8/5|8/5]]'''
| [[6/5|6/5]], [[5/3|5/3]]
| style="text-align:center;" | '''5.826'''
| 6.310
|-
|-
| style="text-align:center;" | [[6/5|6/5]], [[5/3|5/3]]
| [[10/9|10/9]], [[9/5|9/5]]
| style="text-align:center;" | 6.310
| 6.794
|-
|-
| style="text-align:center;" | [[10/9|10/9]], [[9/5|9/5]]
| [[18/13|18/13]], [[13/9|13/9]]
| style="text-align:center;" | 6.794
| 7.285
|-
|-
| style="text-align:center;" | [[18/13|18/13]], [[13/9|13/9]]
| [[14/11|14/11]], [[11/7|11/7]]
| style="text-align:center;" | 7.285
| 7.752
|-
|-
| style="text-align:center;" | [[14/11|14/11]], [[11/7|11/7]]
| [[13/12|13/12]], [[24/13|24/13]]
| style="text-align:center;" | 7.752
| 7.769
|-
|-
| style="text-align:center;" | [[13/12|13/12]], [[24/13|24/13]]
| '''[[16/13|16/13]], [[13/8|13/8]]'''
| style="text-align:center;" | 7.769
| '''8.253'''
|-
|-
| style="text-align:center;" | '''[[16/13|16/13]], [[13/8|13/8]]'''
| [[15/11|15/11]], [[22/15|22/15]]
| style="text-align:center;" | '''8.253'''
| 10.122
|-
|-
| style="text-align:center;" | [[15/11|15/11]], [[22/15|22/15]]
| [[11/10|11/10]], [[20/11|20/11]]
| style="text-align:center;" | 10.122
| 10.606
|-
|-
| style="text-align:center;" | [[11/10|11/10]], [[20/11|20/11]]
| [[14/13|14/13]], [[13/7|13/7]]
| style="text-align:center;" | 10.606
| 11.225
|-
|-
| style="text-align:center;" | [[14/13|14/13]], [[13/7|13/7]]
| [[15/13|15/13]], [[26/15|26/15]]
| style="text-align:center;" | 11.225
| 13.595
|-
|-
| style="text-align:center;" | [[15/13|15/13]], [[26/15|26/15]]
| [[13/10|13/10]], [[20/13|20/13]]
| style="text-align:center;" | 13.595
| 14.079
|-
| style="text-align:center;" | [[13/10|13/10]], [[20/13|20/13]]
| style="text-align:center;" | 14.079
|}
|}


Line 622: Line 620:


{| class="wikitable"
{| class="wikitable"
|-
! [[Prime limit|Prime]] <br> [[Prime limit|Limit]]
![[Prime limit|Prime]]
! [[Ratio]]
[[Prime limit|Limit]]
! [[Cents]]
! | [[Ratio]]
! [[Monzo]]
! | [[Cents]]
! colspan="2" | [[Color notation/Temperament Names|color name]]
! | [[Monzo]]
! Name
! colspan="2" |[[Color notation/Temperament Names|color name]]
! | Name
|-
|-
| 3
| 3
| style="text-align:center;" |  
| style="text-align:center;" |  
| | 19.84
| 19.84
| |<nowiki> | 65 -41 </nowiki>&gt;
| <nowiki> | 65 -41 </nowiki>&gt;
| Wa-41
| Wa-41
| 41-edo
| 41-edo
| | '41-tone' comma
| '41-tone' comma
|-
|-
| 5
| 5
| style="text-align:center;" |  
| style="text-align:center;" |  
| | 57.27
| 57.27
| |<nowiki> | -5 -10 9 </nowiki>&gt;
| <nowiki> | -5 -10 9 </nowiki>&gt;
| Tritriyo
| Tritriyo
| y<sup>9</sup>
| y<sup>9</sup>
| | shibboleth
| shibboleth
|-
|-
| "
| "
Line 657: Line 653:
| "
| "
| style="text-align:center;" | 3125/3072
| style="text-align:center;" | 3125/3072
| | 29.61
| 29.61
| |<nowiki> | -10 -1 5 </nowiki>&gt;
| <nowiki> | -10 -1 5 </nowiki>&gt;
| Laquinyo
| Laquinyo
| Ly<sup>5</sup>
| Ly<sup>5</sup>
| | small diesis, magic comma
| small diesis, magic comma
|-
|-
| "
| "
| style="text-align:center;" | 20000/19683
| style="text-align:center;" | 20000/19683
| | 27.66
| 27.66
| |<nowiki> | 5 -9 4 </nowiki>&gt;
| <nowiki> | 5 -9 4 </nowiki>&gt;
| Saquadyo
| Saquadyo
| sy<sup>4</sup>
| sy<sup>4</sup>
| | minimal diesis, tetracot comma
| minimal diesis, tetracot comma
|-
|-
| "
| "
| style="text-align:center;" |  
| style="text-align:center;" |  
| | 25.71
| 25.71
| |<nowiki> | 20 -17 3 </nowiki>&gt;
| <nowiki> | 20 -17 3 </nowiki>&gt;
| Sasa-triyo
| Sasa-triyo
| ssy<sup>3</sup>
| ssy<sup>3</sup>
| | roda
| roda
|-
|-
| "
| "
Line 689: Line 685:
| 7
| 7
| style="text-align:center;" | 15625/15309
| style="text-align:center;" | 15625/15309
| | 35.37
| 35.37
| |<nowiki> | 0 -7 6 -1 </nowiki>&gt;
| <nowiki> | 0 -7 6 -1 </nowiki>&gt;
| Rutribiyo
| Rutribiyo
| ry<sup>6</sup>
| ry<sup>6</sup>
| | great BP diesis
| great BP diesis
|-
|-
| "
| "
Line 705: Line 701:
| "
| "
| style="text-align:center;" | 875/864
| style="text-align:center;" | 875/864
| | 21.90
| 21.90
| |<nowiki> | -5 -3 3 1 </nowiki>&gt;
| <nowiki> | -5 -3 3 1 </nowiki>&gt;
| Zotriyo
| Zotriyo
| zy<sup>3</sup>
| zy<sup>3</sup>
| | keema
| keema
|-
|-
| "
| "
Line 881: Line 877:
| "
| "
| style="text-align:center;" | 441/440
| style="text-align:center;" | 441/440
| | 3.93
| 3.93
| |<nowiki> | -3 2 -1 2 -1 </nowiki>&gt;
| <nowiki> | -3 2 -1 2 -1 </nowiki>&gt;
| Luzozogu
| Luzozogu
| 1uzzg
| 1uzzg
| | Werckmeister's undecimal septenarian schisma, werckisma
| Werckmeister's undecimal septenarian schisma, werckisma
|-
|-
| "
| "
| style="text-align:center;" | 1375/1372
| style="text-align:center;" | 1375/1372
| | 3.78
| 3.78
| |<nowiki> | -2 0 3 -3 1 </nowiki>&gt;
| <nowiki> | -2 0 3 -3 1 </nowiki>&gt;
| Lotriruyo
| Lotriruyo
| 1or<sup>3</sup>y
| 1or<sup>3</sup>y
| | moctdel
| moctdel
|-
|-
| "
| "
| style="text-align:center;" | 540/539
| style="text-align:center;" | 540/539
| | 3.21
| 3.21
| |<nowiki> | 2 3 1 -2 -1 </nowiki>&gt;
| <nowiki> | 2 3 1 -2 -1 </nowiki>&gt;
| Lururuyo
| Lururuyo
| 1urry
| 1urry
| | Swets' comma, swetisma
| Swets' comma, swetisma
|-
|-
| "
| "
| style="text-align:center;" | 3025/3024
| style="text-align:center;" | 3025/3024
| | 0.57
| 0.57
| |<nowiki> | -4 -3 2 -1 2 </nowiki>&gt;
| <nowiki> | -4 -3 2 -1 2 </nowiki>&gt;
| Loloruyoyo
| Loloruyoyo
| 1ooryy
| 1ooryy
| | Lehmerisma
| Lehmerisma
|-
|-
| "
| "
| style="text-align:center;" |  
| style="text-align:center;" |  
| | 0.15
| 0.15
| |<nowiki> | -1 2 -4 5 -2 </nowiki>&gt;
| <nowiki> | -1 2 -4 5 -2 </nowiki>&gt;
| Luluquinzo-aquadgu
| Luluquinzo-aquadgu
| 1uuz<sup>5</sup>g<sup>4</sup>
| 1uuz<sup>5</sup>g<sup>4</sup>
| | odiheim
| odiheim
|-
|-
| 13
| 13
| style="text-align:center;" | 105/104
| style="text-align:center;" | 105/104
| | 16.57
| 16.57
| |<nowiki> | -3 1 1 1 0 -1 </nowiki>&gt;
| <nowiki> | -3 1 1 1 0 -1 </nowiki>&gt;
| Thuzoyo
| Thuzoyo
| 3uzy
| 3uzy
| | small tridecimal comma, animist
| small tridecimal comma, animist
|-
|-
| "
| "
| style="text-align:center;" | 28672/28431
| style="text-align:center;" | 28672/28431
| | 14.61
| 14.61
| |<nowiki> | 12 -7 0 1 0 -1 </nowiki>&gt;
| <nowiki> | 12 -7 0 1 0 -1 </nowiki>&gt;
| Sathuzo
| Sathuzo
| s3uz
| s3uz
| | secorian
| secorian
|-
|-
| "
| "
| style="text-align:center;" | 275/273
| style="text-align:center;" | 275/273
| | 12.64
| 12.64
| |<nowiki> | 0 -1 2 -1 1 -1 </nowiki>&gt;
| <nowiki> | 0 -1 2 -1 1 -1 </nowiki>&gt;
| Thuloruyoyo
| Thuloruyoyo
| 3u1oryy
| 3u1oryy
| | gassorma
| gassorma
|-
|-
| "
| "
| style="text-align:center;" | 144/143
| style="text-align:center;" | 144/143
| | 12.06
| 12.06
| |<nowiki> | 4 2 0 0 -1 -1 </nowiki>&gt;
| <nowiki> | 4 2 0 0 -1 -1 </nowiki>&gt;
| Thulu
| Thulu
| 3u1u
| 3u1u
| | grossma
| grossma
|-
|-
| "
| "
| style="text-align:center;" | 196/195
| style="text-align:center;" | 196/195
| | 8.86
| 8.86
| |<nowiki> | 2 -1 -1 2 0 -1 </nowiki>&gt;
| <nowiki> | 2 -1 -1 2 0 -1 </nowiki>&gt;
| Thuzozogu
| Thuzozogu
| 3uzzg
| 3uzzg
| | mynucuma
| mynucuma
|-
|-
| "
| "
| style="text-align:center;" | 640/637
| style="text-align:center;" | 640/637
| | 8.13
| 8.13
| |<nowiki> | 7 0 1 -2 0 -1 </nowiki>&gt;
| <nowiki> | 7 0 1 -2 0 -1 </nowiki>&gt;
| Thururuyo
| Thururuyo
| 3urry
| 3urry
| | huntma
| huntma
|-
|-
| "
| "
| style="text-align:center;" | 1188/1183
| style="text-align:center;" | 1188/1183
| | 7.30
| 7.30
| |<nowiki> | 2 3 0 -1 1 -2 </nowiki>&gt;
| <nowiki> | 2 3 0 -1 1 -2 </nowiki>&gt;
| Thuthuloru
| Thuthuloru
| 3uu1or
| 3uu1or
| | kestrel comma
| kestrel comma
|-
|-
| "
| "
| style="text-align:center;" | 325/324
| style="text-align:center;" | 325/324
| | 5.34
| 5.34
| |<nowiki> | -2 -4 2 0 0 1 </nowiki>&gt;
| <nowiki> | -2 -4 2 0 0 1 </nowiki>&gt;
| Thoyoyo
| Thoyoyo
| 3oyy
| 3oyy
| | marveltwin
| marveltwin
|-
|-
| "
| "
| style="text-align:center;" | 352/351
| style="text-align:center;" | 352/351
| | 4.93
| 4.93
| |<nowiki> | 5 -3 0 0 1 -1 </nowiki>&gt;
| <nowiki> | 5 -3 0 0 1 -1 </nowiki>&gt;
| Thulo
| Thulo
| 3u1o
| 3u1o
| | minthma
| minthma
|-
|-
| "
| "
| style="text-align:center;" | 364/363
| style="text-align:center;" | 364/363
| | 4.76
| 4.76
| |<nowiki> | 2 -1 0 1 -2 1 </nowiki>&gt;
| <nowiki> | 2 -1 0 1 -2 1 </nowiki>&gt;
| Tholuluzo
| Tholuluzo
| 3o1uuz
| 3o1uuz
| | gentle comma
| gentle comma
|-
|-
| "
| "
| style="text-align:center;" | 847/845
| style="text-align:center;" | 847/845
| | 4.09
| 4.09
| |<nowiki> | 0 0 -1 1 2 -2 </nowiki>&gt;
| <nowiki> | 0 0 -1 1 2 -2 </nowiki>&gt;
| Thuthulolozogu
| Thuthulolozogu
| 3uu1oozg
| 3uu1oozg
| | cuthbert
| cuthbert
|-
|-
| "
| "
| style="text-align:center;" | 729/728
| style="text-align:center;" | 729/728
| | 2.38
| 2.38
| |<nowiki> | -3 6 0 -1 0 -1 </nowiki>&gt;
| <nowiki> | -3 6 0 -1 0 -1 </nowiki>&gt;
| Lathuru
| Lathuru
| L3ur
| L3ur
| | squbema
| squbema
|-
|-
| "
| "
| style="text-align:center;" | 4096/4095
| style="text-align:center;" | 4096/4095
| | 0.42
| 0.42
| |<nowiki> | 12 -2 -1 -1 0 -1 </nowiki>&gt;
| <nowiki> | 12 -2 -1 -1 0 -1 </nowiki>&gt;
| Sathurugu
| Sathurugu
| s3urg
| s3urg
| | tridecimal schisma, Sagittal schismina
| tridecimal schisma, Sagittal schismina
|-
|-
| "
| "
| style="text-align:center;" | 10648/10647
| style="text-align:center;" | 10648/10647
| | 0.16
| 0.16
| |<nowiki> | 3 -2 0 -1 3 -2 </nowiki>&gt;
| <nowiki> | 3 -2 0 -1 3 -2 </nowiki>&gt;
| Thuthutrilo-aru
| Thuthutrilo-aru
| 3uu1o<sup>3</sup>r
| 3uu1o<sup>3</sup>r
| | harmonisma
| harmonisma
|-
|-
| 17
| 17
| style="text-align:center;" | 2187/2176
| style="text-align:center;" | 2187/2176
| | 8.73
| 8.73
| |<nowiki> | -7 7 0 0 0 0 -1 </nowiki>&gt;
| <nowiki> | -7 7 0 0 0 0 -1 </nowiki>&gt;
| Lasu
| Lasu
| L17u
| L17u
| | septendecimal comma
| septendecimal comma
|-
|-
| "
| "
Line 1,057: Line 1,053:
| 19
| 19
| style="text-align:center;" | 210/209
| style="text-align:center;" | 210/209
| | 8.26
| 8.26
| |<nowiki> | 1 1 1 1 -1 0 0 -1 </nowiki>&gt;
| <nowiki> | 1 1 1 1 -1 0 0 -1 </nowiki>&gt;
| Nuluzoyo
| Nuluzoyo
| 19u1uzy
| 19u1uzy
| | spleen comma
| spleen comma
|-
|-
| "
| "
Line 1,073: Line 1,069:
| "
| "
| style="text-align:center;" | 513/512
| style="text-align:center;" | 513/512
| | 3.38
| 3.38
| |<nowiki> | -9 3 0 0 0 0 0 1 </nowiki>&gt;
| <nowiki> | -9 3 0 0 0 0 0 1 </nowiki>&gt;
| Lano
| Lano
| L19o
| L19o
| | undevicesimal comma, Boethius' comma
| undevicesimal comma, Boethius' comma
|-
|-
| "
| "
Line 1,111: Line 1,107:


{| class="wikitable"
{| class="wikitable"
|-
! Degree
! |Degree
! Cents
! | Cents
! Temperament(s)
! | Temperament(s)
! [[Pergen]]
![[Pergen]]
! Some MOS Scales Available
! | Some MOS Scales Available
|-
|-
| style="text-align:center;" | 1
| style="text-align:center;" | 1
| style="text-align:center;" | 29.27
| style="text-align:center;" | 29.27
| |Sepla-sezo = [-100 33  0 17>
| Sepla-sezo = [-100 33  0 17>
| (P8, P4/17)
| (P8, P4/17)
| |  
|  
|-
|-
| style="text-align:center;" | 2
| style="text-align:center;" | 2
| style="text-align:center;" | 58.54
| style="text-align:center;" | 58.54
| | [[Hemimiracle|Hemimiracle]]
| [[Hemimiracle|Hemimiracle]]
| (P8, P5/12)
| (P8, P5/12)
| |  
|  
|-
|-
| style="text-align:center;" | 3
| style="text-align:center;" | 3
| style="text-align:center;" | 87.805
| style="text-align:center;" | 87.805
| | 88cET (approx), [[Octacot|octacot]]
| 88cET (approx), [[Octacot|octacot]]
| (P8, P5/8)
| (P8, P5/8)
| |  
|  
|-
|-
| style="text-align:center;" | 4
| style="text-align:center;" | 4
| style="text-align:center;" | 117.07
| style="text-align:center;" | 117.07
| | [[Miracle|Miracle]]
| [[Miracle|Miracle]]
| (P8, P5/6)
| (P8, P5/6)
| |  
|  
|-
|-
| style="text-align:center;" | 5
| style="text-align:center;" | 5
| style="text-align:center;" | 146.34
| style="text-align:center;" | 146.34
| | [[Bohlen-Pierce|Bohlen-Pierce]]/[[bohpier|bohpier]]
| [[Bohlen-Pierce|Bohlen-Pierce]]/[[bohpier|bohpier]]
| (P8, P12/13)
| (P8, P12/13)
| |  
|  
|-
|-
| style="text-align:center;" | 6
| style="text-align:center;" | 6
| style="text-align:center;" | 175.61
| style="text-align:center;" | 175.61
| | [[Tetracot|Tetracot]]/[[bunya|bunya]]/[[Monkey|monkey]]
| [[Tetracot|Tetracot]]/[[bunya|bunya]]/[[Monkey|monkey]]
| (P8, P5/4)
| (P8, P5/4)
| | 13-tone MOS: 1 5 1 5 1 5 1 5 5 1 5 1 5
| 13-tone MOS: 1 5 1 5 1 5 1 5 5 1 5 1 5
|-
|-
| style="text-align:center;" | 7
| style="text-align:center;" | 7
| style="text-align:center;" | 204.88
| style="text-align:center;" | 204.88
| | [[Baldy|Baldy]]
| [[Baldy|Baldy]]
| (P8, c<sup>3</sup>P4/20)
| (P8, c<sup>3</sup>P4/20)
| | 11-tone MOS: 6 1 6 6 1 6 1 6 1 6 1
| 11-tone MOS: 6 1 6 6 1 6 1 6 1 6 1
|-
|-
| style="text-align:center;" | 8
| style="text-align:center;" | 8
| style="text-align:center;" | 234.15
| style="text-align:center;" | 234.15
| | [[Rodan|Rodan]]/[[guiron|guiron]]
| [[Rodan|Rodan]]/[[guiron|guiron]]
| (P8, P5/3)
| (P8, P5/3)
| | 11-tone MOS: 7 1 7 1 7 1 7 1 1 7 1
| 11-tone MOS: 7 1 7 1 7 1 7 1 1 7 1
|-
|-
| style="text-align:center;" | 9
| style="text-align:center;" | 9
| style="text-align:center;" | 263.415
| style="text-align:center;" | 263.415
| | [[Septimin|Septimin]]
| [[Septimin|Septimin]]
| (P8, ccP4/11)
| (P8, ccP4/11)
| | 9-tone MOS: 5 4 5 5 4 5 4 5 4
| 9-tone MOS: 5 4 5 5 4 5 4 5 4
|-
|-
| style="text-align:center;" | 10
| style="text-align:center;" | 10
| style="text-align:center;" | 292.68
| style="text-align:center;" | 292.68
| | [[Quasitemp|Quasitemp]]
| [[Quasitemp|Quasitemp]]
| (P8, c<sup>3</sup>P4/14)
| (P8, c<sup>3</sup>P4/14)
| |  
|  
|-
|-
| style="text-align:center;" | 11
| style="text-align:center;" | 11
| style="text-align:center;" | 321.95
| style="text-align:center;" | 321.95
| | [[Superkleismic|Superkleismic]]
| [[Superkleismic|Superkleismic]]
| (P8, ccP4/9)
| (P8, ccP4/9)
| | 11-tone MOS: 5 3 5 3 3 5 3 3 5 3 3
| 11-tone MOS: 5 3 5 3 3 5 3 3 5 3 3
|-
|-
| style="text-align:center;" | 12
| style="text-align:center;" | 12
| style="text-align:center;" | 351.22
| style="text-align:center;" | 351.22
| | [[Hemififths|Hemififths]]/[[karadeniz|karadeniz]]
| [[Hemififths|Hemififths]]/[[karadeniz|karadeniz]]
| (P8, P5/2)
| (P8, P5/2)
| | 10-tone MOS: 5 2 5 5 2 5 5 5 2 5
| 10-tone MOS: 5 2 5 5 2 5 5 5 2 5
|-
|-
| style="text-align:center;" | 13
| style="text-align:center;" | 13
| style="text-align:center;" | 380.49
| style="text-align:center;" | 380.49
| | [[Magic|Magic]]/[[witchcraft|witchcraft]]
| [[Magic|Magic]]/[[witchcraft|witchcraft]]
| (P8, P12/5)
| (P8, P12/5)
| | 10-tone MOS: 2 9 2 2 9 2 2 9 2 2
| 10-tone MOS: 2 9 2 2 9 2 2 9 2 2
|-
|-
| style="text-align:center;" | 14
| style="text-align:center;" | 14
| style="text-align:center;" | 409.76
| style="text-align:center;" | 409.76
| | [[Hocus|Hocus]]
| [[Hocus|Hocus]]
| (P8, c<sup>3</sup>P4/10)
| (P8, c<sup>3</sup>P4/10)
| |  
|  
|-
|-
| style="text-align:center;" | 15
| style="text-align:center;" | 15
| style="text-align:center;" | 439.02
| style="text-align:center;" | 439.02
| |Sasa-tritribizo = [5 -35 0 18>
| Sasa-tritribizo = [5 -35 0 18>
