600edo: Difference between revisions

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 {{Infobox ET}}
-The '''600 equal divisions of the octave''' ('''600edo'''), or the '''1200(-tone) equal temperament''' ('''600tet''', '''600et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 600 [[equal]] parts of exactly 2 [[cent]]s each. Because the step size is 2 cents, it is the smallest EDO where every possible interval is tuned within 1 cent of error.
+{{EDO intro|600}} Because the step size is 2 cents, it is the smallest edo where every possible interval is tuned within 1 cent of error.
 == Theory ==
+edo tempers out the [[tricot comma]], {{monzo| 39 -29 3 }}, and the mutt comma, {{monzo| -44 -3 21 }} in the 5-limit, 65625/65536, [[250047/250000]], 5250987/5242880, and 28824005/28697814 in the 7-limit, supporting septimal [[mutt]].
+=== Prime harmonics ===
 {{Harmonics in equal|600}}
-edo has the same mapping as [[1200edo]] in the 5-limit.
+=== Subsets and supersets ===
+Since 600 factors into 2<sup>3</sup> × 3 × 5<sup>2</sup>, it has subset edos {{EDOs| 2, 3, 4, 5, 6, 8, 10, 12, 15, 24, 25, 30, 40, 60, 100, 200, and 300 }}.
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+== Regular temperament properties ==
+=== Rank-2 temperaments ===
+{| class="wikitable center-all left-5"
+|+Table of rank-2 temperaments by generator
+! Periods<br>per 8ve
+! Generator<br>(Reduced)
+! Cents<br>(Reduced)
+! Associated<br>Ratio
+! Temperaments
+|-
+| 1
+| 283\600
+| 566.00
+| 81920/59049
+| [[Tricot]]
+|-
+| 3
+| 193\600<br>(7\600)
+| 386.00<br>(14.00)
+| 5/4<br>(126/125)
+| [[Mutt]]
+|-
+| 12
+| 249\600<br>(1\600)
+| 498.00<br>(2.00)
+| 4/3<br>(32805/32768)
+| [[Atomic]] (600e)
+|}