1944edo: Difference between revisions

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== Theory ==

1944edo is [[consistent]] in the [[5-odd-limit]] to which it provides good approximation, and a near-perfect [[15/8]], but it is only consistent that far since [[harmonic]] [[7/1|7]] is about halfway between its steps. In the 5-limit, it [[tempering out|tempers out]] the [[luna comma]], {{monzo| 38 -2 -15 }}. In the 1944d [[val]] in the 7-limit, it is a [[landscape]] system, tempering out [[250047/250000]], and as a consequence it tunes the 24th-octave [[chromium]] temperament.

1944edo is [[consistent]] in the [[5-odd-limit]] to which it provides good approximation, and a near-perfect [[15/8]], but it is only consistent that far since [[harmonic]] [[7/1|7]] is about halfway between its steps. In the 5-limit, it [[tempering out|tempers out]] the [[luna comma]], {{monzo| 38 -2 -15 }}. In the 1944d [[val]] in the 7-limit, it is a [[landscape]] system tempering out [[250047/250000]], and as a consequence it tunes the 24th-octave [[chromium]] temperament, providing a tuning close to [[POTE]] tuning.

In higher limits, 1944edo is a tuning for the [[jamala]] temperament in the 2.5.11.13.19.41.47 [[subgroup]], for which 1944edo provides good approximation (except for the 13th harmonic). Overall, the best subgroup for 1944edo is 2.3.5.11.17.19.29.31.41.47.

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=== Subsets and supersets ===

Since 1944 factors into {{factorization|1944}}, 1944edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, and 972 }}.

== Regular temperament properties ==

=== Rank-2 temperaments ===

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

! Periods per 8ve

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

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! Temperaments

|-

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|-

| 24

| 944\1944 (53\1944)

| 944\1944 (53\1944)

| 582.716 (32.716)

| 582.716 (32.716)

| 7/5 (?)

| 7/5 (?)

| [[Chromium]] (1944d)

|-

| 72

| 892\1944 (1\1944)

| 892\1944 (1\1944)

| 550.617 (0.617)

| 550.617 (0.617)

| 73205/53248 (?)

| 73205/53248 (?)

| [[Jamala]]

|}

<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|1944}}
+{{ED intro}}
 == Theory ==
-edo is [[consistent]] in the [[5-odd-limit]] to which it provides good approximation, and a near-perfect [[15/8]], but it is only consistent that far since [[harmonic]] [[7/1|7]] is about halfway between its steps. In the 5-limit, it [[tempering out|tempers out]] the [[luna comma]], {{monzo| 38 -2 -15 }}. In the 1944d [[val]] in the 7-limit, it is a [[landscape]] system, tempering out [[250047/250000]], and as a consequence it tunes the 24th-octave [[chromium]] temperament.
+edo is [[consistent]] in the [[5-odd-limit]] to which it provides good approximation, and a near-perfect [[15/8]], but it is only consistent that far since [[harmonic]] [[7/1|7]] is about halfway between its steps. In the 5-limit, it [[tempering out|tempers out]] the [[luna comma]], {{monzo| 38 -2 -15 }}. In the 1944d [[val]] in the 7-limit, it is a [[landscape]] system tempering out [[250047/250000]], and as a consequence it tunes the 24th-octave [[chromium]] temperament, providing a tuning close to [[POTE]] tuning.
 In higher limits, 1944edo is a tuning for the [[jamala]] temperament in the 2.5.11.13.19.41.47 [[subgroup]], for which 1944edo provides good approximation (except for the 13th harmonic). Overall, the best subgroup for 1944edo is 2.3.5.11.17.19.29.31.41.47.
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
 Since 1944 factors into {{factorization|1944}}, 1944edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, and 972 }}.
 == Regular temperament properties ==
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-! Periods<br>per 8ve
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 29: / Line 31: @@
 |-
 | 24
-| 944\1944<br>(53\1944)
+| 944\1944<br />(53\1944)
-| 582.716<br>(32.716)
+| 582.716<br />(32.716)
-| 7/5<br>(?)
+| 7/5<br />(?)
 | [[Chromium]] (1944d)
 |-
 | 72
-| 892\1944<br>(1\1944)
+| 892\1944<br />(1\1944)
-| 550.617<br>(0.617)
+| 550.617<br />(0.617)
-| 73205/53248<br>(?)
+| 73205/53248<br />(?)
 | [[Jamala]]
 |}
-<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