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41edo: Difference between revisions

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→Theory: shorten the prime harmonics table (per discussion on Discord). Mappings -> as a tuning of other temperaments (following 19edo article). Misc. cleanup
→Intervals: cleanup. Reduced to one decimal place for cent values, per discussion on Discord
Line 41: Line 41:
! #
! #
! Cents
! Cents
! Approximate Ratios*
! Approximate ratios*
! colspan="3" | [[Ups and Downs Notation|Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and ^d2)
! colspan="3" | [[Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>4</sup>A1 and ^d2)
! colspan="3" | [[SKULO interval names | SKULO notation]] (K or S = 1, U = 2)
! colspan="3" | [[SKULO interval names|SKULO notation]] (K or S = 1, U = 2)
! [[41edo solfege | Kite's<br>Solfege]]
! [[41edo solfege|Kite's<br>solfege]]
! [[41edo solfege |Andrew's<br>Solfege]]
! [[41edo solfege|Andrew's<br>solfege]]
|-
|-
| 0
| 0
| 0.00
| 0.0
| [[1/1]]
| [[1/1]]
| perfect unison
| perfect unison
Line 60: Line 60:
|-
|-
| 1
| 1
| 29.27
| 29.3
| [[81/80]], [[64/63]], [[49/48]]
| [[81/80]], [[64/63]], [[49/48]]
| up-unison
| up-unison
Line 72: Line 72:
|-
|-
| 2
| 2
| 58.54
| 58.5
| [[25/24]], [[28/27]], [[36/35]], [[33/32]]
| [[25/24]], [[28/27]], [[36/35]], [[33/32]]
| dup-unison, downminor 2nd
| dup-unison, downminor 2nd
Line 84: Line 84:
|-
|-
| 3
| 3
| 87.80
| 87.8
| [[21/20]], [[22/21]], [[19/18]], [[20/19]]
| [[21/20]], [[22/21]], [[19/18]], [[20/19]]
| down-aug 1sn, minor 2nd
| down-aug 1sn, minor 2nd
Line 96: Line 96:
|-
|-
| 4
| 4
| 117.07
| 117.1
| [[16/15]], [[15/14]], [[14/13]]
| [[16/15]], [[15/14]], [[14/13]]
| augmented 1sn, upminor 2nd
| augmented 1sn, upminor 2nd
Line 108: Line 108:
|-
|-
| 5
| 5
| 146.34
| 146.3
| [[12/11]], [[13/12]]
| [[12/11]], [[13/12]]
| mid 2nd
| mid 2nd
Line 120: Line 120:
|-
|-
| 6
| 6
| 175.61
| 175.6
| [[10/9]], [[11/10]], [[21/19]]
| [[10/9]], [[11/10]], [[21/19]]
| downmajor 2nd
| downmajor 2nd
Line 132: Line 132:
|-
|-
| 7
| 7
| 204.88
| 204.9
| [[9/8]]
| [[9/8]]
| major 2nd
| major 2nd
Line 144: Line 144:
|-
|-
| 8
| 8
| 234.15
| 234.1
| [[8/7]], [[15/13]]
| [[8/7]], [[15/13]]
| upmajor 2nd
| upmajor 2nd
Line 156: Line 156:
|-
|-
| 9
| 9
| 263.41
| 263.4
| [[7/6]], [[22/19]]
| [[7/6]], [[22/19]]
| downminor 3rd
| downminor 3rd
Line 168: Line 168:
|-
|-
| 10
| 10
| 292.68
| 292.7
| [[32/27]], [[13/11]], [[19/16]]
| [[32/27]], [[13/11]], [[19/16]]
| minor 3rd
| minor 3rd
Line 180: Line 180:
|-
|-
| 11
| 11
| 321.95
| 322.0
| [[6/5]]
| [[6/5]]
| upminor 3rd
| upminor 3rd
Line 192: Line 192:
|-
|-
| 12
| 12
| 351.22
| 351.2
| [[11/9]], [[27/22]], [[16/13]]
| [[11/9]], [[27/22]], [[16/13]]
| mid 3rd
| mid 3rd
Line 204: Line 204:
|-
|-
| 13
| 13
| 380.49
| 380.5
| [[5/4]], [[26/21]]
| [[5/4]], [[26/21]]
| downmajor 3rd
| downmajor 3rd
Line 216: Line 216:
|-
|-
| 14
| 14
| 409.76
| 409.8
| [[81/64]], [[14/11]], [[24/19]], [[19/15]]
| [[81/64]], [[14/11]], [[24/19]], [[19/15]]
| major 3rd
| major 3rd
Line 228: Line 228:
|-
|-
| 15
| 15
| 439.02
| 439.0
| [[9/7]], [[32/25]]
| [[9/7]], [[32/25]]
| upmajor 3rd
| upmajor 3rd
Line 240: Line 240:
|-
|-
| 16
| 16
| 468.29
| 468.3
| [[21/16]], [[13/10]]
| [[21/16]], [[13/10]]
| down-4th
| down-4th
Line 252: Line 252:
|-
|-
| 17
| 17
| 497.56
| 497.6
| [[4/3]]
| [[4/3]]
| perfect 4th
| perfect 4th
Line 264: Line 264:
|-
|-
| 18
| 18
| 526.83
| 526.8
| [[27/20]], [[15/11]], [[19/14]]
| [[27/20]], [[15/11]], [[19/14]]
| up-4th
| up-4th
Line 276: Line 276:
|-
|-
| 19
| 19
| 556.10
| 556.1
| [[11/8]], [[18/13]], [[26/19]]
| [[11/8]], [[18/13]], [[26/19]]
| mid-4th, downdim 5th
| mid-4th, downdim 5th
Line 288: Line 288:
|-
|-
| 20
| 20
| 585.37
| 585.4
| [[7/5]], [[45/32]]
| [[7/5]], [[45/32]]
| downaug 4th, dim 5th
| downaug 4th, dim 5th
Line 300: Line 300:
|-
|-
| 21
| 21
| 614.63
| 614.6
| [[10/7]], [[64/45]]
| [[10/7]], [[64/45]]
| aug 4th, updim 5th
| aug 4th, updim 5th
Line 312: Line 312:
|-
|-
| 22
| 22
| 643.90
| 643.9
| [[16/11]], [[13/9]], [[19/13]]
| [[16/11]], [[13/9]], [[19/13]]
| mid-5th, upaug 4th
| mid-5th, upaug 4th
Line 324: Line 324:
|-
|-
| 23
| 23
| 673.17
| 673.2
| [[40/27]], [[22/15]], [[28/19]]
| [[40/27]], [[22/15]], [[28/19]]
| down-5th
| down-5th
Line 336: Line 336:
|-
|-
| 24
| 24
| 702.44
| 702.4
| [[3/2]]
| [[3/2]]
| perfect 5th
| perfect 5th
Line 348: Line 348:
|-
|-
| 25
| 25
| 731.71
| 731.7
| [[32/21]], [[20/13]]
| [[32/21]], [[20/13]]
| up-5th
| up-5th
Line 360: Line 360:
|-
|-
| 26
| 26
| 760.98
| 761.0
| [[14/9]], [[25/16]]
| [[14/9]], [[25/16]]
| downminor 6th
| downminor 6th
Line 372: Line 372:
|-
|-
| 27
| 27
| 790.24
| 790.2
| [[128/81]], [[11/7]], [[19/12]], [[30/19]]
| [[128/81]], [[11/7]], [[19/12]], [[30/19]]
| minor 6th
| minor 6th
Line 384: Line 384:
|-
|-
| 28
| 28
| 819.51
| 819.5
| [[8/5]], [[21/13]]
| [[8/5]], [[21/13]]
| upminor 6th
| upminor 6th
Line 396: Line 396:
|-
|-
| 29
| 29
| 848.78
| 848.8
| [[18/11]], [[44/27]], [[13/8]]
| [[18/11]], [[44/27]], [[13/8]]
| mid 6th
| mid 6th
Line 408: Line 408:
|-
|-
| 30
| 30
| 878.05
| 878.0
| [[5/3]]
| [[5/3]]
| downmajor 6th
| downmajor 6th
Line 420: Line 420:
|-
|-
| 31
| 31
| 907.32
| 907.3
| [[27/16]], [[22/13]], [[32/19]]
| [[27/16]], [[22/13]], [[32/19]]
| major 6th
| major 6th
Line 432: Line 432:
|-
|-
| 32
| 32
| 936.59
| 936.6
| [[12/7]], [[19/11]]
| [[12/7]], [[19/11]]
| upmajor 6th
| upmajor 6th
Line 444: Line 444:
|-
|-
| 33
| 33
| 965.85
| 965.9
| [[7/4]], [[26/15]]
| [[7/4]], [[26/15]]
| downminor 7th
| downminor 7th
Line 456: Line 456:
|-
|-
| 34
| 34
| 995.12
| 995.1
| [[16/9]]
| [[16/9]]
| minor 7th
| minor 7th
Line 468: Line 468:
|-
|-
| 35
| 35
| 1024.39
| 1024.4
| [[9/5]], [[20/11]], [[38/21]]
| [[9/5]], [[20/11]], [[38/21]]
| upminor 7th
| upminor 7th
Line 480: Line 480:
|-
|-
| 36
| 36
| 1053.66
| 1053.7
| [[11/6]], [[24/13]]
| [[11/6]], [[24/13]]
| mid 7th
| mid 7th
Line 492: Line 492:
|-
|-
| 37
| 37
| 1082.93
| 1082.9
| [[15/8]], [[28/15]], [[13/7]]
| [[15/8]], [[28/15]], [[13/7]]
| downmajor 7th
| downmajor 7th
Line 504: Line 504:
|-
|-
| 38
| 38
| 1112.20
| 1112.2
| [[40/21]], [[21/11]], [[36/19]], [[19/10]]
| [[40/21]], [[21/11]], [[36/19]], [[19/10]]
| major 7th
| major 7th
Line 516: Line 516:
|-
|-
| 39
| 39
| 1141.46
| 1141.5
| [[48/25]], [[27/14]], [[35/18]], [[64/33]]
| [[48/25]], [[27/14]], [[35/18]], [[64/33]]
| upmajor 7th
| upmajor 7th
Line 528: Line 528:
|-
|-
| 40
| 40
| 1170.73
| 1170.7
| [[160/81]], [[63/32]], [[96/49]]
| [[160/81]], [[63/32]], [[96/49]]
| dim 8ve
| dim 8ve
Line 540: Line 540:
|-
|-
| 41
| 41
| 1200.00
| 1200.0
| 2/1
| 2/1
| perfect 8ve
| perfect 8ve
Line 556: Line 556:
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:


{| class="wikitable" style="text-align: center;"
{| class="wikitable center-all"
|-
|-
! Quality
! Quality
! [[Color notation|Color]]
! [[Color notation|Color]]
! Monzo Format
! Monzo format
! Examples
! Examples
|-
|-
Line 570: Line 570:
| minor
| minor
| fourthward wa
| fourthward wa
| (a, b) with b &lt; -1
| (a, b) with b < -1
| 32/27, 16/9
| 32/27, 16/9
|-
|-
Line 595: Line 595:
| major
| major
| fifthward wa
| fifthward wa
| (a, b) with b &gt; 1
| (a, b) with b > 1
| 9/8, 27/16
| 9/8, 27/16
|-
|-
Line 606: Line 606:
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" style="text-align: center;"
{| class="wikitable center-all"
|-
|-
! [[Color notation|Color of the 3rd]]
! [[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 (7-over)
| zo (7-over)
Line 663: Line 663:
* 0-14-28 = D F# A# = Da = D aug
* 0-14-28 = D F# A# = Da = D aug


For a more complete list, see [[41edo Chord Names]] and [[Ups and Downs Notation #Chords and Chord Progressions]].
For a more complete list, see [[41edo Chord Names]] and [[Ups and downs notation #Chords and chord progressions]].


== Notations ==
== Notations ==
Retrieved from "https://en.xen.wiki/w/41edo"