243/242: Difference between revisions
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'''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma|small]] [[11-limit]] (also [[2.3.11 subgroup|2.3.11-subgroup]]) [[comma]] with a value of roughly 7.1 [[cent]]s. 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 | '''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma|small]] [[11-limit]] (also [[2.3.11 subgroup|2.3.11-subgroup]]) [[comma]] with a value of roughly 7.1 [[cent]]s. 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 [[2187/2048|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 [[ | [[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 [[2187/2048|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 [[subchromatic|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 == | == Temperaments == | ||
Revision as of 14:36, 3 June 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 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.