Buzzard: Difference between revisions

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Finally, it is possible to extend buzzard to the [[19-limit]], where it merges [[17/16]] and [[16/15]], tempering out [[256/255]] ({{S|16}}), and merges [[26/15]] and [[19/11]], tempering out [[286/285]].

Buzzard can be tuned to [[53edo]], [[58edo]], or [[111edo]]. [[Mos scale]]s of buzzard cluster strongly around [[5edo]], similar to those of [[rodan]]. Rather than directly using mos scales, which are either extremely imbalanced or overly large, an approach to buzzard may involve picking and choosing which intervals from each pentatonic category to keep in the scale.

Buzzard can be tuned to [[53edo]], [[58edo]], or [[111edo]]. [[Mos scale]]s of buzzard cluster strongly around [[5edo]], similar to those of [[rodan]] (see [[#As a detemperament of 5et]]). Rather than directly using mos scales, which are either extremely imbalanced or overly large, an approach to buzzard may involve picking and choosing which intervals from each pentatonic category to keep in the scale.

Alternative extensions of [[2.3.7 subgroup|2.3.7-]][[subgroup]] buzzard include [[subfourth]] (58 & 63) and [[lemongrass]] (63 & 68).

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<nowiki/>* In 13-limit CWE tuning

=== As a detemperament of 5et ===

[[File: Buzzard 5et Detempering.png|thumb|Buzzard as a 58-tone 5et detempering]]

Buzzard is naturally a [[detemperament]] of the [[5edo|5 equal temperament]]. The diagram on the right shows a 58-tone detempered scale, with a generator range of -28 to +29. 58 is the largest number of tones for a mos where intervals in the 5 categories do not overlap. Each category is divided into eleven or twelve qualities separated by 5 generator steps, which represent the generic comma step.

Notice also the little interval between the largest of a category and the smallest of the next, which represents the differences between 16/15 and 15/14, between 16/13 and 26/21, between 7/5 and 45/32, between 21/13 and 13/8, and between 28/15 and 15/8. It spans 53 generator steps, so it vanishes in 53edo, but is tuned to the same size as the comma step in 58edo. 111edo tunes it to one half the size of the comma step, which may be seen as a good compromise.

== Chords and harmony ==

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 Finally, it is possible to extend buzzard to the [[19-limit]], where it merges [[17/16]] and [[16/15]], tempering out [[256/255]] ({{S|16}}), and merges [[26/15]] and [[19/11]], tempering out [[286/285]].
-Buzzard can be tuned to [[53edo]], [[58edo]], or [[111edo]]. [[Mos scale]]s of buzzard cluster strongly around [[5edo]], similar to those of [[rodan]]. Rather than directly using mos scales, which are either extremely imbalanced or overly large, an approach to buzzard may involve picking and choosing which intervals from each pentatonic category to keep in the scale.
+Buzzard can be tuned to [[53edo]], [[58edo]], or [[111edo]]. [[Mos scale]]s of buzzard cluster strongly around [[5edo]], similar to those of [[rodan]] (see [[#As a detemperament of 5et]]). Rather than directly using mos scales, which are either extremely imbalanced or overly large, an approach to buzzard may involve picking and choosing which intervals from each pentatonic category to keep in the scale.
 Alternative extensions of [[2.3.7 subgroup|2.3.7-]][[subgroup]] buzzard include [[subfourth]] (58 & 63) and [[lemongrass]] (63 & 68).
@@ Line 192: / Line 192: @@
 |}
 <nowiki/>* In 13-limit CWE tuning
+=== As a detemperament of 5et ===
+[[File: Buzzard 5et Detempering.png|thumb|Buzzard as a 58-tone 5et detempering]]
+Buzzard is naturally a [[detemperament]] of the [[5edo|5 equal temperament]]. The diagram on the right shows a 58-tone detempered scale, with a generator range of -28 to +29. 58 is the largest number of tones for a mos where intervals in the 5 categories do not overlap. Each category is divided into eleven or twelve qualities separated by 5 generator steps, which represent the generic comma step.
+Notice also the little interval between the largest of a category and the smallest of the next, which represents the differences between 16/15 and 15/14, between 16/13 and 26/21, between 7/5 and 45/32, between 21/13 and 13/8, and between 28/15 and 15/8. It spans 53 generator steps, so it vanishes in 53edo, but is tuned to the same size as the comma step in 58edo. 111edo tunes it to one half the size of the comma step, which may be seen as a good compromise.
 == Chords and harmony ==