Rodan: Difference between revisions

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See also [[Gamelismic clan #Rodan]]
See also [[Gamelismic clan #Rodan]].


Gencom: [2 8/7; 154/153 196/195 245/243 273/272 364/363]
Gencom: [2 8/7; 154/153 196/195 245/243 273/272 364/363]
Line 11: Line 11:
! colspan="2" | Approximate Ratios
! colspan="2" | Approximate Ratios
|-
|-
!11-limit
! 11-limit
!13- and 17-limit
! 13- and 17-limit
|-
|-
|0
| 0
|0.000
| 0.000
|1/1
| 1/1
|
|
|-
|-
|1
| 1
|234.482
| 234.482
|8/7
| 8/7
|
|
|-
|-
|2
| 2
|468.964
| 468.964
|21/16
| 21/16
|17/13
| 17/13
|-
|-
|3
| 3
|703.446
| 703.446
|3/2
| 3/2
|
|
|-
|-
|4
| 4
|937.929
| 937.929
|12/7
| 12/7
|
|
|-
|-
|5
| 5
|1172.411
| 1172.411
|63/32~160/81
| 63/32~160/81
|
|
|-
|-
|6
| 6
|206.893
| 206.893
|9/8
| 9/8
|
|
|-
|-
|7
| 7
|441.375
| 441.375
|9/7
| 9/7
|22/17
| 22/17
|-
|-
|8
| 8
|675.857
| 675.857
|40/27
| 40/27
|
|
|-
|-
|9
| 9
|910.339
| 910.339
|27/16
| 27/16
|22/13
| 22/13
|-
|-
|10
| 10
|1144.821
| 1144.821
|27/14~35/18~64/33
| 27/14~35/18~64/33
|33/17
| 33/17
|-
|-
|11
| 11
|179.304
| 179.304
|10/9
| 10/9
|
|
|-
|-
|12
| 12
|413.786
| 413.786
|14/11~81/64~80/63
| 14/11~81/64~80/63
|33/26
| 33/26
|-
|-
|13
| 13
|648.268
| 648.268
|16/11
| 16/11
|
|
|-
|-
|14
| 14
|882.750
| 882.750
|5/3
| 5/3
|
|
|-
|-
|15
| 15
|1117.232
| 1117.232
|21/11~40/21
| 21/11~40/21
|
|
|-
|-
|16
| 16
|151.714
| 151.714
|12/11
| 12/11
|
|
|-
|-
|17
| 17
|386.196
| 386.196
|5/4
| 5/4
|
|
|-
|-
|18
| 18
|620.679
| 620.679
|10/7
| 10/7
|
|
|-
|-
|19
| 19
|855.161
| 855.161
|18/11
| 18/11
|64/39~28/17
| 64/39~28/17
|-
|-
|20
| 20
|1089.643
| 1089.643
|15/8
| 15/8
|32/17
| 32/17
|-
|-
|21
| 21
|124.125
| 124.125
|15/14
| 15/14
|14/13
| 14/13
|-
|-
|22
| 22
|358.607
| 358.607
|27/22
| 27/22
|16/13~21/17
| 16/13~21/17
|}
|}
<nowiki>*</nowiki> in 13-limit POTE tuning
<nowiki>*</nowiki> in 13-limit POTE tuning
Line 133: Line 133:
== Spectrum of Rodan Tunings by Eigenmonzos ==
== Spectrum of Rodan Tunings by Eigenmonzos ==


