17edo: Difference between revisions

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=== Subsets and supersets ===

17edo is the seventh [[prime edo]], following [[13edo]] and coming before [[19edo]]~~, so it~~ does not contain any nontrivial subset edos, though it contains [[17ed4]]. [[34edo]], which doubles it, provides a good correction to harmonics 5 and 17; while [[68edo]], which quadruples it, provides additionally the primes 7, 19, and 31.

17edo is the seventh [[prime edo]], following [[13edo]] and coming before [[19edo]]. It does not contain any nontrivial subset edos, though it contains [[17ed4]] and [[17ed8]]. 17ed8 is a system where all odd harmonics up to the 21st are mapped exactly as in 17edo, except for the 11th. Beyond that, the 27th, 31st, 35th, and 39th harmonics are likewise mapped identically.

[[34edo]], which doubles 17edo, provides a good correction to harmonics 5 and 17; while [[68edo]], which quadruples it, provides additionally the primes 7, 19, and 31.

== Intervals ==

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* [[User:CritDeathX/Sam's 17-note Well Temperament|Nicolai's 17-note well temperament]]

* [[User:FloraC/Flora's 17-note well temperament|Flora's 17-note well temperament]]

~~=== Non-octave scales ===~~

Taking '''every 3 degrees of 17edo''' (or [[17ed8]]) produces a scale in which all odd harmonics up to the 21st are mapped exactly as in 17edo, except for the 11th harmonic. Beyond that, the 27th, 31st, 35th, and 39th harmonics are likewise mapped identically.

== Introductory materials ==

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 === Subsets and supersets ===
-edo is the seventh [[prime edo]], following [[13edo]] and coming before [[19edo]], so it does not contain any nontrivial subset edos, though it contains [[17ed4]]. [[34edo]], which doubles it, provides a good correction to harmonics 5 and 17; while [[68edo]], which quadruples it, provides additionally the primes 7, 19, and 31.
+edo is the seventh [[prime edo]], following [[13edo]] and coming before [[19edo]]. It does not contain any nontrivial subset edos, though it contains [[17ed4]] and [[17ed8]]. 17ed8 is a system where all odd harmonics up to the 21st are mapped exactly as in 17edo, except for the 11th. Beyond that, the 27th, 31st, 35th, and 39th harmonics are likewise mapped identically.
+[[34edo]], which doubles 17edo, provides a good correction to harmonics 5 and 17; while [[68edo]], which quadruples it, provides additionally the primes 7, 19, and 31.
 == Intervals ==
@@ Line 786: / Line 788: @@
 * [[User:CritDeathX/Sam's 17-note Well Temperament|Nicolai's 17-note well temperament]]
 * [[User:FloraC/Flora's 17-note well temperament|Flora's 17-note well temperament]]
-=== Non-octave scales ===
-Taking '''every 3 degrees of 17edo''' (or [[17ed8]]) produces a scale in which all odd harmonics up to the 21st are mapped exactly as in 17edo, except for the 11th harmonic. Beyond that, the 27th, 31st, 35th, and 39th harmonics are likewise mapped identically.
 == Introductory materials ==