Blackville: Difference between revisions
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'''Blackville''' is a rank-3 [[ | '''Blackville''' is a rank-3 [[Bipentatonic scale|bipentatonic]] [[generator-offset]] and [[step-nested scale]] with step signature and mapping [[SNS ((2/1, 3/2)-5, 16/15)-10|2L 5m 3s = (10/9, 16/15, 135/128)]]. It may be generated as a generator offset scale by two chains of 3/2, offset by 16/15, or by the variable generator sequences GS(15/8, 8/5) or GS(16/15, 45/32); or as a step-nested scale by adding 16/15 above the bottom or below the top of every step of the Pythagorean pentatonic scale, which is generated by 3/2. | ||
Tempering ''L'' = ''s'' leads to [[Blackwood]][10], and tempering out ''s'' leads to [[Mavila]][7]. Since tempering ''s'' = ''m'' leads to the pentachordal decatonic of [[Diaschismic family|Srutal/diaschsimic]] temperament, we may name Blackville's modes through extrapolating the modes of the pentachordal decatonic. The first edo to represent Blackville without redundancy is [[17edo]] using the 17c [[val]], where in the standard major mode (smLmsmLmsm) it is 2131213121, i.e., 2L 5m 3s = (3, 1, 2). It may also be tuned without redundancy to [[19edo]] as 1232123212 with 2L 5m 3s = (3, 2, 1), [[26edo]] as 1343134313 with 2L 5m 3s = (4, 3, 1), [[27edo]] as 3242324232 with 2L 5m 3s = (4, 2, 3), [[29edo]] as 2343234323 with 2L 5m 3s = (4, 3, 2), [[31edo]] as 2353235323 with 2L 5m 3s = (5, 3, 2), and [[41edo]] as 3464346434 with 2L 5m 3s = (6, 4, 3), for example. | Tempering ''L'' = ''s'' leads to [[Blackwood]][10], and tempering out ''s'' leads to [[Mavila]][7]. Since tempering ''s'' = ''m'' leads to the pentachordal decatonic of [[Diaschismic family|Srutal/diaschsimic]] temperament, we may name Blackville's modes through extrapolating the modes of the pentachordal decatonic. The first edo to represent Blackville without redundancy is [[17edo]] using the 17c [[val]], where in the standard major mode (smLmsmLmsm) it is 2131213121, i.e., 2L 5m 3s = (3, 1, 2). It may also be tuned without redundancy to [[19edo]] as 1232123212 with 2L 5m 3s = (3, 2, 1), [[26edo]] as 1343134313 with 2L 5m 3s = (4, 3, 1), [[27edo]] as 3242324232 with 2L 5m 3s = (4, 2, 3), [[29edo]] as 2343234323 with 2L 5m 3s = (4, 3, 2), [[31edo]] as 2353235323 with 2L 5m 3s = (5, 3, 2), and [[41edo]] as 3464346434 with 2L 5m 3s = (6, 4, 3), for example. | ||
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[[Category:10-tone scales]] | [[Category:10-tone scales]] | ||
[[Category: | [[Category:GO scales]] | ||
[[Category:Step-nested scales]] | [[Category:Step-nested scales]] | ||