4096/3993: Difference between revisions

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'''4096/3993''', the '''Alpharabian subminor second''', is notable for being one of only two [[11-limit]] quartertone intervals needed in order to add up to a familiar [[9/8]] whole tone. Specifically, it is the quartertone that forms the difference between the whole tone and a stack of three [[33/32]] quartertones, and can thus be regarded as a sort of subminor second.  Remarkably, it 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.
'''4096/3993''', the '''Alpharabian subminor second''', around 44.1 cents in size, is notable for being one of only two [[11-limit]] quartertone intervals needed in order to add up to a familiar [[9/8]] whole tone. Specifically, it is the quartertone that forms the difference between the whole tone and a stack of three [[33/32]] quartertones, and can thus be regarded as a sort of subminor second.  Remarkably, it 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.
 
Its monzo is {{Monzo| 12 -1 0 0 -3 }}.
 
[[Category:11-limit]]
[[Category:Quartertone]]
[[Category:Alpharabian]]

Revision as of 23:19, 4 November 2020

4096/3993, the Alpharabian subminor second, around 44.1 cents in size, is notable for being one of only two 11-limit quartertone intervals needed in order to add up to a familiar 9/8 whole tone. Specifically, it is the quartertone that forms the difference between the whole tone and a stack of three 33/32 quartertones, and can thus be regarded as a sort of subminor second. Remarkably, it 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.

Its monzo is [12 -1 0 0 -3⟩.