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Golden magic: Difference between revisions

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Line 5: Line 5:
Golden magic approximates simple intervals in the 2,3,7,11 subgroup very closely and 5 somewhat less closely (in fact 5 has the highest error of any identity in the 11 limit). Here's the 41 tone MOS with a JI detempering in the 2,3,7,11 subgroup:
Golden magic approximates simple intervals in the 2,3,7,11 subgroup very closely and 5 somewhat less closely (in fact 5 has the highest error of any identity in the 11 limit). Here's the 41 tone MOS with a JI detempering in the 2,3,7,11 subgroup:
{| class="wikitable"
{| class="wikitable"
|Scale Degree
|'''Scale Degree'''
|Ratio
|'''Ratio'''
|Golden Magic
|'''Golden Magic'''
|Detempered
|'''Detempered'''
|Error
|'''Error'''
|'''Color Notation'''
|-
|-
|0
|0
Line 16: Line 17:
|0.000
|0.000
|0.000
|0.000
|w1
|-
|-
|1
|1
Line 22: Line 24:
|35.697
|35.697
| -0.134
| -0.134
|zz2
|-
|-
|2
|2
Line 28: Line 31:
|53.273
|53.273
|4.270
|4.270
|1o1
|-
|-
|3
|3
Line 34: Line 38:
|87.676
|87.676
|5.430
|5.430
|1ur1
|-
|-
|4
|4
Line 40: Line 45:
|116.234
|116.234
| -1.149
| -1.149
|1oz2
|-
|-
|5
|5
Line 46: Line 52:
|150.637
|150.637
|0.012
|0.012
|1u2
|-
|-
|6
|6
Line 52: Line 59:
|168.213
|168.213
|4.415
|4.415
|rr1
|-
|-
|7
|7
Line 58: Line 66:
|203.910
|203.910
|4.281
|4.281
|w2
|-
|-
|8
|8
Line 64: Line 73:
|231.174
|231.174
| -1.004
| -1.004
|r2
|-
|-
|9
|9
Line 70: Line 80:
|266.871
|266.871
| -1.137
| -1.137
|z3
|-
|-
|10
|10
Line 76: Line 87:
|284.447
|284.447
|3.266
|3.266
|1or2
|-
|-
|11
|11
Line 82: Line 94:
|320.144
|320.144
|3.133
|3.133
|1oz3
|-
|-
|12
|12
Line 88: Line 101:
|347.408
|347.408
| -2.152
| -2.152
|1o3
|-
|-
|13
|13
Line 94: Line 108:
|381.811
|381.811
| -0.992
| -0.992
|1ur3
|-
|-
|14
|14
Line 100: Line 115:
|417.508
|417.508
| -1.126
| -1.126
|1uz4
|-
|-
|15
|15
Line 106: Line 122:
|435.084
|435.084
|3.278
|3.278
|r3
|-
|-
|16
|16
Line 112: Line 129:
|470.781
|470.781
|3.144
|3.144
|z4
|-
|-
|17
|17
Line 118: Line 136:
|498.045
|498.045
| -2.141
| -2.141
|w4
|-
|-
|18
|18
Line 124: Line 143:
|533.742
|533.742
| -2.274
| -2.274
|zz5
|-
|-
|19
|19
Line 130: Line 150:
|551.318
|551.318
|2.129
|2.129
|1o4
|-
|-
|20
|20
Line 136: Line 157:
|585.721
|585.721
|3.289
|3.289
|1ur4
|-
|-
|21
|21
Line 142: Line 164:
|614.279
|614.279
| -3.289
| -3.289
|1oz5
|-
|-
|22
|22
Line 148: Line 171:
|648.682
|648.682
| -2.129
| -2.129
|1u5
|-
|-
|23
|23
Line 154: Line 178:
|666.258
|666.258
|2.274
|2.274
|rr4
|-
|-
|24
|24
Line 160: Line 185:
|701.955
|701.955
|2.141
|2.141
|w5
|-
|-
|25
|25
Line 166: Line 192:
|729.219
|729.219
| -3.144
| -3.144
|r5
|-
|-
|26
|26
Line 172: Line 199:
|764.916
|764.916
| -3.278
| -3.278
|z6
|-
|-
|27
|27
Line 178: Line 206:
|782.492
|782.492
|1.126
|1.126
|1or5
|-
|-
|28
|28
Line 184: Line 213:
|818.189
|818.189
|0.992
|0.992
|1oz6
|-
|-
|29
|29
Line 190: Line 220:
|852.592
|852.592
|2.152
|2.152
|1u6
|-
|-
|30
|30
Line 196: Line 227:
|879.856
|879.856
| -3.133
| -3.133
|1ur6
|-
|-
|31
|31
Line 202: Line 234:
|915.553
|915.553
| -3.266
| -3.266
|1uz7
|-
|-
|32
|32
Line 208: Line 241:
|933.129
|933.129
|1.137
|1.137
|r6
|-
|-
|33
|33
Line 214: Line 248:
|968.826
|968.826
|1.004
|1.004
|z7
|-
|-
|34
|34
Line 220: Line 255:
|996.090
|996.090
| -4.281
| -4.281
|w7
|-
|-
|35
|35
Line 226: Line 262:
|1031.787
|1031.787
| -4.415
| -4.415
|zz8
|-
|-
|36
|36
Line 232: Line 269:
|1049.363
|1049.363
| -0.012
| -0.012
|1o7
|-
|-
|37
|37
Line 238: Line 276:
|1083.766
|1083.766
|1.149
|1.149
|1ur7
|-
|-
|38
|38
Line 244: Line 283:
|1112.324
|1112.324
| -5.430
| -5.430
|1oz8
|-
|-
|39
|39
Line 250: Line 290:
|1146.727
|1146.727
| -4.270
| -4.270
|1u8
|-
|-
|40
|40
Line 256: Line 297:
|1164.303
|1164.303
|0.134
|0.134
|rr7
|-
|-
|41
|41
Line 262: Line 304:
|1200.000
|1200.000
|0.000
|0.000
|w8
|}
|}
The highest error of any interval in the 1,3,7,9,11 tonality diamond is 9/8, which is 4.281 cents sharp.
The highest error of any interval in the 1,3,7,9,11 tonality diamond is 9/8, which is 4.281 cents sharp.
Retrieved from "https://en.xen.wiki/w/Golden_magic"