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Line 14: Line 14:
== Intervals ==
== Intervals ==


{| class="wikitable" style="text-align:center"
{| class="wikitable center-1 right-2 center-5 center-6 center-7"
! #
! #
! Cents
! Cents
Line 22: Line 22:
|-
|-
| 0
| 0
| style="text-align:right" | 0.00
| 0.00
| style="text-align:left" | [[1/1]]
| [[1/1]]
| perfect unison
| perfect unison
| P1
| P1
Line 30: Line 30:
|-
|-
| 1
| 1
| style="text-align:right" | 29.27
| 29.27
| style="text-align:left" | [[81/80]], [[64/63]]
| [[81/80]], [[64/63]]
| up-unison
| up-unison
| ^1
| ^1
Line 38: Line 38:
|-
|-
| 2
| 2
| style="text-align:right" | 58.54
| 58.54
| style="text-align:left" | [[25/24]], [[28/27]], [[33/32]]
| [[25/24]], [[28/27]], [[33/32]]
| double-up unison, downminor 2nd
| double-up unison, downminor 2nd
| ^^1, vm2
| ^^1, vm2
Line 46: Line 46:
|-
|-
| 3
| 3
| style="text-align:right" | 87.80
| 87.80
| style="text-align:left" | [[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
| vA1, m2
| vA1, m2
Line 54: Line 54:
|-
|-
| 4
| 4
| style="text-align:right" | 117.07
| 117.07
| style="text-align:left" | [[16/15]], [[15/14]], [[14/13]]
| [[16/15]], [[15/14]], [[14/13]]
| augmented 1sn, upminor 2nd
| augmented 1sn, upminor 2nd
| A1, ^m2
| A1, ^m2
Line 62: Line 62:
|-
|-
| 5
| 5
| style="text-align:right" | 146.34
| 146.34
| style="text-align:left" | [[12/11]], [[13/12]]
| [[12/11]], [[13/12]]
| mid 2nd
| mid 2nd
| ~2
| ~2
Line 70: Line 70:
|-
|-
| 6
| 6
| style="text-align:right" | 175.61
| 175.61
| style="text-align:left" | [[10/9]], [[11/10]], [[21/19]]
| [[10/9]], [[11/10]], [[21/19]]
| downmajor 2nd
| downmajor 2nd
| vM2
| vM2
Line 78: Line 78:
|-
|-
| 7
| 7
| style="text-align:right" | 204.88
| 204.88
| style="text-align:left" | [[9/8]]
| [[9/8]]
| major 2nd
| major 2nd
| M2
| M2
Line 86: Line 86:
|-
|-
| 8
| 8
| style="text-align:right" | 234.15
| 234.15
| style="text-align:left" | [[8/7]], [[15/13]]
| [[8/7]], [[15/13]]
| upmajor 2nd
| upmajor 2nd
| ^M2
| ^M2
Line 94: Line 94:
|-
|-
| 9
| 9
| style="text-align:right" | 263.41
| 263.41
| style="text-align:left" | [[7/6]], [[22/19]]
| [[7/6]], [[22/19]]
| downminor 3rd
| downminor 3rd
| vm3
| vm3
Line 102: Line 102:
|-
|-
| 10
| 10
| style="text-align:right" | 292.68
| 292.68
| style="text-align:left" | [[32/27]], [[13/11]], [[19/16]]
| [[32/27]], [[13/11]], [[19/16]]
| minor 3rd
| minor 3rd
| m3
| m3
Line 110: Line 110:
|-
|-
| 11
| 11
| style="text-align:right" | 321.95
| 321.95
| style="text-align:left" | [[6/5]]
| [[6/5]]
| upminor 3rd
| upminor 3rd
| ^m3
| ^m3
Line 118: Line 118:
|-
|-
| 12
| 12
| style="text-align:right" | 351.22
| 351.22
| style="text-align:left" | [[11/9]], [[27/22]], [[16/13]]
| [[11/9]], [[27/22]], [[16/13]]
| mid 3rd
| mid 3rd
| ~3
| ~3
Line 126: Line 126:
|-
|-
| 13
| 13
| style="text-align:right" | 380.49
| 380.49
| style="text-align:left" | [[5/4]], [[26/21]]
| [[5/4]], [[26/21]]
| downmajor 3rd
| downmajor 3rd
| vM3
| vM3
Line 134: Line 134:
|-
|-
| 14
| 14
| style="text-align:right" | 409.76
| 409.76
| style="text-align:left" | [[81/64]], [[14/11]], [[24/19]], [[19/15]]
| [[81/64]], [[14/11]], [[24/19]], [[19/15]]
| major 3rd
| major 3rd
| M3
| M3
Line 142: Line 142:
|-
|-
| 15
| 15
| style="text-align:right" | 439.02
| 439.02
| style="text-align:left" | [[9/7]], [[32/25]]
| [[9/7]], [[32/25]]
| upmajor 3rd
| upmajor 3rd
| ^M3
| ^M3
Line 150: Line 150:
|-
|-
| 16
| 16
| style="text-align:right" | 468.29
| 468.29
| style="text-align:left" | [[21/16]], [[13/10]]
| [[21/16]], [[13/10]]
| down-4th
| down-4th
| v4
| v4
Line 158: Line 158:
|-
|-
| 17
| 17
| style="text-align:right" | 497.56
| 497.56
| style="text-align:left" | [[4/3]]
| [[4/3]]
| perfect 4th
| perfect 4th
| P4
| P4
Line 166: Line 166:
|-
|-
| 18
| 18
| style="text-align:right" | 526.83
| 526.83
| style="text-align:left" | [[15/11]], [[27/20]], [[19/14]]
| [[15/11]], [[27/20]], [[19/14]]
| up-4th
| up-4th
| ^4
| ^4
Line 174: Line 174:
|-
|-
| 19
| 19
| style="text-align:right" | 556.10
| 556.10
| style="text-align:left" | [[11/8]], [[18/13]], [[26/19]]
| [[11/8]], [[18/13]], [[26/19]]
| mid-4th
| mid-4th
| ~4
| ~4
Line 182: Line 182:
|-
|-
| 20
| 20
| style="text-align:right" | 585.37
| 585.37
| style="text-align:left" | [[7/5]]
| [[7/5]]
| downaug 4th, dim 5th
| downaug 4th, dim 5th
| vA4, d5
| vA4, d5
Line 190: Line 190:
|-
|-
| 21
| 21
| style="text-align:right" | 614.63
| 614.63
| style="text-align:left" | [[10/7]]
| [[10/7]]
| aug 4th, updim 5th
| aug 4th, updim 5th
| A4, ^d5
| A4, ^d5
Line 198: Line 198:
|-
|-
| 22
| 22
| style="text-align:right" | 643.90
| 643.90
| style="text-align:left" | [[16/11]], [[13/9]], [[19/13]]
| [[16/11]], [[13/9]], [[19/13]]
| mid-5th
| mid-5th
| ~5
| ~5
Line 206: Line 206:
|-
|-
| 23
| 23
| style="text-align:right" | 673.17
| 673.17
| style="text-align:left" | [[22/15]], [[40/27]], [[28/19]]
| [[22/15]], [[40/27]], [[28/19]]
| down-5th
| down-5th
| v5
| v5
Line 214: Line 214:
|-
|-
| 24
| 24
| style="text-align:right" | 702.44
| 702.44
| style="text-align:left" | [[3/2]]
| [[3/2]]
| perfect 5th
| perfect 5th
| P5
| P5
Line 222: Line 222:
|-
|-
| 25
| 25
| style="text-align:right" | 731.71
| 731.71
| style="text-align:left" | [[32/21]], [[20/13]]
| [[32/21]], [[20/13]]
| up-5th
| up-5th
| ^5
| ^5
Line 230: Line 230:
|-
|-
| 26
| 26
| style="text-align:right" | 760.98
| 760.98
| style="text-align:left" | [[14/9]], [[25/16]]
| [[14/9]], [[25/16]]
| downminor 6th
| downminor 6th
| vm6
| vm6
Line 238: Line 238:
|-
|-
| 27
| 27
| style="text-align:right" | 790.24
| 790.24
| style="text-align:left" | [[128/81]], [[11/7]], [[19/12]], [[30/19]]
| [[128/81]], [[11/7]], [[19/12]], [[30/19]]
| minor 6th
| minor 6th
| m6
| m6
Line 246: Line 246:
|-
|-
| 28
| 28
| style="text-align:right" | 819.51
| 819.51
| style="text-align:left" | [[8/5]], [[21/13]]
| [[8/5]], [[21/13]]
| upminor 6th
| upminor 6th
| ^m6
| ^m6
Line 254: Line 254:
|-
|-
| 29
| 29
| style="text-align:right" | 848.78
| 848.78
| style="text-align:left" | [[18/11]], [[44/27]], [[13/8]]
| [[18/11]], [[44/27]], [[13/8]]
| mid 6th
| mid 6th
| ~6
| ~6
Line 262: Line 262:
|-
|-
| 30
| 30
| style="text-align:right" | 878.05
| 878.05
| style="text-align:left" | [[5/3]]
| [[5/3]]
| downmajor 6th
| downmajor 6th
| vM6
| vM6
Line 270: Line 270:
|-
|-
| 31
| 31
| style="text-align:right" | 907.32
| 907.32
| style="text-align:left" | [[27/16]], [[22/13]], [[32/19]]
| [[27/16]], [[22/13]], [[32/19]]
| major 6th
| major 6th
| M6
| M6
Line 278: Line 278:
|-
|-
| 32
| 32
| style="text-align:right" | 936.59
| 936.59
| style="text-align:left" | [[12/7]], [[19/11]]
| [[12/7]], [[19/11]]
| upmajor 6th
| upmajor 6th
| ^M6
| ^M6
Line 286: Line 286:
|-
|-
| 33
| 33
| style="text-align:right" | 965.85
| 965.85
| style="text-align:left" | [[7/4]], [[26/15]]
| [[7/4]], [[26/15]]
| downminor 7th
| downminor 7th
| vm7
| vm7
Line 294: Line 294:
|-
|-
| 34
| 34
| style="text-align:right" | 995.12
| 995.12
| style="text-align:left" | [[16/9]]
| [[16/9]]
| minor 7th
| minor 7th
| m7
| m7
Line 302: Line 302:
|-
|-
| 35
| 35
| style="text-align:right" | 1024.39
| 1024.39
| style="text-align:left" | [[9/5]], [[20/11]], [[38/21]]
| [[9/5]], [[20/11]], [[38/21]]
| upminor 7th
| upminor 7th
| ^m7
| ^m7
Line 310: Line 310:
|-
|-
| 36
| 36
| style="text-align:right" | 1053.66
| 1053.66
| style="text-align:left" | [[11/6]], [[24/13]]
| [[11/6]], [[24/13]]
| mid 7th
| mid 7th
| ~7
| ~7
Line 318: Line 318:
|-
|-
| 37
| 37
| style="text-align:right" | 1082.93
| 1082.93
| style="text-align:left" | [[15/8]], [[28/15]], [[13/7]]
| [[15/8]], [[28/15]], [[13/7]]
| downmajor 7th
| downmajor 7th
| vM7
| vM7
Line 326: Line 326:
|-
|-
| 38
| 38
| style="text-align:right" | 1112.20
| 1112.20
| style="text-align:left" | [[40/21]], [[21/11]], [[36/19]], [[19/10]]
| [[40/21]], [[21/11]], [[36/19]], [[19/10]]
| major 7th
| major 7th
| M7
| M7
Line 334: Line 334:
|-
|-
| 39
| 39
| style="text-align:right" | 1141.46
| 1141.46
| style="text-align:left" | [[48/25]], [[27/14]], [[64/33]]
| [[48/25]], [[27/14]], [[64/33]]
| upmajor 7th
| upmajor 7th
| ^M7
| ^M7
Line 342: Line 342:
|-
|-
| 40
| 40
| style="text-align:right" | 1170.73
| 1170.73
| style="text-align:left" | [[160/81]], [[63/32]]
| [[160/81]], [[63/32]]
| dim 8ve
| dim 8ve
| v8
| v8
Line 350: Line 350:
|-
|-
| 41
| 41
| style="text-align:right" | 1200.00
| 1200.00
| style="text-align:left" | 2/1
| 2/1
| perfect 8ve
| perfect 8ve
| P8
| P8
Line 617: Line 617:
== Commas ==
== Commas ==


41 EDO tempers out the following commas using its patent val, < 41 65 95 115 142 152 168 174 185 199 203 |.
41 EDO tempers out the following commas using its patent val, {{val|41 65 95 115 142 152 168 174 185 199 203}}.


{| class="wikitable"
{| class="wikitable center-1 center-2 right-3 center-6"
! [[Prime limit|Prime <br> limit]]
! [[Prime limit|Prime <br> limit]]
! [[Ratio]]
! [[Ratio]]
Line 628: Line 628:
|-
|-
| 3
| 3
| style="text-align:center;" |  
|  
| 19.84
| 19.84
| {{monzo| 65 -41 }}
| {{monzo| 65 -41 }}
Line 636: Line 636:
|-
|-
| 5
| 5
| style="text-align:center;" |  
|  
| 57.27
| 57.27
| {{Monzo| -5 -10 9 }}
| {{Monzo| -5 -10 9 }}
Line 644: Line 644:
|-
|-
| "
| "
| style="text-align:center;" |  
|  
| 31.57
| 31.57
| {{Monzo| -25 7 6 }}
| {{Monzo| -25 7 6 }}
Line 652: Line 652:
|-
|-
| "
| "
| style="text-align:center;" | 3125/3072
| 3125/3072
| 29.61
| 29.61
| {{Monzo| -10 -1 5 }}
| {{Monzo| -10 -1 5 }}
Line 660: Line 660:
|-
|-
| "
| "
| style="text-align:center;" | 20000/19683
| 20000/19683
| 27.66
| 27.66
| {{Monzo| 5 -9 4 }}
| {{Monzo| 5 -9 4 }}
Line 668: Line 668:
|-
|-
| "
| "
| style="text-align:center;" |  
|  
| 25.71
| 25.71
| {{Monzo| 20 -17 3 }}
| {{Monzo| 20 -17 3 }}
Line 676: Line 676:
|-
|-
| "
| "
| style="text-align:center;" | 32805/32768
| 32805/32768
| 1.95
| 1.95
| {{Monzo| -15 8 1 }}
| {{Monzo| -15 8 1 }}
Line 684: Line 684:
|-
|-
| 7
| 7
| style="text-align:center;" | 15625/15309
| 15625/15309
| 35.37
| 35.37
| {{Monzo| 0 -7 6 -1 }}
| {{Monzo| 0 -7 6 -1 }}
Line 692: Line 692:
|-
|-
| "
| "
| style="text-align:center;" |  
|  
| 22.41
| 22.41
| {{Monzo| -10 7 8 -7 }}
| {{Monzo| -10 7 8 -7 }}
Line 700: Line 700:
|-
|-
| "
| "
| style="text-align:center;" | 875/864
| 875/864
| 21.90
| 21.90
| {{Monzo| -5 -3 3 1 }}
| {{Monzo| -5 -3 3 1 }}
Line 708: Line 708:
|-
|-
| "
| "
| style="text-align:center;" | 3125/3087
| 3125/3087
| 21.18
| 21.18
| {{Monzo| 0 -2 5 -3 }}
| {{Monzo| 0 -2 5 -3 }}
Line 716: Line 716:
|-
|-
| "
| "
| style="text-align:center;" |
|  
| 19.95
| 19.95
| {{Monzo| 10 -11 2 1 }}
| {{Monzo| 10 -11 2 1 }}
Line 724: Line 724:
|-
|-
| "
| "
| style="text-align:center;" | 33075/32768
| 33075/32768
| 16.14
| 16.14
| {{Monzo| -15 3 2 2 }}
| {{Monzo| -15 3 2 2 }}
Line 732: Line 732:
|-
|-
| "
| "
| style="text-align:center;" | 245/243
| 245/243
| 14.19
| 14.19
| {{Monzo| 0 -5 1 2 }}
| {{Monzo| 0 -5 1 2 }}
Line 740: Line 740:
|-
|-
| "
| "
| style="text-align:center;" | 4000/3969
| 4000/3969
| 13.47
| 13.47
| {{Monzo| 5 -4 3 -2 }}
| {{Monzo| 5 -4 3 -2 }}
Line 748: Line 748:
|-
|-
| "
| "
| style="text-align:center;" |  
|  
| 9.15
| 9.15
| {{Monzo| -15 0 -2 7 }}
| {{Monzo| -15 0 -2 7 }}
Line 756: Line 756:
|-
|-
| "
| "
| style="text-align:center;" | 1029/1024
| 1029/1024
| 8.43
| 8.43
| {{Monzo| -10 1 0 3 }}
| {{Monzo| -10 1 0 3 }}
Line 764: Line 764:
|-
|-
| "
| "
| style="text-align:center;" | 225/224
| 225/224
| 7.71
| 7.71
| {{Monzo| -5 2 2 -1 }}
| {{Monzo| -5 2 2 -1 }}
Line 772: Line 772:
|-
|-
| "
| "
| style="text-align:center;" | 16875/16807
| 16875/16807
| 6.99
| 6.99
| {{Monzo| 0 3 4 -5 }}
| {{Monzo| 0 3 4 -5 }}
Line 780: Line 780:
|-
|-
| "
| "
| style="text-align:center;" | 10976/10935
| 10976/10935
| 6.48
| 6.48
| {{Monzo| 5 -7 -1 3 }}
| {{Monzo| 5 -7 -1 3 }}
Line 788: Line 788:
|-
|-
| "
| "
| style="text-align:center;" | 5120/5103
| 5120/5103
| 5.76
| 5.76
| {{Monzo| 10 -6 1 -1 }}
| {{Monzo| 10 -6 1 -1 }}
Line 796: Line 796:
|-
|-
| "
| "
| style="text-align:center;" |  
|  
| 3.80
| 3.80
| {{Monzo| 25 -14 0 -1 }}
| {{Monzo| 25 -14 0 -1 }}
Line 804: Line 804:
|-
|-
| "
| "
| style="text-align:center;" | 2401/2400
| 2401/2400
| 0.72
| 0.72
| {{Monzo| -5 -1 -2 4 }}
| {{Monzo| -5 -1 -2 4 }}
Line 812: Line 812:
|-
|-
| 11
| 11
| style="text-align:center;" |  
|  
| 29.72
| 29.72
| {{Monzo| 15 0 1 0 -5 }}
| {{Monzo| 15 0 1 0 -5 }}
Line 820: Line 820:
|-
|-
| "
| "
| style="text-align:center;" | 245/242
| 245/242
| 21.33
| 21.33
| {{Monzo| -1 0 1 2 -2 }}
| {{Monzo| -1 0 1 2 -2 }}
Line 828: Line 828:
|-
|-
| "
| "
| style="text-align:center;" | 100/99
| 100/99
| 17.40
| 17.40
| {{Monzo| 2 -2 2 0 -1 }}
| {{Monzo| 2 -2 2 0 -1 }}
Line 836: Line 836:
|-
|-
| "
| "
| style="text-align:center;" | 1344/1331
| 1344/1331
| 16.83
| 16.83
| {{Monzo| 6 1 0 1 -3 }}
| {{Monzo| 6 1 0 1 -3 }}
Line 844: Line 844:
|-
|-
| "
| "
| style="text-align:center;" | 896/891
| 896/891
| 9.69
| 9.69
| {{Monzo| 7 -4 0 1 -1 }}
| {{Monzo| 7 -4 0 1 -1 }}
Line 852: Line 852:
|-
|-
| "
| "
| style="text-align:center;" | 65536/65219
| 65536/65219
| 8.39
| 8.39
| {{Monzo| 16 0 0 -2 -3 }}
| {{Monzo| 16 0 0 -2 -3 }}
Line 860: Line 860:
|-
|-
| "
| "
| style="text-align:center;" | 243/242
| 243/242
| 7.14
| 7.14
| {{Monzo| -1 5 0 0 -2 }}
| {{Monzo| -1 5 0 0 -2 }}
Line 868: Line 868:
|-
|-
| "
| "
| style="text-align:center;" | 385/384
| 385/384
| 4.50
| 4.50
| {{Monzo| -7 -1 1 1 1 }}
| {{Monzo| -7 -1 1 1 1 }}
Line 876: Line 876:
|-
|-
| "
| "
| style="text-align:center;" | 441/440
| 441/440
| 3.93
| 3.93
| {{Monzo| -3 2 -1 2 -1 }}
| {{Monzo| -3 2 -1 2 -1 }}
Line 884: Line 884:
|-
|-
| "
| "
| style="text-align:center;" | 1375/1372
| 1375/1372
| 3.78
| 3.78
| {{Monzo| -2 0 3 -3 1 }}
| {{Monzo| -2 0 3 -3 1 }}
Line 892: Line 892:
|-
|-
| "
| "
| style="text-align:center;" | 540/539
| 540/539
| 3.21
| 3.21
| {{Monzo| 2 3 1 -2 -1 }}
| {{Monzo| 2 3 1 -2 -1 }}
Line 900: Line 900:
|-
|-
| "
| "
| style="text-align:center;" | 3025/3024
| 3025/3024
| 0.57
| 0.57
| {{Monzo| -4 -3 2 -1 2 }}
| {{Monzo| -4 -3 2 -1 2 }}
Line 908: Line 908:
|-
|-
| "
| "
| style="text-align:center;" |  
|  
| 0.15
| 0.15
| {{Monzo| -1 2 -4 5 -2 }}
| {{Monzo| -1 2 -4 5 -2 }}
Line 916: Line 916:
|-
|-
| 13
| 13
| style="text-align:center;" | 105/104
| 105/104
| 16.57
| 16.57
| {{Monzo| -3 1 1 1 0 -1 }}
| {{Monzo| -3 1 1 1 0 -1 }}
Line 924: Line 924:
|-
|-
| "
| "
| style="text-align:center;" | 28672/28431
| 28672/28431
| 14.61
| 14.61
| {{Monzo| 12 -7 0 1 0 -1 }}
| {{Monzo| 12 -7 0 1 0 -1 }}
Line 932: Line 932:
|-
|-
| "
| "
| style="text-align:center;" | 275/273
| 275/273
| 12.64
| 12.64
| {{Monzo| 0 -1 2 -1 1 -1 }}
| {{Monzo| 0 -1 2 -1 1 -1 }}
Line 940: Line 940:
|-
|-
| "
| "
| style="text-align:center;" | 144/143
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| {{Monzo| 4 2 0 0 -1 -1 }}
| {{Monzo| 4 2 0 0 -1 -1 }}
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| style="text-align:center;" | 196/195
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| 8.86
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| {{Monzo| 2 -1 -1 2 0 -1 }}
| {{Monzo| 2 -1 -1 2 0 -1 }}
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| style="text-align:center;" | 640/637
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| 8.13
| 8.13
| {{Monzo| 7 0 1 -2 0 -1 }}
