5120/5103: Difference between revisions

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'''5120/5103''', the '''aberschisma''' (formerly ''hemifamity comma''), is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 5.76 [[cent]]s. It is the difference between [[7/5]] (small septimal tritone) and [[1024/729]] (Pythagorean diminished fifth), or between [[10/7]] (large septimal tritone) and [[729/512]] (Pythagorean augmented fourth). It is also the difference between [[15/14]] and [[2187/2048]], between [[21/20]] and [[256/243]], between [[80/63]] and [[81/64]], etc., hence, between the septimal comma of [[64/63]] and the syntonic comma of [[81/80]].

In terms of smaller commas, it is the difference between the [[marvel comma]] and the [[32805/32768|schisma]], as well as the sum of the schisma and the [[septischisma]]. In terms of [[S-expression]]s, this can be seen through the fact that one way of expressing the schisma is {{nowrap~~| [[225/224~~|S15]]/(~~[[5120/5103|~~S8/S9]]) }} while the septischisma can be expressed as {{nowrap| (S8/S9)<sup>2</sup>/S15 }}, that is, the reciprocal of the septischisma~~, 33480783/33554432,~~ is ~~{{nowrap| S8/S9 {{=}} 5120/5103 }}~~ below the schisma.

In terms of smaller commas, it is the difference between the [[marvel comma]] and the [[32805/32768|schisma]], as well as the sum of the schisma and the [[septischisma]]. In terms of [[S-expression]]s, this can be seen through the fact that one way of expressing the schisma is {{nowrap| S15/(S8/S9) }} while the septischisma can be expressed as {{nowrap| (S8/S9)<sup>2</sup>/S15 }}, that is, the reciprocal of the septischisma is an aberschisma below the schisma.

== Temperaments ==

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 '''5120/5103''', the '''aberschisma''' (formerly ''hemifamity comma''), is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 5.76 [[cent]]s. It is the difference between [[7/5]] (small septimal tritone) and [[1024/729]] (Pythagorean diminished fifth), or between [[10/7]] (large septimal tritone) and [[729/512]] (Pythagorean augmented fourth). It is also the difference between [[15/14]] and [[2187/2048]], between [[21/20]] and [[256/243]], between [[80/63]] and [[81/64]], etc., hence, between the septimal comma of [[64/63]] and the syntonic comma of [[81/80]].
-In terms of smaller commas, it is the difference between the [[marvel comma]] and the [[32805/32768|schisma]], as well as the sum of the schisma and the [[septischisma]]. In terms of [[S-expression]]s, this can be seen through the fact that one way of expressing the schisma is {{nowrap| [[225/224|S15]]/([[5120/5103|S8/S9]]) }} while the septischisma can be expressed as {{nowrap| (S8/S9)<sup>2</sup>/S15 }}, that is, the reciprocal of the septischisma, 33480783/33554432, is {{nowrap| S8/S9 {{=}} 5120/5103 }} below the schisma.
+In terms of smaller commas, it is the difference between the [[marvel comma]] and the [[32805/32768|schisma]], as well as the sum of the schisma and the [[septischisma]]. In terms of [[S-expression]]s, this can be seen through the fact that one way of expressing the schisma is {{nowrap| S15/(S8/S9) }} while the septischisma can be expressed as {{nowrap| (S8/S9)<sup>2</sup>/S15 }}, that is, the reciprocal of the septischisma is an aberschisma below the schisma.
 == Temperaments ==