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User:Moremajorthanmajor/5L 3s (minor ninth-equivalent): Difference between revisions

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The author suggests the name '''Neapolitan'''-'''oneirotonic'''.
The author suggests the name '''Neapolitan'''-'''oneirotonic'''.
==Intervals==
==Intervals==
The table of Neapolitan-oneirotonic intervals below takes the fourth as the generator. Given the size of the fourth generator ''g'', any oneirotonic interval can easily be found by noting what multiple of ''g'' it is, and multiplying the size by the number ''k'' of generators it takes to reach the interval and reducing mod 1300 (for relative cents) if necessary (so you can use "''k''*''g'' % 1300" for search engines, for plugged-in values of ''k'' and ''g''). For example, since the major third is reached by six fourth generators, 18edIX's major third is 6*505.56 mod 1300 = 3033.33 mod 1300 = 433.33r¢.
The table of Neapolitan-oneirotonic intervals below takes the fourth as the generator. Given the size of the fourth generator ''g'', any oneirotonic interval can easily be found by noting what multiple of ''g'' it is, and multiplying the size by the number ''k'' of generators it takes to reach the interval and reducing if necessary (so you can use "''k''*''g'' % ''x''" for search engines, for plugged-in values of ''k'' and ''g''). For example, since the major third is reached by six fourth generators, 18edIX's major third is 6*494.12 mod 1270.59 = 2964.71 mod 1270.59 = 423.53¢.
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
Line 184: Line 184:
|major 2nd
|major 2nd
|2\13, 200.00
|2\13, 200.00
|3\18, 211.765
|3\18, 211.76
|3\21, 189.47
|3\21, 189.47
|A
|A
Line 258: Line 258:
|major 7th
|major 7th
|10\13, 1000.00
|10\13, 1000.00
|14\18, 988.235
|14\18, 988.24
|16\21, 1017.53
|16\21, 1017.53
|E
|E
Line 338: Line 338:
|major 2nd
|major 2nd
|2\13, 200.00
|2\13, 200.00
|3\18, 211.765
|3\18, 211.76
|5\31, 206.87
|5\31, 206.87
|A
|A
Line 347: Line 347:
|3\13, 300.00
|3\13, 300.00
|4\18, 282.35
|4\18, 282.35
|7\31, 289.655
|7\31, 289.66
|Bf
|Bf
|13/11, 33/28
|13/11, 33/28
Line 409: Line 409:
| rowspan="2" |9\13, 900.00
| rowspan="2" |9\13, 900.00
|13\18, 917.65
|13\18, 917.65
|22\31, 910.345
|22\31, 910.34
|D
|D
|56/33, 22/17
|56/33, 22/17
Line 423: Line 423:
|major 7th
|major 7th
|10\13, 1000.00
|10\13, 1000.00
|14\18, 988.235
|14\18, 988.24
|24\31, 993.13  
|24\31, 993.13  
|E
|E
Line 798: Line 798:
|}
|}
===Parahard===
===Parahard===
23edIX Neapolitan-oneiro combines the sound of the 32/15 minor ninth and the [[8/7]] whole tone. This is because 23edIX Neapolitan-oneirotonic a large step of 218.2¢, 22edIX's superpythagorean major second, which is both a warped Pythagorean [[9/8]] whole tone and a warped [[8/7]] septimal whole tone.
23edIX Neapolitan-oneiro combines the sound of the 32/15 minor ninth and the [[8/7]] whole tone. This is because 23edIX Neapolitan-oneirotonic has a large step of 218.2¢, 22edIX's superpythagorean major second, which is both a warped Pythagorean [[9/8]] whole tone and a warped [[8/7]] septimal whole tone.
====Intervals====
====Intervals====
The intervals of the extended generator chain (-12 to +12 generators) are as follows in various Neapolitan-oneirotonic tunings close to 23edIX.
The intervals of the extended generator chain (-12 to +12 generators) are as follows in various Neapolitan-oneirotonic tunings close to 23edIX.
Line 1,134: Line 1,134:
!Comments
!Comments
|-
|-
| colspan="3" |3\(8\7)||514.286||1||1||1.000||
| colspan="3" |3\8||514.286||1||1||1.000||
|-
|-
| colspan="3" |17\(45\40)||510||6||5||1.200||
| colspan="3" |17\45||510.000||6||5||1.200||
|-
|-
| colspan="3" |14\(37\33)||509.091||5||4||1.250||
| colspan="3" |14\37||509.091||5||4||1.250||
|-
|-
| colspan="3" |25\(66\59)||508.475||9||7||1.286||
| colspan="3" |25\66||508.475||9||7||1.286||
|-
|-
| colspan="3" |11\(29\26)||507.692||4||3||1.333||
| colspan="3" |11\29||507.692||4||3||1.333||
|-
|-
| colspan="3" |30\(79\71)||507.042||11||8||1.375||
