1178edo: Difference between revisions

Line 3:

== Theory ==

1178edo is a very strong 19-limit system, ~~and is a [[zeta edo|zeta peak, integral and gap edo]]. It is also~~ [[consistency|distinctly consistent]] through to the [[21-odd-limit]], and is the first edo past [[742edo|742]] with a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. A [[~~comma basis~~|~~basis~~]] ~~for its~~ 19-limit [[~~comma~~]]s ~~consists of~~ [[~~2500/2499~~]], [[3025/3024]], ~~3250~~/~~3249~~, ~~4200~~/~~4199~~, [[4225/4224]], [[~~4375~~/~~4374~~]], ~~and~~ [[4914/4913]]~~. It~~ [[~~support~~]]s and ~~provides a great tuning for~~ [[~~semihemienneadecal~~]].

1178edo is a very strong [[19-limit]] system, [[consistency|distinctly consistent]] through to the [[21-odd-limit]], and is the first edo past [[742edo|742]] with a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It is a [[zeta peak edo|zeta peak]], [[zeta integral edo|integral]] and [[zeta gap edo|gap edo]].

As an equal temperament, it tempers out {{monzo| -14 -19-19 }} ([[enneadeca]]) in the [[5-limit]], 4375/4374 ([[ragisma]]) and 703125/702464 ([[meter]]) in the [[7-limit]], so that it [[support]]s [[enneadecal]]. In the [[11-limit]] it tempers out [[3025/3024]], [[9801/9800]], and [[234375/234256]], supporting [[hemienneadecal]], and in the [[13-limit]] [[4225/4224]] and [[10648/10647]], supporting and providing a great tuning for [[semihemienneadecal]]. It further tempers out [[2500/2499]], [[4914/4913]] in the [[17-limit]]; [[3250/3249]], [[4200/4199]] in the 19-limit; and [[2025/2024]] among others in the [[23-limit]].

=== Prime harmonics ===

{{Harmonics in equal|1178|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 1178edo (continued)}}

=== Subsets and supersets ===

Since 1178 factors into {{~~factorization~~|~~1178~~}}, 1178edo is notable for containing both 19 and 31. Its subset edos are {{EDOs| 2, 19, 31, 38, 62, and 589 }}.

Since 1178 factors into primes as {{nowrap| 2 × 19 × 31 }}, 1178edo is notable for containing both 19 and 31. Its subset edos are {{EDOs| 2, 19, 31, 38, 62, and 589 }}.

== Regular temperament properties ==

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is a very strong 19-limit system, and is a [[zeta edo|zeta peak, integral and gap edo]]. It is also [[consistency|distinctly consistent]] through to the [[21-odd-limit]], and is the first edo past [[742edo|742]] with a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. A [[comma basis|basis]] for its 19-limit [[comma]]s consists of [[2500/2499]], [[3025/3024]], 3250/3249, 4200/4199, [[4225/4224]], [[4375/4374]], and [[4914/4913]]. It [[support]]s and provides a great tuning for [[semihemienneadecal]].
+edo is a very strong [[19-limit]] system, [[consistency|distinctly consistent]] through to the [[21-odd-limit]], and is the first edo past [[742edo|742]] with a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. It is a [[zeta peak edo|zeta peak]], [[zeta integral edo|integral]] and [[zeta gap edo|gap edo]].
+As an equal temperament, it tempers out {{monzo| -14 -19-19 }} ([[enneadeca]]) in the [[5-limit]], 4375/4374 ([[ragisma]]) and 703125/702464  ([[meter]]) in the [[7-limit]], so that it [[support]]s [[enneadecal]]. In the [[11-limit]] it tempers out [[3025/3024]], [[9801/9800]], and [[234375/234256]], supporting [[hemienneadecal]], and in the [[13-limit]] [[4225/4224]] and [[10648/10647]], supporting and providing a great tuning for [[semihemienneadecal]]. It further tempers out [[2500/2499]], [[4914/4913]] in the [[17-limit]]; [[3250/3249]], [[4200/4199]] in the 19-limit; and [[2025/2024]] among others in the [[23-limit]].
 === Prime harmonics ===
 {{Harmonics in equal|1178|columns=11}}
+{{Harmonics in equal|1178|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 1178edo (continued)}}
 === Subsets and supersets ===
-Since 1178 factors into {{factorization|1178}}, 1178edo is notable for containing both 19 and 31. Its subset edos are {{EDOs| 2, 19, 31, 38, 62, and 589 }}.
+Since 1178 factors into primes as {{nowrap| 2 × 19 × 31 }}, 1178edo is notable for containing both 19 and 31. Its subset edos are {{EDOs| 2, 19, 31, 38, 62, and 589 }}.
 == Regular temperament properties ==