Nicetone: Difference between revisions
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* [[Blackdye]], a 10-note scale that is an extension to nicetone. | * [[Blackdye]], a 10-note scale that is an extension to nicetone. | ||
* [[Zarlino]], a 5-limit JI scale with the same pattern. | * [[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 | * [[5L 2s]] - LM-equalized version of nicetone | ||
** [[5L 2s Muddles]] - other diatonic muddles | ** [[5L 2s Muddles]] - other diatonic muddles | ||
Revision as of 11:43, 18 May 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.
| 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 | ├──────┼──────┼──┼──────┼──────┼──────┼──┤ |
| 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 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.
| Left handed | Right handed |
|---|---|
| LmLsmLs
LH NiceLydian |
LmLsLms
RH NiceLydian |
| mLsLmLs
LH NiceIonian |
LmsLmLs
RH NiceIonian |
| mLsmLsL
LH NiceMixo |
mLsLmsL
RH NiceMixo |
| LsLmLsm
LH NiceDorian |
msLmLsL
RH NiceDorian |
| LsmLsLm
LH NiceAolian |
LsLmsLm
RH NiceAolian |
| sLmLsmL
LH NicePhrygian |
sLmLsLm
RH NicePhrygian |
| smLsLmL
LH NiceLocrian |
sLmsLmL
RH NiceLocrian |
Tunings
| Tuning range | |
|---|---|
| Outer generator (G1 = 2L + m + s) |
[math]\displaystyle{ \displaystyle \frac{4}{7} < G_\text{1} < \frac{2}{3} }[/math] |
| RH inner generator (G2 = L + m) |
[math]\displaystyle{ \displaystyle \frac{1}{2} G_\text{1} < G_\text{2} < 4 G_\text{1} - 2 \text{ for } \frac{4}{7} < G_\text{1} ≤ \frac{3}{5} }[/math] [math]\displaystyle{ \displaystyle \frac{1}{2} G_\text{1} < G_\text{2} < 1 - G_\text{1} \text{ for }\frac{3}{5} ≤ G_\text{1} < \frac{2}{3} }[/math] |
| LH inner generator (G2 = L + s) |
[math]\displaystyle{ \displaystyle 2 - 3 G_\text{1} < G_\text{2} < \frac{1}{2} G_\text{1} \text{ for }\frac{4}{7} < G_\text{1} ≤ \frac{3}{5} }[/math] [math]\displaystyle{ \displaystyle 2 G_\text{1} - 1 < G_\text{2} < \frac{1}{2} G_\text{1} \text{ for }\frac{3}{5} ≤ G_\text{1} < \frac{2}{3} }[/math] |
| Tuning | L:m:s | Good Just Approximations | Other comments | Degrees | |||||
|---|---|---|---|---|---|---|---|---|---|
| D(~9/8) | vE(~5/4) | F(~4/3) | G(~3/2) | vA(~5/3) | vB(~15/8) | ||||
| 5-limit JI | (~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 | 3:2:1 | 240 | 400 | 480 | 720 | 880 | 1120 | ||
| 18edo | 4:2:1 | Wolf fourth and fifth | 266.667 | 466.667 | 733.333 | 866.667 | 1133.333 | ||
| 20edo | 4:3:1 | 240 | 420 | 480 | 720 | 900 | 1140 | ||
| 21edo | 5:2:1 | Wolf fourth and fifth | 285.714 | 400 | 457.143 | 742.857 | 857.143 | 1142.857 | |
| 22edo | 4:3:2 | Also has diatonic MOS | 218.182 | 381.182 | 490.909 | 709.091 | 872.727 | 1090.909 | |
| 23edo | 5:3:1 | 14/11 | Wolf fourth and fifth | 260.87 | 417.391 | 469.565 | 730.435 | 886.9565 | 1147.826 |
| 24edo | 6:2:1 | Also has neutral diatonic MOS | 300 | 400 | 450 | 750 | 850 | 1050 | |
| 25edo | 5:3:2
5:4:1 |
240 | 384
432 |
480 | 720 | 864
912 |
1104 | ||
| 26edo | 6:3:1 | Also has diatonic MOS | 276.923 | 415.385 | 461.5385 | 738.4615 | 876.923 | 1153.846 | |
| 27edo | 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 | 6:3:2
6:4:1 |
257.143 | 385.714
428.571 |
471.429 | 728.571 | 857.143
900 |
1114.286
1157.143 | ||
| 29edo | 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 | 6:5:1
8:2:1 |
240
320 |
440
400 |
480
440 |
720
760 |
920
840 |
1160 | ||
| 31edo | 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 | 6:4:3
6:5:2 8:3:1 |
Also has diatonic MOS | 225
300 |
375
412.5 |
487.5
450 |
712.5
750 |
862.5
900 |
1087.5
1125 1162.5 | |
| 33edo | 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 | 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 | 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 | 6:5:4 | 27/25 | Also has Porcupine MOS | 200 | 366.667 | 500 | 700 | 866.667 | 1066.667 |
| 37edo | 7:5:3
7:6:2 |
Has 37edo just major triad | 227.027 | 389.189 | 486.4865 | 713.5135 | 875.676 | 1102.703 | |
| 38edo | 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 | 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 | 8:5:3
8:7:1 |
Golden Nicetone
Also has diatonic MOS |
240 | 390
450 |
480 | 720 | 870
930 |
1110
1170 | |
| 41edo | 7:6:4 | Also has diatonic MOS | 204.878 | 380.488 | 497.561 | 702.439 | 878.049 | 1082.927 | |
| 42edo | 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 | 7:6:5 | Also has diatonic MOS | 195.349 | 362.791 | 502.326 | 697.674 | 865.116 | 1060.465 | |
| 44edo | 8:7:3 | Also has neutral diatonic MOS | 218.182 | 409.091 | 490.909 | 709.091 | 900 | 1118.182 | |
| 46edo | 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 | 8:7:5 | 200 | 375 | 500 | 700 | 875 | 1075 | ||
| 50edo | 8:7:6 | Also has diatonic MOS | 192 | 360 | 504 | 696 | 864 | 1056 | |
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
- 5L 2s Muddles - other diatonic muddles
- 3L 4s - MS-equalized version of nicetone
- 3L 2s - collapsed version of nicetone