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Line 8: Line 8:
! | cents value
! | cents value
! | ratio
! | ratio
!JI approximation
|-
|-
| | 0
| | 0
| | 0.0000
| | 0.0000
| | '''[[1/1]]'''
| | '''[[1/1]]'''
|[[1/1]]
|-
|-
| | 1
| | 1
| | 96.5784
| | 96.5784
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">1/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">1/4</font>
|[[18/17]], [[19/18]]
|-
|-
| | 2
| | 2
| | 193.1569
| | 193.1569
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">1/2</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">1/2</font>
|[[19/17]]
|-
|-
| | 3
| | 3
| | 289.7353
| | 289.7353
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">3/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">3/4</font>
|[[13/11]]
|-
|-
| | 4
| | 4
| | 386.3137
| | 386.3137
| | '''[[5/4]]'''
| | '''[[5/4]]'''
|[[5/4]]
|-
|-
| | 5
| | 5
| | 482.8921
| | 482.8921
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">5/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">5/4</font>
|[[4/3]]
|-
|-
| | 6
| | 6
| | 579.4706
| | 579.4706
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">3/2</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">3/2</font>
|[[7/5]]
|-
|-
| | 7
| | 7
| | 676.0490
| | 676.0490
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">7/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">7/4</font>
|
|-
|-
| | 8
| | 8
| | 772.6274
| | 772.6274
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">2</font> = [[25/16]]
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">2</font> = [[25/16]]
|[[14/9]], [[25/16]], [[11/7]]
|-
|-
| | 9
| | 9
| | 869.2059
| | 869.2059
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">9/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">9/4</font>
|[[5/3]]
|-
|-
| | 10
| | 10
| | 965.7843
| | 965.7843
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">5/2</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">5/2</font>
|[[7/4]]
|-
|-
| | 11
| | 11
| | 1062.3627
| | 1062.3627
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">11/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">11/4</font>
|[[11/6]]
|-
|-
| | 12
| | 12
| | 1158.9411
| | 1158.9411
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">3</font> = 125/64
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">3</font> = 125/64
|
|-
|-
| | 13
| | 13
| | 1255.5196
| | 1255.5196
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">13/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">13/4</font>
|
|-
|-
| | 14
| | 14
| | 1352.0980
| | 1352.0980
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">7/2</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">7/2</font>
|[[11/5]]
|-
|-
| | 15
| | 15
| | 1448.6764
| | 1448.6764
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">15/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">15/4</font>
|
|-
|-
| | 16
| | 16
| | 1545.2549
| | 1545.2549
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">4</font> = 625/256
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">4</font> = 625/256
|
|-
|-
| | 17
| | 17
| | 1641.8333
| | 1641.8333
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">17/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">17/4</font>
|[[13/5]]
|-
|-
| | 18
| | 18
| | 1738.4117
| | 1738.4117
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">9/2</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">9/2</font>
|[[11/4]]
|-
|-
| | 19
| | 19
| | 1834.9901
| | 1834.9901
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">19/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">19/4</font>
|
|-
|-
| | 20
| | 20
| | 1931.5686
| | 1931.5686
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">5</font> = 3125/1024
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">5</font> = 3125/1024
|
|-
|-
| | 21
| | 21
| | 2028.1470
| | 2028.1470
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">21/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">21/4</font>
|[[13/4]]
|-
|-
| | 22
| | 22
| | 2124.7254
| | 2124.7254
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">11/2</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">11/2</font>
|[[17/5]]
|-
|-
| | 23
| | 23
| | 2221.3039
| | 2221.3039
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">23/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">23/4</font>
|[[18/5]]
|-
|-
| | 24
| | 24
| | 2317.8823
| | 2317.8823
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">6</font> = 15625/4096
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">6</font> = 15625/4096
|[[19/5]]
|-
|-
| | 25
| | 25
| | 2414.4607
| | 2414.4607
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">25/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">25/4</font>
|[[4/1]]
|-
|-
| | 26
| | 26
| | 2511.0391
| | 2511.0391
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">13/2</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">13/2</font>
|[[17/4]]
|-
|-
| | 27
| | 27
| | 2607.6176
| | 2607.6176
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">27/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">27/4</font>
|[[9/2]]
|-
|-
| | 28
| | 28
| | 2704.1960
| | 2704.1960
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">7</font> = 78125/16384
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">7</font> = 78125/16384
|[[19/4]]
|-
|-
| | 29
| | 29
| | 2800.7744
| | 2800.7744
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">29/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">29/4</font>
|[[5/1]]
|-
|-
| | 30
| | 30
| | 2897.3529
| | 2897.3529
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">15/2</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">15/2</font>
|[[16/3]]
|-
|-
| | 31
| | 31
