User:Unque/Buzzard: Difference between revisions

Line 9:

=== Canonical Buzzard ===

The interval at five generators up falls short of the octave by a small interval (namely [[64/63]], the septimal comma), which in Buzzard functions as an [[aberrisma]]. In 2.3.7 Buzzard, this aberrisma can be used to inflect between 3-limit and 7-limit consonances, such as between 21/16 and 4/3, or between 9/8 and 8/7. The canonical extension to include prime 5 is created by using this ~~amerrisma~~ as an all-purpose inflection, allowing 5-limit consonances to be accessed by inflecting in the opposite direction; for instance, 9/8 can be inflected upwards to reach 8/7, or downwards to reach 10/9. To do this, it tempers out [[5120/5103]], equating 64/63 with [[81/80]].

The interval at five generators up falls short of the octave by a small interval (namely [[64/63]], the septimal comma), which in Buzzard functions as an [[aberrisma]]. In 2.3.7 Buzzard, this aberrisma can be used to inflect between 3-limit and 7-limit consonances, such as between 21/16 and 4/3, or between 9/8 and 8/7. The canonical extension to include prime 5 is created by using this aberrisma as an all-purpose inflection, allowing 5-limit consonances to be accessed by inflecting in the opposite direction; for instance, 9/8 can be inflected upwards to reach 8/7, or downwards to reach 10/9. To do this, it tempers out [[5120/5103]], equating 64/63 with [[81/80]].

The canonical extension to 11-limit further equates this aberrisma with [[100/99]] (thus tempering out [[176/175]]), allowing 11-limit consonances to be reached via similar inflections; for instance, 11/9 can be found as an inflection downwards from 5/4 (or equivalently, two inflections below 81/64, or three below 9/7), and [[15/11]] can be found as an inflection upwards from 27/20 (or two inflections above 4/3, or three above 21/16).

@@ Line 9: / Line 9: @@
 === Canonical Buzzard ===
-The interval at five generators up falls short of the octave by a small interval (namely [[64/63]], the septimal comma), which in Buzzard functions as an [[aberrisma]].  In 2.3.7 Buzzard, this aberrisma can be used to inflect between 3-limit and 7-limit consonances, such as between 21/16 and 4/3, or between 9/8 and 8/7.  The canonical extension to include prime 5 is created by using this amerrisma as an all-purpose inflection, allowing 5-limit consonances to be accessed by inflecting in the opposite direction; for instance, 9/8 can be inflected upwards to reach 8/7, or downwards to reach 10/9.  To do this, it tempers out [[5120/5103]], equating 64/63 with [[81/80]].
+The interval at five generators up falls short of the octave by a small interval (namely [[64/63]], the septimal comma), which in Buzzard functions as an [[aberrisma]].  In 2.3.7 Buzzard, this aberrisma can be used to inflect between 3-limit and 7-limit consonances, such as between 21/16 and 4/3, or between 9/8 and 8/7.  The canonical extension to include prime 5 is created by using this aberrisma as an all-purpose inflection, allowing 5-limit consonances to be accessed by inflecting in the opposite direction; for instance, 9/8 can be inflected upwards to reach 8/7, or downwards to reach 10/9.  To do this, it tempers out [[5120/5103]], equating 64/63 with [[81/80]].
 The canonical extension to 11-limit further equates this aberrisma with [[100/99]] (thus tempering out [[176/175]]), allowing 11-limit consonances to be reached via similar inflections; for instance, 11/9 can be found as an inflection downwards from 5/4 (or equivalently, two inflections below 81/64, or three below 9/7), and [[15/11]] can be found as an inflection upwards from 27/20 (or two inflections above 4/3, or three above 21/16).