Buzzardsmic clan: Difference between revisions

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= Weak extensions =

== ~~Submajor~~ ==

== Demibuzzard ==

: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum#Submajor]].''

~~Submajor~~ may be described as the {{nowrap| 10 & 53 }} temperament. It is generated by a submajor third~~, hence the name~~; note that in the data below, the generator is the [[octave complement]], a supraminor sixth, since two of it minus an octave make buzzard's generator of ~21/16. The ploidacot for this temperament is epsilon-octacot.

Demibuzzard may be described as the {{nowrap| 10 & 53 }} temperament. It is generated by a submajor third; note that in the data below, the generator is the [[octave complement]], a supraminor sixth, since two of it minus an octave make buzzard's generator of ~21/16. The ploidacot for this temperament is epsilon-octacot.

~~Submajor~~ naturally comes about from a structure in edos like [[43edo|43-]], [[53edo|53-]], and [[63edo]] where two flattened ~[[13/8]] intervals reach the buzzard generator of ~21/16, two of which produce a semitritave that can here be equated to [[26/15]] – providing a mapping of 5 significantly less complex than the [[vulture]] mapping – and two of those finally reach [[3/1]].

This temperament naturally comes about from a structure in edos like [[43edo|43-]], [[53edo|53-]], and [[63edo]] where two flattened ~[[13/8]] intervals reach the buzzard generator of ~21/16, two of which produce a semitritave that can here be equated to [[26/15]] – providing a mapping of 5 significantly less complex than the [[vulture]] mapping – and two of those finally reach [[3/1]].

It diverges into two extensions for prime 11: ~~the canonical one~~ ({{nowrap| 53 & 63 }}) favoring sharp fifths, and interpental ({{nowrap| 43 & 53 }}), favoring flat fifths; the two mappings meet at [[53edo]].

It diverges into two extensions for prime 11: submajor ({{nowrap| 53 & 63 }}) favoring sharp fifths, and interpental ({{nowrap| 43 & 53 }}), favoring flat fifths; the two mappings meet at [[53edo]].

=== 7-limit ===

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Badness (Sintel): 0.847

=== ~~11-limit~~ ===

=== Submajor ===

Subgroup: 2.3.5.7.11

@@ Line 218: / Line 218: @@
 = Weak extensions =
-== Submajor ==
+== Demibuzzard ==
 : ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum#Submajor]].''
-Submajor may be described as the {{nowrap| 10 & 53 }} temperament. It is generated by a submajor third, hence the name; note that in the data below, the generator is the [[octave complement]], a supraminor sixth, since two of it minus an octave make buzzard's generator of ~21/16. The ploidacot for this temperament is epsilon-octacot.
+Demibuzzard may be described as the {{nowrap| 10 & 53 }} temperament. It is generated by a submajor third; note that in the data below, the generator is the [[octave complement]], a supraminor sixth, since two of it minus an octave make buzzard's generator of ~21/16. The ploidacot for this temperament is epsilon-octacot.
-Submajor naturally comes about from a structure in edos like [[43edo|43-]], [[53edo|53-]], and [[63edo]] where two flattened ~[[13/8]] intervals reach the buzzard generator of ~21/16, two of which produce a semitritave that can here be equated to [[26/15]] – providing a mapping of 5 significantly less complex than the [[vulture]] mapping – and two of those finally reach [[3/1]].
+This temperament naturally comes about from a structure in edos like [[43edo|43-]], [[53edo|53-]], and [[63edo]] where two flattened ~[[13/8]] intervals reach the buzzard generator of ~21/16, two of which produce a semitritave that can here be equated to [[26/15]] – providing a mapping of 5 significantly less complex than the [[vulture]] mapping – and two of those finally reach [[3/1]].
-It diverges into two extensions for prime 11: the canonical one ({{nowrap| 53 & 63 }}) favoring sharp fifths, and interpental ({{nowrap| 43 & 53 }}), favoring flat fifths; the two mappings meet at [[53edo]].
+It diverges into two extensions for prime 11: submajor ({{nowrap| 53 & 63 }}) favoring sharp fifths, and interpental ({{nowrap| 43 & 53 }}), favoring flat fifths; the two mappings meet at [[53edo]].
 === 7-limit ===
@@ Line 261: / Line 261: @@
 Badness (Sintel): 0.847
-=== 11-limit ===
+=== Submajor ===
 Subgroup: 2.3.5.7.11