Lucky scale
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This page presents a novelty topic. It features ideas which are less likely to find practical applications in xenharmonic music. It may contain numbers that are impractically large, exceedingly complex, or chosen arbitrarily. Novelty topics are often developed by a single person or a small group. As such, this page may also feature idiosyncratic terms, notations, or conceptual frameworks. |
A lucky scale [idiosyncratic term ] (ed777c) is an equal-step tuning in which the interval 777 cents is divided in a given number of equal steps.
Examples
7ed777c
Close to 11edo.
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +21.0 | -15.0 | +42.0 | -11.3 | +6.0 | -38.8 | -48.0 | -29.9 | +9.7 | -44.3 | +27.0 |
Relative (%) | +18.9 | -13.5 | +37.8 | -10.2 | +5.4 | -35.0 | -43.3 | -27.0 | +8.7 | -39.9 | +24.4 | |
Steps (reduced) |
11 (4) |
17 (3) |
22 (1) |
25 (4) |
28 (0) |
30 (2) |
32 (4) |
34 (6) |
36 (1) |
37 (2) |
39 (4) |
Intervals
- 111.
- 222.
- 333.
- 444.
- 555.
- 666.
- 777.
- 888.
- 999.
- 1110.
- 1221.
- 1332.
- 1443.
- 1554.
9ed777c
Close to 14edo.
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +8.7 | -2.6 | +17.3 | -23.7 | +6.0 | -1.8 | +26.0 | -5.3 | -15.0 | -7.3 | +14.7 |
Relative (%) | +10.0 | -3.0 | +20.1 | -27.4 | +7.0 | -2.1 | +30.1 | -6.1 | -17.4 | -8.5 | +17.0 | |
Steps (reduced) |
14 (5) |
22 (4) |
28 (1) |
32 (5) |
36 (0) |
39 (3) |
42 (6) |
44 (8) |
46 (1) |
48 (3) |
50 (5) |
Intervals
- 86.333
- 172.667
- 259.
- 345.333
- 431.667
- 518.
- 604.333
- 690.667
- 777.
- 863.333
- 949.667
- 1036.
- 1122.333
- 1208.667
- 1295.
- 1381.333
- 1467.667
- 1554.
11ed777c
Close to 17edo.
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | +0.8 | +5.2 | +1.6 | -31.5 | +6.0 | +21.7 | +2.4 | +10.4 | -30.7 | +16.2 | +6.8 |
Relative (%) | +1.2 | +7.4 | +2.3 | -44.6 | +8.5 | +30.7 | +3.5 | +14.8 | -43.5 | +23.0 | +9.7 | |
Steps (reduced) |
17 (6) |
27 (5) |
34 (1) |
39 (6) |
44 (0) |
48 (4) |
51 (7) |
54 (10) |
56 (1) |
59 (4) |
61 (6) |
Intervals
- 70.636
- 141.273
- 211.909
- 282.545
- 353.182
- 423.818
- 494.455
- 565.091
- 635.727
- 706.364
- 777.
- 847.636
- 918.273
- 988.909
- 1059.545
- 1130.182
- 1200.818
- 1271.455
- 1342.091
- 1412.727
- 1483.364
- 1554.
13ed777c
Close to 20edo.
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -4.6 | +10.7 | -9.2 | +22.8 | +6.0 | -21.8 | -13.9 | +21.3 | +18.2 | -27.3 | +1.4 |
Relative (%) | -7.7 | +17.8 | -15.5 | +38.2 | +10.1 | -36.4 | -23.2 | +35.6 | +30.5 | -45.6 | +2.4 | |
Steps (reduced) |
20 (7) |
32 (6) |
40 (1) |
47 (8) |
52 (0) |
56 (4) |
60 (8) |
64 (12) |
67 (2) |
69 (4) |
72 (7) |
Intervals
- 59.769
- 119.538
- 179.308
- 239.077
- 298.846
- 358.615
- 418.385
- 478.154
- 537.923
- 597.692
- 657.462
- 717.231
- 777.
- 836.769
- 896.538
- 956.308
- 1016.077
- 1075.846
- 1135.615
- 1195.385
- 1255.154
- 1314.923
- 1374.692
- 1434.462
- 1494.231
- 1554.