# Lucky scale

 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.