243/242: Difference between revisions
CompactStar (talk | contribs) |
Restore prose format, which better shows the logical relation in these equations; also note the last equation isn't 2.3.11. |
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'''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma|small]] [[11-limit]] ( [[2.3.11 subgroup|2.3.11-subgroup]]) [[comma]] of roughly 7.1 [[cent]]s. It is significant in [[just intonation]] as the difference between many 2.3.11 intervals, namely: | '''243/242''', the '''rastma''' or the '''neutral third comma''', is a [[small comma|small]] [[11-limit]] (specifically [[2.3.11 subgroup|2.3.11-subgroup]]) [[comma]] of roughly 7.1 [[cent]]s. It is significant in [[just intonation]] as the difference between many 2.3.11-subgroup intervals, namely: between [[11/9]] and its [[fifth complement]], [[27/22]], between [[3/2]] and a stack of two [[11/9]]'s (as a [[semiparticular]] comma), or equivalently between a [[2187/2048|Pythagorean apotome (2187/2048)]] and a stack of two [[33/32]]'s. | ||
In the full 11-limit, it is also the difference between [[45/44]] and [[55/54]], which shows it as the [[subchromatic|subchroma]] that separates greater and lesser 11-limit [[chroma]]s – a demonstration that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit. | |||
Its square rooted value, about 3.57 cents, is also a tiny comma that is used in [[Neutral FJS]] as the formal comma of prime 11; the difference between [[11/8]] and the half-augmented fourth sqrt(243/128), or between 11/9 or 27/22 and the hemipythagorean neutral third [[sqrt(3/2)]]. | Its square rooted value, about 3.57 cents, is also a tiny comma that is used in [[Neutral FJS]] as the formal comma of prime 11; the difference between [[11/8]] and the half-augmented fourth sqrt(243/128), or between 11/9 or 27/22 and the hemipythagorean neutral third [[sqrt(3/2)]]. | ||