User:MisterShafXen/1ed13/10
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Prime factorization
2 × 5
Step size
120 ¢
Fifth
6\10 (720 ¢) (→ 3\5)
Semitones (A1:m2)
2:0 (240 ¢ : 0 ¢)
Consistency limit
7
Distinct consistency limit
3
Special properties
|
This page presents a niche topic.
While not arbitrary, it may contain ideas whose practical applications in music are unknown or narrow in scope. Niche topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
| ← 9edo | 10 | 11edo → |
1 equal division of 13/10 (abbreviated 1ed13/10) is a nonoctave tuning system that uses equal steps of 13/10, or about 454 ¢.
It does not lend itself to familiar tonal harmony due to having no meaningful approximation of the octave (2/1), tritave (3/1), perfect fifth (3/2), nor any of the first 17 harmonics.
This necessitates a very experimental approach, which is perhaps atonal or perhaps uses instruments with a heavily modified, inharmonic timbre.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +163 | -85 | -129 | -61 | +78 | -189 | +34 | -170 | +102 |
| Relative (%) | +35.8 | -18.7 | -28.4 | -13.4 | +17.1 | -41.7 | +7.4 | -37.5 | +22.4 | |
| Step | 3 | 4 | 5 | 6 | 7 | 7 | 8 | 8 | 9 | |
| Harmonic | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -63 | -214 | +102 | -27 | -146 | +196 | +91 | -8 | -101 |
| Relative (%) | -14.0 | -47.1 | +22.4 | -5.9 | -32.2 | +43.2 | +20.1 | -1.7 | -22.3 | |
| Step | 9 | 9 | 10 | 10 | 10 | 11 | 11 | 11 | 11 | |