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== Intervals and notation ==
== Intervals and notation ==
There are multiple ways to approach notation. The simplest method is to use the notations from [[41edo]]. However, this approach will not preserve octave compression when the audio is rendered by notation software. To address this, consider using the ups and downs notation from [[124edo]] at every 3-degree step (i.e., the [[edonoi]] [[124ed8]]).
There are multiple ways to approach notation. The simplest method is to use the notations from [[41edo]]. However, this approach will not preserve octave compression when the audio is rendered by notation software. To address this, consider using the ups and downs notation from [[124edo]] at every 3-degree step (i.e., the [[edonoi]] [[124ed8]]).
{| class="wikitable center-all right-2 left-3"
|-
! Step
! Cents
! Ratios
|-
| 0
| 0.000
|
|-
| 1
| 29.025
|
|-
| 2
| 58.050
| '''32/31''', '''<u>31/30'''</u>, '''<u>30/29'''</u>, '''29/28''', 28/27, <small>27/26</small>, <small><small>26/25</small></small>, <small><small><small>25/24</small></small></small>
|-
| 3
| 87.075
| <small><small><small>24/23</small></small></small>, <small><small>23/22</small></small>, 22/21, '''21/20''', '''<u>20/19'''</u>, 19/18, <small><small>18/17</small></small>
|-
| 4
| 116.100
| <small><small>17/16</small></small>, '''16/15''', '''<u>31/29'''</u>, '''15/14''', <small>29/27</small>, <small><small><small>14/13</small></small></small>
|-
| 5
| 145.124
| <small><small>27/25</small></small>, 13/12, '''<u>25/23'''</u>, 12/11, <small><small><small>23/21</small></small></small>
|-
| 6
| 174.149
| <small>11/10</small>, '''32/29''', '''<u>21/19'''</u>, '''<u>31/28'''</u>, <small>10/9</small>
|-
| 7
| 203.174
| <small><small><small>29/26</small></small></small>, <small><small>19/17</small></small>, 28/25, '''<u>9/8'''</u>, <small>26/23</small>, <small><small><small>17/15</small></small></small>
|-
| 8
| 232.199
| <small><small>25/22</small></small>, '''<u>8/7'''</u>, 31/27, <small><small>23/20</small></small>
|-
| 9
| 261.224
| <small><small><small>15/13</small></small></small>, <small>22/19</small>, '''29/25''', 7/6
|-
| 10
| 290.249
| <small><small><small>27/23</small></small></small>, <small>20/17</small>, '''<u>13/11'''</u>, '''32/27''', <small>19/16</small>, <small><small>25/21</small></small>, <small><small><small>31/26</small></small></small>
|-
| 11
| 319.274
| '''6/5''', <small>29/24</small>, <small><small>23/19</small></small>
|-
| 12
| 348.299
| <small><small><small>17/14</small></small></small>, <small>28/23</small>, '''<u>11/9'''</u>, 27/22, <small><small>16/13</small></small>
|-
| 13
| 377.323
| <small><small>21/17</small></small>, <small>26/21</small>, 31/25, <small>5/4</small>
|-
| 14
| 406.348
| 29/23, '''<u>24/19'''</u>, '''19/15''', <small><small>14/11</small></small>
|-
| 15
| 435.373
| <small><small>23/18</small></small>, <small>32/25</small>, '''<u>9/7'''</u>, <small>31/24</small>, <small><small>22/17</small></small>
|-
| 16
| 464.398
| <small><small>13/10</small></small>, '''30/23''', '''<u>17/13'''</u>, 21/16, <small><small>25/19</small></small>, <small><small><small>29/22</small></small></small>
|-
| 17
| 493.423
| '''4/3'''
|-
| 18
| 522.448
| 31/23, '''27/20''', '''<u>23/17'''</u>, 19/14, <small><small><small>15/11</small></small></small>
|-
| 19
| 551.473
| <small>26/19</small>, '''<u>11/8'''</u>, <small>29/21</small>, <small><small>18/13</small></small>
|-
| 20
| 580.498
| <small><small>25/18</small></small>, <small>32/23</small>, '''<u>7/5'''</u>, <small><small><small>31/22</small></small></small>
|-
| 21
| 609.523
| <small><small><small>24/17</small></small></small>, 17/12, '''<u>27/19'''</u>, <small>10/7</small>
|-
| 22
| 638.547
| <small><small>23/16</small></small>, '''<u>13/9'''</u>, '''29/20''', <small><small>16/11</small></small>
|-
| 23
| 667.572
| <small><small>19/13</small></small>, '''22/15''', '''<u>25/17'''</u>, '''28/19''', 31/21
|-
| 24
| 696.597
| 3/2
|-
| 25
| 725.622
| '''32/21''', 29/19, <small><small>26/17</small></small>, <small><small><small>23/15</small></small></small>
|-
| 26
| 754.647
| <small>20/13</small>, '''<u>17/11'''</u>, '''31/20''', <small><small>14/9</small></small>
|-
| 27
| 783.672
| <small><small>25/16</small></small>, '''<u>11/7'''</u>, 30/19, <small><small>19/12</small></small>
|-
| 28
| 812.697
| <small><small>27/17</small></small>, '''<u>8/5'''</u>, <small><small><small>29/18</small></small></small>
|-
| 29
| 841.722
| <small><small>21/13</small></small>, '''<u>13/8'''</u>, 31/19, <small><small>18/11</small></small>
|-
| 30
| 870.746
| <small><small>23/14</small></small>, 28/17, <small><small><small>5/3</small></small></small>
|-
| 31
| 899.771
| '''32/19''', 27/16, <small><small>22/13</small></small>
|-
| 32
| 928.796
| <small><small>17/10</small></small>, '''29/17''', '''12/7''', <small><small><small>31/18</small></small></small>
|-
| 33
| 957.821
| <small><small>19/11</small></small>, 26/15, <small><small>7/4</small></small>
|-
| 34
| 986.846
| '''30/17''', '''<u>23/13'''</u>, <small>16/9</small>
|-
| 35
| 1015.871
| <small><small>25/14</small></small>, '''<u>9/5'''</u>, <small><small><small>29/16</small></small></small>
|-
| 36
| 1044.896
| <small><small>20/11</small></small>, '''31/17''', '''11/6'''
|-
| 37
| 1073.921
| <small><small><small>24/13</small></small></small>, '''<u>13/7'''</u>, 28/15, <small><small><small>15/8</small></small></small>
|-
| 38
| 1102.946
| <small>32/17</small>, '''<u>17/9'''</u>, <small>19/10</small>
|-
| 39
| 1131.970
| <small><small><small>21/11</small></small></small>, 23/12, '''<u>25/13'''</u>, 27/14, <small>29/15</small>, <small><small><small>31/16</small></small></small>
|-
| 40
| 1160.995
|
|-
| 41
| 1190.020
| <small><small>2/1</small></small>
|-
| 42
| 1219.045
|
|-
| 43
| 1248.070
| <small>31/15</small>, <small><small><small>29/14</small></small></small>
|-
| 44
| 1277.095
| <small><small>27/13</small></small>, 25/12, '''<u>23/11'''</u>, <small>21/10</small>
|-
| 45
| 1306.120
| <small><small><small>19/9</small></small></small>, '''<u>17/8'''</u>, 32/15, <small><small><small>15/7</small></small></small>
|-
| 46
| 1335.145
| 28/13, '''13/6'''
|-
| 47
| 1364.170
| <small><small><small>24/11</small></small></small>, '''<u>11/5'''</u>, <small><small>31/14</small></small>
|-
| 48
| 1393.194
| <small><small>20/9</small></small>, '''29/13''', <small><small>9/4</small></small>
|-
| 49
| 1422.219
| '''<u>25/11'''</u>, <small>16/7</small>
|-
| 50
| 1451.244
| <small>23/10</small>, '''30/13'''
|-
| 51
| 1480.269
| <small><small><small>7/3</small></small></small>, <small>26/11</small>
|-
| 52
| 1509.294
| <small><small>19/8</small></small>, '''31/13''', 12/5
|-
| 53
| 1538.319
| <small><small>29/12</small></small>, '''<u>17/7'''</u>, <small>22/9</small>
|-
| 54
| 1567.344
| <small><small><small>27/11</small></small></small>, <small>32/13</small>
|-
| 55
| 1596.369
| <small><small>5/2</small></small>
|-
| 56
| 1625.393
| <small>28/11</small>, '''<u>23/9'''</u>, <small><small>18/7</small></small>
|-
| 57
| 1654.418
| <small><small>31/12</small></small>, '''<u>13/5'''</u>
|-
| 58
| 1683.443
| <small><small><small>21/8</small></small></small>, 29/11
|-
| 59
| 1712.468
| <small><small><small>8/3</small></small></small>, 27/10
|-
| 60
| 1741.493
| <small><small><small>19/7</small></small></small>, '''30/11''', <small><small>11/4</small></small>
|-
| 61
| 1770.518
| '''<u>25/9'''</u>, <small><small>14/5</small></small>
|-
| 62
| 1799.543
| 31/11, '''17/6'''
|-
| 63
| 1828.568
| <small><small>20/7</small></small>, '''<u>23/8'''</u>, <small>26/9</small>
|-
| 64
| 1857.593
| <small><small><small>29/10</small></small></small>, <small>32/11</small>
|-
| 65
| 1886.617
|
|-
| 66
| 1915.642
| <small><small><small>3/1</small></small></small>
|-
| 67
| 1944.667
| <small><small><small>31/10</small></small></small>
|-
| 68
| 1973.692
| <small>28/9</small>, '''<u>25/8'''</u>, <small>22/7</small>
|-
| 69
| 2002.717
| 19/6, <small><small>16/5</small></small>
|-
| 70
| 2031.742
| 29/9, <small>13/4</small>
|-
| 71
| 2060.767
| '''<u>23/7'''</u>
|-
| 72
| 2089.792
| 10/3
|-
| 73
| 2118.816
| <small><small><small>27/8</small></small></small>, '''<u>17/5'''</u>, <small><small><small>24/7</small></small></small>
|-
| 74
| 2147.841
| 31/9
|-
| 75
| 2176.866
| <small>7/2</small>
|-
| 76
| 2205.891
| <small><small>32/9</small></small>, '''<u>25/7'''</u>, <small><small>18/5</small></small>
|-
| 77
| 2234.916
| 29/8, <small><small><small>11/3</small></small></small>
|-
| 78
| 2263.941
| <small>26/7</small>
|-
| 79
| 2292.966
| '''15/4'''
|-
| 80
| 2321.991
| <small><small>19/5</small></small>, '''23/6'''
|-
| 81
| 2351.016
| <small><small><small>27/7</small></small></small>, 31/8
|-
| 82
| 2380.040
|
|-
| 83
| 2409.065
| <small>4/1</small>
|-
| 84
| 2438.090
|
|-
| 85
| 2467.115
| 29/7, '''25/6'''
|-
| 86
| 2496.140
| <small><small>21/5</small></small>, <small>17/4</small>
|-
| 87
| 2525.165
| 30/7, <small><small><small>13/3</small></small></small>
|-
| 88
| 2554.190
| <small><small>22/5</small></small>
|-
| 89
| 2583.215
| 31/7
|-
| 90
| 2612.239
| <small>9/2</small>
|-
| 91
| 2641.264
| <small><small>32/7</small></small>, '''<u>23/5'''</u>
|-
| 92
| 2670.289
| '''14/3'''
|-
| 93
| 2699.314
| '''<u>19/4'''</u>
|-
| 94
| 2728.339
| <small><small><small>24/5</small></small></small>, '''<u>29/6'''</u>
|-
| 95
| 2757.364
|
|-
| 96
| 2786.389
| '''<u>5/1'''</u>
|-
| 97
| 2815.414
|
|-
| 98
| 2844.439
| '''<u>31/6'''</u>, <small><small>26/5</small></small>
|-
| 99
| 2873.463
| '''21/4'''
|-
| 100
| 2902.488
| '''16/3'''
|-
| 101
| 2931.513
| <small><small>27/5</small></small>
|-
| 102
| 2960.538
| <small>11/2</small>
|-
| 103
| 2989.563
| 28/5, <small><small><small>17/3</small></small></small>
|-
| 104
| 3018.588
| <small><small>23/4</small></small>
|-
| 105
| 3047.613
| '''29/5'''
|-
| 106
| 3076.638
|
|-
| 107
| 3105.663
| '''6/1'''
|-
| 108
| 3134.687
|
|-
| 109
| 3163.712
| 31/5, <small>25/4</small>
|-
| 110
| 3192.737
| '''19/3'''
|-
| 111
| 3221.762
| <small>32/5</small>
|-
| 112
| 3250.787
| <small><small>13/2</small></small>
|-
| 113
| 3279.812
| '''20/3'''
|-
| 114
| 3308.837
| '''27/4'''
|-
| 115
| 3337.862
|
|-
| 116
| 3366.886
| '''<u>7/1'''</u>
|-
| 117
| 3395.911
|
|-
| 118
| 3424.936
| '''29/4'''
|-
| 119
| 3453.961
| '''22/3'''
|-
| 120
| 3482.986
| 15/2
|-
| 121
| 3512.011
| <small><small><small>23/3</small></small></small>
|-
| 122
| 3541.036
| '''31/4'''
|-
| 123
| 3570.061
|
|-
| 124
| 3599.086
| '''<u>8/1'''</u>
|-
| 125
| 3628.110
|
|-
| 126
| 3657.135
| <small><small><small>25/3</small></small></small>
|-
| 127
| 3686.160
|
|-
| 128
| 3715.185
| <small><small>17/2</small></small>
|-
| 129
| 3744.210
| 26/3
|-
| 130
| 3773.235
|
|-
| 131
| 3802.260
| '''<u>9/1'''</u>
|-
| 132
| 3831.285
|
|-
| 133
| 3860.309
| 28/3
|-
| 134
| 3889.334
| <small>19/2</small>
|-
| 135
| 3918.359
| <small>29/3</small>
|-
| 136
| 3947.384
|
|-
| 137
| 3976.409
| <small><small>10/1</small></small>
|-
| 138
| 4005.434
|
|-
| 139
| 4034.459
| <small>31/3</small>
|-
| 140
| 4063.484
| <small>21/2</small>
|-
| 141
| 4092.509
| 32/3
|-
| 142
| 4121.533
|
|-
| 143
| 4150.558
| '''<u>11/1'''</u>
|-
| 144
| 4179.583
|
|-
| 145
| 4208.608
|
|-
| 146
| 4237.633
| <small>23/2</small>
|-
| 147
| 4266.658
|
|-
| 148
| 4295.683
| 12/1
|-
| 149
| 4324.708
|
|-
| 150
| 4353.732
|
|-
| 151
| 4382.757
| <small><small>25/2</small></small>
|-
| 152
| 4411.782
|
|-
| 153
| 4440.807
| '''<u>13/1'''</u>
|-
| 154
| 4469.832
|
|-
| 155
| 4498.857
| 27/2
|-
| 156
| 4527.882
|
|-
| 157
| 4556.907
| <small><small>14/1</small></small>
|-
| 158
| 4585.932
|
|-
| 159
| 4614.956
|
|-
| 160
| 4643.981
| <small><small><small>29/2</small></small></small>
|-
| 161
| 4673.006
|
|-
| 162
| 4702.031
| <small><small><small>15/1</small></small></small>
|-
| 163
| 4731.056
| <small><small><small>31/2</small></small></small>
|-
| 164
| 4760.081
|
|-
| 165
| 4789.106
| <small><small>16/1</small></small>
|-
| 166
| 4818.131
|
|-
| 167
| 4847.156
|
|-
| 168
| 4876.180
|
|-
| 169
| 4905.205
| '''<u>17/1'''</u>
|-
| 170
| 4934.230
|
|-
| 171
| 4963.255
|
|-
| 172
| 4992.280
| <small><small>18/1</small></small>
|-
| 173
| 5021.305
|
|-
| 174
| 5050.330
|
|-
| 175
| 5079.355
|
|-
| 176
| 5108.379
| <small><small>19/1</small></small>
|-
| 177
| 5137.404
|
|-
| 178
| 5166.429
|
|-
| 179
| 5195.454
| <small>20/1</small>
|-
| 180
| 5224.479
|
|-
| 181
| 5253.504
|
|-
| 182
| 5282.529
| <small><small>21/1</small></small>
|-
| 183
| 5311.554
|
|-
| 184
| 5340.579
| <small><small>22/1</small></small>
|-
| 185
| 5369.603
|
|-
| 186
| 5398.628
|
|-
| 187
| 5427.653
| '''<u>23/1'''</u>
|-
| 188
| 5456.678
|
|-
| 189
| 5485.703
|
|-
| 190
| 5514.728
| <small><small><small>24/1</small></small></small>
|-
| 191
| 5543.753
|
|-
| 192
| 5572.778
| '''<u>25/1'''</u>
|-
| 193
| 5601.802
|
|-
| 194
| 5630.827
| <small><small>26/1</small></small>
|-
| 195
| 5659.852
|
|-
| 196
| 5688.877
|
|-
| 197
| 5717.902
| <small><small>27/1</small></small>
|-
| 198
| 5746.927
|
|-
| 199
| 5775.952
| 28/1
|-
| 200
| 5804.977
|
|-
| 201
| 5834.002
| '''29/1'''
|-
| 202
| 5863.026
|
|-
| 203
| 5892.051
| '''30/1'''
|-
| 204
| 5921.076
|
|-
| 205
| 5950.101
| 31/1
|-
| 206
| 5979.126
|
|-
| 207
| 6008.151
| <small>32/1</small>
|}


=== Approximation to JI ===
=== Approximation to JI ===
Retrieved from "https://en.xen.wiki/w/186zpi"