33/32: Difference between revisions

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The interval 33/32 is significant in [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the undecimal formal comma which translates a Pythagorean interval to a nearby undecimal interval. However, it should be noted that in some significant respects, treating 33/32 as a comma rather than as an important musical interval in its own right sells it short, and results in the failure to correctly define the properties of certain intervals. Namely, a stack of two 33/32 intervals equals [[1089/1024]], a type of chromatic semitone that has [[128/121]] as its diatonic counterpart. Furthermore, 33/32 is one of two distinct 11-limit quartertone intervals required to add up to a whole tone, with [[4096/3993]] being the other- specifically, adding 4096/3993 to a stack of three 33/32 quartertones yields [[9/8]]. In addition to all this, 33/32 finds a special place in the theory of [[User:Aura|Aura]] not only in terms of [[Alpharabian tuning]], but also in terms of his ideas on how [[diatonic functional harmony]] extends to the realm of microtonality, and it is from these areas of microtonal theory that 33/32 acquires the names '''Alpharabian parachroma''' and '''Alphrabian ultraprime''', names that are at this point mainly used by Aura himself.

== See also ==

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	The interval 33/32 is significant in [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the undecimal formal comma which translates a Pythagorean interval to a nearby undecimal interval. However, it should be noted that in some significant respects, treating 33/32 as a comma rather than as an important musical interval in its own right sells it short, and results in the failure to correctly define the properties of certain intervals. Namely, a stack of two 33/32 intervals equals [[1089/1024]], a type of chromatic semitone that has [[128/121]] as its diatonic counterpart. Furthermore, 33/32 is one of two distinct 11-limit quartertone intervals required to add up to a whole tone, with [[4096/3993]] being the other- specifically, adding 4096/3993 to a stack of three 33/32 quartertones yields [[9/8]]. In addition to all this, 33/32 finds a special place in the theory of [[User:Aura\|Aura]] not only in terms of [[Alpharabian tuning]], but also in terms of his ideas on how [[diatonic functional harmony]] extends to the realm of microtonality, and it is from these areas of microtonal theory that 33/32 acquires the names '''Alpharabian parachroma''' and '''Alphrabian ultraprime''', names that are at this point mainly used by Aura himself.		The interval 33/32 is significant in [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the undecimal formal comma which translates a Pythagorean interval to a nearby undecimal interval. However, it should be noted that in some significant respects, treating 33/32 as a comma rather than as an important musical interval in its own right sells it short, and results in the failure to correctly define the properties of certain intervals. Namely, a stack of two 33/32 intervals equals [[1089/1024]], a type of chromatic semitone that has [[128/121]] as its diatonic counterpart. Furthermore, 33/32 is one of two distinct 11-limit quartertone intervals required to add up to a whole tone, with [[4096/3993]] being the other- specifically, adding 4096/3993 to a stack of three 33/32 quartertones yields [[9/8]]. In addition to all this, 33/32 finds a special place in the theory of [[User:Aura\|Aura]] not only in terms of [[Alpharabian tuning]], but also in terms of his ideas on how [[diatonic functional harmony]] extends to the realm of microtonality, and it is from these areas of microtonal theory that 33/32 acquires the names '''Alpharabian parachroma''' and '''Alphrabian ultraprime''', names that are at this point mainly used by Aura himself.



	== See also ==		== See also ==