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Table of 311edo intervals: Difference between revisions

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Godtone (talk | contribs)
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2,289 edits
m removed the table i generated and added the skeletons for two tables to be generated for aesthetic comparison before finalisation
Line 1: Line 1:
{{delete|comprehensive collapsible table that is an improved and prettified superset of both tables here has been put on the 311edo page}}
{{delete|comprehensive collapsible table that is an improved and prettified superset of both tables here has been put on the 311edo page}}
== marker < cent < gene ==
{| class="mw-collapsible mw-collapsed wikitable center-1"
|+ style=white-space:nowrap | Table of 311edo intervals
| style="text-align:center;" | marks
| style="text-align:center;" | cents
| style="text-align:center;" | genes
| style="text-align:center;" | [[41-limit]] add-73 add-89 add-101 add-109 add-113 123-odd-limit intervals (/2^n and 2^n/ in bold & linked, inconsistent in italics, else, if [[23-limit]], linked)
|-
| P1
| 0.0000
| 0
| '''1/1''', [[1681/1680|S41]], [[1600/1599|S40]], [[1444/1443|S38]], [[1369/1368|S37]], [[1225/1224|S35 = S49*S50]], [[1156/1155|S34]], [[1024/1023|S32]], [[900/899|S30]], ''[[784/783|S28]]'', ''[[625/624|S25]]'',
|-
|
| 3.8585
| 1
| ''[[1521/1520|S39]]'', ''[[1296/1295|S36]]'', ''[[1089/1088|S33]]'', ''[[961/960|S31]]'', [[841/840|S29]], [[729/728|S27]], [[676/675|S26 = S13/S15]], [[576/575|S24]], [[529/528|S23]], [[484/483|S22]], [[441/440|S21]], [[400/399|S20]], [[361/360|S19]], ''[[289/288|S17]]''
|-
|
| 7.7170
| 2
| ''[[324/323|S18]]'', [[256/255|S16]], [[225/224|S15]], [[196/195|S14]], ''170/169''
|-
|
| 11.575
| 3
| [[169/168|S13 = 169/168]], [[144/143|S12 = 144/143]], 171/170
|-
| P8
| 1200.0
| 311
| '''2/1'''
|}
== gene < cent < marker ==
{| class="mw-collapsible mw-collapsed wikitable center-1"
|+ style=white-space:nowrap | Table of 311edo intervals
| style="text-align:center;" | genes
| style="text-align:center;" | cents
| style="text-align:center;" | marks
| style="text-align:center;" | [[41-limit]] add-73 add-89 add-101 add-109 add-113 123-odd-limit intervals (/2^n and 2^n/ in bold & linked, inconsistent in italics, else, if [[23-limit]], linked)
|-
| 0
| 0.0000
| P1
| '''1/1''', [[1681/1680|S41]], [[1600/1599|S40]], [[1444/1443|S38]], [[1369/1368|S37]], [[1225/1224|S35 = S49*S50]], [[1156/1155|S34]], [[1024/1023|S32]], [[900/899|S30]], ''[[784/783|S28]]'', ''[[625/624|S25]]'',
|-
| 1
| 3.8585
|
| ''[[1521/1520|S39]]'', ''[[1296/1295|S36]]'', ''[[1089/1088|S33]]'', ''[[961/960|S31]]'', [[841/840|S29]], [[729/728|S27]], [[676/675|S26 = S13/S15]], [[576/575|S24]], [[529/528|S23]], [[484/483|S22]], [[441/440|S21]], [[400/399|S20]], [[361/360|S19]], ''[[289/288|S17]]''
|-
| 2
| 7.7170
|
| ''[[324/323|S18]]'', [[256/255|S16]], [[225/224|S15]], [[196/195|S14]], ''170/169''
|-
| 3
| 11.575
|
| [[169/168|S13 = 169/168]], [[144/143|S12 = 144/143]], 171/170
|-
| 311
| 1200.0
| P8
| '''2/1'''
|}


{| class="wikitable"
{| class="wikitable"
Line 937: Line 1,005:
|-
|-
| style="text-align:center;" | 311
| style="text-align:center;" | 311
| | 2/1
|}
Alternatively, here is only the intervals of the 41-prime-limited 77-odd-limit add-73, with others left blank.
The content of this table was generated with a small amount of Python 3 code, shown first:
<syntaxhighlight lang="python">
import math
h = [39,40,41,42,44,45,46,48,49,50,51,52,54,55,56,57,58,60,62,63,64,65,66,68,69,70,72,73,74,75,76,77,78]
m311 = {}
for i in range(311+1):
  m311[i] = []
for i in range(len(h)):
  for j in range(i,len(h)):
    f = math.gcd(h[i],h[j])
    numer = h[j] // f
    denom = h[i] // f
    interval = str(numer) + '/' + str(denom)
    complement = ''
    if math.gcd(2*denom,numer)==1:
      complement = str(2*denom) + '/' + str(numer)
    else:
      complement = str(denom) + '/' + str(numer//2)
    steps = round(311*math.log(h[j]/h[i],2))
    if interval not in m311[steps]:
      m311[steps].append(interval)
    if complement not in m311[311-steps]:
      m311[311-steps].append(complement)
for i in range(311+1):
  m311[i] = '|-\n| | '+str(i)+'\n| | '+ (', '.join(m311[i]) if len(m311[i])>0 else '')
print( '\n'.join([s for s in m311.values()]) )
</syntaxhighlight>
Note that the intervals listed for each interval of 311 EDO are in no particular order, so read carefully.
Also note that the blankness of intervals 1\311 to 5\311 and 306\311 to 310\311 show how 311 EDO is a sixth-comma system, with a generic 'comma' being 6\311, which is also what 81/80 is mapped to consistently, although the 81st harmonic is the first in the 41-limit to cause inconsistency.
{| class="wikitable"
|-
| | steps
| | intervals
|-
| | 0
| | 1/1
|-
| | 1
| |
|-
| | 2
| |
|-
| | 3
| |
|-
| | 4
| |
|-
| | 5
| |
|-
| | 6
| | 78/77, 70/69, 73/72, 74/73, 75/74, 76/75, 77/76
|-
| | 7
| | 63/62, 64/63, 65/64, 66/65, 69/68
|-
| | 8
| | 55/54, 56/55, 57/56, 58/57
|-
| | 9
| | 49/48, 50/49, 51/50, 52/51
|-
| | 10
| | 45/44, 46/45
|-
| | 11
| | 40/39, 41/40, 42/41
|-
| | 12
| | 39/38, 37/36, 75/73, 38/37, 77/75
|-
| | 13
| | 34/33, 35/34, 36/35
|-
| | 14
| | 32/31, 65/63, 33/32
|-
| | 15
| | 30/29, 31/30
|-
| | 16
| | 28/27, 57/55, 29/28
|-
| | 17
| | 80/77, 27/26
|-
| | 18
| | 26/25, 25/24, 51/49, 76/73, 77/74
|-
| | 19
| | 24/23, 73/70
|-
| | 20
| | 23/22, 68/65
|-
| | 21
| | 22/21, 65/62
|-
| | 22
| | 41/39, 21/20
|-
| | 23
| | 20/19
|-
| | 24
| | 39/37, 19/18, 58/55, 77/73
|-
| | 25
| | 55/52, 73/69, 37/35
|-
| | 26
| | 18/17, 35/33
|-
| | 27
| | 17/16, 52/49, 69/65
|-
| | 28
| | 82/77, 49/46, 33/31
|-
| | 29
| | 16/15
|-
| | 30
| | 78/73, 31/29, 77/72
|-
| | 31
| | 15/14, 74/69
|-
| | 32
| | 44/41, 29/27, 73/68
|-
| | 33
| | 14/13
|-
| | 34
| | 41/38, 55/51, 68/63, 69/64
|-
| | 35
| | 40/37, 27/25
|-
| | 36
| | 13/12
|-
| | 37
| | 25/23, 63/58, 38/35
|-
| | 38
| | 49/45, 62/57, 37/34
|-
| | 39
| | 12/11
|-
| | 40
| | 82/75, 35/32
|-
| | 41
| | 80/73, 23/21, 57/52, 34/31
|-
| | 42
| | 45/41, 56/51
|-
| | 43
| | 11/10, 76/69
|-
| | 44
| | 54/49, 32/29, 75/68
|-
| | 45
| | 21/19, 73/66
|-
| | 46
| | 41/37, 51/46, 31/28, 72/65
|-
| | 47
| | 10/9
|-
| | 48
| | 49/44, 69/62
|-
| | 49
| | 39/35, 29/26, 77/69
|-
| | 50
| | 19/17
|-
| | 51
| | 28/25, 65/58, 37/33
|-
| | 52
| | 46/41, 82/73, 55/49, 64/57, 73/65
|-
| | 53
| | 9/8
|-
| | 54
| | 44/39, 62/55, 35/31
|-
| | 55
| | 26/23
|-
| | 56
| | 17/15, 77/68
|-
| | 57
| | 42/37, 25/22
|-
| | 58
| | 41/36, 58/51, 33/29, 74/65
|-
| | 59
| | 57/50, 65/57, 73/64
|-
| | 60
| | 8/7
|-
| | 61
| | 55/48, 63/55
|-
| | 62
| | 39/34, 31/27
|-
| | 63
| | 23/20, 84/73, 38/33
|-
| | 64
| | 15/13
|-
| | 65
| | 52/45, 37/32
|-
| | 66
| | 80/69, 51/44, 22/19, 73/63
|-
| | 67
| | 29/25, 65/56, 36/31
|-
| | 68
| | 57/49, 64/55
|-
| | 69
| | 7/6
|-
| | 70
| | 90/77, 76/65
|-
| | 71
| | 48/41, 41/35, 34/29, 75/64
|-
| | 72
| | 88/75, 27/23, 74/63
|-
| | 73
| | 20/17, 73/62
|-
| | 74
| | 46/39, 33/28
|-
| | 75
| | 13/11
|-
| | 76
| | 45/38, 58/49, 32/27, 77/65
|-
| | 77
| | 82/69, 19/16
|-
| | 78
| | 25/21, 44/37, 69/58
|-
| | 79
| | 31/26, 68/57, 37/31
|-
| | 80
| | 49/41, 55/46, 92/77
|-
| | 81
| |
|-
| | 82
| | 6/5
|-
| | 83
| | 65/54, 77/64
|-
| | 84
| | 41/34, 88/73, 35/29, 76/63
|-
| | 85
| | 29/24, 75/62
|-
| | 86
| | 40/33, 23/19, 63/52
|-
| | 87
| | 17/14
|-
| | 88
| | 28/23, 45/37, 62/51, 73/60
|-
| | 89
| | 39/32, 50/41
|-
| | 90
| | 11/9
|-
| | 91
| | 49/40, 60/49, 38/31
|-
| | 92
| | 27/22, 92/75, 70/57
|-
| | 93
| | 16/13
|-
| | 94
| | 90/73, 69/56, 37/30
|-
| | 95
| | 21/17, 68/55
|-
| | 96
| | 26/21, 57/46
|-
| | 97
| | 41/33, 31/25, 36/29, 77/62
|-
| | 98
| | 51/41, 56/45, 46/37
|-
| | 99
| | 96/77
|-
| | 100
| | 5/4
|-
| | 101
| |
|-
| | 102
| | 49/39, 64/51, 69/55
|-
| | 103
| | 39/31, 44/35, 34/27, 73/58
|-
| | 104
| | 82/65, 29/23, 92/73, 63/50
|-
| | 105
| | 24/19
|-
| | 106
| | 19/15, 62/49
|-
| | 107
| | 80/63, 52/41, 33/26
|-
| | 108
| | 14/11
|-
| | 109
| | 51/40, 88/69, 65/51, 37/29
|-
| | 110
| | 23/18
|-
| | 111
| | 50/39, 41/32, 32/25, 73/57
|-
| | 112
| | 77/60
|-
| | 113
| | 9/7
|-
| | 114
| | 40/31, 58/45, 49/38
|-
| | 115
| | 84/65, 31/24, 75/58
|-
| | 116
| | 57/44, 22/17, 35/27
|-
| | 117
| | 48/37, 100/77, 74/57
|-
| | 118
| | 13/10, 82/63
|-
| | 119
| | 30/23, 73/56
|-
| | 120
| | 17/13, 64/49, 98/75
|-
| | 121
| | 55/42, 72/55, 38/29
|-
| | 122
| | 21/16
|-
| | 123
| | 46/35, 96/73, 25/19
|-
| | 124
| | 54/41, 29/22
|-
| | 125
| | 41/31, 33/25, 37/28
|-
| | 126
| | 45/34, 49/37, 102/77
|-
| | 127
| | 65/49, 69/52, 73/55, 77/58
|-
| | 128
| |
|-
| | 129
| | 4/3
|-
| | 130
| |
|-
| | 131
| | 75/56
|-
| | 132
| | 55/41, 98/73, 51/38
|-
| | 133
| | 39/29, 35/26, 74/55
|-
| | 134
| | 31/23, 66/49
|-
| | 135
| | 27/20, 50/37, 104/77, 73/54, 77/57
|-
| | 136
| | 42/31, 88/65, 23/17, 65/48
|-
| | 137
| | 19/14
|-
| | 138
| | 49/36, 34/25
|-
| | 139
| | 15/11
|-
| | 140
| | 56/41, 41/30
|-
| | 141
| | 26/19, 63/46, 100/73, 37/27
|-
| | 142
| | 48/35, 70/51
|-
| | 143
| | 11/8
|-
| | 144
| | 40/29, 62/45, 51/37
|-
| | 145
| | 29/21, 69/50, 76/55
|-
| | 146
| | 18/13
|-
| | 147
| | 68/49, 25/18, 104/75
|-
| | 148
| | 57/41, 32/23
|-
| | 149
| | 39/28, 46/33
|-
| | 150
| | 88/63, 102/73
|-
| | 151
| | 7/5
|-
| | 152
| | 80/57, 73/52, 108/77
|-
| | 153
| | 45/32, 52/37, 38/27
|-
| | 154
| | 55/39, 31/22, 69/49
|-
| | 155
| | 41/29, 65/46, 24/17
|-
| | 156
| | 58/41, 92/65, 17/12
|-
| | 157
| | 78/55, 44/31, 98/69
|-
| | 158
| | 64/45, 37/26, 27/19
|-
| | 159
| | 57/40, 104/73, 77/54
|-
| | 160
| | 10/7
|-
| | 161
| | 63/44, 73/51
|-
| | 162
| | 56/39, 33/23
|-
| | 163
| | 82/57, 23/16
|-
| | 164
| | 49/34, 36/25, 75/52
|-
| | 165
| | 13/9
|-
| | 166
| | 42/29, 100/69, 55/38
|-
| | 167
| | 29/20, 45/31, 74/51
|-
| | 168
| | 16/11
|-
| | 169
| | 35/24, 51/35
|-
| | 170
| | 19/13, 92/63, 73/50, 54/37
|-
| | 171
| | 41/28, 60/41
|-
| | 172
| | 22/15
|-
| | 173
| | 72/49, 25/17
|-
| | 174
| | 28/19
|-
| | 175
| | 31/21, 65/44, 34/23, 96/65
|-
| | 176
| | 40/27, 37/25, 77/52, 108/73, 114/77
|-
| | 177
| | 46/31, 49/33
|-
| | 178
| | 58/39, 52/35, 55/37
|-
| | 179
| | 82/55, 73/49, 76/51
|-
| | 180
| | 112/75
|-
| | 181
| |
|-
| | 182
| | 3/2
|-
| | 183
| |
|-
| | 184
| | 98/65, 104/69, 110/73, 116/77
|-
| | 185
| | 68/45, 74/49, 77/51
|-
| | 186
| | 62/41, 50/33, 56/37
|-
| | 187
| | 41/27, 44/29
|-
| | 188
| | 35/23, 73/48, 38/25
|-
| | 189
| | 32/21
|-
| | 190
| | 84/55, 55/36, 29/19
|-
| | 191
| | 26/17, 49/32, 75/49
|-
| | 192
| | 23/15, 112/73
|-
| | 193
| | 20/13, 63/41
|-
| | 194
| | 37/24, 77/50, 57/37
|-
| | 195
| | 88/57, 17/11, 54/35
|-
| | 196
| | 65/42, 48/31, 116/75
|-
| | 197
| | 31/20, 45/29, 76/49
|-
| | 198
| | 14/9
|-
| | 199
| | 120/77
|-
| | 200
| | 39/25, 64/41, 25/16, 114/73
|-
| | 201
| | 36/23
|-
| | 202
| | 80/51, 69/44, 102/65, 58/37
|-
| | 203
| | 11/7
|-
| | 204
| | 63/40, 41/26, 52/33
|-
| | 205
| | 30/19, 49/31
|-
| | 206
| | 19/12
|-
| | 207
| | 65/41, 46/29, 73/46, 100/63
|-
| | 208
| | 62/39, 35/22, 27/17, 116/73
|-
| | 209
| | 78/49, 51/32, 110/69
|-
| | 210
| |
|-
| | 211
| | 8/5
|-
| | 212
| | 77/48
|-
| | 213
| | 82/51, 45/28, 37/23
|-
| | 214
| | 66/41, 50/31, 29/18, 124/77
|-
| | 215
| | 21/13, 92/57
|-
| | 216
| | 34/21, 55/34
|-
| | 217
| | 73/45, 112/69, 60/37
|-
| | 218
| | 13/8
|-
| | 219
| | 44/27, 75/46, 57/35
|-
| | 220
| | 80/49, 49/30, 31/19
|-
| | 221
| | 18/11
|-
| | 222
| | 64/39, 41/25
|-
| | 223
| | 23/14, 74/45, 51/31, 120/73
|-
| | 224
| | 28/17
|-
| | 225
| | 33/20, 38/23, 104/63
|-
| | 226
| | 48/29, 124/75
|-
| | 227
| | 68/41, 73/44, 58/35, 63/38
|-
| | 228
| | 108/65, 128/77
|-
| | 229
| | 5/3
|-
| | 230
| |
|-
| | 231
| | 82/49, 92/55, 77/46
|-
| | 232
| | 52/31, 57/34, 62/37
|-
| | 233
| | 42/25, 37/22, 116/69
|-
| | 234
| | 69/41, 32/19
|-
| | 235
| | 76/45, 49/29, 27/16, 130/77
|-
| | 236
| | 22/13
|-
| | 237
| | 39/23, 56/33
|-
| | 238
| | 17/10, 124/73
|-
| | 239
| | 75/44, 46/27, 63/37
|-
| | 240
| | 41/24, 70/41, 29/17, 128/75
|-
| | 241
| | 77/45, 65/38
|-
| | 242
| | 12/7
|-
| | 243
| | 98/57, 55/32
|-
| | 244
| | 50/29, 112/65, 31/18
|-
| | 245
| | 69/40, 88/51, 19/11, 126/73
|-
| | 246
| | 45/26, 64/37
|-
| | 247
| | 26/15
|-
| | 248
| | 40/23, 73/42, 33/19
|-
| | 249
| | 68/39, 54/31
|-
| | 250
| | 96/55, 110/63
|-
| | 251
| | 7/4
|-
| | 252
| | 100/57, 114/65, 128/73
|-
| | 253
| | 72/41, 51/29, 58/33, 65/37
|-
| | 254
| | 37/21, 44/25
|-
| | 255
| | 30/17, 136/77
|-
| | 256
| | 23/13
|-
| | 257
| | 39/22, 55/31, 62/35
|-
| | 258
| | 16/9
|-
| | 259
| | 41/23, 73/41, 98/55, 57/32, 130/73
|-
| | 260
| | 25/14, 116/65, 66/37
|-
| | 261
| | 34/19
|-
| | 262
| | 70/39, 52/29, 138/77
|-
| | 263
| | 88/49, 124/69
|-
| | 264
| | 9/5
|-
| | 265
| | 74/41, 92/51, 56/31, 65/36
|-
| | 266
| | 38/21, 132/73
|-
| | 267
| | 49/27, 29/16, 136/75
|-
| | 268
| | 20/11, 69/38
|-
| | 269
| | 82/45, 51/28
|-
| | 270
| | 73/40, 42/23, 104/57, 31/17
|-
| | 271
| | 75/41, 64/35
|-
| | 272
| | 11/6
|-
| | 273
| | 90/49, 57/31, 68/37
|-
| | 274
| | 46/25, 116/63, 35/19
|-
| | 275
| | 24/13
|-
| | 276
| | 37/20, 50/27
|-
| | 277
| | 76/41, 102/55, 63/34, 128/69
|-
| | 278
| | 13/7
|-
| | 279
| | 41/22, 54/29, 136/73
|-
| | 280
| | 28/15, 69/37
|-
| | 281
| | 73/39, 58/31, 144/77
|-
| | 282
| | 15/8
|-
| | 283
| | 77/41, 92/49, 62/33
|-
| | 284
| | 32/17, 49/26, 130/69
|-
| | 285
| | 17/9, 66/35
|-
| | 286
| | 104/55, 138/73, 70/37
|-
| | 287
| | 74/39, 36/19, 55/29, 146/77
|-
| | 288
| | 19/10
|-
| | 289
| | 78/41, 40/21
|-
| | 290
| | 21/11, 124/65
|-
| | 291
| | 44/23, 65/34
|-
| | 292
| | 23/12, 140/73
|-
| | 293
| | 25/13, 48/25, 98/51, 73/38, 148/77
|-
| | 294
| | 77/40, 52/27
|-
| | 295
| | 27/14, 110/57, 56/29
|-
| | 296
| | 29/15, 60/31
|-
| | 297
| | 31/16, 126/65, 64/33
|-
| | 298
| | 33/17, 68/35, 35/18
|-
| | 299
| | 76/39, 72/37, 146/75, 37/19, 150/77
|-
| | 300
| | 39/20, 80/41, 41/21
|-
| | 301
| | 88/45, 45/23
|-
| | 302
| | 96/49, 49/25, 100/51, 51/26
|-
| | 303
| | 108/55, 55/28, 112/57, 57/29
|-
| | 304
| | 124/63, 63/32, 128/65, 65/33, 136/69
|-
| | 305
| | 77/39, 69/35, 144/73, 73/37, 148/75, 75/38, 152/77
|-
| | 306
| |
|-
| | 307
| |
|-
| | 308
| |
|-
| | 309
| |
|-
| | 310
| |
|-
| | 311
| | 2/1
| | 2/1
|}
|}
[[Category:311edo]]
[[Category:311edo]]
Retrieved from "https://en.xen.wiki/w/Table_of_311edo_intervals"