4096/3993: Difference between revisions
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Remarkably, 4096/3993 is currently the simplest interval in terms of odd-limit that is known to result from stacking three identical quartertones with rational intervals and subtracting said stack from a 9/8 whole tone. Furthermore, although [[38/37]], [[35/34]], [[32/31]] and [[28/27]] are all simpler intervals that can be called "quarter tones" and can safely be regarded as some kind of second, subtracting any one of these intervals from 9/8 yields an interval that has a ratio lacking a cubed number in the numerator and or the denominator, and such an interval cannot be split into three equal quartertones with rational intervals. | Remarkably, 4096/3993 is currently the simplest interval in terms of odd-limit that is known to result from stacking three identical quartertones with rational intervals and subtracting said stack from a 9/8 whole tone. Furthermore, although [[38/37]], [[35/34]], [[32/31]] and [[28/27]] are all simpler intervals that can be called "quarter tones" and can safely be regarded as some kind of second, subtracting any one of these intervals from 9/8 yields an interval that has a ratio lacking a cubed number in the numerator and or the denominator, and such an interval cannot be split into three equal quartertones with rational intervals. | ||
== Temperaments == | |||
[[Tempering out]] the paralimma in the 2.3.11 subgroup results in paralimmic temperament, where [[3/1]] is divided into 3 flat [[16/11]]s. | |||
== See also == | == See also == | ||
* [[3993/2048]] – its [[octave complement]] | * [[3993/2048]] – its [[octave complement]] | ||
* [[1331/1024]] – its [[fourth complement]] | * [[1331/1024]] – its [[fourth complement]] | ||