Wikispaces Classroom is now free, social, and easier than ever. Try it today.

Contributions to http://xenharmonic.wikispaces.com/ are licensed under a Creative Commons Attribution Share-Alike Non-Commercial 3.0 License.

Portions not contributed by visitors are Copyright 2016 Tangient LLC

TES: The largest network of teachers in the world

Portions not contributed by visitors are Copyright 2016 Tangient LLC

TES: The largest network of teachers in the world

Loading...

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 105-110 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. 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.

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.

## Interval chains

There are two different mappings of the 11 limit. One is just called "pajara" and is slightly more complex but suffers almost no loss of accuracy compared to the 7 limit. The other, called "pajarous" to avoid confusion, loses some accuracy and there's little reason to use it unless you're using 22edo, which is the intersection of both systems.## Basic 7-limit pajara

## 11-limit pajara

## Pajarous

## MOSes

## 10-note (proper)

See 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.

## 12-note (proper)

See 10L 2s.## Spectrum of Pajara Tunings by Eigenmonzos

## References

## Music

12-22hexachordal Dirge and12-22hexachordal Sonatina both by Joel Grant Taylor, in the hexachordal dodecatonic MODMOS.

Smoke Filled Bar by Chris Vaisvil, also in 12-22h.