Bohlen–Pierce scale: Difference between revisions
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<span style="display: block; text-align: right;">[[:de:Bohlen-Pierce Deutsch]]</span> | <span style="display: block; text-align: right;">[[:de:Bohlen-Pierce|Deutsch]]</span> | ||
The '''Bohlen-Pierce''' ('''BP''') scale is a [[nonoctave|nonoctave]] scale, a 13-part equal division of the perfect-twelfth ([[3/1|3/1]]) or [[Tritave|Tritave]] ('''13edt'''). Each step is about 146 ¢, making it a [[macrotonal|macrotonal]] scale. It is closely related to the rank two temperament [[Sensamagic_clan#Bohpier|bohpier]]. Bohlen-Pierce is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 [[Just_intonation_subgroups|subgroup]]. However, it (or at least 3.5.7-limit [[edt|13edt]]) can be extended to the 3.5.7.11/4 subgroup. This extension is controversial because of the presence of 2 in the denominator of 11/4, but the interval is present in the sense that 3^(12\13) provides an approximation to it. Chords of Bohlen-Pierce, from this extended perspective, may be found listed on the page [[Chords_of_bohpier|chords of bohpier]]. Bohlen-Pierce was discovered independently by [[Heinz_Bohlen|Heinz Bohlen]], [[John_Pierce|John Pierce]], [[Kees_van_Prooijen|Kees van Prooijen]], and perhaps others, usually noticed for its good approximation of odd-number just ratios 3:5, 5:7, 3:7, etc.; but not necessarily 4:11, 5:6, 6:7, etc. | The '''Bohlen-Pierce''' ('''BP''') scale is a [[nonoctave|nonoctave]] scale, a 13-part equal division of the perfect-twelfth ([[3/1|3/1]]) or [[Tritave|Tritave]] ('''13edt'''). Each step is about 146 ¢, making it a [[macrotonal|macrotonal]] scale. It is closely related to the rank two temperament [[Sensamagic_clan#Bohpier|bohpier]]. Bohlen-Pierce is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 [[Just_intonation_subgroups|subgroup]]. However, it (or at least 3.5.7-limit [[edt|13edt]]) can be extended to the 3.5.7.11/4 subgroup. This extension is controversial because of the presence of 2 in the denominator of 11/4, but the interval is present in the sense that 3^(12\13) provides an approximation to it. Chords of Bohlen-Pierce, from this extended perspective, may be found listed on the page [[Chords_of_bohpier|chords of bohpier]]. Bohlen-Pierce was discovered independently by [[Heinz_Bohlen|Heinz Bohlen]], [[John_Pierce|John Pierce]], [[Kees_van_Prooijen|Kees van Prooijen]], and perhaps others, usually noticed for its good approximation of odd-number just ratios 3:5, 5:7, 3:7, etc.; but not necessarily 4:11, 5:6, 6:7, etc. | ||