1700edo: Difference between revisions

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== Theory ==

1700edo 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.

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.

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

=== Odd harmonics ===

== Regular temperament properties ==

=== Rank-2 temperaments===

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

!Periods

! Periods per 8ve

per 8ve

! Generator*

!Generator

! Cents*

~~(Reduced)~~

! Associated Ratio

!Cents

! Temperament

~~(Reduced)~~

!Associated

Ratio

!Temperament

|-

|17

| 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]]

| [[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

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{EDO intro|1700}}
 == 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 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.
 One step of 1700edo is the [[relative cent]] for [[17edo]]. It has been named '''iota''' by [[Margo Schulter]] and [[George Secor]].
 === Odd harmonics ===
-{{harmonics in equal|1700}}
+{{Harmonics in equal|1700}}
 == Regular temperament properties ==
 === Rank-2 temperaments===
 {| class="wikitable center-all left-5"
-!Periods
+! Periods<br>per 8ve
-per 8ve
+! Generator*
-!Generator
+! Cents*
-(Reduced)
+! Associated<br>Ratio
-!Cents
+! Temperament
-(Reduced)
-!Associated
-Ratio
-!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>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct