1665edo: Difference between revisions

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== Theory ==

1665edo is a very strong 5-limit (as well as 2.3.5.11 [[subgroup]]) tuning and it is [[consistent]] in the [[15-odd-limit]]. In the 5-limit, 1665edo is a tuning for the [[gross]] temperament.

1665edo provides the [[optimal patent val]] for the [[rhodium]] temperament in the 11-limit and also in the 13-limit. In addition, it provides the optimal patent val for [[~~dzelic~~]] temperament in the 13-limit.

1665edo provides the [[optimal patent val]] for the [[rhodium]] temperament in the 11-limit and also in the 13-limit. In addition, it provides the optimal patent val for [[ludidzelic]] temperament in the 13-limit.

The 1665cc val is a tuning for the [[roentgenium]] temperament, and the patent val tunes the unnamed 111 & 1665 temperament in the 13-limit which has a comma basis {6656/6655, 123201/123200, 250047/250000, 91182091/91125000}.

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== Regular temperament properties ==

=== Rank-2 temperaments ===

{{rank-2 ~~begin}}~~

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

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

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ratio*

! Temperaments

|-

| 1

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| 271.711 (12.252)

| 117/100 (?)

| [[~~Dzelic~~]]

| [[Ludidzelic]]

|-

| 45

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| 55/32 (?)

| [[Rhodium]]

~~{{rank-2 end}~~}

|}

~~{{orf}}~~

<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

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1665}}
+{{ED intro}}
 == Theory ==
 edo is a very strong 5-limit (as well as 2.3.5.11 [[subgroup]]) tuning and it is [[consistent]] in the [[15-odd-limit]]. In the 5-limit, 1665edo is a tuning for the [[gross]] temperament.
-edo provides the [[optimal patent val]] for the [[rhodium]] temperament in the 11-limit and also in the 13-limit. In addition, it provides the optimal patent val for [[dzelic]] temperament in the 13-limit.
+edo provides the [[optimal patent val]] for the [[rhodium]] temperament in the 11-limit and also in the 13-limit. In addition, it provides the optimal patent val for [[ludidzelic]] temperament in the 13-limit.
 The 1665cc val is a tuning for the [[roentgenium]] temperament, and the patent val tunes the unnamed 111 & 1665 temperament in the 13-limit which has a comma basis {6656/6655, 123201/123200, 250047/250000, 91182091/91125000}.
@@ Line 17: / Line 17: @@
 == Regular temperament properties ==
 === Rank-2 temperaments ===
-{{rank-2 begin}}
+{| class="wikitable center-all left-5"
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
+! Generator*
+! Cents*
+! Associated<br />ratio*
+! Temperaments
 |-
 | 1
@@ Line 29: / Line 36: @@
 | 271.711<br />(12.252)
 | 117/100<br />(?)
-| [[Dzelic]]
+| [[Ludidzelic]]
 |-
 | 45
@@ Line 36: / Line 43: @@
 | 55/32<br />(?)
 | [[Rhodium]]
-{{rank-2 end}}
+|}
-{{orf}}
+<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