Rodan: Difference between revisions

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Line 13: Line 13:
! colspan="2" | Approximate Ratios
! colspan="2" | Approximate Ratios
|-
|-
! 11-limit
! 13-limit
! 13- and 17-limit
! 17-limit extension
|-
|-
| 0
| 0
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| 9
| 9
| 910.339
| 910.339
| 27/16
| 22/13, 27/16, 33/28
| 22/13
|  
|-
|-
| 10
| 10
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| 12
| 12
| 413.786
| 413.786
| 14/11, 81/64, 80/63
| 14/11, 33/26, 80/63
| 33/26
|  
|-
|-
| 13
| 13
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| 19
| 19
| 855.161
| 855.161
| 18/11
| 18/11, 64/39
| 64/39, 28/17
| 28/17
|-
|-
| 20
| 20
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| 21
| 21
| 124.125
| 124.125
| 15/14
| 14/13, 15/14
| 14/13
|  
|-
|-
| 22
| 22
| 358.607
| 358.607
| 27/22
| '''16/13''', 27/22
| '''16/13''', 21/17
| 21/17
|-
| 23
| 593.088
| 45/32
| 24/17
|-
| 24
| 827.570
| 21/13
|
|-
| 25
| 1062.052
| 24/13
|
|}
|}
<nowiki>*</nowiki> in 13-limit POTE tuning
<nowiki>*</nowiki> in 13-limit POTE tuning
Line 144: Line 159:
* [[Rodan41opt]]
* [[Rodan41opt]]


== Spectrum of Rodan Tunings by Eigenmonzos ==
== Spectrum of rodan tunings by eigenmonzos ==


{| class="wikitable center-all left-3"
{| class="wikitable center-all left-3"
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|  
|  
|-
|-
| (24\41)
| ([[41edo|24\41]])
| 702.439
| 702.439
|  
|  
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| 11-odd-limit minimax
| 11-odd-limit minimax
|-
|-
| (75\128)
| ([[128edo|75\128]])
| 703.125
| 703.125
|
|
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|  
|  
|-
|-
| (51\87)
| ([[87edo|51\87]])
| 703.448
| 703.448
|  
|  
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|  
|  
|-
|-
| (78\133)
| ([[133edo|78\133]])
| 703.759
| 703.759
|  
|  
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|  
|  
|-
|-
| (27\46)
| ([[46edo|27\46]])
| 704.348
| 704.348
|  
|  

Revision as of 09:23, 7 March 2021

See Gamelismic clan #Rodan for more information.

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

Primes harmonics are in bold.

# Cents* Approximate Ratios
13-limit 17-limit extension
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 22/13, 27/16, 33/28
10 1144.821 27/14, 35/18, 64/33 33/17
11 179.304 10/9
12 413.786 14/11, 33/26, 80/63
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 14/13, 15/14
22 358.607 16/13, 27/22 21/17
23 593.088 45/32 24/17
24 827.570 21/13
25 1062.052 24/13

* in 13-limit POTE tuning

Chords

Main article: Chords of rodan

Scales

Spectrum of rodan tunings by eigenmonzos

Eigenmonzo Fifth Comments
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-odd-limit minimax
11/9 703.041 11-odd-limit minimax
(75\128) 703.125
18/13 703.220 13- and 15-odd-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-odd-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-odd-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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