| (P8, c<sup>6</sup>P5/18)
| (P8, c<sup>6</sup>P5/18)
| | 11-tone MOS: 4 3 4 4 4 3 4 4 3 4 4
| 11-tone MOS: 4 3 4 4 4 3 4 4 3 4 4
|-
|-
| style="text-align:center;" | 16
| style="text-align:center;" | 16
| style="text-align:center;" | 468.29
| style="text-align:center;" | 468.29
| | [[Barbad|Barbad]]
| [[Barbad|Barbad]]
| (P8, c<sup>7</sup>P4/19)
| (P8, c<sup>7</sup>P4/19)
| |  
|  
|-
|-
| style="text-align:center;" | 17
| style="text-align:center;" | 17
| style="text-align:center;" | 497.56
| style="text-align:center;" | 497.56
| | [[Schismatic|Schismatic]] ([[Helmholtz|helmholtz]], [[Garibaldi_temperament|garibaldi]], [[cassandra|cassandra]])
| [[Schismatic|Schismatic]] ([[Helmholtz|helmholtz]], [[Garibaldi_temperament|garibaldi]], [[cassandra|cassandra]])
| (P8, P5)
| (P8, P5)
| |  
|  
|-
|-
| style="text-align:center;" | 18
| style="text-align:center;" | 18
| style="text-align:center;" | 526.83
| style="text-align:center;" | 526.83
| | [[Trismegistus|Trismegistus]]
| [[Trismegistus|Trismegistus]]
| (P8, c<sup>6</sup>P5/15)
| (P8, c<sup>6</sup>P5/15)
| | 9-tone MOS: 5 5 3 5 5 5 5 3 5
| 9-tone MOS: 5 5 3 5 5 5 5 3 5
|-
|-
| style="text-align:center;" | 19
| style="text-align:center;" | 19
| style="text-align:center;" | 556.1
| style="text-align:center;" | 556.1
| |Sasa-quadquadlu = [57 -1 0 0 -16>
| Sasa-quadquadlu = [57 -1 0 0 -16>
| (P8, c<sup>7</sup>P4/16)
| (P8, c<sup>7</sup>P4/16)
| |  
|  
|-
|-
| style="text-align:center;" | 20
| style="text-align:center;" | 20
| style="text-align:center;" | 585.37
| style="text-align:center;" | 585.37
| | [[Pluto|Pluto]]
| [[Pluto|Pluto]]
| (P8, c<sup>3</sup>P4/7)
| (P8, c<sup>3</sup>P4/7)
| |  
|  
|}
|}


Line 1,248: Line 1,243:


{| class="wikitable"
{| class="wikitable"
| Overtones in "Mode 8":
| 8
| 9
| 10
| 11
| 12
| 13
| 14
| 15
| 16
|-
|-
| | Overtones in "Mode 8":
| ...as JI Ratio from 1/1:
| | 8
| 1/1
| | 9
| 9/8
| | 10
| 5/4
| | 11
| 11/8
| | 12
| 3/2
| | 13
| 13/8
| | 14
| 7/4
| | 15
| 15/8
| | 16
| 2/1
|-
|-
| | ...as JI Ratio from 1/1:
| ...in cents:
| | 1/1
| 0
| | 9/8
| 203.9
| | 5/4
| 386.3
| | 11/8
| 551.3
| | 3/2
| 702.0
| | 13/8
| 840.5
| | 7/4
| 968.8
| | 15/8
| 1088.3
| | 2/1
| 1200.0
|-
|-
| | ...in cents:
| Nearest degree of 41edo:
| | 0
| 0
| | 203.9
| 7
| | 386.3
| 13
| | 551.3
| 19
| | 702.0
| 24
| | 840.5
| 29
| | 968.8
| 33
| | 1088.3
| 37
| | 1200.0
| 41
|-
|-
| | Nearest degree of 41edo:
| ...in cents:
| | 0
| 0
| | 7
| 204.9
| | 13
| 380.5
| | 19
| 556.1
| | 24
| 702.4
| | 29
| 848.8
| | 33
| 965.9
| | 37
| 1082.9
| | 41
| 1200.0
|-
| | ...in cents:
| | 0
| | 204.9
| | 380.5
| | 556.1
| | 702.4
| | 848.8
| | 965.9
| | 1082.9
| | 1200.0
|}
|}


Line 1,321: Line 1,315:
Taking every third degree of 41edo produces a scale extremely close to [[88cET|88cET]] or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered <span style="">[[BP|Bohlen-Pierce]]</span>[[BP| Scale]] (or the 13th root of 3). See chart:
Taking every third degree of 41edo produces a scale extremely close to [[88cET|88cET]] or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered <span style="">[[BP|Bohlen-Pierce]]</span>[[BP| Scale]] (or the 13th root of 3). See chart:


{| class="wikitable"
{| class="wikitable" style="text-align:center"
| colspan="3" | 3 degrees of 41edo (near 88cET)
| overlap
| colspan="3" | 5 degrees of 41edo (near BP)
|-
|-
| colspan="3" style="text-align:center;" | 3 degrees of 41edo (near 88cET)
! deg of 41edo
| style="text-align:center;" | overlap
! deg of 88cET
| colspan="3" style="text-align:center;" | 5 degrees of 41edo (near BP)
! cents
! cents
! cents
! deg of BP
! deg of 41edo
|-
|-
! | deg of 41edo
| 0
! | deg of 88cET
| 0
! | cents
|  
! | cents
| 0
! | cents
|  
