Pajara: Difference between revisions

'''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.  

== MOSes ==

{{Main|2L 8s}}

The true MOS is called the "symmetric" decatonic scale, because it repeats exactly at the half-octave, so the symmetric scale starting from 7/5~10/7 is the same as the symmetric scale starting from 1/1. The near-MOS, LsssLsssss, in which only the 5-step interval violates the "no more than 2 intervals per class" rule, is called the "pentachordal" decatonic, because it consists of two identical "pentachords" plus a split 9/8~8/7 whole tone to complete the octave.

{{main|10L 2s}}

! ET<br />generator

! [[eigenmonzo|Eigenmonzo<br />(unchanged-interval]])

! decatonic<br />seventh (¢)

! comments