| {{Monzo| 7 0 1 -2 0 -1 }}
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| style="text-align:center;" | 1188/1183
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| 7.30
| 7.30
| {{Monzo| 2 3 0 -1 1 -2 }}
| {{Monzo| 2 3 0 -1 1 -2 }}
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| style="text-align:center;" | 325/324
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| 5.34
| {{Monzo| -2 -4 2 0 0 1 }}
| {{Monzo| -2 -4 2 0 0 1 }}
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| style="text-align:center;" | 352/351
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| 4.93
| 4.93
| {{Monzo| 5 -3 0 0 1 -1 }}
| {{Monzo| 5 -3 0 0 1 -1 }}
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| style="text-align:center;" | 364/363
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| {{Monzo| 2 -1 0 1 -2 1 }}
| {{Monzo| 2 -1 0 1 -2 1 }}
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| style="text-align:center;" | 847/845
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| 4.09
| 4.09
| {{Monzo| 0 0 -1 1 2 -2 }}
| {{Monzo| 0 0 -1 1 2 -2 }}
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| style="text-align:center;" | 729/728
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| 2.38
| 2.38
| {{Monzo| -3 6 0 -1 0 -1 }}
| {{Monzo| -3 6 0 -1 0 -1 }}
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| style="text-align:center;" | 4096/4095
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| 0.42
| 0.42
| {{Monzo| 12 -2 -1 -1 0 -1 }}
| {{Monzo| 12 -2 -1 -1 0 -1 }}
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| style="text-align:center;" | 10648/10647
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| 0.16
| 0.16
| {{Monzo| 3 -2 0 -1 3 -2 }}
| {{Monzo| 3 -2 0 -1 3 -2 }}
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| 17
| 17
| style="text-align:center;" | 2187/2176
| 2187/2176
| 8.73
| 8.73
| {{Monzo| -7 7 0 0 0 0 -1 }}
| {{Monzo| -7 7 0 0 0 0 -1 }}
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| style="text-align:center;" | 256/255
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| 6.78
| 6.78
| {{Monzo| 8 -1 -1 0 0 0 -1 }}
| {{Monzo| 8 -1 -1 0 0 0 -1 }}
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| style="text-align:center;" | 715/714
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| 2.42
| {{Monzo| -1 -1 1 -1 1 1 -1 }}
| {{Monzo| -1 -1 1 -1 1 1 -1 }}
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| 8.26
| {{Monzo| 1 1 1 1 -1 0 0 -1 }}
| {{Monzo| 1 1 1 1 -1 0 0 -1 }}
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| {{Monzo| -3 -2 -1 0 0 0 0 2 }}
| {{Monzo| -3 -2 -1 0 0 0 0 2 }}
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| 3.38
| {{Monzo| -9 3 0 0 0 0 0 1 }}
| {{Monzo| -9 3 0 0 0 0 0 1 }}
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| style="text-align:center;" | 1216/1215
| 1216/1215
| 1.42
| 1.42
| {{Monzo| 6 -5 -1 0 0 0 0 1 }}
| {{Monzo| 6 -5 -1 0 0 0 0 1 }}
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| 23
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| 16.54
| {{Monzo| 5 -6 0 0 0 0 0 0 1 }}
| {{Monzo| 5 -6 0 0 0 0 0 0 1 }}
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| 29
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| 11.98
| {{Monzo| -4 -2 1 0 0 0 0 0 0 1 }}
| {{Monzo| -4 -2 1 0 0 0 0 0 0 1 }}
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== Temperaments ==
== Temperaments ==


