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 fall short of [[3/2]] just perfect fifth as well as the amount by which a stack of two [[27/22]] neutral thirds 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 [[~~diatonic, chromatic, enharmonic,~~ 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.

'''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 [[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 ==

[[Tempering out]] this comma in the full 11-limit leads to the [[rastmic]] 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 [[Rastmic rank three clan|Rastmic rank-3 clan]] for the clan of rank-3 temperaments where it is tempered out.

== See also ==

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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 fall short of [[3/2]] just perfect fifth as well as the amount by which a stack of two [[27/22]] neutral thirds 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 [[diatonic, chromatic, enharmonic, 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.
+'''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 [[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 ==
-[[Tempering out]] this comma in the full 11-limit leads to the [[rastmic]] 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 [[Rastmic rank three clan|Rastmic rank-3 clan]] for the clan of rank-3 temperaments where it is tempered out.
 == See also ==