User:MisterShafXen/17ed9/2: Difference between revisions
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Prime factorization
2 (prime)
Step size
600 ¢
Fifth
1\2 (600 ¢)
(convergent)
Semitones (A1:m2)
-1:1 (-600 ¢ : 600 ¢)
Consistency limit
3
Distinct consistency limit
1
Special properties
Created page with "{{Infobox ET}} {{ED intro}} == Theory == This tuning tempers out 9/8 in the 3-limit, 25/24 and 27/25 in the 5-limit, and 21/20, 35/32, 36/35, and 15/14 in the 7-limit. == Harmonics == {{Harmonics in equal | 17 | 9 | 2}}" Tags: Visual edit Mobile edit Mobile web edit |
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This tuning tempers out [[9/8]] in the [[3-limit]], [[25/24]] and [[27/25]] in the [[5-limit]], and [[21/20]], [[35/32]], [[36/35]], and [[15/14]] in the [[7-limit]]. | This tuning tempers out [[9/8]] in the [[3-limit]], [[25/24]] and [[27/25]] in the [[5-limit]], and [[21/20]], [[35/32]], [[36/35]], and [[15/14]] in the [[7-limit]]. | ||
== Harmonics == | === Harmonics === | ||
{{Harmonics in equal | 17 | 9 | 2}} | {{Harmonics in equal|17|9|2}} | ||
Revision as of 14:09, 20 July 2025
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| ← 1edo | 2 | 3edo → |
(convergent)
17 equal divisions of 9/2 (abbreviated 17ed9/2) is a nonoctave tuning system that divides the interval of 9/2 into 17 equal parts of about 153 ¢ each. Each step represents a frequency ratio of (9/2)1/17, or the 17th root of 9/2.
This tuning tempers out 9/8 in the 3-limit, 25/24 and 27/25 in the 5-limit, and 21/20, 35/32, 36/35, and 15/14 in the 7-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +25.4 | -63.9 | +50.7 | -29.2 | -38.5 | +0.9 | +76.1 | +25.4 | -3.9 | -15.7 | -13.2 |
| Relative (%) | +16.6 | -41.7 | +33.1 | -19.1 | -25.2 | +0.6 | +49.7 | +16.6 | -2.5 | -10.2 | -8.6 | |
| Steps (reduced) |
8 (8) |
12 (12) |
16 (16) |
18 (1) |
20 (3) |
22 (5) |
24 (7) |
25 (8) |
26 (9) |
27 (10) |
28 (11) | |