9ed5/2: Difference between revisions
Jump to navigation
Jump to search
m Marked page as stub |
Standardize the layout & expand |
||
| (2 intermediate revisions by one other user not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | |||
9ed5/2 can function as a generator chain for the [[tetracot]] temperament. | |||
=== Harmonics === | |||
{{Harmonics in equal|9|5|2|columns=11}} | |||
{{Harmonics in equal|9|5|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 9ed5/2 (continued)}} | |||
== Intervals == | |||
{| class="wikitable center-1 right-2" | |||
! # | |||
! Cents | |||
! Approximated ratios | |||
|- | |||
| 0 | |||
| 0 | |||
| 1/1 | |||
|- | |||
| 1 | |||
| 176 | |||
| 10/9, 11/10, 21/19 | |||
|- | |||
| 2 | |||
| 353 | |||
| 11/9, 16/13 | |||
|- | |||
| 3 | |||
| 529 | |||
| 15/11, 19/14, 27/20 | |||
|- | |||
| 4 | |||
| 705 | |||
| 3/2 | |||
|- | |||
| 5 | |||
| 881 | |||
| 5/3 | |||
|- | |||
| 6 | |||
| 1058 | |||
| 11/6, 24/13 | |||
|- | |||
| 7 | |||
| 1234 | |||
| 45/22 | |||
|- | |||
| 8 | |||
| 1410 | |||
| 9/4 | |||
|- | |||
| 9 | |||
| 1586 | |||
| 5/2 | |||
|} | |||
Latest revision as of 14:34, 27 May 2026
| ← 8ed5/2 | 9ed5/2 | 10ed5/2 → |
(semiconvergent)
9 equal divisions of 5/2 (abbreviated 9ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 9 equal parts of about 176 ¢ each. Each step represents a frequency ratio of (5/2)1/9, or the 9th root of 5/2.
Theory
9ed5/2 can function as a generator chain for the tetracot temperament.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +33.8 | +36.9 | +67.6 | +33.8 | +70.7 | -19.9 | -74.9 | +73.7 | +67.6 | +78.9 | -71.8 |
| Relative (%) | +19.2 | +20.9 | +38.4 | +19.2 | +40.1 | -11.3 | -42.5 | +41.8 | +38.4 | +44.7 | -40.7 | |
| Steps (reduced) |
7 (7) |
11 (2) |
14 (5) |
16 (7) |
18 (0) |
19 (1) |
20 (2) |
22 (4) |
23 (5) |
24 (6) |
24 (6) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -34.1 | +13.9 | +70.7 | -41.1 | +30.2 | -68.7 | +13.9 | -74.9 | +16.9 | -63.6 | +35.7 | -38.0 |
| Relative (%) | -19.3 | +7.9 | +40.1 | -23.3 | +17.2 | -39.0 | +7.9 | -42.5 | +9.6 | -36.1 | +20.3 | -21.6 | |
| Steps (reduced) |
25 (7) |
26 (8) |
27 (0) |
27 (0) |
28 (1) |
28 (1) |
29 (2) |
29 (2) |
30 (3) |
30 (3) |
31 (4) |
31 (4) | |
Intervals
| # | Cents | Approximated ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 176 | 10/9, 11/10, 21/19 |
| 2 | 353 | 11/9, 16/13 |
| 3 | 529 | 15/11, 19/14, 27/20 |
| 4 | 705 | 3/2 |
| 5 | 881 | 5/3 |
| 6 | 1058 | 11/6, 24/13 |
| 7 | 1234 | 45/22 |
| 8 | 1410 | 9/4 |
| 9 | 1586 | 5/2 |