Buzzard: Difference between revisions
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{{Infobox | {{Infobox regtemp | ||
| Title = Buzzard | | Title = Buzzard | ||
| Subgroups = 2.3.7, 2.3.5.7, 2.3.5.7.11.13 | | Subgroups = 2.3.7, 2.3.5.7, 2.3.5.7.11.13 | ||
| Comma basis = [[65536/64827]] (2.3.7);<br>[[1728/1715]], [[5120/5103]] (7-limit);<br>[[176/175]], [[351/350]], [[540/539]], [[676/675]] (13-limit) | | Comma basis = [[65536/64827]] (2.3.7); <br>[[1728/1715]], [[5120/5103]] (7-limit);<br>[[176/175]], [[351/350]], [[540/539]], [[676/675]]<br>(13-limit) | ||
| Edo join 1 = 53 | Edo join 2 = 58 | | Edo join 1 = 53 | Edo join 2 = 58 | ||
| Mapping = 1; 4 21 -3 39 27 | | Mapping = 1; 4 21 -3 39 27 | ||
| | | Generators = 21/16 | ||
| | | Generators tuning = 475.7 | ||
| Optimization method = CWE | | Optimization method = CWE | ||
| MOS scales = 3L 2s | | MOS scales = 3L 2s | ||
| Line 12: | Line 12: | ||
| Pergen = | | Pergen = | ||
| Color name = | | Color name = | ||
| Odd limit 1 = | | Odd limit 1 = 2.3.7 9 | Mistuning 1 = 3.42 | Complexity 1 = 13 | ||
| Odd limit 2 = 15 | Mistuning 2 = 4.09 | Complexity 2 = 43 | | Odd limit 2 = 15 | Mistuning 2 = 4.09 | Complexity 2 = 43 | ||
}} | }} | ||
'''Buzzard''' is a [[regular temperament|temperament]] that splits a tempered [[3/1|perfect twelfth (3/1)]] into four [[generator]]s of [[21/16]] subfourths, [[tempering out]] the [[buzzardsma]] ([[ratio]]: 65536/64827). Two generators therefore give us a [[semitwelfth]], and five give us a sub-octave just short of the [[ | '''Buzzard''' is a [[regular temperament|temperament]] that splits a tempered [[3/1|perfect twelfth (3/1)]] into four [[generator]]s of [[21/16]] subfourths, [[tempering out]] the [[buzzardsma]] ([[ratio]]: 65536/64827). Two generators therefore give us a [[semitwelfth]], and five give us a sub-octave just short of the [[octave]] by a [[64/63|septimal comma]]. Bending the semitwelfth up by a septimal comma results in ~[[7/4]], and down results in ~[[12/7]], with the implication that the septimal diesis of [[49/48]] is equated to two septimal commas. In fact, buzzard slices the [[256/243|Pythagorean limma]] into four, one for 64/63, two for 49/48, and three for [[28/27]]. | ||
By finding [[harmonic]] [[5/1|5]] twenty-one generators away, buzzard is [[extension and restriction|extended]] to the full [[7-limit]], where it tempers out [[1728/1715]] and [[5120/5103]]. This equates the [[81/80|syntonic comma]] with the septimal comma and turns it into a generic comma step that can be used to bridge Pythagorean intervals with both classical and septimal intervals. Buzzard then extends naturally to the [[13-limit]] by identifying the semitwelfth as [[26/15]], and identifying the comma step as the [[100/99|ptolemisma]] (100/99, {{S|10}}). This means [[176/175]], [[351/350]], [[540/539]], and [[676/675]] all vanish. | By finding [[harmonic]] [[5/1|5]] twenty-one generators away, buzzard is [[extension and restriction|extended]] to the full [[7-limit]], where it tempers out [[1728/1715]] and [[5120/5103]]. This equates the [[81/80|syntonic comma]] with the septimal comma and turns it into a generic comma step that can be used to bridge Pythagorean intervals with both classical and septimal intervals. Buzzard then extends naturally to the [[13-limit]] by identifying the semitwelfth as [[26/15]], and identifying the comma step as the [[100/99|ptolemisma]] (100/99, {{S|10}}). This means [[176/175]], [[351/350]], [[540/539]], and [[676/675]] all vanish. | ||
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[[Category:Buzzardsmic clan]] | [[Category:Buzzardsmic clan]] | ||
[[Category:Orwellismic temperaments]] | [[Category:Orwellismic temperaments]] | ||
[[Category: | [[Category:Aberschismic temperaments]] | ||