! | deg of BP
| 0
! | deg of 41edo
| 0
|-
|-
| style="text-align:center;" | 0
| 3
| style="text-align:center;" | 0
| 1
| style="text-align:center;" |
| 87.8
| style="text-align:center;" | 0
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | 0
|  
| style="text-align:center;" | 0
|  
|-
|-
| style="text-align:center;" | 3
|  
| style="text-align:center;" | 1
|  
| style="text-align:center;" | 87.8
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |
| 146.3
| style="text-align:center;" |
| 1
| style="text-align:center;" |
| 5
|-
|-
| style="text-align:center;" |
| 6
| style="text-align:center;" |
| 2
| style="text-align:center;" |
| 175.6
| style="text-align:center;" |  
|  
| style="text-align:center;" | 146.3
|  
| style="text-align:center;" | 1
|  
| style="text-align:center;" | 5
|  
|-
|-
| style="text-align:center;" | 6
| 9
| style="text-align:center;" | 2
| 3
| style="text-align:center;" | 175.6
| 263.4
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 9
|  
| style="text-align:center;" | 3
|  
| style="text-align:center;" | 263.4
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |
| 292.7
| style="text-align:center;" |
| 2
| style="text-align:center;" |
| 10
|-
|-
| style="text-align:center;" |
| 12
| style="text-align:center;" |
| 4
| style="text-align:center;" |
| 351.2
| style="text-align:center;" |  
|  
| style="text-align:center;" | 292.7
|  
| style="text-align:center;" | 2
|  
| style="text-align:center;" | 10
|  
|-
|-
| style="text-align:center;" | 12
| 15
| style="text-align:center;" | 4
| 5
| style="text-align:center;" | 351.2
|  
| style="text-align:center;" |  
| 439.0
| style="text-align:center;" |
|  
| style="text-align:center;" |
| 3
| style="text-align:center;" |
| 15
|-
|-
| style="text-align:center;" | 15
| 18
| style="text-align:center;" | 5
| 6
| style="text-align:center;" |
| 526.8
| style="text-align:center;" | 439.0
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | 3
|  
| style="text-align:center;" | 15
|  
|-
|-
| style="text-align:center;" | 18
|  
| style="text-align:center;" | 6
|  
| style="text-align:center;" | 526.8
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |
| 585.4
| style="text-align:center;" |
| 4
| style="text-align:center;" |
| 20
|-
|-
| style="text-align:center;" |
| 21
| style="text-align:center;" |
| 7
| style="text-align:center;" |
| 614.6
| style="text-align:center;" |  
|  
| style="text-align:center;" | 585.4
|  
| style="text-align:center;" | 4
|  
| style="text-align:center;" | 20
|  
|-
|-
| style="text-align:center;" | 21
| 24
| style="text-align:center;" | 7
| 8
| style="text-align:center;" | 614.6
| 702.4
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 24
|  
| style="text-align:center;" | 8
|  
| style="text-align:center;" | 702.4
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |
| 731.7
| style="text-align:center;" |
| 5
| style="text-align:center;" |
| 25
|-
|-
| style="text-align:center;" |
| 27
| style="text-align:center;" |
| 9
| style="text-align:center;" |
| 790.2
| style="text-align:center;" |  
|  
| style="text-align:center;" | 731.7
|  
| style="text-align:center;" | 5
|  
| style="text-align:center;" | 25
|  
|-
|-
| style="text-align:center;" | 27
| 30
| style="text-align:center;" | 9
| 10
| style="text-align:center;" | 790.2
|  
| style="text-align:center;" |  
| 878.0
| style="text-align:center;" |
|  
| style="text-align:center;" |
| 6
| style="text-align:center;" |
| 30
|-
|-
| style="text-align:center;" | 30
| 33
| style="text-align:center;" | 10
| 11
| style="text-align:center;" |
| 965.9
| style="text-align:center;" | 878.0
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | 6
|  
| style="text-align:center;" | 30
|  
|-
|-
| style="text-align:center;" | 33
|  
| style="text-align:center;" | 11
|  
| style="text-align:center;" | 965.9
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |
| 1024.4
| style="text-align:center;" |
| 7
| style="text-align:center;" |
| 35
|-
|-
| style="text-align:center;" |
| 36
| style="text-align:center;" |
| 12
| style="text-align:center;" |
| 1053.7
| style="text-align:center;" |  
|  
| style="text-align:center;" | 1024.4
|  
| style="text-align:center;" | 7
|  
| style="text-align:center;" | 35
|  
|-
|-
| style="text-align:center;" | 36
| 39
| style="text-align:center;" | 12
| 13
| style="text-align:center;" | 1053.7
| 1141.5
| style="text-align:center;" |
|  
| style="text-align:center;" |
|  
| style="text-align:center;" |
|  
| style="text-align:center;" |
|  
|-
| style="text-align:center;" | 39
| style="text-align:center;" | 13
| style="text-align:center;" | 1141.5
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
| style="text-align:center;" |  
|-
|-
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | 1170.7
| 1170.7
| style="text-align:center;" | 8
| 8
| style="text-align:center;" | 40
| 40
|-
|-
! colspan="7" | [ second octave ]
! colspan="7" | [ second octave ]
|-
|-
| style="text-align:center;" | 1
| 1
| style="text-align:center;" | 14
| 14
| style="text-align:center;" | 29.2
| 29.2
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 4
| 4
| style="text-align:center;" | 15
| 15
| style="text-align:center;" |  
|  
| style="text-align:center;" | 117.1
| 117.1
| style="text-align:center;" |  
|  
| style="text-align:center;" | 9
| 9
| style="text-align:center;" | 4
| 4
|-
|-
| style="text-align:center;" | 7
| 7
| style="text-align:center;" | 16
| 16
| style="text-align:center;" | 204.9
| 204.9
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | 263.4
| 263.4
| style="text-align:center;" | 10
| 10
| style="text-align:center;" | 9
| 9
|-
|-
| style="text-align:center;" | 10
| 10
| style="text-align:center;" | 17
| 17
| style="text-align:center;" | 292.7
| 292.7
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 13
| 13
| style="text-align:center;" | 18
| 18
| style="text-align:center;" | 380.5
| 380.5
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | 409.8
| 409.8
| style="text-align:center;" | 11
| 11
| style="text-align:center;" | 14
| 14
|-
|-
| style="text-align:center;" | 16
| 16
| style="text-align:center;" | 19
| 19
| style="text-align:center;" | 468.3
| 468.3
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 19
| 19
| style="text-align:center;" | 20
| 20
| style="text-align:center;" |  
|  
| style="text-align:center;" | 556.1
| 556.1
| style="text-align:center;" |  
|  
| style="text-align:center;" | 12
| 12
| style="text-align:center;" | 19
| 19
|-
|-
| style="text-align:center;" | 22
| 22
| style="text-align:center;" | 21
| 21
| style="text-align:center;" | 643.9
| 643.9
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | 702.4
| 702.4
| style="text-align:center;" | 13
| 13
| style="text-align:center;" | 24
| 24
|-
|-
| style="text-align:center;" | 25
| 25
| style="text-align:center;" | 22
| 22
| style="text-align:center;" | 731.7
| 731.7
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 28
| 28
| style="text-align:center;" | 23
| 23
| style="text-align:center;" | 819.5
| 819.5
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | 848.8
| 848.8
| style="text-align:center;" | 14
| 14
| style="text-align:center;" | 29
| 29
|-
|-
| style="text-align:center;" | 31
| 31
| style="text-align:center;" | 24
| 24
| style="text-align:center;" | 907.3
| 907.3
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 34
| 34
| style="text-align:center;" | 25
| 25
| style="text-align:center;" |  