{| class="wikitable"
{| class="wikitable center-all left-3"
|-
|-
! | Eigenmonzo
! Eigenmonzo
! | Fifth
! Fifth
! Comment
|-
|-
| | 8/7
| 8/7
| | 693.522
| 693.522
|
|-
|-
| | 17/13
| 17/13
| | 696.642
| 696.642
|
|-
|-
| | 7/6
| 7/6
| | 699.847
| 699.847
|
|-
|-
| | 9/7
| 9/7
| | 700.750
| 700.750
|
|-
|-
| | 4/3
| 4/3
| | 701.955
| 701.955
|
|-
|-
| | 24\41
| (24\41)
| | 702.439
| 702.439
|
|-
|-
| | 15/14
| 15/14
| | 702.778
| 702.778
|
|-
|-
| | 7/5
| 7/5
| | 702.915 (7 and 9 limit minimax)
| 702.915
| 7 and 9 limit minimax
|-
|-
| | 11/9
| 11/9
| | 703.041 (11 limit minimax)
| 703.041
| 11 limit minimax
|-
|-
| | 75\128
| (75\128)
| | 703.125
| 703.125
|-
|-
| | 18/13
| 18/13
| | 703.220 (13 and 15 limit minimax)
| 703.220
| 13 and 15 limit minimax
|-
|-
| | 16/15
| 16/15
| | 703.240
| 703.240
|
|-
|-
| | 12/11
| 12/11
| | 703.244
| 703.244
|
|-
|-
| | 15/11
| 15/11
| | 703.359
| 703.359
|
|-
|-
| | 13/12
| 13/12
| | 703.371
| 703.371
|
|-
|-
| | 15/13
| 15/13
| | 703.410
| 703.410
|
|-
|-
| | 51\87
| (51\87)
| | 703.448
| 703.448
|
|-
|-
| | 5/4
| 5/4
| | 703.467 (5 limit minimax)
| 703.467
| 5 limit minimax
|-
|-
| | 11/10
| 11/10
| | 703.500
| 703.500
|
|-
|-
| | 13/10
| 13/10
| | 703.522
| 703.522
|
|-
|-
| | 11/8
| 11/8
| | 703.542
| 703.542
|
|-
|-
| | 16/13
| 16/13
| | 703.564
| 703.564
|
|-
|-
| | 13/11
| 13/11
| | 703.597
| 703.597
|
|-
|-
| | 18/17
| 18/17
| | 703.726 (17 limit minimax)
| 703.726
| 17 limit minimax
|-
|-
| | 17/15
| 17/15
| | 703.748
| 703.748
|
|-
|-
| | 78\133
| (78\133)
| | 703.759
| 703.759
|
|-
|-
| | 6/5
| 6/5
| | 703.791
| 703.791
|
|-
|-
| | 20/17
| 20/17
| | 703.894
| 703.894
|
|-
|-
| | 24/17
| 24/17
| | 703.956
| 703.956
|
|-
|-
|17/16
| 17/16
|704.257
| 704.257
|
|-
|-
| | 10/9
| 10/9
| | 704.292
| 704.292
|
|-
|-
|27\46
| (27\46)
|704.348
| 704.348
|
|-
|-
| | 14/11
| 14/11
| | 704.377
| 704.377
|
|}
|}


[[Category:Temperament]]
[[Category:Rodan| ]] <!-- main article -->
[[Category:Rodan| ]] <!-- main article -->
[[Category:Sensamagic]]
[[Category:Gamelismic]]

Revision as of 08:19, 12 October 2020

See also Gamelismic clan #Rodan.

Gencom: [2 8/7; 154/153 196/195 245/243 273/272 364/363]

Gencom map: [<1 1 -1 3 6 8 8|, <0 3 17 -1 -13 -22 -20|]

Interval Chain

# Cents* Approximate Ratios
11-limit 13- and 17-limit
0 0.000 1/1
1 234.482 8/7
2 468.964 21/16 17/13
3 703.446 3/2
4 937.929 12/7
5 1172.411 63/32~160/81
6 206.893 9/8
7 441.375 9/7 22/17
8 675.857 40/27
9 910.339 27/16 22/13
10 1144.821 27/14~35/18~64/33 33/17
11 179.304 10/9
12 413.786 14/11~81/64~80/63 33/26
13 648.268 16/11
14 882.750 5/3
15 1117.232 21/11~40/21
16 151.714 12/11
17 386.196 5/4
18 620.679 10/7
19 855.161 18/11 64/39~28/17
20 1089.643 15/8 32/17
21 124.125 15/14 14/13
22 358.607 27/22 16/13~21/17

* in 13-limit POTE tuning

Spectrum of Rodan Tunings by Eigenmonzos

Eigenmonzo Fifth Comment
8/7 693.522
17/13 696.642
7/6 699.847
9/7 700.750
4/3 701.955
(24\41) 702.439
15/14 702.778
7/5 702.915 7 and 9 limit minimax
11/9 703.041 11 limit minimax
(75\128) 703.125
18/13 703.220 13 and 15 limit minimax
16/15 703.240
12/11 703.244
15/11 703.359
13/12 703.371
15/13 703.410
(51\87) 703.448
5/4 703.467 5 limit minimax
11/10 703.500
13/10 703.522
11/8 703.542
16/13 703.564
13/11 703.597
18/17 703.726 17 limit minimax
17/15 703.748
(78\133) 703.759
6/5 703.791
20/17 703.894
24/17 703.956
17/16 704.257
10/9 704.292
(27\46) 704.348
14/11 704.377
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