243/242: Difference between revisions

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'''243/242''', ~~otherwise known as~~ the '''rastma''' or the '''neutral third comma''', is an [[11-limit]] comma with a value of roughly 7.~~13912~~ [[cent~~|cents~~]]. It is significant in ~~Just Intonation~~ as the amount by which a stack of two [[33/32]] quartertones falls short of an [[2187/2048|apotome]] as well as the difference between [[11/9]] and [[27/22]], and, the difference between [[45/44]] and [[55/54]]. Tempering it out leads to ~~a form of '''~~[[rastmic ~~temperaments|rastmic temperament~~]]~~'''~~ or ~~'''~~neutral temperament~~'''~~. ~~When not~~ tempered out~~, the rastma behaves much like an 11-limit counterpart to the 5-limit's~~ [[~~81/80~~|~~syntonic comma~~]] ~~– a property that becomes especially apparent when one works extensively with 33/32 quartertones~~.

{{interwiki

| de = 243/242

| en = 243/242

| es =

| ja =

}}

{{Infobox Interval

| Name = rastma, neutral third comma

| Color name = 1uu1, lulu 1sn,<br>Lulu comma

| Comma = yes

}}

'''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]] 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 ==

* [[Rastmic chords]]

* [[Comma]]

* [[List of superparticular intervals]]

~~[[Category:11-limit]]~~

~~[[Category:Small comma]]~~

~~[[Category:Superparticular]]~~

[[Category:Rastmic]]

[[Category:Neutral]]

[[Category:Commas named after musical traditions]]

[[Category:Commas named for the generator of their temperament]]

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-'''243/242''', otherwise known as the '''rastma''' or the '''neutral third comma''', is an [[11-limit]] comma with a value of roughly 7.13912 [[cent|cents]]. It is significant in Just Intonation as the amount by which a stack of two [[33/32]] quartertones falls short of an [[2187/2048|apotome]] as well as the difference between [[11/9]] and [[27/22]], and, the difference between [[45/44]] and [[55/54]]. Tempering it out leads to a form of '''[[rastmic temperaments|rastmic temperament]]''' or '''neutral temperament'''. When not tempered out, the rastma behaves much like an 11-limit counterpart to the 5-limit's [[81/80|syntonic comma]] – a property that becomes especially apparent when one works extensively with 33/32 quartertones.
+{{interwiki
+| de = 243/242
+| en = 243/242
+| es =
+| ja =
+}}
+{{Infobox Interval
+| Name = rastma, neutral third comma
+| Color name = 1uu1, lulu 1sn,<br>Lulu comma
+| Comma = yes
+}}
+'''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]] 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 ==
-* [[Rastmic chords]]
-* [[Comma]]
 * [[List of superparticular intervals]]
-[[Category:11-limit]]
-[[Category:Small comma]]
-[[Category:Superparticular]]
 [[Category:Rastmic]]
 [[Category:Neutral]]
+[[Category:Commas named after musical traditions]]
+[[Category:Commas named for the generator of their temperament]]