6th-octave temperaments: Difference between revisions

VisualWikitext

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+{{Technical data page}}
+{{Infobox fractional-octave|6}}
+[[6edo]] is called the whole tone scale, therefore 6th-octave temperaments include various temperaments where the period is an interval classified as a "tone".
+Temperaments discussed elsewhere include [[Augmented family #Hexe|hexe]], [[Misty family #Semimist|semimist]], [[Schismatic family #Semiterm|semiterm]], [[Garischismic clan #Sextile|sextile]], and [[Stearnsmic clan #Stearnscape|stearnscape]].
+Considered below is spoob.
 == Spoob ==
-[[Spoob]] temperament is named after an emoji on Xenharmonic Discord and is defined by associating the werckismic tone [[55/49]] with 1/6th of the octave.
+{{Main|Spoob}}
 [[Subgroup]]: 2.3.5.7.11
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 [[Comma list]]: 27682574402/27680640625
-{{mapping|legend=1|6 0 0 0 1|0 1 0 0 0|0 0 1 0 -1|0 0 0 1 2}}
+{{mapping|legend=1| 6 0 0 0 1 | 0 1 0 0 0 | 0 0 1 0 -1 | 0 0 0 1 2 }}
+: mapping generators: ~55/49, ~3, ~5, ~7
+{{Optimal ET sequence|legend=1| 72, 198, 270, 342, 612, 954, 1236, 1506, 1578, 1848, 3426, 4038, 5616, 6390, 6660, 7002, 7626, 7896, 8238, 8850, 9744, 9816, 10086, 10428, 11664, 11934, 12276, 36216, 48492, 60768, 84978, 97254, 98832d }}
+[[Badness]] (Sintel): 3.91
+=== Spoob retraction ===
+[[Subgroup]]: 2.5.7.11
+[[Comma list]]: 27682574402/27680640625
+{{Mapping|legend=2| 6 0 0 1 | 0 1 0 -1 | 0 0 1 2 }}
+: mapping generators: ~55/49, ~5, ~7
+{{Optimal ET sequence|legend=1| 72, 150, 186, 192, 198, 264, 270, 342, 348, 612, 618, 960, 1578, 7542, 8160, 9120, 10698, 12276, 13854, 23592, 25170, 26748, 28326, 40602, 42180, 67350, 68928 }}
+[[Badness]] (Sintel): 0.165
-: mapping generators: ~55/49 = 1\6, ~3, ~5, ~7
+{{Navbox fractional-octave}}
-[[Support]]ing [[ET]]s: {{EDOs|6, 12, 72, 78, 84, 126, 240, 342, 612, 1236, 1506, 1578, 1848, 1920, 2190, 3426}}
+[[Category:6edo]]