243/242: Difference between revisions
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[[Tempering out]] this comma in the full 11-limit leads to the [[rastmic]] rank-4 temperament, or in the 2.3.11 subgroup, the [[neutral (temperament)|neutral]] temperament, enabling [[rastmic chords]] in either case. | [[Tempering out]] this comma in the full 11-limit leads to the [[rastmic]] rank-4 temperament, or in the 2.3.11 subgroup, the [[neutral (temperament)|neutral]] temperament, enabling [[rastmic chords]] in either case. | ||
See [[Rastmic clan]] for the clan of rank-2 temperaments where it is tempered out. See [[ | See [[Rastmic clan]] for the clan of rank-2 temperaments where it is tempered out. See [[Rastmic rank-3 clan]] for the clan of rank-3 temperaments where it is tempered out. | ||
== See also == | == See also == | ||
Latest revision as of 13:56, 27 August 2025
| Interval information |
neutral third comma
Lulu comma
reduced
243/242, the rastma or the neutral third comma, is a small 11-limit (also 2.3.11-subgroup) comma with a value of roughly 7.1 cents. It is significant in just intonation as the amount by which a stack of two 11/9 neutral thirds (that is an Alpharabian narrow fifth 121/81) fall short of 3/2 just perfect fifth as well as the amount by which a stack of two 27/22 neutral thirds (that is an Alpharabian wide fifth 729/484) exceeds a 3/2 just perfect fifth, the amount by which a stack of two 33/32 quartertones falls short of an apotome (2187/2048) as well as the difference between 11/9 and 27/22, and the difference between 45/44 and 55/54. The last makes the theory where the rastma serves as the subchroma that separates greater and lesser 11-limit chromas – a theory that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.
Temperaments
Tempering out this comma in the full 11-limit leads to the rastmic rank-4 temperament, or in the 2.3.11 subgroup, the neutral temperament, enabling rastmic chords in either case.
See Rastmic clan for the clan of rank-2 temperaments where it is tempered out. See Rastmic rank-3 clan for the clan of rank-3 temperaments where it is tempered out.