99/98: Difference between revisions

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

'''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.

== 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 ==

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-'''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)<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.
+'''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.
 == 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 ==