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 [[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]].

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 ===

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=== Rank-2 temperaments===

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

|+Table of rank-2 temperaments by generator

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Periods per 8ve

! Periods per 8ve

! Generator*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! Temperament

|-

| 17

| 121\1700 (21\1700)

| 121\1700 (21\1700)

| 85.412 (14.824)

| 85.412 (14.824)

| 1024/975 (8192/8125)

| 1024/975 (8192/8125)

| [[Leaves]]

|}

<nowiki>*~~</nowiki>~~ [[Normal lists|~~octave~~-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if ~~it is~~ distinct

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1700}}
+{{ED intro}}
 == Theory ==
-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]].
+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 {{nowrap|323 &amp; 2023}} temperament [[leaves]] in the 17-limit on the [[patent val]].
 === Odd harmonics ===
@@ Line 16: / Line 16: @@
 === Rank-2 temperaments===
 {| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
 |-
-! Periods<br>per 8ve
+! Periods<br />per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio*
+! Associated<br />ratio*
 ! Temperament
 |-
 | 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]]
 |}
-<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct