Pajara: Difference between revisions
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'''Pajara''' (pronounced /pəˈd͡ʒɑːrə/, with the J as in "jar") is a temperament with a half-octave period that represents both [[7/5]] and [[10/7]], so [[50/49]] is tempered out and it is in the [[jubilismic clan]]. The generator is in the neighborhood of | '''Pajara''' (pronounced /pəˈd͡ʒɑːrə/, with the J as in "jar") is a temperament with a half-octave period that represents both [[7/5]] and [[10/7]], so [[50/49]] is tempered out and it is in the [[jubilismic clan]]. The generator is in the neighborhood of 107-111 cents, so that period + generator represents [[3/2]]. Period minus 2 generators is 5/4, which, if you work it out, implies that [[2048/2025]] is tempered out, so pajara is also in the [[diaschismic family]]. In fact, it shares the same structure as 5-limit [[srutal]]. Finally, two 4/3s (or a 2/1 minus two generators) represents 7/4 as well as 16/9, so 64/63 is tempered out and pajara is in the [[Archytas clan]]. Tempering out any two of these commas (among others) produces the unique temperament pajara. | ||
Pajara loses some accuracy overall, due to 5/4 and 7/4 necessarily being separated by 600 cents. This means that [[49/48]] and [[25/24]] are tempered to the same interval. As such, pajara has fundamentally different categories, as a conventional semifourth (~250 cents) is now a neutral interval of some variety. As a result, a unique feature of pajara is a well-defined "minor" version of the [[4:5:6:7|harmonic tetrad]] (as the 7th harmonic is now a major interval), consisting of [1/1 6/5 3/2 12/7], as an essentially tempered alteration to [1/1 5/4 3/2 7/4] where both the third and the harmonic seventh are flattened by a chroma. | |||
The 10-note MOS and LsssLsssss almost-MOS are called the symmetric and pentachordal decatonic scales and were independently invented/discovered by [[Paul Erlich]] and [[Gene Ward Smith]]. They are often thought of as subsets of [[22edo]], without much loss of generality and accuracy. | The 10-note MOS and LsssLsssss almost-MOS are called the symmetric and pentachordal decatonic scales and were independently invented/discovered by [[Paul Erlich]] and [[Gene Ward Smith]]. They are often thought of as subsets of [[22edo]], without much loss of generality and accuracy. | ||
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<nowiki /> | <nowiki>*</nowiki> In 11-limit POTE tuning | ||
== Theoretical properties == | |||
Pajara is unique in that it introduces a well-defined "minor" analogue to the [[harmonic tetrad]], because | |||
== MOSes == | == MOSes == | ||