17100edo: Difference between revisions
Created page with "{{Infobox ET}} {{ED intro}} == Theory == This EDO's step size is the relative cent of 171edo. It notably provides the optimal patent val for 13-limit harmonismic temperament, tempering out 10648/10647. === Subsets and Supersets === Since 17100 = 2<sup>2</sup> * 3<sup>2</sup> * 5<sup>2</sup> * 19, it contains subset edos {{edos| 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 25, 30, 36, 38, 45, 50, 57, 60, 75, 76, 90, 95, 100, 114, 150, 171, 180, 190, 22..." |
Cleanup |
||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} | {{ED intro}} | ||
This | This edo's step size is the [[relative cent]] of [[171edo]], an excellent [[7-limit]] [[microtemperament]]. It also notably provides the [[optimal patent val]] for [[13-limit]] [[harmonisma|harmonismic]] temperament, which [[tempering out|tempers out]] [[10648/10647]]. | ||
=== | |||
=== Prime harmonics === | |||
{{Harmonics in equal|17100}} | {{Harmonics in equal|17100}} | ||
=== Subsets and supersets === | |||
Since 17100 factors into primes as {{nowrap| 2<sup>2</sup> × 3<sup>2</sup> × 5<sup>2</sup> × 19 }}, 17100edo contains subset edos {{EDOs| 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 25, 30, 36, 38, 45, 50, 57, 60, 75, 76, 90, 95, 100, 114, 150, 171, 180, 190, 225, 228, 285, 300, 342, 380, 450, 475, 570, 684, 855, 900, 950, 1140, 1425, 1710, 1900, 2850, 3420, 4275, 5700, and 8550 }}. | |||
[[Category:Harmonismic]] | [[Category:Harmonismic]] | ||
[[Category:171edo]] | [[Category:171edo]] | ||
Latest revision as of 06:27, 25 February 2026
| ← 17099edo | 17100edo | 17101edo → |
17100 equal divisions of the octave (abbreviated 17100edo or 17100ed2), also called 17100-tone equal temperament (17100tet) or 17100 equal temperament (17100et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 17100 equal parts of about 0.0702 ¢ each. Each step represents a frequency ratio of 21/17100, or the 17100th root of 2.
This edo's step size is the relative cent of 171edo, an excellent 7-limit microtemperament. It also notably provides the optimal patent val for 13-limit harmonismic temperament, which tempers out 10648/10647.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0099 | +0.0021 | +0.0162 | -0.0197 | +0.0337 | +0.0270 | +0.0308 | +0.0064 | -0.0333 | +0.0171 |
| Relative (%) | +0.0 | +14.1 | +3.0 | +23.1 | -28.1 | +48.1 | +38.5 | +44.0 | +9.1 | -47.5 | +24.3 | |
| Steps (reduced) |
17100 (0) |
27103 (10003) |
39705 (5505) |
48006 (13806) |
59156 (7856) |
63278 (11978) |
69896 (1496) |
72640 (4240) |
77353 (8953) |
83071 (14671) |
84717 (16317) | |
Subsets and supersets
Since 17100 factors into primes as 22 × 32 × 52 × 19, 17100edo contains subset edos 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 25, 30, 36, 38, 45, 50, 57, 60, 75, 76, 90, 95, 100, 114, 150, 171, 180, 190, 225, 228, 285, 300, 342, 380, 450, 475, 570, 684, 855, 900, 950, 1140, 1425, 1710, 1900, 2850, 3420, 4275, 5700, and 8550.