112edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|112}} | |||
== Theory == | == Theory == | ||
112edo has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which- the [[patent fifth]]- is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27|28:27]] while -8 fifths gives a near-just [[39/32|32:39]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17|17:21]]. | |||
One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure. | One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure. | ||
Revision as of 21:16, 30 May 2023
| ← 111edo | 112edo | 113edo → |
Theory
112edo has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which- the patent fifth- is identical to the perfect fifth of 56edo, a great inverse gentle fifth where +5 fifths gives a near-just 28:27 while -8 fifths gives a near-just 32:39 (identical to 2 degrees of 7edo) and +9 fifths gives a close approximation to 17:21.
One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from 17edo, but sharing a similar structure.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.19 | -0.60 | -4.54 | -0.34 | -4.89 | -4.81 | +4.59 | +2.19 | +2.49 | +0.65 | +3.87 |
| Relative (%) | +48.4 | -5.6 | -42.4 | -3.2 | -45.6 | -44.9 | +42.8 | +20.4 | +23.2 | +6.0 | +36.1 | |
| Steps (reduced) |
178 (66) |
260 (36) |
314 (90) |
355 (19) |
387 (51) |
414 (78) |
438 (102) |
458 (10) |
476 (28) |
492 (44) |
507 (59) | |