150edo: Difference between revisions

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-'''150edo''' is the [[equal division of the octave]] into 150 equal steps exactly 8 cents each. This means eleven such steps are 88 cents, relating 150edo to the [[88cET|88cET]] nonoctave tuning. It tempers out 245/243, 4000/3969 and 2401/2400 in the 7-limit, 896/891, 385/384 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675 and 1575/1573 in the 134-limit. It is [[contorted]] in the 5-limit, tempering out the same commas as [[75edo|75edo]], including 20000/19683 and 2109375/2097152. It provides a good tuning for [[Tetracot_family#Octacot|Tetracot family]], for which 88 cents provides a generator.
+{{Infobox ET}}
-[[Category:Equal divisions of the octave]]
+{{ED intro}}
+== Theory ==
+edo is [[contorted]] in the 5-limit, [[tempering out]] the same commas as [[75edo]], including [[20000/19683]] and [[2109375/2097152]]. However, every 11th step of 150edo is equal to the [[88cET]] nonoctave tuning, which is also represented as [[octacot]] through a regular temperament theory perspective. It provides a good tuning for octacot, for which 88{{c}} provides a generator.
+The equal temperament tempers out [[245/243]], [[2401/2400]], and [[4000/3969]] in the 7-limit, [[385/384]], [[896/891]], and [[1375/1372]] in the 11-limit, and [[352/351]], [[364/363]], [[676/675]] and [[1575/1573]] in the 13-limit.
+=== Odd harmonics ===
+{{Harmonics in equal|150|columns=10}}
+=== Subsets and supersets ===
+Since 150 factors into 2 × 3 × 5<sup>2</sup>, 150edo has subset edos {{EDOs| 2, 3, 5, 6, 10, 15, 25, 30, 50, and 75 }}.
+== Regular temperament properties ==
+=== Rank-2 temperaments ===
+{| class="wikitable center-all left-5"
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
+! Generator*
+! Cents*
+! Associated<br />ratio*
+! Temperaments
+|-
+| 1
+| 11\150
+| 88.00
+| 21/20
+| [[Octacot]] (150e) / [[october]] (150)
+|-
+| 1
+| 29\150
+| 232.00
+| 8/7
+| [[Quadrawell]]
+|-
+| 10
+| 31\150<br />(1\150)
+| 248.00<br />(8.00)
+| 15/13<br />(176/175)
+| [[Decoid]] (150e)
+|}
+<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct