1700edo: Difference between revisions

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== Theory ==

1700edo is only [[consistent]] in the [[5-odd-limit]], and there is a large relative delta on the ~~3rd~~ harmonic. ~~From~~ a ~~regular temperament theory perspective~~, ~~its best usage~~ is ~~as a~~ 2.9.11.21.23.31 [[subgroup]] ~~tuning because all other harmonics up to 29th have more than 25% error~~. Nonetheless, it tunes the 323 & 2023 temperament [[leaves]] in the 17-limit on the patent val.

1700edo is only [[consistent]] in the [[5-odd-limit]], and there is a large relative delta on the [[harmonic]] [[3/1|3]]. It has a reasonable approximation to the 2.9.15.21.11.13.17.23 [[subgroup]], or if the harmonic [[5/1|5]] is desired, the 2.9.5.21.11.23 subgroup. Otherwise, it can be considered in the 2.9.21.11.23.31 [[subgroup]] (not including either 5 or 15). Nonetheless, it tunes the 323 & 2023 temperament [[leaves]] in the 17-limit on the [[patent val]].

One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]].

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=== Odd harmonics ===

=== Subsets and supersets ===

Since 1700 factors into {{factorization|1700}}, 1700edo has subset edos {{EDOs| 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, and 850 }}.

== Regular temperament properties ==

=== Rank-2 temperaments===

{| class="wikitable center-all left-5"

|+Table of rank-2 temperaments by generator

|-

! Periods<br>per 8ve

! Generator*

! Cents*

! Associated<br>Ratio

! Associated<br>Ratio*

! Temperament

|-

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is only [[consistent]] in the [[5-odd-limit]], and there is a large relative delta on the 3rd harmonic. From a regular temperament theory perspective, its best usage is as a 2.9.11.21.23.31 [[subgroup]] tuning because all other harmonics up to 29th have more than 25% error. Nonetheless, it tunes the 323 & 2023 temperament [[leaves]] in the 17-limit on the patent val.
+edo is only [[consistent]] in the [[5-odd-limit]], and there is a large relative delta on the [[harmonic]] [[3/1|3]]. It has a reasonable approximation to the 2.9.15.21.11.13.17.23 [[subgroup]], or if the harmonic [[5/1|5]] is desired, the 2.9.5.21.11.23 subgroup. Otherwise, it can be considered in the 2.9.21.11.23.31 [[subgroup]] (not including either 5 or 15). Nonetheless, it tunes the 323 & 2023 temperament [[leaves]] in the 17-limit on the [[patent val]].
 One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]].
@@ Line 9: / Line 9: @@
 === Odd harmonics ===
 {{Harmonics in equal|1700}}
+=== Subsets and supersets ===
+Since 1700 factors into {{factorization|1700}}, 1700edo has subset edos {{EDOs| 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, and 850 }}.
 == Regular temperament properties ==
 === Rank-2 temperaments===
 {| class="wikitable center-all left-5"
+|+Table of rank-2 temperaments by generator
+|-
 ! Periods<br>per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio
+! Associated<br>Ratio*
 ! Temperament
 |-