User:2^67-1/Sandbox II

Revision as of 03:02, 4 August 2026 by 2^67-1 (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Notes Step pattern Name
0 1# 2 3# 4 5 6# 7 8# 9 LsLssLsLss Atlantic
0 1# 2 3 4 5 6# 7 8 9 LssLsLssLs Lumian
0 1 2 3 4 5 6 7 8 9 sLsLssLsLs Pacific
0 1 2 3 4b 5 6 7 8 9b sLssLsLssL Taliesin
0 1 2b 3 4b 5 6 7b 8 9b ssLsLssLsL Dresden


3-limit uniform maps between 0 and 10
Min. size Max. size Wart notation Map
0.0000 0.3155 0 0 0]
0.3155 0.5000 0bb 0 1]
0.5000 0.9464 1b 1 1]
0.9464 1.5000 1 1 2]
1.5000 1.5773 2bb 2 2]
1.5773 2.2083 2 2 3]
2.2083 2.5000 2b 2 4]
2.5000 2.8392 3b 3 4]
2.8392 3.4701 3 3 5]
3.4701 3.5000 3bb 3 6]
3.5000 4.1010 4 4 6]
4.1010 4.5000 4b 4 7]
4.5000 4.7320 5b 5 7]
4.7320 5.3629 5 5 8]
5.3629 5.5000 5bb 5 9]
5.5000 5.9938 6b 6 9]
5.9938 6.5000 6 6 10]
6.5000 6.6248 7bb 7 10]
6.6248 7.2557 7 7 11]
7.2557 7.5000 7b 7 12]
7.5000 7.8866 8b 8 12]
7.8866 8.5000 8 8 13]
8.5000 8.5176 9bb 9 13]
8.5176 9.1485 9 9 14]
9.1485 9.5000 9b 9 15]
9.5000 9.7794 10b 10 15]
9.7794 10.4103 10 10 16]


Approximation of odd harmonics in 3570edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.106 -0.095 -0.086 +0.124 -0.057 +0.145 +0.135 -0.081 -0.034 +0.143 -0.039
Relative (%) -31.6 -28.3 -25.7 +36.8 -17.1 +43.0 +40.1 -24.2 -10.1 +42.7 -11.6
Steps
(reduced)
5658
(2088)
8289
(1149)
10022
(2882)
11317
(607)
12350
(1640)
13211
(2501)
13948
(3238)
14592
(312)
15165
(885)
15681
(1401)
16149
(1869)


Approximation of odd harmonics in 4410edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.086 +0.081 -0.118 -0.100 -0.025 +0.017 -0.105 +0.079 -0.098 -0.033 +0.025
Relative (%) +31.5 +29.7 -43.5 -36.9 -9.3 +6.1 -38.8 +28.9 -36.0 -12.0 +9.2
Steps
(reduced)
6990
(2580)
10240
(1420)
12380
(3560)
13979
(749)
15256
(2026)
16319
(3089)
17229
(3999)
18026
(386)
18733
(1093)
19370
(1730)
19949
(2309)


Approximation of prime harmonics in 7980edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000 -0.0001 +0.0021 +0.0463 -0.0397 +0.0738 +0.0070 -0.0694 -0.0037 +0.0469 -0.0732
Relative (%) +0.0 -0.1 +1.4 +30.8 -26.4 +49.1 +4.7 -46.2 -2.4 +31.2 -48.7
Steps
(reduced)
7980
(0)
12648
(4668)
18529
(2569)
22403
(6443)
27606
(3666)
29530
(5590)
32618
(698)
33898
(1978)
36098
(4178)
38767
(6847)
39534
(7614)


Approximation of harmonics in 34ed30
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Error Absolute (¢) +12.3 +3.1 +24.6 -15.4 +15.4 -78.3 +36.9 +6.1 -3.1 +5.1 +27.7 +62.3 -66.0 -12.3 +49.2
Relative (%) +7.1 +1.8 +14.2 -8.9 +8.9 -45.2 +21.3 +3.5 -1.8 +2.9 +16.0 +36.0 -38.1 -7.1 +28.4
Steps
(reduced)
7
(7)
11
(11)
14
(14)
16
(16)
18
(18)
19
(19)
21
(21)
22
(22)
23
(23)
24
(24)
25
(25)
26
(26)
26
(26)
27
(27)
28
(28)