87edo/13-limit detempering: Difference between revisions

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In this table, "Difference in Cents" indicates whether the 87-interval is flat (negative) or sharp (positive) of the detempered interval. For example, 15 steps, at 206.89655 cents, corresponds to [[9/8]] and is 3.0 cents sharp.  
{{breadcrumb}}
In this table, "Difference in Cents" indicates whether the 87-edo interval is flat (negative) or sharp (positive) of the detempered interval. For example, 15 steps, at 206.90{{c}}, corresponds to [[9/8]] and is about 3 cents sharp.  


{| class="wikitable center-all right-2 right-4"
{| class="wikitable center-all right-2 right-4"
! #
|-
! #
! [[Cent]]s
! [[Cent]]s
! Detempered <br> Interval
! Detempered<br />Interval
! Difference <br>in Cents
! Difference<br />in cents
|-
|-
| 0
| 0
Line 15: Line 17:
| 13.79
| 13.79
| [[91/90]]
| [[91/90]]
| -5.34
| −5.34
|-
|-
| 2
| 2
| 27.59
| 27.59
| [[49/48]]
| [[49/48]]
| -8.11
| −8.11
|-
|-
| 3
| 3
| 41.38
| 41.38
| [[40/39]]
| [[40/39]]
| -2.45
| −2.45
|-
|-
| 4
| 4
| 55.17
| 55.17
| [[28/27]]
| [[28/27]]
| -7.79
| −7.79
|-
|-
| 5
| 5
| 68.97
| 68.97
| [[25/24]]
| [[25/24]]
| -1.71
| −1.71
|-
|-
| 6
| 6
| 82.76
| 82.76
| [[21/20]]
| [[21/20]]
| -1.71
| −1.71
|-
|-
| 7
| 7
| 96.55
| 96.55
| [[35/33]]
| [[35/33]]
| -5.31
| −5.31
|-
|-
| 8
| 8
| 110.34
| 110.34
| [[16/15]]
| [[16/15]]
| -1.39
| −1.39
|-
|-
| 9
| 9
| 124.14
| 124.14
| [[14/13]]
| [[14/13]]
| -4.16
| −4.16
|-
|-
| 10
| 10
| 137.93
| 137.93
| [[13/12]]
| [[13/12]]
| -0.64
| −0.64
|-
|-
| 11
| 11
Line 75: Line 77:
| 179.31
| 179.31
| [[10/9]]
| [[10/9]]
| -3.09
| −3.09
|-
|-
| 14
| 14
| 193.10
| 193.10
| [[28/25]]
| [[28/25]]
| -3.10
| −3.10
|-
|-
| 15
| 15
Line 90: Line 92:
| 220.69
| 220.69
| [[25/22]]
| [[25/22]]
| -0.62
| −0.62
|-
|-
| 17
| 17
Line 105: Line 107:
| 262.07
| 262.07
| [[7/6]]
| [[7/6]]
| -4.80
| −4.80
|-
|-
| 20
| 20
Line 130: Line 132:
| 331.03
| 331.03
| [[40/33]]
| [[40/33]]
| -2.01
| −2.01
|-
|-
| 25
| 25
| 344.83
| 344.83
| [[11/9]]
| [[11/9]]
| -2.58
| −2.58
|-
|-
| 26
| 26
| 358.62
| 358.62
| [[16/13]]
| [[16/13]]
| -0.85
| −0.85
|-
|-
| 27
| 27
Line 150: Line 152:
| 386.21
| 386.21
| [[5/4]]
| [[5/4]]
| -0.11
| −0.11
|-
|-
| 29
| 29
Line 160: Line 162:
| 413.79
| 413.79
| [[14/11]]
| [[14/11]]
| -3.71
| −3.71
|-
|-
| 31
| 31
Line 180: Line 182:
| 468.97
| 468.97
| [[21/16]]
| [[21/16]]
| -1.82
| −1.82
|-
|-
| 35
| 35
Line 190: Line 192:
| 496.55
| 496.55
| [[4/3]]
| [[4/3]]
| -1.49
| −1.49
|-
|-
| 37
| 37
| 510.34
| 510.34
| [[35/26]]
| [[35/26]]
| -4.27
| −4.27
|-
|-
| 38
| 38
Line 220: Line 222:
| 579.31
| 579.31
| [[7/5]]
| [[7/5]]
| -3.20
| −3.20
|-
|-
| 43
| 43
Line 230: Line 232:
| 606.90
| 606.90
| [[64/45]]
| [[64/45]]
| -2.88
| −2.88
|-
|-
| 45
| 45
Line 240: Line 242:
| 634.48
| 634.48
| [[13/9]]
| [[13/9]]
| -2.13
| −2.13
|-
|-
| 47
| 47
| 648.28
| 648.28
| [[16/11]]
| [[16/11]]
| -0.41
| −0.41
|-
|-
| 48
| 48
| 662.07
| 662.07
| [[22/15]]
| [[22/15]]
| -0.98
| −0.98
|-
|-
| 49
| 49
| 675.86
| 675.86
| [[40/27]]
| [[40/27]]
| -4.59
| −4.59
|-
|-
| 50
| 50
Line 270: Line 272:
| 717.24
| 717.24
| [[50/33]]
| [[50/33]]
| -2.11
| −2.11
|-
|-
| 53
| 53
Line 280: Line 282:
| 744.83
| 744.83
| [[20/13]]
| [[20/13]]
| -0.96
| −0.96
|-
|-
| 55
| 55
| 758.62
| 758.62
| [[14/9]]
| [[14/9]]
| -6.30
| −6.30
|-
|-
| 56
| 56
| 772.41
| 772.41
| [[25/16]]
| [[25/16]]
| -0.21
| −0.21
|-
|-
| 57
| 57
Line 300: Line 302:
| 800.00
| 800.00
| [[35/22]]
| [[35/22]]
| -3.82
| −3.82
|-
|-
| 59
| 59
Line 310: Line 312:
| 827.59
| 827.59
| [[21/13]]
| [[21/13]]
| -2.67
| −2.67
|-
|-
| 61
| 61
Line 330: Line 332:
| 882.76
| 882.76
| [[5/3]]
| [[5/3]]
| -1.60
| −1.60
|-
|-
| 65
| 65
| 896.55
| 896.55
| [[42/25]]
| [[42/25]]
| -1.60
| −1.60
|-
|-
| 66
| 66
| 910.34
| 910.34
| [[22/13]]
| [[22/13]]
| -0.45
| −0.45
|-
|-
| 67
| 67
Line 355: Line 357:
| 951.72
| 951.72
| [[26/15]]
| [[26/15]]
| -0.53
| −0.53
|-
|-
| 70
| 70
| 965.52
| 965.52
| [[7/4]]
| [[7/4]]
| -3.31
| −3.31
|-
|-
| 71
| 71
Line 370: Line 372:
| 993.10
| 993.10
| [[16/9]]
| [[16/9]]
| -2.99
| −2.99
|-
|-
| 73
| 73
Line 385: Line 387:
| 1034.48
| 1034.48
| [[20/11]]
| [[20/11]]
| -0.51
| −0.51
|-
|-
| 76
| 76
| 1048.28
| 1048.28
| [[11/6]]
| [[11/6]]
| -1.09
| −1.09
|-
|-
| 77
| 77
Line 415: Line 417:
| 1117.24
| 1117.24
| [[21/11]]
| [[21/11]]
| -2.22
| −2.22
|-
|-
| 82
| 82
| 1131.03
| 1131.03
| [[25/13]]
| [[25/13]]
| -1.07
| −1.07
|-
|-
| 83
| 83
Line 448: Line 450:
|}
|}


[[Category:Interval collection]]
[[Category:Lists of intervals]]
[[Category:87edo]]
[[Category:87edo]]
[[Category:Detempering]]

Latest revision as of 14:05, 20 January 2025

< 87edo

In this table, "Difference in Cents" indicates whether the 87-edo interval is flat (negative) or sharp (positive) of the detempered interval. For example, 15 steps, at 206.90 ¢, corresponds to 9/8 and is about 3 cents sharp.

# Cents Detempered
Interval 		Difference
in cents
0 0.00 1/1 0.00
1 13.79 91/90 −5.34
2 27.59 49/48 −8.11
3 41.38 40/39 −2.45
4 55.17 28/27 −7.79
5 68.97 25/24 −1.71
6 82.76 21/20 −1.71
7 96.55 35/33 −5.31
8 110.34 16/15 −1.39
9 124.14 14/13 −4.16
10 137.93 13/12 −0.64
11 151.72 12/11 +1.09
12 165.52 11/10 +0.51
13 179.31 10/9 −3.09
14 193.10 28/25 −3.10
15 206.90 9/8 +2.99
16 220.69 25/22 −0.62
17 234.48 8/7 +3.31
18 248.28 15/13 +0.53
19 262.07 7/6 −4.80
20 275.86 75/64 +1.28
21 289.66 13/11 +0.45
22 303.45 25/21 +1.60
23 317.24 6/5 +1.60
24 331.03 40/33 −2.01
25 344.83 11/9 −2.58
26 358.62 16/13 −0.85
27 372.41 26/21 +2.67
28 386.21 5/4 −0.11
29 400.00 44/35 +3.82
30 413.79 14/11 −3.71
31 427.59 32/25 +0.21
32 441.38 9/7 +6.30
33 455.17 13/10 +0.96
34 468.97 21/16 −1.82
35 482.76 33/25 +2.11
36 496.55 4/3 −1.49
37 510.34 35/26 −4.27
38 524.14 27/20 +4.59
39 537.93 15/11 +0.98
40 551.72 11/8 +0.41
41 565.52 18/13 +2.13
42 579.31 7/5 −3.20
43 593.10 45/32 +2.88
44 606.90 64/45 −2.88
45 620.69 10/7 +3.20
46 634.48 13/9 −2.13
47 648.28 16/11 −0.41
48 662.07 22/15 −0.98
49 675.86 40/27 −4.59
50 689.66 52/35 +4.27
51 703.45 3/2 +1.49
52 717.24 50/33 −2.11
53 731.03 32/21 +1.82
54 744.83 20/13 −0.96
55 758.62 14/9 −6.30
56 772.41 25/16 −0.21
57 786.22 11/7 +3.71
58 800.00 35/22 −3.82
59 813.79 8/5 +0.11
60 827.59 21/13 −2.67
61 841.38 13/8 +0.85
62 855.17 18/11 +2.58
63 868.97 33/20 +2.01
64 882.76 5/3 −1.60
65 896.55 42/25 −1.60
66 910.34 22/13 −0.45
67 924.14 75/44 +0.87
68 937.93 12/7 +4.80
69 951.72 26/15 −0.53
70 965.52 7/4 −3.31
71 979.31 44/25 +0.62
72 993.10 16/9 −2.99
73 1006.90 25/14 +3.10
74 1020.69 9/5 +3.09
75 1034.48 20/11 −0.51
76 1048.28 11/6 −1.09
77 1062.07 24/13 +0.64
78 1075.86 13/7 +4.16
79 1089.66 15/8 +1.39
80 1103.45 66/35 +5.31
81 1117.24 21/11 −2.22
82 1131.03 25/13 −1.07
83 1144.83 27/14 +7.79
84 1158.62 39/20 +2.45
85 1172.41 55/28 +3.61
86 1186.21 99/50 +3.61
87 1200.00 2/1 0.00
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