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'''[[EDF|Division of the just perfect fifth]] into 45 equal parts''' (45EDF) is related to [[77edo|77 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 1.123 cents stretched and the step size is about 15.599 cents. The patent val has a generally sharp tendency for harmonics up to 16, with the exception for 11.
{{Infobox ET}}
'''[[EDF|Division of the just perfect fifth]] into 45 equal parts''' (45EDF) is related to [[77edo]], but with the [[3/2]] rather than the [[2/1]] being [[just]]. The octave is [[Octave stretch|stretched]] by about 1.123 [[cents]] and the step size is about 15.599 cents.  
 
The [[patent val]] has a generally sharp tendency for [[harmonic]]s up to 16, with the exception for 11.


Lookalikes: [[77edo]], [[122edt]]
Lookalikes: [[77edo]], [[122edt]]
== Harmonics ==
{{Harmonics in equal|45|3|2|intervals=prime|columns=9}}
{{Harmonics in equal|45|3|2|intervals=prime|columns=9|start=10|collapsed=1}}


== Intervals ==
== Intervals ==
Line 12: Line 19:
in the 13-limit
in the 13-limit
|-
|-
| style="text-align:right;" |0
| colspan="2" style="text-align:right;" |0
| style="text-align:right;" |0.000
| style="text-align:center;" |1/1
| style="text-align:center;" |1/1
|-
|-
| style="text-align:right;" |1
|1
| style="text-align:right;" |15.599
|15.599
| style="text-align:center;" |81/80, 99/98
|81/80, 99/98
|-
|2
|31.198
|64/63, 49/48
|-
|3
|46.797
|33/32, 36/35
|-
|4
|62.396
|28/27, 27/26, 26/25
|-
|5
|77.995
|21/20, 22/21, 25/24
|-
|6
|93.594
|135/128
|-
|7
|109.193
|16/15
|-
|8
|124.792
|15/14, 14/13
|-
|9
|140.391
|13/12
|-
|10
|155.99
|12/11, 11/10
|-
|11
|171.589
|72/65
|-
|12
|187.188
|10/9
|-
|13
|202.787
|9/8
|-
|14
|218.386
|256/225
|-
|-
| style="text-align:right;" |2
|15
| style="text-align:right;" |31.198
|233.985
| style="text-align:center;" |64/63, 49/48
|8/7
|-
|-
| style="text-align:right;" |3
|16
| style="text-align:right;" |46.797
|249.584
| style="text-align:center;" |33/32, 36/35
|15/13
|-
|-
| style="text-align:right;" |4
|17
| style="text-align:right;" |62.395
|265.183
| style="text-align:center;" |28/27, 26/25
|7/6
|-
|-
| style="text-align:right;" |5
|18
| style="text-align:right;" |77.995
|280.782
| style="text-align:center;" |21/20, 25/24
|33/28
|-
|-
| style="text-align:right;" |6
|19
| style="text-align:right;" |93.594
|296.381
| style="text-align:center;" |135/128
|32/27, 13/11
|-
|-
| style="text-align:right;" |7
|20
| style="text-align:right;" |109.193
|311.98
| style="text-align:center;" |16/15
|6/5
|-
|-
| style="text-align:right;" |8
|21
| style="text-align:right;" |124.792
|327.579
| style="text-align:center;" |15/14
|98/81
|-
|-
| style="text-align:right;" |9
|22
| style="text-align:right;" |140.391
|343.178
| style="text-align:center;" |13/12
|11/9, 39/32
|-
|-
| style="text-align:right;" |10
|23
| style="text-align:right;" |155.99
|358.777
| style="text-align:center;" |12/11, 11/10
|16/13
|-
|-
| style="text-align:right;" |11
|24
| style="text-align:right;" |171.589
|374.376
| style="text-align:center;" |72/65
|56/45, 26/21
|-
|-
| style="text-align:right;" |12
|25
| style="text-align:right;" |187.188
|389.975
| style="text-align:center;" |10/9
|5/4
|-
|-
| style="text-align:right;" |13
|26
| style="text-align:right;" |202.787
|405.574
| style="text-align:center;" |9/8
|33/26, 81/64
|-
|-
| style="text-align:right;" |14
|27
| style="text-align:right;" |218.386
|420.173
| style="text-align:center;" |256/225
|14/11, 32/25
|-
|-
| style="text-align:right;" |15
|28
| style="text-align:right;" |233.985
|436.772
| style="text-align:center;" |8/7
|9/7
|-
|-
| style="text-align:right;" |16
|29
| style="text-align:right;" |249.584
|452.371
| style="text-align:center;" |15/13
|13/10
|-
|-
| style="text-align:right;" |17
|30
| style="text-align:right;" |265.183
|467.97
| style="text-align:center;" |7/6
|21/16
|-
|-
| style="text-align:right;" |18
|31
| style="text-align:right;" |280.782
|483.569
| style="text-align:center;" |33/28
|120/91
|-
|-
| style="text-align:right;" |19
