6edt: Difference between revisions
Jump to navigation
Jump to search
m Infobox ET added |
clean up |
||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro}} | |||
Since 6edt contains one | |||
6edt is therefore the smallest edt other than [[5edt]] to accurately approximate [[5-limit]] harmony. 6edt allows for construction of chords such as 2:5:6:15:18:26:31:45:54... | == Theory == | ||
Since 6edt contains one interval of [[2edt]] and two intervals of [[3edt]], it introduces 2 new notes unseen in previous edts. These new notes happen to approximate [[6/5]] and [[5/2]] very well, the former being only 1.351 [[cents]] sharp. | |||
6edt is therefore the smallest edt other than [[5edt]] to accurately approximate [[5-limit]] harmony, as well as some elements from the [[13-limit]] inherited from [[3edt]]. 6edt allows for construction of chords such as 2:5:6:15:18:26:31:45:54... | |||
=== Harmonics === | |||
{{Harmonics in equal|5|3|1}} | |||
== Intervals == | == Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 46: | Line 51: | ||
| [[3/1]] | | [[3/1]] | ||
|} | |} | ||
[[Category:Edt]] | [[Category:Edt]] | ||
Revision as of 13:53, 28 April 2024
| ← 5edt | 6edt | 7edt → |
Theory
Since 6edt contains one interval of 2edt and two intervals of 3edt, it introduces 2 new notes unseen in previous edts. These new notes happen to approximate 6/5 and 5/2 very well, the former being only 1.351 cents sharp. 6edt is therefore the smallest edt other than 5edt to accurately approximate 5-limit harmony, as well as some elements from the 13-limit inherited from 3edt. 6edt allows for construction of chords such as 2:5:6:15:18:26:31:45:54...
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -59 | +0 | -118 | -124 | -59 | +55 | -176 | +0 | -182 | +33 | -118 |
| Relative (%) | -15.5 | +0.0 | -30.9 | -32.5 | -15.5 | +14.4 | -46.4 | +0.0 | -48.0 | +8.7 | -30.9 | |
| Steps (reduced) |
3 (3) |
5 (0) |
6 (1) |
7 (2) |
8 (3) |
9 (4) |
9 (4) |
10 (0) |
10 (0) |
11 (1) |
11 (1) | |
Intervals
| Degrees | Cents | hekts | ApproximateRatios |
|---|---|---|---|
| 0 | 1/1 | ||
| 1 | 316.993 | 216.667 | 6/5, 65/54 |
| 2 | 633.985 | 433.333 | 13/9 |
| 3 | 950.978 | 650 | 19/11, 26/15 |
| 4 | 1267.97 | 866.667 | 27/13 |
| 5 | 1584.963 | 1093.333 | 5/2 (5/4 plus an octave) |
| 6 | 1901.955 | 1300 | 3/1 |