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. [[Ben Johnston's notation]] denotes this interval with ↑, and its reciprocal as ↓. 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 [[Alpharabian tuning]] and it is from this area of microtonal theory, among a select few others, that 33/32 acquires the names "'''Alpharabian parachroma'''" and "'''Alpharabian ultraprime'''", names that at this point are only used in said theoretical contexts. While many may be accustomed to thinking of 33/32 and [[729/704]] as "semiaugmented primes", this analysis is only completely accurate when [[243/242]] is tempered out. | 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. [[Ben Johnston's notation]] denotes this interval with ↑, and its reciprocal as ↓. 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 [[Alpharabian tuning]] and it is from this area of microtonal theory, among a select few others, that 33/32 acquires the names "'''Alpharabian parachroma'''" and "'''Alpharabian ultraprime'''", names that at this point are only used in said theoretical contexts. While many may be accustomed to thinking of 33/32 and [[729/704]] as "semiaugmented primes", this analysis is only completely accurate when [[243/242]] is tempered out. | ||
== Approximation == | |||
[[23edo]]'s step size is a good albeit in[[consistent]] approximation of this interval. 46edo contains the same approximation mapped consistently. | |||
== See also == | == See also == | ||
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* [[16/11]] – its [[fifth complement]] | * [[16/11]] – its [[fifth complement]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[32/31]] | * [[32/31]] – the tricesimoprimal counterpart | ||
* [[:File:Ji-33-32-csound-foscil-220hz.mp3 | * [[:File:Ji-33-32-csound-foscil-220hz.mp3]] – alternative sound example | ||
== References == | == References == | ||