| | 2993.9313
| | 2993.9313
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">31/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">31/4</font>
|[[17/3]]
|-
|-
| | 32
| | 32
| | 3090.5097
| | 3090.5097
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">8</font> = 390625/65536
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">8</font> = 390625/65536
|[[6/1]]
|-
|-
| | 33
| | 33
| | 3187.0881
| | 3187.0881
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">33/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">33/4</font>
|[[19/3]]
|-
|-
| | 34
| | 34
| | 3283.6666
| | 3283.6666
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">17/2</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">17/2</font>
|[[20/3]]
|-
|-
| | 35
| | 35
| | 3380.2450
| | 3380.2450
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">35/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">35/4</font>
|[[7/1]]
|-
|-
| | 36
| | 36
| | 3476.8234
| | 3476.8234
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">9</font> = 1953125/262144
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">9</font> = 1953125/262144
|[[15/2]]
|-
|-
| | 37
| | 37
| | 3573.4019
| | 3573.4019
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">37/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">37/4</font>
|
|-
|-
| | 38
| | 38
| | 3669.9803
| | 3669.9803
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">19/2</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">19/2</font>
|
|-
|-
| | 39
| | 39
| | 3766.5587
| | 3766.5587
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">39/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">39/4</font>
|
|-
|-
| | 40
| | 40
| | 3863.1371
| | 3863.1371
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">10</font> = 9765625/1048576
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">10</font> = 9765625/1048576
|
|-
|-
| | 41
| | 41
| | 3959.7156
| | 3959.7156
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">41/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">41/4</font>
|
|-
|-
| | 42
| | 42
| | 4056.2940
| | 4056.2940
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">21/2</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">21/2</font>
|[[21/2]]
|-
|-
| | 43
| | 43
| | 4152.8724
| | 4152.8724
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">43/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">43/4</font>
|[[11/1]]
|-
|-
| | 44
| | 44
| | 4249.4509
| | 4249.4509
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">11</font> = 48828125/4194304
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">11</font> = 48828125/4194304
|
|-
|-
| | 45
| | 45
| | 4346.0293
| | 4346.0293
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">45/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">45/4</font>
|
|-
|-
| | 46
| | 46
| | 4442.6077
| | 4442.6077
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">23/2</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">23/2</font>
|[[13/1]]
|-
|-
| | 47
| | 47
| | 4539.1861
| | 4539.1861
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">47/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">47/4</font>
|
|-
|-
| | 48
| | 48
| | 4635.7646
| | 4635.7646
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">12</font> = 244140625/16777216
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">12</font> = 244140625/16777216
|
|-
|-
| | 49
| | 49
| | 4732.3430
| | 4732.3430
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">49/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">49/4</font>
|
|-
|-
| | 50
| | 50
| | 4828.9214
| | 4828.9214
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">25/2</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">25/2</font>
|[[16/1]]
|-
|-
| | 51
| | 51
| | 4925.4999
| | 4925.4999
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">51/4</font>
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">51/4</font>
|
|-
|-
| | 52
| | 52
| | 5022.0783
| | 5022.0783
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">13</font> = 1220703125/67108864
| | (5/4)<font style="vertical-align:super;font-size:0.8em;">13</font> = 1220703125/67108864
|
|}
|}
== Harmonics ==
{{Harmonics in equal
| steps = 4
| num = 5
| denom = 4
}}
{{Harmonics in equal
| steps = 4
| num = 5
| denom = 4
| start = 12
| collapsed = 1
}}


== Related regular temperament ==
== Related regular temperament ==
Line 231: Line 299:
Mapping: [{{val|1 4 2 -5}}, {{val|0 -30 4 97}}]<br>
Mapping: [{{val|1 4 2 -5}}, {{val|0 -30 4 97}}]<br>
POTE generator: ~200/189 = 96.591<br>
POTE generator: ~200/189 = 96.591<br>
Vals: 87, 236, 323, 410, 733<br>
{{Optimal ET sequence|legend=1|87, 236, 323, 410, 733}}<br>
Badness: 0.179304<br><br>
Badness: 0.179304<br><br>
'''11-limit'''<br>
'''11-limit'''<br>
Line 237: Line 305:
Mapping: [{{val|1 4 2 -5 7}}, {{val|0 -30 4 97 -44}}]<br>
Mapping: [{{val|1 4 2 -5 7}}, {{val|0 -30 4 97 -44}}]<br>
POTE generator: ~200/189 = 96.587<br>
POTE generator: ~200/189 = 96.587<br>
Vals: 87, 236, 323, 410<br>
{{Optimal ET sequence|legend=1|87, 236, 323, 410}}<br>
Badness: 0.100077<br><br>
Badness: 0.100077<br><br>
'''13-limit'''<br>
'''13-limit'''<br>
Line 243: Line 311:
Mapping: [{{val|1 4 2 -5 7 7}}, {{val|0 -30 4 97 -44 -41}}]<br>
Mapping: [{{val|1 4 2 -5 7 7}}, {{val|0 -30 4 97 -44 -41}}]<br>
POTE generator: ~143/135 = 96.586<br>
POTE generator: ~143/135 = 96.586<br>
Vals: 87, 236, 323, 410<br>
{{Optimal ET sequence|legend=1|87, 236, 323, 410}}<br>
Badness: 0.046151<br><br>
Badness: 0.046151<br><br>


[[Category:Major third]]
[[Category:Major third]]
[[Category:Equal-step tuning]]
[[Category:Equal-step tuning]]
[[Category:Edonoi]]
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