6th-octave temperaments: Difference between revisions

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{{~~Fractional~~-octave ~~navigation~~|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".

~~== Spoob (rank-4) ==~~

[[~~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~~.

[[6edo]] is called the whole tone scale, therefore 6th-octave temperaments include various temperaments where the period is an interval classified as a "tone".

Considered below is spoob.

== 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 generators: ~55/49, ~3, ~5, ~7

~~: mapping generators: ~55/49~~ = 1\6, ~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 }}

[[~~Support~~]]~~ing [[ET]]s~~: ~~{{EDOs|6, 12, 72, 78, 84, 126, 240, 342, 612, 1236, 1506, 1578, 1848, 1920, 2190, 3426}}~~

[[Badness]] (Sintel): 3.91

=== ~~2.5.7.11 spoob~~ ===

=== Spoob retraction ===

[[Subgroup]]: 2.5.7.11

[[Comma list]]: 27682574402/27680640625

: 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 }}

: ~~mapping generators: ~55/49 = 1\6, ~5, ~7~~

[[Badness]] (Sintel): 0.165

[[Category:6edo]]

@@ Line 1: / Line 1: @@
-{{Fractional-octave navigation|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".
+{{Technical data page}}
-== Spoob (rank-4) ==
+{{Infobox fractional-octave|6}}
-[[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.
+[[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 ==
+{{Main|Spoob}}
 [[Subgroup]]: 2.3.5.7.11
@@ Line 7: / Line 14: @@
 [[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
-: mapping generators: ~55/49 = 1\6, ~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 }}
-[[Support]]ing [[ET]]s: {{EDOs|6, 12, 72, 78, 84, 126, 240, 342, 612, 1236, 1506, 1578, 1848, 1920, 2190, 3426}}
+[[Badness]] (Sintel): 3.91
-=== 2.5.7.11 spoob ===
+=== Spoob retraction ===
 [[Subgroup]]: 2.5.7.11
 [[Comma list]]: 27682574402/27680640625
-{{mapping|legend=2|6 0 0 1|3=0 1 0 -1|4=0 0 1 2}}
+{{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 }}
-: mapping generators: ~55/49 = 1\6, ~5, ~7
+[[Badness]] (Sintel): 0.165
 {{Navbox fractional-octave}}
 [[Category:6edo]]