|32
| style="text-align:right;" |296.381
|499.168
| style="text-align:center;" |32/27, 13/11
|4/3
|-
|-
| style="text-align:right;" |20
|33
| style="text-align:right;" |311.98
|514.767
| style="text-align:center;" |6/5
|27/20
|-
|-
| style="text-align:right;" |21
|34
| style="text-align:right;" |327.579
|530.366
| style="text-align:center;" |98/81
|49/36
|-
|-
| style="text-align:right;" |22
|35
| style="text-align:right;" |343.178
|545.965
| style="text-align:center;" |11/9, 39/32
|11/8, 15/11
|-
|-
| style="text-align:right;" |23
|36
| style="text-align:right;" |358.777
|561.564
| style="text-align:center;" |16/13
|18/13
|-
|-
| style="text-align:right;" |24
|37
| style="text-align:right;" |374.376
|577.163
| style="text-align:center;" |56/45, 26/21
|7/5
|-
|-
| style="text-align:right;" |25
|38
| style="text-align:right;" |389.975
|592.762
| style="text-align:center;" |5/4
|45/32
|-
|-
| style="text-align:right;" |26
|39
| style="text-align:right;" |405.574
|608.361
| style="text-align:center;" |33/26, 81/64
|64/45
|-
|-
| style="text-align:right;" |27
|40
| style="text-align:right;" |420.173
|623.96
| style="text-align:center;" |14/11, 32/25
|10/7
|-
|-
| style="text-align:right;" |28
|41
| style="text-align:right;" |436.772
|639.559
| style="text-align:center;" |9/7
|13/9
|-
|-
| style="text-align:right;" |29
|42
| style="text-align:right;" |452.371
|655.158
| style="text-align:center;" |13/10
|16/11, 22/15
|-
|-
| style="text-align:right;" |30
|43
| style="text-align:right;" |467.97
|670.757
| style="text-align:center;" |21/16
|72/49
|-
|-
| style="text-align:right;" |31
|44
| style="text-align:right;" |483.569
|686.356
| style="text-align:center;" |120/91
|40/27
|-
|-
| style="text-align:right;" |32
|45
| style="text-align:right;" |499.168
|701.955
| style="text-align:center;" |4/3
|3/2
|-
|-
| style="text-align:right;" |33
|46
| style="text-align:right;" |514.767
|717.554
| style="text-align:center;" |27/20
|91/60
|-
|-
| style="text-align:right;" |34
|47
| style="text-align:right;" |530.366
|733.153
| style="text-align:center;" |49/36
|32/21
|-
|-
| style="text-align:right;" |35
|48
| style="text-align:right;" |545.965
|748.752
| style="text-align:center;" |11/8, 15/11
|20/13
|-
|-
| style="text-align:right;" |36
|49
| style="text-align:right;" |561.564
|764.351
| style="text-align:center;" |18/13
|14/9
|-
|-
| style="text-align:right;" |37
|50
| style="text-align:right;" |577.163
|779.95
| style="text-align:center;" |7/5
|11/7, 25/16
|-
|-
| style="text-align:right;" |38
|51
| style="text-align:right;" |592.762
|795.549
| style="text-align:center;" |45/32
|52/33, 128/81
|-
|-
| style="text-align:right;" |39
|52
| style="text-align:right;" |608.361
|818.148
| style="text-align:center;" |64/45
|8/5
|-
|-
| style="text-align:right;" |40
|53
| style="text-align:right;" |623.96
|826.747
| style="text-align:center;" |10/7
|45/28, 21/13
|-
|-
| style="text-align:right;" |41
|54
| style="text-align:right;" |639.559
|842.346
| style="text-align:center;" |13/9
|13/8
|-
|-
| style="text-align:right;" |42
|55
| style="text-align:right;" |655.158
|857.945
| style="text-align:center;" |16/11, 22/15
|18/11, 64/39
|-
|-
| style="text-align:right;" |43
|56
| style="text-align:right;" |670.757
|873.544
| style="text-align:center;" |72/49
|81/49
|-
|-
| style="text-align:right;" |44
|57
| style="text-align:right;" |686.356
|889.143
| style="text-align:center;" |40/27
|5/3
|-
|-
| style="text-align:right;" |45
|58
| style="text-align:right;" |701.955
|904.742
| style="text-align:center;" |3/2
|27/16, 22/13
|-
|-
| style="text-align:right;" |46
|59
| style="text-align:right;" |717.554
|920.341
| style="text-align:center;" |91/60
|56/33
|-
|-
| style="text-align:right;" |47
|60
| style="text-align:right;" |733.153
|935.84
| style="text-align:center;" |32/21
|12/7
|-
|-
| style="text-align:right;" |48
|61
| style="text-align:right;" |748.752
|951.539
| style="text-align:center;" |20/13
|26/15
|-
|-
| style="text-align:right;" |49
|62
| style="text-align:right;" |764.351
|967.138
| style="text-align:center;" |14/9
|7/4
|-
|-
| style="text-align:right;" |50
|63
| style="text-align:right;" |779.95
|982.737
| style="text-align:center;" |11/7, 25/16
|225/128
|-
|-
| style="text-align:right;" |51
|64
| style="text-align:right;" |795.549
|998.336
| style="text-align:center;" |52/33, 128/81
|16/9
|-
|-
| style="text-align:right;" |52
|65
| style="text-align:right;" |818.148
|1013.935
| style="text-align:center;" |8/5
|9/5
|-
|-
| style="text-align:right;" |53
|66
| style="text-align:right;" |826.747
|1029.534
| style="text-align:center;" |45/28, 21/13
|65/36
|-
|-
| style="text-align:right;" |54
|67
| style="text-align:right;" |842.346
|1045.133
| style="text-align:center;" |13/8
|11/6, 20/11
|-
|-
| style="text-align:right;" |55
|68
| style="text-align:right;" |857.945
|1060.732
| style="text-align:center;" |18/11, 64/39
|24/13
|-
|-
| style="text-align:right;" |56
|69
| style="text-align:right;" |873.544
|1076.331
| style="text-align:center;" |81/49
|28/15
|-
|-
| style="text-align:right;" |57
|70
| style="text-align:right;" |889.143
|1091.93
| style="text-align:center;" |5/3
|15/8
|-
|-
| style="text-align:right;" |58
|71
| style="text-align:right;" |904.742
|1107.529
| style="text-align:center;" |27/16, 22/13
|256/135
|-
|-
| style="text-align:right;" |59
|72
| style="text-align:right;" |920.341
|1123.128
| style="text-align:center;" |56/33
|40/21, 48/25
|-
|-
| style="text-align:right;" |60
|73
| style="text-align:right;" |935.84
|1138.727
| style="text-align:center;" |12/7
|27/14, 25/13
|-
|-
| style="text-align:right;" |61
|74
| style="text-align:right;" |951.539
|1154.326
| style="text-align:center;" |26/15
|64/33, 35/18
|-
|-
| style="text-align:right;" |62
|75
| style="text-align:right;" |967.138
|1169.925
| style="text-align:center;" |7/4
|63/32, 96/49
|-
|-
| style="text-align:right;" |63
|76
| style="text-align:right;" |982.737
|1185.524
| style="text-align:center;" |225/128
|160/81, 196/99
|-
|-
| style="text-align:right;" |64
|77
| style="text-align:right;" |998.336
|1201.123
| style="text-align:center;" |16/9
|/1
|-
|-
| style="text-align:right;" |65
|78
| style="text-align:right;" |1013.935
|1216.722
| style="text-align:center;" |9/5
|81/40, 99/49
|-
|-
| style="text-align:right;" |66
|79
| style="text-align:right;" |1029.534
|1232.321
| style="text-align:center;" |65/36
|128/63, 49/24
|-
|-
| style="text-align:right;" |67
|80
| style="text-align:right;" |1045.133
|1247.92
| style="text-align:center;" |11/6, 20/11
|33/16, 72/35
|-
|-
| style="text-align:right;" |68
|81
| style="text-align:right;" |1060.732
|1263.519
| style="text-align:center;" |24/13
|56/27, 27/13, 52/25
|-
|-
| style="text-align:right;" |69
|82
| style="text-align:right;" |1076.331
|1279.118
| style="text-align:center;" |28/15
|21/10, 44/21,25/12
|-
|-
| style="text-align:right;" |70
|83
| style="text-align:right;" |1091.93
|1294.717
| style="text-align:center;" |15/8
|135/64
|-
|-
| style="text-align:right;" |71
|84
| style="text-align:right;" |1107.529
|1310.316
| style="text-align:center;" |256/135
|32/15
|-
|-
| style="text-align:right;" |72
|85
| style="text-align:right;" |1123.128
|1325.915
| style="text-align:center;" |40/21, 48/25
|15/7, 28/13
|-
|-
| style="text-align:right;" |73
|86
| style="text-align:right;" |1138.727
|1341.514
| style="text-align:center;" |27/14, 25/13
|13/6
|-
|-
| style="text-align:right;" |74
|87
| style="text-align:right;" |1154.326
|1357.113
| style="text-align:center;" |64/33, 35/18
|24/11, 11/5
|-
|-
| style="text-align:right;" |75
|88
| style="text-align:right;" |1169.925
|1372.712
| style="text-align:center;" |63/32, 96/49
|144/65
|-
|-
| style="text-align:right;" |76
|89
| style="text-align:right;" |1185.524
|1388.311
| style="text-align:center;" |160/81, 196/99
|20/9
|-
|-
| style="text-align:right;" |77
|90
| style="text-align:right;" |1201.123
|1403.91
| style="text-align:center;" |2/1
|9/4
|}
|}
[[Category:Edf]]
 
[[Category:Edonoi]]
{{todo|expand}}
Retrieved from "https://en.xen.wiki/w/45edf"