1944edo: Difference between revisions

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== Theory ==

1944edo is consistent in the 5-limit to which it provides good approximation, and a near-perfect [[15/8]], but it is only consistent that far. In the 5-limit, it ~~does temper~~ 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) ~~and which is named after an [[wikipedia:Jamala|artist]] who performed a [[wikipedia:1944 (song)|song about the same year as the edo number]]~~. Overall, the best subgroup for 1944edo is 2.3.5.11.17.19.29.31.41.47.

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.

=== Odd harmonics ===

=== 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

!Generator~~ (reduced)~~

|-

!Cents ~~(reduced)~~

! Periods per 8ve

~~!Associated~~ ratio

! Generator*

!Temperaments

! Cents*

! Associated ratio*

! Temperaments

|-

|1

| 1

|313\1944

| 313\1944

|193.210

| 193.210

|262144/234375

| 262144/234375

|[[Luna]] (5-limit)

| [[Luna]] (5-limit)

|-

|24

| 24

|944\1944 (53\1944)

| 944\1944 (53\1944)

|582.716 (32.716)

| 582.716 (32.716)

|7/5 (?)

| 7/5 (?)

|[[Chromium]] (1944d)

| [[Chromium]] (1944d)

|-

|72

| 72

|892\1944 (1\1944)

| 892\1944 (1\1944)

|550.617 (0.617)

| 550.617 (0.617)

|73205/53248 (?)

| 73205/53248 (?)

|[[Jamala]]

| [[Jamala]]

|}

<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-limit to which it provides good approximation, and a near-perfect [[15/8]], but it is only consistent that far. In the 5-limit, it does temper 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) and which is named after an [[wikipedia:Jamala|artist]] who performed a [[wikipedia:1944 (song)|song about the same year as the edo number]]. Overall, the best subgroup for 1944edo is 2.3.5.11.17.19.29.31.41.47.
+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.
 === Odd harmonics ===
-{{harmonics in equal|1944}}
+{{Harmonics in equal|1944}}
+=== 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
-!Generator<br>(reduced)
+|-
-!Cents<br>(reduced)
+! Periods<br />per 8ve
-!Associated ratio
+! Generator*
-!Temperaments
+! Cents*
+! Associated<br />ratio*
+! Temperaments
 |-
-|1
+| 1
-|313\1944
+| 313\1944
-|193.210
+| 193.210
-|262144/234375
+| 262144/234375
-|[[Luna]] (5-limit)
+| [[Luna]] (5-limit)
 |-
-|24
+| 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)
+| [[Chromium]] (1944d)
 |-
-|72
+| 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]]
+| [[Jamala]]
 |}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct