1700edo: Difference between revisions

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-{{novelty}}{{stub}}{{Infobox ET}}
+{{Infobox ET}}
-{{EDO intro|1700}}
+{{ED intro}}
 == Theory ==
-edo is consistent in the 5-odd-limit, although there is a large relative delta on the 3rd harmonic. From a regular temperament theory perspective, it's 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).
+=== Odd harmonics ===
+{{Harmonics in equal|1700}}
-One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]].
+=== 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 }}.
-=== Odd harmonics ===
+One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]].
-{{harmonics in equal|1700}}
-== Regular temperament properties ==
-=== Rank-2 temperaments===
-{| class="wikitable center-all left-5"
-!Periods
-per 8ve
-!Generator
-(Reduced)
-!Cents
-(Reduced)
-!Associated
-Ratio
-!Temperament
-|-
-|17
-|121\1700<br>(21\1700)
-|85.412<br>(14.824)
-|1024/975<br>(8192/8125)
-|[[Leaves]]
-|}