| colspan="3" |19\50||506.667||7||5||1.400||
|-
|-
| colspan="3" |19\(50\45)||506.667||7||5||1.400||
| colspan="3" |8\21||505.263||3||2||1.500||L/s = 3/2
|-
|-
| colspan="3" |27\(71\64)||506.25||10||7||1.429||
| colspan="3" |29\76||504.348||11||7||1.571||
|-
|-
| colspan="3" |8\(21\19)||505.263||3||2||1.500||L/s = 3/2
| colspan="3" |21\55||504.000||8||5||1.600||
|-
|-
| colspan="3" |29\(76\69)||504.348||11||7||1.571||
| colspan="3" |34\89||503.704||13||8||1.625||Golden Neapolitan-oneirotonic
|-
|-
| colspan="3" |21\(55\50)||504.000||8||5||1.600||
| colspan="3" |13\34||503.226||5||3||1.667||
|-
|-
| colspan="3" |34\(89\81)||503.704||13||8||1.625||Golden Neapolitan-oneirotonic
| colspan="3" |31\81||502.703||12||7||1.714||
|-
|-
| colspan="3" |13\(34\31)||503.226||5||3||1.667||
| colspan="3" |18\47||502.326||7||4||1.750||
|-
|-
| colspan="3" |31\(81\74)||502.703||12||7||1.714||
| colspan="3" |23\60||501.818||9||5||1.800||
|-
|-
| colspan="3" |18\(47\43)||502.326||7||4||1.750||
| colspan="3" |28\73
|-
| colspan="3" |23\(60\55)||501.818||9||5||1.800||
|-
| colspan="3" |28\(73/67)
|501.493
|501.493
|11
|11
Line 1,173: Line 1,169:
|
|
|-
|-
| colspan="3" |33\(86\79)
| colspan="3" |33\86
|501.265
|501.265
|13
|13
Line 1,180: Line 1,176:
|
|
|-
|-
| colspan="3" |38\(99\91)
| colspan="3" |38\99
|501.099
|501.099
|15
|15
Line 1,187: Line 1,183:
|
|
|-
|-
| colspan="3" |43\(112\103)
| colspan="3" |43\112
|500.971
|500.971
|17
|17
Line 1,194: Line 1,190:
|
|
|-
|-
| colspan="3" |5\(13\12)||500||2||1||2.000||Basic Neapolitan-oneirotonic
| colspan="3" |5\13||500||2||1||2.000||Basic Neapolitan-oneirotonic
(generators smaller than this are proper)
(generators smaller than this are proper)
|-
|-
| colspan="3" |42\(109\101)
| colspan="3" |42\109
|499.010
|499.010
|17
|17
Line 1,204: Line 1,200:
|
|
|-
|-
| colspan="3" |37\(96\89)
| colspan="3" |37\96
|498.876
|498.876
|15
|15
Line 1,211: Line 1,207:
|
|
|-
|-
| colspan="3" |32\(83\77)
| colspan="3" |32\83
|498.701
|498.701
|13
|13
Line 1,218: Line 1,214:
|
|
|-
|-
| colspan="3" |27\(70\65)
| colspan="3" |27\70
|498.462
|498.462
|11
|11
Line 1,225: Line 1,221:
|
|
|-
|-
| colspan="3" |22\(57\53)||498.113||9||4||2.250||
| colspan="3" |22\57||498.113||9||4||2.250||
|-
|-
| colspan="3" |17\(44\41)||497.561||7||3||2.333||
| colspan="3" |17\44||497.561||7||3||2.333||
|-
|-
| colspan="3" |29\(75\70)||497.143||12||5||2.400||
| colspan="3" |29\75||497.143||12||5||2.400||
|-
|-
| colspan="3" |12\(31\29)||496.552||5||2||2.500||
| colspan="3" |12\31||496.552||5||2||2.500||
|-
|-
| colspan="3" |31\(80\75)||496.000||13||5||2.600||
| colspan="3" |31\80||496.000||13||5||2.600||
|-
|-
| colspan="3" |19\(49\46)||495.652||8||3||2.667||
| colspan="3" |19\49||495.652||8||3||2.667||
|-
|-
| colspan="3" |26\(67\63)||495.238||11||4||2.750||
| colspan="3" |26\67||495.238||11||4||2.750||
|-
|-
| colspan="3" |7\(18\17)||494.118||3||1||3.000||L/s = 3/1
| colspan="3" |7\18||494.118||3||1||3.000||L/s = 3/1
|-
|-
| colspan="3" |30\(77\73)
| colspan="3" |30\77
|493.151
|493.151
|13
|13
Line 1,248: Line 1,244:
|
|
|-
|-
| colspan="3" |23\[59\56]||492.857||10||3||3.333||
| colspan="3" |23\59||492.857||10||3||3.333||
|-
|-
| colspan="3" |16\(41\39)||492.308||7||2||3.500||
| colspan="3" |16\41||492.308||7||2||3.500||
|-
|-
| colspan="3" |25\(64\61)||491.803||11||3||3.667||
| colspan="3" |25\64||491.803||11||3||3.667||
|-
|-
| colspan="3" |9\(23\22)||490.909||4||1||4.000||
| colspan="3" |9\23||490.909||4||1||4.000||
|-
|-
| colspan="3" |20\(51\49)||489.796||9||2||4.500||
| colspan="3" |20\51||489.796||9||2||4.500||
|-
|-
| colspan="3" |11\(28\27)||488.889||5||1||5.000||
| colspan="3" |11\28||488.889||5||1||5.000||
|-
|-
| colspan="3" |24\(61\59)
| colspan="3" |24\61
|488.136
|488.136
|11
|11
Line 1,267: Line 1,263:
|
|
|-
|-
| colspan="3" |13\(33\32)||487.500||6||1||6.000||
| colspan="3" |13\33||487.500||6||1||6.000||
|-
|-
| colspan="3" |2\5||480.000||1||0||→ inf||
| colspan="3" |2\5||480.000||1||0||→ inf||
Line 1,273: Line 1,269:


== See also ==
== See also ==
[[5L 3s (45/22-equivalent)]] - undecimal small diesis tuning
[[5L 3s (33/16-equivalent)]] - harmonic subminor ninth tuning  
[[5L 3s (33/16-equivalent)]] - harmonic subminor ninth tuning  


[[5L 3s (44/21-equivalent)]] - Neogothic minor ninth tuning  
[[5L 3s (56/27-equivalent)]] - Archytas diatonic minor ninth tuning
 
[[5L 3s (25/12-equivalent)]] - classical chromatic minor ninth tuning
 
[[5L 3s (44/21-equivalent)]], [[5L 3s (208/99-equivalent)]] - Neogothic undecimal diatonic minor ninth tuning  


[[5L 3s (21/10-equivalent)]] - septimal chromatic minor ninth tuning
[[5L 3s (21/10-equivalent)]] - septimal chromatic minor ninth tuning
[[5L 3s (32/15-equivalent)]] - classical diatonic minor ninth tuning
[[5L 3s (891/416-equivalent)]], [[5L 3s (189/88-equivalent)]] - Neogothic chromatic minor ninth tuning


[[5L 3s (15/7-equivalent)]] - septimal diatonic minor ninth tuning
[[5L 3s (15/7-equivalent)]] - septimal diatonic minor ninth tuning
[[5L 3s (243/112-equivalent)]] - Archytas chromatic minor ninth tuning


[[5L 3s (11/5-equivalent)]] - undecimal neutral ninth tuning
[[5L 3s (11/5-equivalent)]] - undecimal neutral ninth tuning
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