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m →Tuning ranges: Made interval tables more user-friendly by including both major and minor intervals in one table
Line 74: Line 74:


==== Intervals ====
==== Intervals ====
Sortable table of intervals in the Dylathian mode in hypohard oneiro tunings:
Sortable table of major and minor intervals in hypohard oneiro tunings:


{| class="wikitable right-2 right-3 right-4 sortable"
{| class="wikitable right-2 right-3 right-4 sortable "
|-
|-
! Degree
! class="unsortable"|Degree
! Size in 13edo
! Size in 13edo
! Size in 18edo
! Size in 18edo
! Size in 31edo
! Size in 31edo
! Note name on Q
! Note name on J
! class="unsortable"| Approximate ratios<ref>The ratio interpretations that are not valid for 18edo are italicized.</ref>
! class="unsortable"| Approximate ratios<ref>The ratio interpretations that are not valid for 18edo are italicized.</ref>
! #Gens up
! #Gens up
|-
|-
| 1
| unison
| 0\13, 0.00
| 0\13, 0.00
| 0\18, 0.00
| 0\18, 0.00
| 0\31, 0.00
| 0\31, 0.00
| Q
| J
| 1/1
| 1/1
| 0
| 0
|-
|-
| 2
| min. o2nd
| 1\13, 92.31
| 1\18, 66.67
| 2\31, 77.42
| K@
| 21/20, ''22/21''
| -5
|-
| maj. o2nd
| 2\13, 184.62
| 2\13, 184.62
| 3\18, 200.00
| 3\18, 200.00
| 5\31, 193.55
| 5\31, 193.55
| J
| K
| 9/8, 10/9
| 9/8, 10/9
| +3
| +3
|-
|-
| 3
| min. o3rd
| 3\13, 276.92
| 4\18, 266.67
| 7\31, 270.97
| L
| 7/6
| -2
|-
| maj. o3rd
| 4\13, 369.23
| 4\13, 369.23
| 6\18, 400.00
| 6\18, 400.00
| 10\31, 387.10
| 10\31, 387.10
| K
| L&
| 5/4
| 5/4
| +6
| +6
|-
|-
| 4
| dim. o4th
| 4\13, 369.23
| 5\18, 333.33
| 9\31, 348.39
| M@
| ''16/13, 11/9''
| -7
|-
| perf. o4th
| 5\13, 461.54  
| 5\13, 461.54  
| 7\18, 466.67
| 7\18, 466.67
| 12\31, 464.52
| 12\31, 464.52
| L
| M
| 21/16, ''13/10''
| 21/16, ''13/10'', 17/13
| +1
| +1
|-
|-
| 5
| min. o5th
| 6\13, 553.85
| 8\18, 533.33
| 14\31, 541.94
| N@
| ''11/8''
| -4
|-
| maj. o5th
| 7\13, 646.15
| 7\13, 646.15
| 10\18, 666.66
| 10\18, 666.66
| 17\31, 658.06
| 17\31, 658.06
| M
| N
| ''13/9'', ''16/11''
| ''13/9'', ''16/11''
| +4
| +4
|-
|-
| 6
| perf. o6th
| 8\13, 738.46
| 11\18, 733.33
| 19\31, 735.48
| O
| 26/17
| -1
|-
| aug. o6th
| 9\13, 830.77
| 9\13, 830.77
| 13\18, 866.66
| 13\18, 866.66
| 22\31, 851.61
| 22\31, 851.61
| N
| O&
| ''13/8'', ''18/11''
| ''13/8'', ''18/11''
| +7
| +7
|-
|-
| 7
| min. o7th
| 9\13, 830.77
| 12\18, 800.00
| 21\31, 812.90
| P@
| 8/5
| -6
|-
| maj. o7th
| 10\13, 923.08
| 10\13, 923.08
| 14\18, 933.33
| 14\18, 933.33
| 24\31, 929.03
| 24\31, 929.03
| O
| P
| 12/7
| 12/7
| +2
| +2
|-
|-
| 8
| min. o8th
| 11\13, 1015.39
| 15\18, 1000.00
| 26\31, 1006.45
| Q
| 9/5, 16/9
| -3
|-
| maj. o8th
| 12\13, 1107.69
| 12\13, 1107.69
| 17\18, 1133.33
| 17\18, 1133.33
| 29\31, 1122.58  
| 29\31, 1122.58  
| P
| Q&
|  
|  
| +5
| +5
|}
|}
<references/>
<references/>
=== Hyposoft ===
=== Hyposoft ===
[[Hyposoft]] oneirotonic tunings (with generator between 8\21 and 5\13) have step ratios between 3/2 and 2/1. The 8\21-to-5\13 range of oneirotonic tunings remains relatively unexplored. In these tunings,  
[[Hyposoft]] oneirotonic tunings (with generator between 8\21 and 5\13) have step ratios between 3/2 and 2/1. The 8\21-to-5\13 range of oneirotonic tunings remains relatively unexplored. In these tunings,  
Line 160: Line 215:
* [[34edo]]'s 9:10:11:13 is even better.
* [[34edo]]'s 9:10:11:13 is even better.


The sizes of the generator, large step and small step of oneirotonic are as follows in various hyposoft oneiro tunings.
The sizes of the generator, large step and small step of oneirotonic are as follows in various hyposoft oneiro tunings (13edo not shown).
{| class="wikitable right-2 right-3 right-4 right-5"
{| class="wikitable right-2 right-3 right-4 right-5"
|-
|-
!  
!  
! [[13edo]]
! [[21edo]]
! [[21edo]]
! [[34edo]]
! [[34edo]]
|-
|-
| generator (g)
| generator (g)
| 5\13, 461.54
| 8\21, 457.14
| 8\21, 457.14
| 13\34, 458.82
| 13\34, 458.82
|-
|-
| L (3g - octave)
| L (3g - octave)
| 2\13, 184.62
| 3\21, 171.43
| 3\21, 171.43
| 5\34, 176.47
| 5\34, 176.47
|-
|-
| s (-5g + 2 octaves)
| s (-5g + 2 octaves)
| 1\13, 92.31
| 2\21, 114.29
| 2\21, 114.29
| 3\34, 105.88
| 3\34, 105.88
Line 185: Line 236:


==== Intervals ====
==== Intervals ====
Sortable table of intervals in the Dylathian mode in hyposoft tunings:
Sortable table of intervals in the Dylathian mode in hyposoft tunings (13edo not shown):
{| class="wikitable right-2 right-3 right-4 right-5 sortable"
 
{| class="wikitable right-2 right-3 sortable "
|-
|-
! Degree
! class="unsortable"|Degree
! Size in 13edo
! Size in 21edo
! Size in 21edo
! Size in 34edo
! Size in 34edo
! Note name on Q
! Note name on J
! class="unsortable"| Approximate ratios
! class="unsortable"| Approximate ratios
! #Gens up
! #Gens up
|-
|-
| 1
| unison
| 0\13, 0.00
| 0\21, 0.00
| 0\21, 0.00
| 0\34, 0.00
| 0\34, 0.00
| Q
| J
| 1/1
| 1/1
| 0
| 0
|-
|-
| 2
| min. o2nd
| 2\13, 184.62
| 2\21, 114.29
| 3\34, 105.88
| K@
| 17/16, 16/15
| -5
|-
| maj. o2nd
| 3\21, 171.43
| 3\21, 171.43
| 5\34, 176.47
| 5\34, 176.47
| J
| K
| 10/9, 11/10
| 10/9, 11/10
| +3
| +3
|-
|-
| 3
| min. o3rd
| 4\13, 369.23
| 5\21, 285.71
| 8\34, 282.35
| L
| 13/11, 20/17
| -2
|-
| maj. o3rd
| 6\21, 342.86
| 6\21, 342.86
| 10\34, 352.94
| 10\34, 352.94
| K
| L&
| 11/9, 16/13
| 11/9
| +6
| +6
|-
|-
| 4
| dim. o4th
| 5\13, 461.54
| 7\21, 400.00
| 8\21, 457.14
| 11\34, 388.24
| 13\34, 458.82
| M@
| L
| 5/4
| 13/10, 17/13, 22/17
| -7
|-
| perf. o4th
| 7\18, 457.14
| 12\31, 458.82
| M
| 13/10
| +1
| +1
|-
|-
| 5
| min. o5th
| 7\13, 646.15
| 10\21, 571.43
| 16\34, 564.72
| N@
| 18/13, 32/23
| -4
|-
| maj. o5th
| 11\21, 628.57
| 11\21, 628.57
| 18\34, 635.294
| 18\34, 635.29
| M
| N
| 13/9, 16/11, 23/16 (esp. 21edo)
| 13/9, 23/16
| +4
| +4
|-
|-
| 6
| perf. o6th
| 9\13, 830.77
| 13\21, 742.86
| 21\34, 741.18
| O
| 20/13
| -1
|-
| aug. o6th
| 14\21, 800.00
| 14\21, 800.00
| 23\34, 811.77
| 23\34, 811.77
| N
| O&
| 8/5
| 8/5
| +7
| +7
|-
|-
| 7
| min. o7th
| 10\13, 923.08
| 15\21, 857.14
| 24\34, 847.06
| P@
| 18/11
| -6
|-
| maj. o7th
| 16\21, 914.29
| 16\21, 914.29
| 26\34, 917.65
| 26\34, 917.65
| O
| P
| 17/10
| 22/13, 17/10
| +2
| +2
|-
|-
| 8
| maj. o8th
| 12\13, 1107.69
| 18\21, 1028.57
| 29\34, 1023.53
| Q
| 9/5
| -3
|-
| maj. o8th
| 19\21, 1085.71
| 19\21, 1085.71
| 31\34, 1094.12
| 31\34, 1094.12
| P
| Q&
| 17/9, 32/17, 15/8
| ''15/8''
| +5
| +5
|}
|}
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