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5L 3s: Difference between revisions

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m (1) Standardizing temperament entry format (2) changing A-Team's POTE generator to subgroup TE. Please add the badnesses!
Line 10: Line 10:
# When the generator is between 461.54¢ (5\13) and 466.67¢ (7\18): [[A-Team]] (13&18, a 4:5:9:21 or 2.9.5.21 temperament)
# When the generator is between 461.54¢ (5\13) and 466.67¢ (7\18): [[A-Team]] (13&18, a 4:5:9:21 or 2.9.5.21 temperament)
# When the generator is between 457.14¢ (8\21) and 461.54¢ (5\13): [[Chromatic_pairs#Petrtri|Petrtri]] (13&21, a 4:5:9:11:13:17 or 2.5.9.11.13.17 temperament)
# When the generator is between 457.14¢ (8\21) and 461.54¢ (5\13): [[Chromatic_pairs#Petrtri|Petrtri]] (13&21, a 4:5:9:11:13:17 or 2.5.9.11.13.17 temperament)
[[13edo]] represents both temperaments.
In a sense, these two temperaments represent the middle of the oneirotonic spectrum; [[13edo]] represents both temperaments, with a L/s ratio of 2/1.


More extreme oneirotonic temperaments include:
More extreme oneirotonic temperaments include:
Line 430: Line 430:
EDOs that support A-Team include [[13edo]], [[18edo]], and [[31edo]].
EDOs that support A-Team include [[13edo]], [[18edo]], and [[31edo]].
* 18edo can be used for a large L/s ratio of 3, (thus 18edo oneirotonic is distorted 17edo diatonic), or for nearly pure 9/8 and 7/6.
* 18edo can be used for a large L/s ratio of 3, (thus 18edo oneirotonic is distorted 17edo diatonic), or for nearly pure 9/8 and 7/6.
* 31edo can be used to make the major mos3rd a near-just 5/4.
* 31edo is very close to the POTE tuning, and can be used to make the major mos3rd a near-just 5/4.


The sizes of the generator, large step and small step of oneirotonic are as follows in various A-Team tunings.  
The sizes of the generator, large step and small step of oneirotonic are as follows in various A-Team tunings.  
Line 446: Line 446:
| 7\18, 466.67
| 7\18, 466.67
| 12\31, 464.52
| 12\31, 464.52
| 464.14
| 464.39
| 21/16
| 21/16
|-
|-
Line 453: Line 453:
| 3\18, 200.00
| 3\18, 200.00
| 5\31, 193.55
| 5\31, 193.55
| 192.42
| 193.16
| 9/8, 10/9
| 9/8, 10/9
|-
|-
Line 460: Line 460:
| 1\18, 66.66
| 1\18, 66.66
| 2\31, 77.42
| 2\31, 77.42
| 79.30
| 78.07
| 21/20
| 21/20
|}
|}
Line 939: Line 939:
Todo: Add temperament data
Todo: Add temperament data
=== Tridec (21&29, 2.7/5.11/5.13/5) ===
=== Tridec (21&29, 2.7/5.11/5.13/5) ===
=== A-Team (13&18, 2.5.9.21) ===
Period: 1\1
Sortable table of intervals in the Dylathian mode and their A-Team interpretations:
 
Optimal ([[POTE]] generator: 454.5555
 
EDO generators: [[21edo|8\21]], [[29edo|11\29]], [[37edo|14\37]]
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
[[Comma]] list: 847/845, 1001/1000
 
[[Mapping]] (for 2, 7/5, 11/5, 13/5): [{{val|1 2 0 1}}, {{val|0 -4 3 1}}]
 
Mapping generators: ~2, ~13/10
 
{{Vals|legend=1| 21, 29, 37 }}
 
</div></div>
=== Petrtri (13&21, 2.5.9.11.13.17) ===
Period: 1\1
 
Optimal ([[POTE]]) generator: 459.1502
 
EDO generators: [[13edo|5\13]], [[21edo|8\21]], [[34edo|13\34]]
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
[[Comma]] list: 100/99, 144/143, 170/169, 221/220
 
[[Mapping]] (for 2, 5, 9, 11, 13, 17): [{{val|1 5 7 5 6 6}}, {{val|0 -7 -10 -4 -6 -5}}]
 
Mapping generators: ~2, ~13/10
 
{{Vals|legend=1| 13, 21, 34 }}
 
</div></div>


{| class="wikitable right-2 right-3 right-4 sortable"
{| class="wikitable right-2 right-3 right-4 right-5 sortable"
|-
|-
! Degree
! Degree
! Size in 13edo
! Size in 13edo
! Size in 18edo
! Size in 21edo
! Size in 31edo
! Size in 34edo
! Size in POTE tuning
! Note name on L
! Note name on L
! class="unsortable"| Approximate ratios<ref>The harmonics over 1/1 are in bold. The ratio interpretations that are not valid for 18edo are italicized.</ref>
! class="unsortable"| Approximate ratios
! #Gens up
! #Gens up
|-
|-
| 1
| 1
| 0\13, 0.00
| 0\13, 0.00
| 0\18, 0.00
| 0\21, 0.00
| 0\31, 0.00
| 0\34, 0.00
| 0.00
| L
| L
| '''1/1'''
| 1/1
| 0
| 0
|-
|-
| 2
| 2
| 2\13, 184.62
| 2\13, 184.62
| 3\18, 200.00
| 3\21, 171.43
| 5\31, 193.55
| 5\34, 176.47
| 177.45
| M
| M
| '''9/8''', 10/9
| 10/9, 11/10
| +3
| +3
|-
|-
| 3
| 3
| 4\13, 369.23
| 4\13, 369.23
| 6\18, 400.00
| 6\21, 342.86
| 10\31, 387.10
| 10\34, 352.94
| 354.90
| N
| N
| '''5/4'''
| 11/9, 16/13
| +6
| +6
|-
|-
| 4
| 4
| 5\13, 461.54  
| 5\13, 461.54  
| 7\18, 466.67
| 8\21, 457.14
| 12\31, 464.52
| 13\34, 458.82
| 459.15
| O
| O
| '''21/16''', ''13/10''
| 13/10, 17/13, 22/17
| +1
| +1
|-
|-
| 5
| 5
| 7\13, 646.15
| 7\13, 646.15
| 10\18, 666.66
| 11\21, 628.57
| 17\31, 658.06
| 18\34, 635.294
| 636.60
| P
| P
| ''13/9'', ''16/11''
| 13/9, 16/11
| +4
| +4
|-
|-
| 6
| 6
| 9\13, 830.77
| 9\13, 830.77
| 13\18, 866.66
| 14\21, 800.00
| 22\31, 851.61
| 23\34, 811.77
| 814.05
| Q
| Q
| '''''13/8''''', ''18/11''
| 8/5
| +7
| +7
|-
|-
| 7
| 7
| 10\13, 923.08
| 10\13, 923.08
| 14\18, 933.33
| 16\21, 914.29
| 24\31, 929.03
| 26\34, 917.65
| 918.30
| J
| J
| 12/7
| 17/10
| +2
| +2
|-
|-
| 8
| 8
| 12\13, 1107.69
| 12\13, 1107.69
| 17\18, 1133.33
| 19\21, 1085.71
| 29\31, 1122.58
| 31\34, 1094.12
| 1095.75
| K
| K
|  
| 17/9, 32/17
| +5
| +5
|}
|}
<references/>
=== A-Team (13&18, 2.5.9.21) ===
Period: 1\1
 
Optimal ([[POTE]]) generator: 464.3865
 
EDO generators: [[13edo|5\13]], [[18edo|7\18]], [[31edo|12\31]], [[44edo|17\44]]
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
[[Comma]] list: 81/80, 1029/1024
 
[[Mapping]] (for 2, 5, 9, 21): [{{val|1 0 2 4}}, {{val|0 6 3 1}}]
 
Mapping generators: ~2, ~21/16


=== Petrtri (13&21, 2.5.9.11.13.17) ===
{{Vals|legend=1| 13, 18, 31, 44 }}


</div></div>
==== Intervals ====
==== Intervals ====
Sortable table of intervals in the Dylathian mode and their Petrtri interpretations:
Sortable table of intervals in the Dylathian mode and their A-Team interpretations:


{| class="wikitable right-2 right-3 right-4 right-5 sortable"
{| class="wikitable right-2 right-3 right-4 sortable"
|-
|-
! Degree
! Degree
! Size in 13edo
! Size in 13edo
! Size in 21edo
! Size in 18edo
! Size in 34edo
! Size in 31edo
! Size in POTE tuning
! Note name on L
! Note name on L
! class="unsortable"| Approximate ratios
! class="unsortable"| Approximate ratios<ref>The harmonics over 1/1 are in bold. The ratio interpretations that are not valid for 18edo are italicized.</ref>
! #Gens up
! #Gens up
|-
|-
| 1
| 1
| 0\13, 0.00
| 0\13, 0.00
| 0\21, 0.00
| 0\18, 0.00
| 0\34, 0.00
| 0\31, 0.00
| 0.00
| L
| L
| 1/1
| '''1/1'''
| 0
| 0
|-
|-
| 2
| 2
| 2\13, 184.62
| 2\13, 184.62
| 3\21, 171.43
| 3\18, 200.00
| 5\34, 176.47
| 5\31, 193.55
| 177.45
| M
| M
| 10/9, 11/10
| '''9/8''', 10/9
| +3
| +3
|-
|-
| 3
| 3
| 4\13, 369.23
| 4\13, 369.23
| 6\21, 342.86
| 6\18, 400.00
| 10\34, 352.94
| 10\31, 387.10
| 354.90
| N
| N
| 11/9, 16/13
| '''5/4'''
| +6
| +6
|-
|-
| 4
| 4
| 5\13, 461.54  
| 5\13, 461.54  
| 8\21, 457.14
| 7\18, 466.67
| 13\34, 458.82
| 12\31, 464.52
| 459.15
| O
| O
| 13/10, 17/13, 22/17
| '''21/16''', ''13/10''
| +1
| +1
|-
|-
| 5
| 5
| 7\13, 646.15
| 7\13, 646.15
| 11\21, 628.57
| 10\18, 666.66
| 18\34, 635.294
| 17\31, 658.06
| 636.60
| P
| P
| 13/9, 16/11
| ''13/9'', ''16/11''
| +4
| +4
|-
|-
| 6
| 6
| 9\13, 830.77
| 9\13, 830.77
| 14\21, 800.00
| 13\18, 866.66
| 23\34, 811.77
| 22\31, 851.61
| 814.05
| Q
| Q
| 8/5
| '''''13/8''''', ''18/11''
| +7
| +7
|-
|-
| 7
| 7
| 10\13, 923.08
| 10\13, 923.08
| 16\21, 914.29
| 14\18, 933.33
| 26\34, 917.65
| 24\31, 929.03
| 918.30
| J
| J
| 17/10
| 12/7
| +2
| +2
|-
|-
| 8
| 8
| 12\13, 1107.69
| 12\13, 1107.69
| 19\21, 1085.71
| 17\18, 1133.33
| 31\34, 1094.12
| 29\31, 1122.58
| 1095.75
| K
| K
| 17/9, 32/17
|  
| +5
| +5
|}
|}
<references/>


=== Buzzard (48&53, 2.3.5.7) ===
=== Buzzard (48&53, 2.3.5.7) ===
Period: 1\1
Optimal ([[POTE]]) generator: ~320/243 = 475.636
EDO generators: [[38edo|15\38]], [[43edo|17\43]], [[48edo|19\48]], [[53edo|21\53]], [[58edo|23\58]], [[63edo|25\63]]
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
Commas: 1728/1715, 5120/5103
Commas: 1728/1715, 5120/5103
[[POTE_tuning|POTE generator]]: ~320/243 = 475.636


Map: [&lt;1 0 -6 4|, &lt;0 4 21 -3|]
Map: [&lt;1 0 -6 4|, &lt;0 4 21 -3|]
Line 1,116: Line 1,178:
Wedgie: &lt;&lt;4 21 -3 24 -16 -66||
Wedgie: &lt;&lt;4 21 -3 24 -16 -66||


EDOs: 48, 53, 111, 164d, 275d
{{Vals| 48, 53, 111, 164d, 275d}}


Badness: 0.0480
Badness: 0.0480
</div></div>


==== Intervals ====
==== Intervals ====
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