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. 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.

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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=== 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 ==

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! Generator*

! Cents*

! Associated<br>Ratio

! Associated<br>Ratio*

! Temperaments

|-

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 == 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. 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.
 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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 === Odd harmonics ===
 {{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 ==
@@ Line 16: / Line 19: @@
 ! Generator*
 ! Cents*
-! Associated<br>Ratio
+! Associated<br>Ratio*
 ! Temperaments
 |-