1700edo: Difference between revisions
Created page with "{{Infobox ET}} {{EDO intro|1700}} == Theory == 1700edo is consistent in the 5-odd-limit, although there is a large relative delta on the 3rd harmonic. From a regular temperame..." |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
1700edo is consistent in the 5-odd-limit, | 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 {{nowrap|323 & 2023}} temperament [[leaves]] in the 17-limit on the [[patent val]]. | ||
=== 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 }}. | |||
One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]]. | One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]]. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments=== | === Rank-2 temperaments=== | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
per 8ve | |- | ||
!Generator | ! Periods<br />per 8ve | ||
! Generator* | |||
!Cents | ! Cents* | ||
! Associated<br />ratio* | |||
!Associated | ! Temperament | ||
!Temperament | |||
|- | |- | ||
|17 | | 17 | ||
|121\1700<br>(21\1700) | | 121\1700<br />(21\1700) | ||
|85.412<br>(14.824) | | 85.412<br />(14.824) | ||
|1024/975<br>(8192/8125) | | 1024/975<br />(8192/8125) | ||
|[[Leaves]] | | [[Leaves]] | ||
|} | |} | ||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||