[[List_of_edo-distinct_41et_rank_two_temperaments|List of edo-distinct 41et rank two temperaments]]
[[List of edo-distinct 41et rank two temperaments]]


Table of Temperaments by generator
Table of Temperaments by generator
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== Scales and modes ==
== Scales and modes ==


A list of [[41edo_modes|41edo modes]] (MOS and others).
A list of [[41edo modes]] (MOS and others).


==== Harmonic Scale ====
=== Harmonic Scale ===


41edo is the first edo to do some justice to Mode 8 of the [[OverToneSeries|harmonic series]], which Dante Rosati calls the "[[overtone_scales|Diatonic Harmonic Series Scale]]," consisting of overtones 8 through 16 (sometimes made to repeat at the octave).
41edo is the first edo to do some justice to Mode 8 of the [[OverToneSeries|harmonic series]], which Dante Rosati calls the "[[overtone_scales|Diatonic Harmonic Series Scale]]," consisting of overtones 8 through 16 (sometimes made to repeat at the octave).


{| class="wikitable"
{| class="wikitable" style="text-align:center"
| Overtones in "Mode 8":
| Overtones in "Mode 8":
| 8
| 8
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The scale in 41, as adjacent steps, thus goes: 7 6 6 5 5 4 4 4.
The scale in 41, as adjacent steps, thus goes: 7 6 6 5 5 4 4 4.


== Nonoctave Temperaments ==
=== Nonoctave Temperaments ===


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:
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|}
|}


=== Instruments ===
== Instruments ==


[[File:41-EDD_elektrische_gitaar.jpg|alt=41-EDD elektrische gitaar.jpg|560x745px|41-EDD elektrische gitaar.jpg]]
[[File:41-EDD_elektrische_gitaar.jpg|alt=41-EDD elektrische gitaar.jpg|560x745px|41-EDD elektrische gitaar.jpg]]
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