Nicetone: Difference between revisions

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Update tables
Line 167: Line 167:
!Right handed
!Right handed
|-
|-
|LmLsmLs
|LmLsmLs <br>LH Nice-Lydian
LH NiceLydian
|LmLsLms <br>RH Nice-Lydian
|LmLsLms
RH NiceLydian
|-
|-
|mLsLmLs
|mLsLmLs <br>LH Nice-Ionian
LH NiceIonian
|LmsLmLs <br>RH Nice-Ionian
|LmsLmLs
RH NiceIonian
|-
|-
|mLsmLsL
|mLsmLsL <br>LH Nice-Mixolydian
LH NiceMixo
|mLsLmsL <br>RH Nice-Mixolydian
|mLsLmsL
RH NiceMixo
|-
|-
|LsLmLsm
|LsLmLsm <br>LH Nice-Dorian
LH NiceDorian
|msLmLsL <br>RH Nice-Dorian
|msLmLsL
RH NiceDorian
|-
|-
|LsmLsLm
|LsmLsLm <br>LH Nice-Aeolian
LH NiceAolian
|LsLmsLm <br>RH Nice-Aeolian
|LsLmsLm
RH NiceAolian
|-
|-
|sLmLsmL
|sLmLsmL <br>LH Nice-Phrygian
LH NicePhrygian
|sLmLsLm <br>RH Nice-Phrygian
|sLmLsLm
RH NicePhrygian
|-
|-
|smLsLmL
|smLsLmL <br>LH Nice-Locrian
LH NiceLocrian
|sLmsLmL <br>RH Nice-Locrian
|sLmsLmL
RH NiceLocrian
|}
|}


Line 207: Line 193:
|+Tuning range of nicetone
|+Tuning range of nicetone
!  
!  
! Tuning range
! Tuning range (in [[octave]]s)
|-
|-
! Outer generator <br>(''G''<sub>1</sub> = 2L + m + s)
! Outer generator <br>(''G''<sub>1</sub> = 2L + m + s)
Line 230: Line 216:
{| class="wikitable"
{| class="wikitable"
|+Common Nicetone tunings
|+Common Nicetone tunings
! rowspan="2" |Tuning
! rowspan="2" | Tuning
! rowspan="2" |L:m:s
! rowspan="2" | L:m:s
! rowspan="2" |Good Just Approximations
! colspan="3" | Size of step (¢)
! rowspan="2" |Other comments
! colspan="2" | Inner generator
! colspan="6" |Degrees
! rowspan="2" | Outer generator <br>(2L+m+s)
! rowspan="2" | Comments
|-
|-
! D(~9/8)
! L
! vE(~5/4)
! m
! F(~4/3)
! s
! G(~3/2)
! LH (L+s)
! vA(~5/3)
! RH (L+m)
! vB(~15/8)
|-
|-
| 5-limit JI
| 5-limit JI || ||203.910||182.404||111.731||315.641||386.314||701.955||L=9/8, m=10/9, s=16/15
| (~1.825):(~1.6325):1
| Just 9/8, 5/4 and 4/3
|
|203.91
|386.314
|498.045
|701.955
|884.359
|1088.269
|-
|-
|[[15edo]]
|[[15edo]]||3:2:1||240.000||160.000||80.000||320.000||400.000||720.000||
|3:2:1
|
|
|240
| rowspan="2" |400
|480
|720
|880
|1120
|-
|-
|[[18edo]]
|[[18edo]]||4:2:1||266.667||133.333||66.667||333.333||400.000||733.333||
|4:2:1
|
|Wolf fourth and fifth
|266.667
|466.667
|733.333
|866.667
|1133.333
|-
|-
|[[20edo]]
|[[20edo]]||4:3:1||240.000||180.000||60.000||300.000||420.000||720.000||
|4:3:1
|
|
|240
|420
|480
|720
|900
|1140
|-
|-
|[[21edo]]
|[[21edo]]||5:2:1||285.714||114.286||57.143||342.857||400.000||742.857||
|5:2:1
|
|Wolf fourth and fifth
|285.714
|400
|457.143
|742.857
|857.143
|1142.857
|-
|-
|[[22edo]]
|[[22edo]]||4:3:2||218.182||163.636||109.091||327.273||381.818||709.091||
|4:3:2
|
|Also has diatonic MOS
|218.182
|381.182
|490.909
|709.091
|872.727
|1090.909
|-
|-
|[[23edo]]
|[[23edo]]||5:3:1||260.870||156.522||52.174||313.043||417.391||730.435||
|5:3:1
|14/11
|Wolf fourth and fifth
|260.87
|417.391
|469.565
|730.435
|886.9565
|1147.826
|-
|-
|[[24edo]]
|[[24edo]]||6:2:1||300.000||100.000||50.000||350.000||400.000||750.000||
|6:2:1
|
|Also has neutral diatonic MOS
|300
|400
|450
|750
|850
|1050
|-
|-
|[[25edo]]
| rowspan="2" |[[25edo]]||5:3:2||240.000||144.000||96.000||336.000||384.000||720.000||
|5:3:2
5:4:1
|
|
|240
|384
432
|480
|720
|864
912
|1104
|-
|-
|[[26edo]]
|5:4:1||240.000||192.000||48.000||288.000||432.000||720.000||
|6:3:1
|
|Also has diatonic MOS
|276.923
|415.385
|461.5385
|738.4615
|876.923
|1153.846
|-
|-
|[[27edo]]
|[[26edo]]||6:3:1||276.923||138.462||46.154||323.077||415.385||738.462||
|5:4:2
7:2:1
|
|Also has diatonic MOS
|222.222
311.111
|400
|488.889
444.444
|711.111
755.556
|888.889
844.444
|1111.111
1155.556
|-
|-
|[[28edo]]
| rowspan="2" |[[27edo]]||5:4:2||222.222||177.778||88.889||311.111||400.000||711.111||
|6:3:2
6:4:1
|
|
|257.143
|385.714
428.571
|471.429
|728.571
|857.143
900
|1114.286
1157.143
|-
|-
|[[29edo]]
|7:2:1||311.111||88.889||44.444||355.556||400.000||755.556||
|5:4:3
7:3:1
|
|Gentle fifth
Also has diatonic MOS
|206.897
289.655
|372.414
413.793
|496.551
455.172
|703.449
745.828
|868.9655
|1075.862
1158.721
|-
|-
|[[30edo]]
| rowspan="2" |[[28edo]]||6:3:2||257.143||128.571||85.714||342.857||385.714||728.571||
|6:5:1
8:2:1
|
|
|240
320
|440
400
|480
440
|720
760
|920
840
|1160
|-
|-
|[[31edo]]
|6:4:1||257.143||171.429||42.857||300.000||428.571||728.571||
|7:3:2
7:4:1
|
|Also has diatonic MOS
|270.968
|386.314
425.8065
|464.516
|735.484
|851.613
890.323
|1122.581
1161.29
|-
|-
|[[32edo]]
| rowspan="2" |[[29edo]]||5:4:3||206.897||165.517||124.138||331.034||372.414||703.448||
|6:4:3
|-
6:5:2
|7:3:1||289.655||124.138||41.379||331.034||413.793||744.828||
 
|-
8:3:1
| rowspan="2" |[[30edo]]||6:5:1||240.000||200.000||40.000||280.000||440.000||720.000||
|
|-
|Also has diatonic MOS
|8:2:1||320.000||80.000||40.000||360.000||400.000||760.000||
|225
|-
300
| rowspan="2" |[[31edo]]||7:3:2||270.968||116.129||77.419||348.387||387.097||735.484||
|375
|-
412.5
|7:4:1||270.968||154.839||38.710||309.677||425.806||735.484||
|487.5
|-
450
| rowspan="3" |[[32edo]]||6:4:3||225.000||150.000||112.500||337.500||375.000||712.500||
|712.5
|-
750
|6:5:2||225.000||187.500||75.000||300.000||412.500||712.500||
|862.5
|-
900
|8:3:1||300.000||112.500||37.500||337.500||412.500||750.000||
|1087.5
|-
1125
| rowspan="3" |[[33edo]]||7:4:2||254.545||145.455||72.727||327.273||400.000||727.273||
 
|-
1162.5
|7:5:1||254.545||181.818||36.364||290.909||436.364||727.273||
|-
|9:2:1||327.273||72.727||36.364||363.636||400.000||763.636||
|-
| rowspan="3" |[[34edo]]||6:5:3||211.765||176.471||105.882||317.647||388.235||705.882||
|-
|8:3:2||282.353||105.882||70.588||352.941||388.235||741.176||
|-
|8:4:1||282.353||141.176||35.294||317.647||423.529||741.176||
|-
| rowspan="4" |[[35edo]]||7:4:3||240.000||137.143||102.857||342.857||377.143||720.000||
|-
|7:5:2||240.000||171.429||68.571||308.571||411.429||720.000||
|-
|7:6:1||240.000||205.714||34.286||274.286||445.714||720.000||
|-
|9:3:1||308.571||102.857||34.286||342.857||411.429||754.286||
|-
| rowspan="3" |[[36edo]]||6:5:4||200.000||166.667||133.333||333.333||366.667||700.000||
|-
|8:5:1||266.667||166.667||33.333||300.000||433.333||733.333||
|-
|10:2:1||333.333||66.667||33.333||366.667||400.000||766.667||
|-
| rowspan="4" |[[37edo]]||7:5:3||227.027||162.162||97.297||324.324||389.189||713.514||
|-
|7:6:2||227.027||194.595||64.865||291.892||421.622||713.514||
|-
|9:3:2||291.892||97.297||64.865||356.757||389.189||745.946||
|-
|9:4:1||291.892||129.730||32.432||324.324||421.622||745.946||
|-
| rowspan="4" |[[38edo]]||8:4:3||252.632||126.316||94.737||347.368||378.947||726.316||
|-
|8:5:2||252.632||157.895||63.158||315.789||410.526||726.316||
|-
|8:6:1||252.632||189.474||31.579||284.211||442.105||726.316||
|-
|10:3:1||315.789||94.737||31.579||347.368||410.526||757.895||
|-
| rowspan="5" |[[39edo]]||7:5:4||215.385||153.846||123.077||338.462||369.231||707.692||
|-
|7:6:3||215.385||184.615||92.308||307.692||400.000||707.692||
|-
|9:4:2||276.923||123.077||61.538||338.462||400.000||738.462||
|-
|9:5:1||276.923||153.846||30.769||307.692||430.769||738.462||
|-
|11:2:1||338.462||61.538||30.769||369.231||400.000||769.231||
|-
| rowspan="4" |[[40edo]]||8:5:3||240.000||150.000||90.000||330.000||390.000||720.000||
|-
|8:7:1||240.000||210.000||30.000||270.000||450.000||720.000||
|-
|10:3:2||300.000||90.000||60.000||360.000||390.000||750.000||
|-
|10:4:1||300.000||120.000||30.000||330.000||420.000||750.000||
|-
| rowspan="5" |[[41edo]]||7:6:4||204.878||175.610||117.073||321.951||380.488||702.439||
|-
|9:4:3||263.415||117.073||87.805||351.220||380.488||731.707||
|-
|9:5:2||263.415||146.341||58.537||321.951||409.756||731.707||
|-
|9:6:1||263.415||175.610||29.268||292.683||439.024||731.707||
|-
|11:3:1||321.951||87.805||29.268||351.220||409.756||760.976||
|-
| rowspan="5" |[[42edo]]||8:5:4||228.571||142.857||114.286||342.857||371.429||714.286||