|  
| style="text-align:center;" | 995.1
| 995.1
| style="text-align:center;" |  
|  
| style="text-align:center;" | 15
| 15
| style="text-align:center;" | 34
| 34
|-
|-
| style="text-align:center;" | 37
| 37
| style="text-align:center;" | 26
| 26
| style="text-align:center;" | 1082.9
| 1082.9
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | 1141.5
| 1141.5
| style="text-align:center;" | 16
| 16
| style="text-align:center;" | 39
| 39
|-
|-
| style="text-align:center;" | 40
| 40
| style="text-align:center;" | 27
| 27
| style="text-align:center;" | 1170.7
| 1170.7
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
! colspan="7" | [ third octave ]
! colspan="7" | [ third octave ]
|-
|-
| style="text-align:center;" | 2
| 2
| style="text-align:center;" | 28
| 28
| style="text-align:center;" | 58.5
| 58.5
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | 87.8
| 87.8
| style="text-align:center;" | 17
| 17
| style="text-align:center;" | 3
| 3
|-
|-
| style="text-align:center;" | 5
| 5
| style="text-align:center;" | 29
| 29
| style="text-align:center;" | 146.3
| 146.3
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 8
| 8
| style="text-align:center;" | 30
| 30
| style="text-align:center;" |  
|  
| style="text-align:center;" | 234.1
| 234.1
| style="text-align:center;" |  
|  
| style="text-align:center;" | 18
| 18
| style="text-align:center;" | 8
| 8
|-
|-
| style="text-align:center;" | 11
| 11
| style="text-align:center;" | 31
| 31
| style="text-align:center;" | 322.0
| 322.0
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | 380.5
| 380.5
| style="text-align:center;" | 19
| 19
| style="text-align:center;" | 13
| 13
|-
|-
| style="text-align:center;" | 14
| 14
| style="text-align:center;" | 32
| 32
| style="text-align:center;" | 409.8
| 409.8
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 17
| 17
| style="text-align:center;" | 33
| 33
| style="text-align:center;" | 497.6
| 497.6
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | 526.8
| 526.8
| style="text-align:center;" | 20
| 20
| style="text-align:center;" | 18
| 18
|-
|-
| style="text-align:center;" | 20
| 20
| style="text-align:center;" | 34
| 34
| style="text-align:center;" | 585.3
| 585.3
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 23
| 23
| style="text-align:center;" | 35
| 35
| style="text-align:center;" |  
|  
| style="text-align:center;" | 673.2
| 673.2
| style="text-align:center;" |  
|  
| style="text-align:center;" | 21
| 21
| style="text-align:center;" | 23
| 23
|-
|-
| style="text-align:center;" | 26
| 26
| style="text-align:center;" | 36
| 36
| style="text-align:center;" | 761.0
| 761.0
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | 819.5
| 819.5
| style="text-align:center;" | 22
| 22
| style="text-align:center;" | 28
| 28
|-
|-
| style="text-align:center;" | 29
| 29
| style="text-align:center;" | 37
| 37
| style="text-align:center;" | 848.8
| 848.8
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 32
| 32
| style="text-align:center;" | 38
| 38
| style="text-align:center;" | 936.6
| 936.6
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" | 965.9
| 965.9
| style="text-align:center;" | 23
| 23
| style="text-align:center;" | 33
| 33
|-
|-
| style="text-align:center;" | 35
| 35
| style="text-align:center;" | 39
| 39
| style="text-align:center;" | 1024.4
| 1024.4
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | 38
| 38
| style="text-align:center;" | 40
| 40
| style="text-align:center;" |  
|  
| style="text-align:center;" | 1112.2
| 1112.2
| style="text-align:center;" |  
|  
| style="text-align:center;" | 24
| 24
| style="text-align:center;" | 38
| 38
|}
|}


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