No-fives subgroup temperaments: Difference between revisions

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=== Boethian ===

Boethian is a diatonic-based temperament that makes [[513/512]] vanish, so that the major third (C-E) is ~[[24/19]] and the minor third (C-E♭) is ~[[19/16]]. Although "undevicesimal schisma" is one of the names of the comma, it functions as a 2.3.19 subgroup analogue of [[meantone]] rather than [[Schismatic family|schismic temperament]], since the major third is at +4 fifths (rather than -8 fifths) from the root note, while the minor third is at -3 fifths (rather than +9 fifths). That said, the equal temperaments in the tuning spectrum up to 1/2-comma (flattened) boethian temperament (very close to [[12edo]]) are included in the schismic tuning spectrum in the 5-limit, and thus Boethian temperament does intersect with schismic in the prime-5 infill extension of Boethian temperament.

Boethian is a diatonic-based temperament that makes [[513/512]] vanish, so that the major third (C-E) is ~[[24/19]] and the minor third (C-E♭) is ~[[19/16]]. Although "undevicesimal schisma" is one of the names of the comma, it functions as a 2.3.19 subgroup analogue of [[meantone]] rather than [[Schismatic family|schismic temperament]], since the major third is at +4 fifths (rather than -8 fifths) from the root note, while the minor third is at -3 fifths (rather than +9 fifths). That said, the equal temperaments in the tuning spectrum up to 1/2-comma (flattened) boethian temperament (very close to [[12edo]]) are included in the schismic tuning spectrum in the 5-limit, and thus Boethian temperament does intersect with schismic in the prime-5 infill extension of Boethian temperament. Additionally tempering out the schisma in the 2.3.5.19 subgroup leads to the [[nestoria]] temperament, which also tempers out [[361/360]], the difference between 19/18 and 20/19 or between 19/15 and 24/19.

[[Subgroup]]: 2.3.19

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 === Boethian ===
-Boethian is a diatonic-based temperament that makes [[513/512]] vanish, so that the major third (C-E) is ~[[24/19]] and the minor third (C-E♭) is ~[[19/16]]. Although "undevicesimal schisma" is one of the names of the comma, it functions as a 2.3.19 subgroup analogue of [[meantone]] rather than [[Schismatic family|schismic temperament]], since the major third is at +4 fifths (rather than -8 fifths) from the root note, while the minor third is at -3 fifths (rather than +9 fifths). That said, the equal temperaments in the tuning spectrum up to 1/2-comma (flattened) boethian temperament (very close to [[12edo]]) are included in the schismic tuning spectrum in the 5-limit, and thus Boethian temperament does intersect with schismic in the prime-5 infill extension of Boethian temperament.
+Boethian is a diatonic-based temperament that makes [[513/512]] vanish, so that the major third (C-E) is ~[[24/19]] and the minor third (C-E♭) is ~[[19/16]]. Although "undevicesimal schisma" is one of the names of the comma, it functions as a 2.3.19 subgroup analogue of [[meantone]] rather than [[Schismatic family|schismic temperament]], since the major third is at +4 fifths (rather than -8 fifths) from the root note, while the minor third is at -3 fifths (rather than +9 fifths). That said, the equal temperaments in the tuning spectrum up to 1/2-comma (flattened) boethian temperament (very close to [[12edo]]) are included in the schismic tuning spectrum in the 5-limit, and thus Boethian temperament does intersect with schismic in the prime-5 infill extension of Boethian temperament. Additionally tempering out the schisma in the 2.3.5.19 subgroup leads to the [[nestoria]] temperament, which also tempers out [[361/360]], the difference between 19/18 and 20/19 or between 19/15 and 24/19.
 [[Subgroup]]: 2.3.19