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

Approximation of harmonics in 7ed777c
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

  1. 111.
  2. 222.
  3. 333.
  4. 444.
  5. 555.
  6. 666.
  7. 777.
  8. 888.
  9. 999.
  10. 1110.
  11. 1221.
  12. 1332.
  13. 1443.
  14. 1554.

9ed777c

Close to 14edo.

Harmonics

Approximation of harmonics in 9ed777c
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

  1. 86.333
  2. 172.667
  3. 259.
  4. 345.333
  5. 431.667
  6. 518.
  7. 604.333
  8. 690.667
  9. 777.
  10. 863.333
  11. 949.667
  12. 1036.
  13. 1122.333
  14. 1208.667
  15. 1295.
  16. 1381.333
  17. 1467.667
  18. 1554.

11ed777c

Close to 17edo.

Harmonics

Approximation of harmonics in 9ed777c
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

  1. 70.636
  2. 141.273
  3. 211.909
  4. 282.545
  5. 353.182
  6. 423.818
  7. 494.455
  8. 565.091
  9. 635.727
  10. 706.364
  11. 777.
  12. 847.636
  13. 918.273
  14. 988.909
  15. 1059.545
  16. 1130.182
  17. 1200.818
  18. 1271.455
  19. 1342.091
  20. 1412.727
  21. 1483.364
  22. 1554.

13ed777c

Close to 20edo.

Harmonics

Approximation of harmonics in 9ed777c
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

  1. 59.769
  2. 119.538
  3. 179.308
  4. 239.077
  5. 298.846
  6. 358.615
  7. 418.385
  8. 478.154
  9. 537.923
  10. 597.692
  11. 657.462
  12. 717.231
  13. 777.
  14. 836.769
  15. 896.538
  16. 956.308
  17. 1016.077
  18. 1075.846
  19. 1135.615
  20. 1195.385
  21. 1255.154
  22. 1314.923
  23. 1374.692
  24. 1434.462
  25. 1494.231
  26. 1554.

See also