2edt: Difference between revisions
Jump to navigation
Jump to search
clean up |
mNo edit summary |
||
| Line 2: | Line 2: | ||
{{EDO intro}} | {{EDO intro}} | ||
== Theory == | |||
As a temperament in the 3.5 [[subgroup]], it tempers out [[27/25]], equating 5/3 with 9/5. | As a temperament in the 3.5 [[subgroup]], it tempers out [[27/25]], equating 5/3 with 9/5. | ||
Since [[26/15]] is a convergent of sqrt(3), 26/15 (and its [[tritave complement]] 45/26) are good rational representations of the square root of 3. 2edt thus tempers out (26/15)<sup>2</sup> / (3/1) = [[676/675]], the island comma. | Since [[26/15]] is a [[convergent]] of sqrt(3), 26/15 (and its [[tritave complement]] 45/26) are good rational representations of the square root of 3. 2edt thus tempers out (26/15)<sup>2</sup> / (3/1) = [[676/675]], the island comma. | ||
One step of 2edt is close to the optimal TE generator of [[Very high accuracy temperaments|monzismic temperament]], which tempers out {{monzo|54 -37 2}}, the monzisma. | One step of 2edt is close to the optimal TE generator of [[Very high accuracy temperaments|monzismic temperament]], which tempers out {{monzo|54 -37 2}}, the monzisma. | ||
Revision as of 12:01, 28 April 2024
| ← 1edt | 2edt | 3edt → |
(convergent)
Theory
As a temperament in the 3.5 subgroup, it tempers out 27/25, equating 5/3 with 9/5.
Since 26/15 is a convergent of sqrt(3), 26/15 (and its tritave complement 45/26) are good rational representations of the square root of 3. 2edt thus tempers out (26/15)2 / (3/1) = 676/675, the island comma.
One step of 2edt is close to the optimal TE generator of monzismic temperament, which tempers out [54 -37 2⟩, the monzisma.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0 | +67 | +435 | +0 | -347 | +314 | +67 | -150 | -343 | +435 | +278 |
| Relative (%) | +0.0 | +7.0 | +45.8 | +0.0 | -36.5 | +33.1 | +7.0 | -15.8 | -36.0 | +45.8 | +29.2 | |
| Steps (reduced) |
2 (0) |
3 (1) |
4 (0) |
4 (0) |
4 (0) |
5 (1) |
5 (1) |
5 (1) |
5 (1) |
6 (0) |
6 (0) | |