178edo: Difference between revisions
Jump to navigation
Jump to search
No edit summary |
Cleanup and +subsets and supersets |
||
| Line 2: | Line 2: | ||
{{EDO intro|178}} | {{EDO intro|178}} | ||
178et [[tempering out|tempers out]] 15625/15555 ([[15625/15552|kleisma]]) and {{monzo| -49 28 2 }} in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], [[4375/4374]], and 40960000/40353607 in the 7-limit; [[243/242]], [[3025/3024]], 4375/4356, and 16896/16807 in the 11-limit; [[640/637]], [[1188/1183]], 1625/1617, [[1716/1715]], and [[4096/4095]] in the 13-limit. Using the 178def val, it tempers out [[10976/10935]], 33075/32768, and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], 4125/4096, and [[8019/8000]] in the 11-limit; [[325/324]], [[625/624]], [[847/845]], [[1287/1280]], and [[1573/1568]] in the 13-limit. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|178}} | {{Harmonics in equal|178}} | ||
=== Subsets and supersets === | |||
Since 178 factors into {{factorization|178}}, 178edo contains [[2edo]] and [[89edo]] as its subsets. | |||
Revision as of 09:39, 25 April 2024
| ← 177edo | 178edo | 179edo → |
178et tempers out 15625/15555 (kleisma) and [-49 28 2⟩ in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.83 | -2.04 | +1.96 | +1.49 | +2.17 | +2.91 | -0.88 | -1.31 | +1.88 | +1.03 |
| Relative (%) | +0.0 | -12.3 | -30.3 | +29.1 | +22.1 | +32.2 | +43.2 | -13.1 | -19.4 | +27.9 | +15.3 | |
| Steps (reduced) |
178 (0) |
282 (104) |
413 (57) |
500 (144) |
616 (82) |
659 (125) |
728 (16) |
756 (44) |
805 (93) |
865 (153) |
882 (170) | |
Subsets and supersets
Since 178 factors into 2 × 89, 178edo contains 2edo and 89edo as its subsets.