CompactStar: Created page with "For archival purposes {| class="wikitable" |- | style="text-align:center;" | note | style="text-align:center;" | interval |- | style="text-align:center;" | 1 | | 289/288 |- |..."

2024-02-25T02:27:06Z

Created page with "For archival purposes {| class="wikitable" |- | style="text-align:center;" | note | style="text-align:center;" | interval |- | style="text-align:center;" | 1 | | 289/288 |- |..."

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| 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
|}
[[Category:311edo]]

← Older revision		Revision as of 01:15, 15 March 2024
Line 1:		Line 1:
	This is an archive of [[table of 311edo intervals]].		This is an archive of [[table of 311edo intervals]].
			<pre>{{delete\|comprehensive collapsible table that is an improved and prettified superset of both tables here has been put on the 311edo page}}</pre>

	== marker < cent < gene ==		== marker < cent < gene ==
	{\| class="mw-collapsible mw-collapsed wikitable center-1 center-2 center-3"		{\| class="mw-collapsible mw-collapsed wikitable center-1 center-2 center-3"

← Older revision		Revision as of 01:14, 15 March 2024
Line 1:		Line 1:
	This is an archive.		This is an archive of [[table of 311edo intervals]].
	== marker < cent < gene ==		== marker < cent < gene ==
	{\| class="mw-collapsible mw-collapsed wikitable center-1 center-2 center-3"		{\| class="mw-collapsible mw-collapsed wikitable center-1 center-2 center-3"
Line 4,067:		Line 4,067:
	\| \| 2/1		\| \| 2/1
	\|}		\|}
			<pre>
	[[Category:311edo]]		[[Category:311edo]]
			</pre>

← Older revision		Revision as of 02:27, 25 February 2024
Line 1:		Line 1:
	~~For archival purposes~~		This is an archive of [[table of 311edo intervals]]

	{\| class="wikitable"		{\| class="wikitable"

User:CompactStar/Table of 311edo intervals - Revision history

CompactStar at 01:15, 15 March 2024

CompactStar at 01:14, 15 March 2024

CompactStar at 01:14, 15 March 2024

CompactStar at 02:27, 25 February 2024

CompactStar: Created page with "For archival purposes {| class="wikitable" |- | style="text-align:center;" | note | style="text-align:center;" | interval |- | style="text-align:center;" | 1 | | 289/288 |- |..."