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]]

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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]]