99/98: Difference between revisions

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'''99/98''', or the '''mothwellsma''' (17.6 [[cent]]s in size), represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. ~~If tempered, it leads to the [[Mothwellsmic triad]], and is related to~~ 11~~-limit [[orwell]], as a generator between~~ 7/6 ~~and (11/8~~)1/2 – is ~~befitting~~ of ~~orwell~~.

'''99/98''', or the '''mothwellsma''', is a [[small comma|small]] [[11-limit]] [[comma]] of 17.6 [[cent]]s in size. It represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. Note that 11/8 = (7/6)2(99/98) and that 7/6 × 99/98 = [[33/28]], which is the fifth complement of 14/11.

(~~Note that~~ (11/8)~~1/2 =~~ 7/6 × (99/98)1/2 and that ~~7/6 × 99/98 = [[33/28]], which is~~ the ~~fifth complement of 14/11~~.)

== Temperaments ==

Tempering out this comma alone in the 11-limit leads to the '''mothwellsmic temperament''' (→ [[Catalog of rank-4 temperaments #Mothwellsmic (99/98)]]) and enables [[mothwellsmic chords]]. It is related to 11-limit [[orwell]], as a generator between 7/6 and (11/8)1/2 is befitting of orwell.

== Etymology ==

This comma's name comes from a contraction of ''mothra'' and ''orwell'', two of the rank-2 temperaments that temper out the comma.

== See also ==

* [[99/49]] – the same interval but one octave higher

* [[Gallery of just intervals]]

* [[Small comma]]

[[Category:Mothwellsmic]]

[[Category:Commas named by combining multiple temperament names]]

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-'''99/98''', or the '''mothwellsma''' (17.6 [[cent]]s in size), represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. If tempered, it leads to the [[Mothwellsmic triad]], and is related to 11-limit [[orwell]], as a generator between 7/6 and (11/8)<sup>1/2</sup> – is befitting of orwell.
+'''99/98''', or the '''mothwellsma''', is a [[small comma|small]] [[11-limit]] [[comma]] of 17.6 [[cent]]s in size. It represents the difference between the [[9/7]] and [[14/11]] supermajor thirds, or the difference between two [[7/6]] subminor thirds and one [[11/8]] semi-augmented fourth. Note that 11/8 = (7/6)<sup>2</sup>(99/98) and that 7/6 × 99/98 = [[33/28]], which is the fifth complement of 14/11.
-(Note that (11/8)<sup>1/2</sup> = 7/6 × (99/98)<sup>1/2</sup> and that 7/6 × 99/98 = [[33/28]], which is the fifth complement of 14/11.)
+== Temperaments ==
+Tempering out this comma alone in the 11-limit leads to the '''mothwellsmic temperament''' (→ [[Catalog of rank-4 temperaments #Mothwellsmic (99/98)]]) and enables [[mothwellsmic chords]]. It is related to 11-limit [[orwell]], as a generator between 7/6 and (11/8)<sup>1/2</sup> is befitting of orwell.
+== Etymology ==
+This comma's name comes from a contraction of ''mothra'' and ''orwell'', two of the rank-2 temperaments that temper out the comma.
 == See also ==
 * [[99/49]] – the same interval but one octave higher
 * [[Gallery of just intervals]]
-* [[Small comma]]
 [[Category:Mothwellsmic]]
+[[Category:Commas named by combining multiple temperament names]]