|-
|8:6:3||228.571||171.429||85.714||314.286||400.000||714.286||
|-
|8:7:2||228.571||200.000||57.143||285.714||428.571||714.286||
|-
|10:5:1||285.714||142.857||28.571||314.286||428.571||742.857||
|-
|12:2:1||342.857||57.143||28.571||371.429||400.000||771.429||
|-
| rowspan="6" |[[43edo]]||7:6:5||195.349||167.442||139.535||334.884||362.791||697.674||
|-
|9:5:3||251.163||139.535||83.721||334.884||390.698||725.581||
|-
|9:6:2||251.163||167.442||55.814||306.977||418.605||725.581||
|-
|9:7:1||251.163||195.349||27.907||279.070||446.512||725.581||
|-
|11:3:2||306.977||83.721||55.814||362.791||390.698||753.488||
|-
|11:4:1||306.977||111.628||27.907||334.884||418.605||753.488||
|-
| rowspan="5" |[[44edo]]||8:7:3||218.182||190.909||81.818||300.000||409.091||709.091||
|-
|10:4:3||272.727||109.091||81.818||354.545||381.818||736.364||
|-
|10:5:2||272.727||136.364||54.545||327.273||409.091||736.364||
|-
|10:6:1||272.727||163.636||27.273||300.000||436.364||736.364||
|-
|12:3:1||327.273||81.818||27.273||354.545||409.091||763.636||
|-
| rowspan="6" |[[45edo]]||9:5:4||240.000||133.333||106.667||346.667||373.333||720.000||
|-
|9:7:2||240.000||186.667||53.333||293.333||426.667||720.000||
|-
|9:8:1||240.000||213.333||26.667||266.667||453.333||720.000||
|-
|11:4:2||293.333||106.667||53.333||346.667||400.000||746.667||
|-
|11:5:1||293.333||133.333||26.667||320.000||426.667||746.667||
|-
|13:2:1||346.667||53.333||26.667||373.333||400.000||773.333||
|-
| rowspan="6" |[[46edo]]||8:6:5||208.696||156.522||130.435||339.130||365.217||704.348||
|-
|8:7:4||208.696||182.609||104.348||313.043||391.304||704.348||
|-
|10:5:3||260.870||130.435||78.261||339.130||391.304||730.435||
|-
|10:7:1||260.870||182.609||26.087||286.957||443.478||730.435||
|-
|12:3:2||313.043||78.261||52.174||365.217||391.304||756.522||
|-
|12:4:1||313.043||104.348||26.087||339.130||417.391||756.522||
|-
| rowspan="7" |[[47edo]]||9:6:4||229.787||153.191||102.128||331.915||382.979||714.894||
|-
|9:7:3||229.787||178.723||76.596||306.383||408.511||714.894||
|-
|9:8:2||229.787||204.255||51.064||280.851||434.043||714.894||
|-
|11:4:3||280.851||102.128||76.596||357.447||382.979||740.426||
|-
|11:5:2||280.851||127.660||51.064||331.915||408.511||740.426||
|-
|11:6:1||280.851||153.191||25.532||306.383||434.043||740.426||
|-
|13:3:1||331.915||76.596||25.532||357.447||408.511||765.957||
|-
| rowspan="7" |[[48edo]]||8:7:5||200.000||175.000||125.000||325.000||375.000||700.000||
|-
|10:5:4||250.000||125.000||100.000||350.000||375.000||725.000||
|-
|10:6:3||250.000||150.000||75.000||325.000||400.000||725.000||
|-
|10:7:2||250.000||175.000||50.000||300.000||425.000||725.000||
|-
|10:8:1||250.000||200.000||25.000||275.000||450.000||725.000||
|-
|12:5:1||300.000||125.000||25.000||325.000||425.000||750.000||
|-
|14:2:1||350.000||50.000||25.000||375.000||400.000||775.000||
|-
|-
|[[33edo]]
| rowspan="8" |[[49edo]]||9:6:5||220.408||146.939||122.449||342.857||367.347||710.204||
|7:4:2
7:5:1
|13/11
|Also has diatonic MOS
|254.5455
|400
436.364
|472.727
|727.272
|872.727
909.091
|1127.273
1163.636
|-
|-
|[[34edo]]
|9:7:4||220.408||171.429||97.959||318.367||391.837||710.204||
|6:5:3
8:3:2
 
8:4:1
|25/24
50/49
|Gentle fifth
Also has neutral diatonic MOS
|211.765
282.353
|388.235
423.529
|494.118
458.8235
|705.882
741.1765
|882.353
847.059
|1094.118
1129.412
 
1164.706
|-
|-
|[[35edo]]
|9:8:3||220.408||195.918||73.469||293.878||416.327||710.204||
|7:4:3
7:5:2
 
7:6:1
|33/26
|
|240
|377.143
411.429
 
445.714
|480
|720
|857.143
891.429
 
925.714
|1097.143
1131.429
 
1165.714
|-
|-
|[[36edo]]
|11:5:3||269.388||122.449||73.469||342.857||391.837||734.694||
|6:5:4
|27/25
|Also has Porcupine MOS
|200
|366.667
|500
|700
|866.667
|1066.667
|-
|-
|[[37edo]]
|11:6:2||269.388||146.939||48.980||318.367||416.327||734.694||
|7:5:3
7:6:2
|
|Has 37edo just major triad
|227.027
|389.189
|486.4865
|713.5135
|875.676
|1102.703
|-
|-
|[[38edo]]
|11:7:1||269.388||171.429||24.490||293.878||440.816||734.694||
|8:4:3
8:5:2
 
8:6:1
|6/5, 33/26 and 14/13 or 28/27
|Has wolf major and minor triads
Also has neutral diatonic MOS
|252.632
|378.947
410.526
 
442.105
|473.684
|726.318
|852.632
884.2105
 
915.7895
|1105.263
1136.842
 
1168.421
|-
|-
|[[39edo]]
|13:3:2||318.367||73.469||48.980||367.347||391.837||759.184||
|7:5:4
7:6:3
|
|Also has diatonic MOS
|215.385
|369.231
400
|492.308
|707.692
|861.5385
892.308
|1076.923
1107.
|-
|-
|[[40edo]]
|13:4:1||318.367||97.959||24.490||342.857||416.327||759.184||
|8:5:3
8:7:1
|
|Golden Nicetone
Also has diatonic MOS
|240
|390
450
|480
|720
|870
930
|1110
1170
|-
|-
|[[41edo]]
| rowspan="7" |[[50edo]]||8:7:6||192.000||168.000||144.000||336.000||360.000||696.000||
|7:6:4
|
|Also has diatonic MOS
|204.878
|380.488
|497.561
|702.439
|878.049
|1082.927
|-
|-
|[[42edo]]
|10:7:3||240.000||168.000||72.000||312.000||408.000||720.000||
|8:5:4
8:6:3
 
8:7:2
|6/5
|Also has diatonic MOS
|228.571
|371.429
400
 
428.571
|485.714
|714.286
|857.143
885.714
 
914.286
|1085.714
1114.286
 
1142.857
|-
|-
|[[43edo]]
|10:9:1||240.000||216.000||24.000||264.000||456.000||720.000||
|7:6:5
|
|Also has diatonic MOS
|195.349
|362.791
|502.326
|697.674
|865.116
|1060.465
|-
|-
|[[44edo]]
|12:4:3||288.000||96.000||72.000||360.000||384.000||744.000||
|8:7:3
|
|Also has neutral diatonic MOS
|218.182
|409.091
|490.909
|709.091
|900
|1118.182
|-
|-
|[[46edo]]
|12:5:2||288.000||120.000||48.000||336.000||408.000||744.000||
|8:6:5
8:7:4
|10/9
|Gentle fifth
Also has diatonic MOS
|208.696
|365.217
391.304
|495.652
|704.348
|860.87
886.9565
|1069.565
1095.652
|-
|-
|[[48edo]]
|12:6:1||288.000||144.000||24.000||312.000||432.000||744.000||
|8:7:5
|
|
|200
|375
|500
|700
|875
|1075
|-
|-
|[[50edo]]
|14:3:1||336.000||72.000||24.000||360.000||408.000||768.000||
|8:7:6
|
|Also has diatonic MOS
|192
|360
|504
|696
|864
|1056
|}
|}


Revision as of 22:22, 1 June 2023

Nicetone (also known as the Zarlino pattern or Ptolemaic-Auric diatonic) is a 7-note Maximum variety 3 scale with the step pattern 3L 2m 2s. Nicetone is a chiral scale with left-handed (LmLsmLs) and right-handed (LmLsLms) variants that are rotationally non-equivalent. 15edo is the first equal division that supports nicetone.

Nicetone has the same pattern of the 5-limit Zarlino scale, though it encompasses the whole range of 3L 2m 2s. It's also a subset of the 5L 2m 3s blackdye scale.

Nicetone is intermediate between the 5L 2s diatonic scale and the 3L 4s neutral scale.

Nicetone can be tuned as a 5-limit JI scale or a tempered version thereof, where L represents 9/8, m represents 10/9, and s represents 16/15.

Comparison with mosh and diatonic in 41edo
Name Structure Step Sizes Graphical Representation
Mosh 3L 4s 7\41, 5\41 ├──────┼────┼────┼──────┼────┼──────┼────┤
Nicetone 3L 2m 2s 7\41, 6\41, 4\41 ├──────┼─────┼───┼──────┼─────┼──────┼───┤
Diatonic 5L 2s 7\41, 3\41 ├──────┼──────┼──┼──────┼──────┼──────┼──┤
Comparison with mosh and antipentic in 33edo
Name Structure Step Sizes Graphical Representation
Mosh 3L 4s 7\33, 3\33 ├──┼──────┼──┼──────┼──┼──┼──────┤
Nicetone 3L 2m 2s 7\33, 4\33, 2\33 ├───┼──────┼─┼──────┼───┼─┼──────┤
Antipentic 3L 2s 7\33, 6\33 ├─────┼──────╫──────┼─────╫──────┤

Intervals

The following is a table of nicetone intervals and their abstract sizes in terms of L, m and s. Given concrete sizes of L, m and s in EDO steps or cents, you can compute the concrete size of any interval in nicetone using the following expressions.

Interval sizes in nicetone
Interval class Sizes 5-limit JI 15edo
(L:m:s = 3:2:1) 		41edo
(L:m:s = 7:6:4)
Second
(1-step) 		small s 16/15, 111.73¢ 1\15, 80.00¢ 4\41, 117.07¢
medium m 10/9, 182.40¢ 2\15, 160.00¢ 6\41, 175.61¢
large L 9/8, 203.91¢ 3\15, 240.00¢ 7\41, 204.88¢
Third
(2-step) 		small m + s 32/27, 294.13¢ 3\15, 240.00¢ 10\41, 292.68¢
medium L + s 6/5, 315.64¢ 4\15, 320.00¢ 11\41, 321.95¢
large L + m 5/4, 386.31¢ 5\15, 400.00¢ 13\41, 380.49¢
Fourth
(3-step) 		small L + m + s 4/3, 498.04¢ 6\15, 480.00¢ 17\41, 497.56¢
medium 2L + s 27/20, 519.55¢ 7\15, 560.00¢ 18\41, 526.83¢
large 2L + m 45/32, 590.22¢ 8\15, 640.00¢ 20\41, 585.37¢
Fifth
(4-step) 		small L + m + 2s 64/45, 609.78¢ 7\15, 560.00¢ 21\41, 614.63¢
medium L + 2m + s 40/27, 680.45¢ 8\15, 640.00¢ 23\41, 673.17¢
large 2L + m + s 3/2, 701.96¢ 9\15, 720.00¢ 24\41, 702.44¢
Sixth
(5-step) 		small 2L + m + 2s 8/5, 813.69¢ 10\15, 800.00¢ 28\41, 819.51¢
medium 2L + 2m + s 5/3, 884.36¢ 11\15, 880.00¢ 30\41, 878.05¢
large 3L + m + s 27/16, 905.87¢ 12\15, 960.00¢ 31\41, 907.32¢
Seventh
(6-step) 		small 2L + 2m + 2s 16/9, 996.09¢ 12\15, 960.00¢ 34\41, 995.12¢
medium 3L + m + 2s 9/5, 1017.60¢ 13\15, 1040.00¢ 35\41, 1024.39¢
large 3L + 2m + s 15/8, 1088.27¢ 14\15, 1120.00¢ 37\41, 1082.93¢

Modes

Nicetone has 14 modes total, with 7 LH and 7 RH modes. The names are based on their diatonic (5L 2s) counterparts.

The modes are arranged by brightest to darkest.

Nicetone modes
Left handed Right handed
LmLsmLs
LH Nice-Lydian 		LmLsLms
RH Nice-Lydian
mLsLmLs
LH Nice-Ionian 		LmsLmLs
RH Nice-Ionian
mLsmLsL
LH Nice-Mixolydian 		mLsLmsL
RH Nice-Mixolydian
LsLmLsm
LH Nice-Dorian 		msLmLsL
RH Nice-Dorian
LsmLsLm
LH Nice-Aeolian 		LsLmsLm
RH Nice-Aeolian
sLmLsmL
LH Nice-Phrygian 		sLmLsLm
RH Nice-Phrygian
smLsLmL
LH Nice-Locrian 		sLmsLmL
RH Nice-Locrian

Tunings

Tuning range of nicetone
Tuning range (in octaves)
Outer generator
(G1 = 2L + m + s) 		[math]\displaystyle{ \displaystyle \frac{4}{7} &lt; G_\text{1} &lt; \frac{2}{3} }[/math]
RH inner generator
(G2R = L + m) 		[math]\displaystyle{ \displaystyle \frac{1}{2} G_\text{1} &lt; G_\text{2R} &lt; 4 G_\text{1} - 2 \text{ for } \frac{4}{7} &lt; G_\text{1} &le; \frac{3}{5} }[/math]
[math]\displaystyle{ \displaystyle \frac{1}{2} G_\text{1} &lt; G_\text{2R} &lt; 1 - G_\text{1} \text{ for }\frac{3}{5} &le; G_\text{1} &lt; \frac{2}{3} }[/math]
LH inner generator
(G2L = L + s) 		[math]\displaystyle{ \displaystyle 2 - 3 G_\text{1} &lt; G_\text{2L} &lt; \frac{1}{2} G_\text{1} \text{ for }\frac{4}{7} &lt; G_\text{1} &le; \frac{3}{5} }[/math]
[math]\displaystyle{ \displaystyle 2 G_\text{1} - 1 &lt; G_\text{2L} &lt; \frac{1}{2} G_\text{1} \text{ for }\frac{3}{5} &le; G_\text{1} &lt; \frac{2}{3} }[/math]
Large step
(L = 2G1 - 1) 		[math]\displaystyle{ \displaystyle \frac{1}{7} &lt; L &lt; \frac{1}{3} }[/math]
Middle step
(m = 1 - G1 - G2L) 		[math]\displaystyle{ \displaystyle \frac{1}{4} (1 - 3 L) &lt; M &lt; L \text{ for } \frac{1}{7} &lt; L &le; \frac{1}{5} }[/math]
[math]\displaystyle{ \displaystyle \frac{1}{4} (1 - 3 L) &lt; M &lt; \frac{1}{2} (1 - 3 L) \text{ for } \frac{1}{5} &le; L &lt; \frac{1}{3} }[/math]
Small step
(s = 1 - G1 - G2R) 		[math]\displaystyle{ \displaystyle \frac{1}{2} (1 - 5 L) &lt; S &lt; \frac{1}{4} (1 - 3 L) \text{ for } \frac{1}{7} &lt; L &le; \frac{1}{5} }[/math]
[math]\displaystyle{ \displaystyle 0 &lt; S &lt; \frac{1}{4} (1 - 3 L) \text{ for } \frac{1}{5} &le; L &lt; \frac{1}{3} }[/math]
Common Nicetone tunings
Tuning L:m:s Size of step (¢) Inner generator Outer generator
(2L+m+s) 		Comments
L m s LH (L+s) RH (L+m)
5-limit JI 203.910 182.404 111.731 315.641 386.314 701.955 L=9/8, m=10/9, s=16/15
15edo 3:2:1 240.000 160.000 80.000 320.000 400.000 720.000
18edo 4:2:1 266.667 133.333 66.667 333.333 400.000 733.333
20edo 4:3:1 240.000 180.000 60.000 300.000 420.000 720.000
21edo 5:2:1 285.714 114.286 57.143 342.857 400.000 742.857
22edo 4:3:2 218.182 163.636 109.091 327.273 381.818 709.091
23edo 5:3:1 260.870 156.522 52.174 313.043 417.391 730.435
24edo 6:2:1 300.000 100.000 50.000 350.000 400.000 750.000
25edo 5:3:2 240.000 144.000 96.000 336.000 384.000 720.000
5:4:1 240.000 192.000 48.000 288.000 432.000 720.000
26edo 6:3:1 276.923 138.462 46.154 323.077 415.385 738.462
27edo 5:4:2 222.222 177.778 88.889 311.111 400.000 711.111
