17edo: Difference between revisions
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{{Infobox ET | {{Infobox ET | ||
| Prime factorization = 17 (prime) | | Prime factorization = 17 (prime) | ||
| Step size = 70. | | Step size = 70.5882¢ | ||
| Fifth = 10\17 ( | | Fifth = 10\17 (705.9¢) | ||
| Major 2nd = 3\17 ( | | Major 2nd = 3\17 (211.8¢) | ||
| Semitones = 2:1 ( | | Semitones = 2:1 (141.2¢ : 71.6¢) | ||
| Consistency = 3 | | Consistency = 3 | ||
}} | }} | ||
'''17 equal divisions of the octave''' ('''17edo'''), or '''17(-tone) equal temperament''' ('''17tet''', '''17et''') when viewed from a [[regular temperament]] perspective, is the tuning system derived from dividing the octave in 17 [[equal]] steps, each around 70.6 [[cent]]s in size. | '''17 equal divisions of the octave''' ('''17edo'''), or '''17(-tone) equal temperament''' ('''17tet''', '''17et''') when viewed from a [[regular temperament]] perspective, is the tuning system derived from dividing the octave in 17 [[equal]] steps, each around 70.6 [[cent]]s in size. | ||
== Theory == | == Theory == | ||
17edo can plausibly be treated as a 2.3.25.7.11.13.23 subgroup temperament, for which it is quite accurate (though the 7-limit ratios are generally not as well-represented as those of the other integers). Because the 3, 7, 11, and 13 are all sharp, it adapts well to octave shrinking; [[27edt]] (a variant of 17edo in which the octaves are flattened by ~2.5 cents) is a good alternative. Another one is [[44ed6]]. | 17edo can plausibly be treated as a 2.3.25.7.11.13.23 subgroup temperament, for which it is quite accurate (though the 7-limit ratios are generally not as well-represented as those of the other integers). Because the 3, 7, 11, and 13 are all sharp, it adapts well to octave shrinking; [[27edt]] (a variant of 17edo in which the octaves are flattened by ~2.5 cents) is a good alternative. Another one is [[44ed6]]. | ||
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== Intervals == | == Intervals == | ||
{| class="wikitable center-all right-2 left-8" | {| class="wikitable center-all right-2 left-8" | ||
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== Introductory materials == | == Introductory materials == | ||
* [[SeventeenTheory]], an introduction to | * [[SeventeenTheory]], an introduction to 17edo theory, through the eyes of the [[SeventeenTonePianoProject]]. | ||
* [http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle] by George Secor, another introduction into | * [http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle] by George Secor, another introduction into 17edo theory. | ||
* [[17edo Solfege]] | * [[17edo Solfege]] | ||
* [[17edo tetrachords]] | * [[17edo tetrachords]] | ||