Pajara: Difference between revisions

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Pajara has fairly low 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, and allows for a simple alteration to produce a "minor" harmonic chord with 6/5 and 12/7 by flattening the third and seventh the same amount.

Pajara has [[mos scale]]s of 10, 12, and 22 notes. The 10-note mos, Pajara[10] is notable for sharing a number of desirable properties with [[5L 2s|diatonic]], while having fundamentally different categories; a [[semifourth]] (~250 cents) is between the two qualities of the decatonic 2-step (so that it is neutral rather than interordinal with respect to that scale) for example. This mos and the LsssLsssss [[modmos]] 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.

Pajara has [[mos scale]]s of 10, 12, and 22 notes. The 10-note mos, Pajara[10] is notable for sharing a number of desirable properties with [[5L 2s|diatonic]], while having fundamentally different categories; a [[semifourth]] (~250 cents) is between the two qualities of the decatonic 2-step (so that it is neutral rather than interordinal with respect to that scale) for example, and 7/4 is intuitively thought of as a major interval, rather than minor. This mos and the LsssLsssss [[modmos]] 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.

See [[Diaschismic family #Pajara]] for technical data. See [[Pajara extensions]] for a discussion on the 11-limit extensions.

@@ Line 9: / Line 9: @@
 Pajara has fairly low 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, and allows for a simple alteration to produce a "minor" harmonic chord with 6/5 and 12/7 by flattening the third and seventh the same amount.
-Pajara has [[mos scale]]s of 10, 12, and 22 notes. The 10-note mos, Pajara[10] is notable for sharing a number of desirable properties with [[5L 2s|diatonic]], while having fundamentally different categories; a  [[semifourth]] (~250 cents) is between the two qualities of the decatonic 2-step (so that it is neutral rather than interordinal with respect to that scale) for example. This mos and the LsssLsssss [[modmos]] 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.
+Pajara has [[mos scale]]s of 10, 12, and 22 notes. The 10-note mos, Pajara[10] is notable for sharing a number of desirable properties with [[5L 2s|diatonic]], while having fundamentally different categories; a  [[semifourth]] (~250 cents) is between the two qualities of the decatonic 2-step (so that it is neutral rather than interordinal with respect to that scale) for example, and 7/4 is intuitively thought of as a major interval, rather than minor. This mos and the LsssLsssss [[modmos]] 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.
 See [[Diaschismic family #Pajara]] for technical data. See [[Pajara extensions]] for a discussion on the 11-limit extensions.