7:2:1 311.111 88.889 44.444 355.556 400.000 755.556
28edo 6:3:2 257.143 128.571 85.714 342.857 385.714 728.571
6:4:1 257.143 171.429 42.857 300.000 428.571 728.571
29edo 5:4:3 206.897 165.517 124.138 331.034 372.414 703.448
7:3:1 289.655 124.138 41.379 331.034 413.793 744.828
30edo 6:5:1 240.000 200.000 40.000 280.000 440.000 720.000
8:2:1 320.000 80.000 40.000 360.000 400.000 760.000
31edo 7:3:2 270.968 116.129 77.419 348.387 387.097 735.484
7:4:1 270.968 154.839 38.710 309.677 425.806 735.484
32edo 6:4:3 225.000 150.000 112.500 337.500 375.000 712.500
6:5:2 225.000 187.500 75.000 300.000 412.500 712.500
8:3:1 300.000 112.500 37.500 337.500 412.500 750.000
33edo 7:4:2 254.545 145.455 72.727 327.273 400.000 727.273
7:5:1 254.545 181.818 36.364 290.909 436.364 727.273
9:2:1 327.273 72.727 36.364 363.636 400.000 763.636
34edo 6:5:3 211.765 176.471 105.882 317.647 388.235 705.882
8:3:2 282.353 105.882 70.588 352.941 388.235 741.176
8:4:1 282.353 141.176 35.294 317.647 423.529 741.176
35edo 7:4:3 240.000 137.143 102.857 342.857 377.143 720.000
7:5:2 240.000 171.429 68.571 308.571 411.429 720.000
7:6:1 240.000 205.714 34.286 274.286 445.714 720.000
9:3:1 308.571 102.857 34.286 342.857 411.429 754.286
36edo 6:5:4 200.000 166.667 133.333 333.333 366.667 700.000
8:5:1 266.667 166.667 33.333 300.000 433.333 733.333
10:2:1 333.333 66.667 33.333 366.667 400.000 766.667
37edo 7:5:3 227.027 162.162 97.297 324.324 389.189 713.514
7:6:2 227.027 194.595 64.865 291.892 421.622 713.514
9:3:2 291.892 97.297 64.865 356.757 389.189 745.946
9:4:1 291.892 129.730 32.432 324.324 421.622 745.946
38edo 8:4:3 252.632 126.316 94.737 347.368 378.947 726.316
8:5:2 252.632 157.895 63.158 315.789 410.526 726.316
8:6:1 252.632 189.474 31.579 284.211 442.105 726.316
10:3:1 315.789 94.737 31.579 347.368 410.526 757.895
39edo 7:5:4 215.385 153.846 123.077 338.462 369.231 707.692
7:6:3 215.385 184.615 92.308 307.692 400.000 707.692
9:4:2 276.923 123.077 61.538 338.462 400.000 738.462
9:5:1 276.923 153.846 30.769 307.692 430.769 738.462
11:2:1 338.462 61.538 30.769 369.231 400.000 769.231
40edo 8:5:3 240.000 150.000 90.000 330.000 390.000 720.000
8:7:1 240.000 210.000 30.000 270.000 450.000 720.000
10:3:2 300.000 90.000 60.000 360.000 390.000 750.000
10:4:1 300.000 120.000 30.000 330.000 420.000 750.000
41edo 7:6:4 204.878 175.610 117.073 321.951 380.488 702.439
9:4:3 263.415 117.073 87.805 351.220 380.488 731.707
9:5:2 263.415 146.341 58.537 321.951 409.756 731.707
9:6:1 263.415 175.610 29.268 292.683 439.024 731.707
11:3:1 321.951 87.805 29.268 351.220 409.756 760.976
42edo 8:5:4 228.571 142.857 114.286 342.857 371.429 714.286
8:6:3 228.571 171.429 85.714 314.286 400.000 714.286
8:7:2 228.571 200.000 57.143 285.714 428.571 714.286
10:5:1 285.714 142.857 28.571 314.286 428.571 742.857
12:2:1 342.857 57.143 28.571 371.429 400.000 771.429
43edo 7:6:5 195.349 167.442 139.535 334.884 362.791 697.674
9:5:3 251.163 139.535 83.721 334.884 390.698 725.581
9:6:2 251.163 167.442 55.814 306.977 418.605 725.581
9:7:1 251.163 195.349 27.907 279.070 446.512 725.581
11:3:2 306.977 83.721 55.814 362.791 390.698 753.488
11:4:1 306.977 111.628 27.907 334.884 418.605 753.488
44edo 8:7:3 218.182 190.909 81.818 300.000 409.091 709.091
10:4:3 272.727 109.091 81.818 354.545 381.818 736.364
10:5:2 272.727 136.364 54.545 327.273 409.091 736.364
10:6:1 272.727 163.636 27.273 300.000 436.364 736.364
12:3:1 327.273 81.818 27.273 354.545 409.091 763.636
45edo 9:5:4 240.000 133.333 106.667 346.667 373.333 720.000
9:7:2 240.000 186.667 53.333 293.333 426.667 720.000
9:8:1 240.000 213.333 26.667 266.667 453.333 720.000
11:4:2 293.333 106.667 53.333 346.667 400.000 746.667
11:5:1 293.333 133.333 26.667 320.000 426.667 746.667
13:2:1 346.667 53.333 26.667 373.333 400.000 773.333
46edo 8:6:5 208.696 156.522 130.435 339.130 365.217 704.348
8:7:4 208.696 182.609 104.348 313.043 391.304 704.348
10:5:3 260.870 130.435 78.261 339.130 391.304 730.435
10:7:1 260.870 182.609 26.087 286.957 443.478 730.435
12:3:2 313.043 78.261 52.174 365.217 391.304 756.522
12:4:1 313.043 104.348 26.087 339.130 417.391 756.522
47edo 9:6:4 229.787 153.191 102.128 331.915 382.979 714.894
9:7:3 229.787 178.723 76.596 306.383 408.511 714.894
9:8:2 229.787 204.255 51.064 280.851 434.043 714.894
11:4:3 280.851 102.128 76.596 357.447 382.979 740.426
11:5:2 280.851 127.660 51.064 331.915 408.511 740.426
11:6:1 280.851 153.191 25.532 306.383 434.043 740.426
13:3:1 331.915 76.596 25.532 357.447 408.511 765.957
48edo 8:7:5 200.000 175.000 125.000 325.000 375.000 700.000
10:5:4 250.000 125.000 100.000 350.000 375.000 725.000
10:6:3 250.000 150.000 75.000 325.000 400.000 725.000
10:7:2 250.000 175.000 50.000 300.000 425.000 725.000
10:8:1 250.000 200.000 25.000 275.000 450.000 725.000
12:5:1 300.000 125.000 25.000 325.000 425.000 750.000
14:2:1 350.000 50.000 25.000 375.000 400.000 775.000
49edo 9:6:5 220.408 146.939 122.449 342.857 367.347 710.204
9:7:4 220.408 171.429 97.959 318.367 391.837 710.204
9:8:3 220.408 195.918 73.469 293.878 416.327 710.204
11:5:3 269.388 122.449 73.469 342.857 391.837 734.694
11:6:2 269.388 146.939 48.980 318.367 416.327 734.694
11:7:1 269.388 171.429 24.490 293.878 440.816 734.694
13:3:2 318.367 73.469 48.980 367.347 391.837 759.184
13:4:1 318.367 97.959 24.490 342.857 416.327 759.184
50edo 8:7:6 192.000 168.000 144.000 336.000 360.000 696.000
10:7:3 240.000 168.000 72.000 312.000 408.000 720.000
10:9:1 240.000 216.000 24.000 264.000 456.000 720.000
12:4:3 288.000 96.000 72.000 360.000 384.000 744.000
12:5:2 288.000 120.000 48.000 336.000 408.000 744.000
12:6:1 288.000 144.000 24.000 312.000 432.000 744.000
14:3:1 336.000 72.000 24.000 360.000 408.000 768.000

See also

  • Blackdye, a 10-note scale that is an extension to nicetone.
  • Zarlino, a 5-limit JI scale with the same pattern.
  • Interdia - sister 2L 3m 2s scale
  • Antinicetone - sister 2L 2m 3s scale
  • 5L 2s - LM-equalized version of nicetone
  • 3L 4s - MS-equalized version of nicetone
  • 3L 2s - collapsed version of nicetone
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