Pajara: Difference between revisions

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Interval chains: reorder info
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2.3.5.7.11.17 in infobox
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{{Infobox regtemp
{{Infobox regtemp
| Title = Pajara
| Title = Pajara
| Subgroups = 2.3.5.7, 2.3.5.7.11
| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.17
| Comma basis = [[50/49]], [[64/63]] (7-limit); <br>[[50/49]], [[64/63]], [[99/98]] (11-limit)
| Comma basis = [[50/49]], [[64/63]] (7-limit);<br>[[50/49]], [[64/63]], [[99/98]] (11-limit);<br>[[50/49]], [[64/63]], [[85/84]], [[99/98]]<br>(2.3.5.7.11.17)
| Edo join 1 = 12 | Edo join 2 = 22
| Edo join 1 = 12 | Edo join 2 = 22
| Mapping = 2; 1 -2 -2 -6
| Mapping = 2; 1 -2 -2 -6 1
| Generators = 3/2 | Generators tuning = 707.2 | Optimization method = CWE
| Generators = 3/2 | Generators tuning = 707.4 | Optimization method = CWE
| MOS scales = [[2L 8s]], [[10L 2s]], [[12L 10s]]
| MOS scales = [[2L 8s]], [[10L 2s]], [[12L 10s]]
| Pergen = (P8/2, P5)
| Pergen = (P8/2, P5)
| Odd limit 1 = 9 | Mistuning 1 = 17.5 | Complexity 1 = 10
| Odd limit 1 = 9 | Mistuning 1 = 17.5 | Complexity 1 = 10
| Odd limit 2 = 11-limit 15 | Mistuning 2 = 17.5 | Complexity 2 = 22
| Odd limit 2 = 2.3.5.7.11.17 17 | Mistuning 2 = 17.5 | Complexity 2 = 22
}}
}}
'''Pajara''' (pronounced /pəˈd͡ʒɑːrə/, with the J as in "jar") is a [[regular temperament|temperament]] with a half-octave [[period]] that represents both [[7/5]] and [[10/7]], so [[50/49]] is [[tempering out|tempered out]] and it is in the [[jubilismic clan]]. The [[generator]] is a [[3/2|perfect fifth]] in the neighborhood of 707–711 [[cent]]s, or that minus a half-octave period, which is a semitone representing [[15/14]] and [[16/15]]. One period minus 2 such semitones 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 [[diaschismic]]. Finally, two 4/3's (or an octave minus two semitones) 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''' (pronounced /pəˈd͡ʒɑːrə/, with the J as in "jar") is a [[regular temperament|temperament]] with a half-octave [[period]] that represents both [[7/5]] and [[10/7]], so [[50/49]] is [[tempering out|tempered out]] and it is in the [[jubilismic clan]]. The [[generator]] is a [[3/2|perfect fifth]] in the neighborhood of 707–711 [[cent]]s, or that minus a half-octave period, which is a semitone representing [[15/14]] and [[16/15]]. One period minus 2 such semitones 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 [[diaschismic]]. Finally, two 4/3's (or an octave minus two semitones) 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.