147edo: Difference between revisions

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'''147edo''' is the [[equal division of the octave]] into 147 parts of 8.1633 [[cent]]s each. It [[tempering out|tempers out]] [[32805/32768]] in the [[5-limit]]; [[225/224]] and [[3125/3087]] in the [[7-limit]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for the 11-limit 41&106 temperament.

~~147~~ = [[~~3edo~~|3]] * [[~~7edo|~~7]]~~<span style="vertical~~-~~align: super~~;">2</~~span>~~, ~~with divisors~~ 3, 7, [[~~21edo~~|21]] and [[~~49edo~~|49]].

== Theory ==

147edo has a very accurate fifth. Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[32805/32768]] in the [[5-limit]], as well as [[225/224]] and [[3125/3087]] in the [[7-limit]], supporting [[garibaldi]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for 11-limit [[karadeniz]], the 41 & 106 temperament. Another val that can be used is the 147c val, with a sharp mapping of [[5/4]] (from [[49edo]]) instead of a slightly flat one, to go along with the sharp tendency of every other prime up to 17. This val tempers out [[126/125]] and [[1728/1715]] in the 7-limit, as well as [[176/175]], 243/242, [[441/440]], and [[540/539]] in the 11-limit, supporting [[myna]] in the 7- and 11-limits.

One particular subgroup that 147edo serves as a [[microtemperament]] in regard to, with errors of less than half a cent for most basic intervals, is 2.3.13.23, which is commonly associated with [[17edo]]. In fact, 147edo is close to the optimal tuning for the remarkable rank-2 temperament [[shoal]] (17 & 113), which tempers out [[3888/3887]] and [[12168/12167]], is generated by the interval of [[26/23]] (less than 0.01{{c}} off in 147edo), divides [[8/3]] into eight equal parts, and serves as a [[circulating temperament]] of 17edo. Additionally, it equates a stack of three [[256/243|pythagorean limmas]] with [[299/256]] and a stack of four with [[16/13]], tempering out 4294967296/4290323193 and the [[tridecapyth comma]].

=== Prime harmonics ===

=== Subsets and supersets ===

Since 147 = 3 × 7<sup>2</sup>, 147edo has subset edos {{EDOs| 3, 7, 21 and 49 }}.

[[441edo]], which triples it, provides strong corrections on the 5th and 7th harmonics and is a very notable 7-limit system.

== Scales ==

* [[Baldy6]]

* [[Baldy11]]

* [[Baldy17]]

* [[baldy6]]

* [[baldy11]]

* [[baldy17]]

~~[[Category:Theory]]~~

~~[[Category:Equal divisions of the octave]]~~

~~[[Category:147edo| ]] ~~

[[Category:Baldy]]

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-'''147edo''' is the [[equal division of the octave]] into 147 parts of 8.1633 [[cent]]s each. It [[tempering out|tempers out]] [[32805/32768]] in the [[5-limit]]; [[225/224]] and [[3125/3087]] in the [[7-limit]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for the 11-limit 41&amp;106 temperament.
+{{Infobox ET}}
+{{ED intro}}
-= [[3edo|3]] * [[7edo|7]]<span style="vertical-align: super;">2</span>, with divisors 3, 7, [[21edo|21]] and [[49edo|49]].
+== Theory ==
+edo has a very accurate fifth. Using the [[patent val]], the equal temperament [[tempering out|tempers out]] [[32805/32768]] in the [[5-limit]], as well as [[225/224]] and [[3125/3087]] in the [[7-limit]], supporting [[garibaldi]]; [[243/242]] in the [[11-limit]]; [[364/363]] in the [[13-limit]]; [[442/441]] and [[595/594]] in the [[17-limit]]. It is the [[optimal patent val]] for 11-limit [[karadeniz]], the 41 &amp; 106 temperament. Another val that can be used is the 147c val, with a sharp mapping of [[5/4]] (from [[49edo]]) instead of a slightly flat one, to go along with the sharp tendency of every other prime up to 17. This val tempers out [[126/125]] and [[1728/1715]] in the 7-limit, as well as [[176/175]], 243/242, [[441/440]], and [[540/539]] in the 11-limit, supporting [[myna]] in the 7- and 11-limits.
+One particular subgroup that 147edo serves as a [[microtemperament]] in regard to, with errors of less than half a cent for most basic intervals, is 2.3.13.23, which is commonly associated with [[17edo]]. In fact, 147edo is close to the optimal tuning for the remarkable rank-2 temperament [[shoal]] (17 & 113), which tempers out [[3888/3887]] and [[12168/12167]], is generated by the interval of [[26/23]] (less than 0.01{{c}} off in 147edo), divides [[8/3]] into eight equal parts, and serves as a [[circulating temperament]] of 17edo. Additionally, it equates a stack of three [[256/243|pythagorean limmas]] with [[299/256]] and a stack of four with [[16/13]], tempering out 4294967296/4290323193 and the [[tridecapyth comma]].
+=== Prime harmonics ===
+{{Harmonics in equal|147}}
+=== Subsets and supersets ===
+Since 147 = 3 × 7<sup>2</sup>, 147edo has subset edos {{EDOs| 3, 7, 21 and 49 }}.
+[[441edo]], which triples it, provides strong corrections on the 5th and 7th harmonics and is a very notable 7-limit system.
 == Scales ==
+* [[Baldy6]]
+* [[Baldy11]]
+* [[Baldy17]]
-* [[baldy6]]
-* [[baldy11]]
-* [[baldy17]]
-[[Category:Theory]]
-[[Category:Equal divisions of the octave]]
-[[Category:147edo| ]] <!-- main arcticle -->
 [[Category:Baldy]]