4096/3993: Difference between revisions
m Misc. edits, categories |
Removed the name "Alpharabian subminor second" for now, as it will eventually be replaced with a more accurate name; also added an additional name showcasing it's relationship to the Pythagorean limma; additional changes |
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| Monzo = 12 -1 0 0 -3 | | Monzo = 12 -1 0 0 -3 | ||
| Cents = 44.09117 | | Cents = 44.09117 | ||
| Name = Alpharabian paralimma, <br> Alpharabian | | Name = Alpharabian paralimma, <br> Alpharabian paradiatonic semilimma | ||
| Color name = Satrilu 2nd | | Color name = Satrilu 2nd | ||
| FJS name = M2<sub>11,11,11</sub> | | FJS name = M2<sub>11,11,11</sub> | ||
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'''4096/3993''', the '''Alpharabian paralimma''' or '''Alpharabian | '''4096/3993''', the '''Alpharabian paralimma''' or '''Alpharabian paradiatonic semilimma''', is notable for being one of only two quartertone intervals in the 2.3.11 [[subgroup]] 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 being some sort of second. It is of further note that this interval is only just shy of being half of [[256/243]]- the Pythagorean limma- being separated from the interval forming the other part of the Pythagorean limma by the nearby [[1331/1296]] by the [[nexus comma]]. | ||
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. | |||
Revision as of 01:10, 26 December 2021
| Interval information |
Alpharabian paradiatonic semilimma
reduced subharmonic
4096/3993, the Alpharabian paralimma or Alpharabian paradiatonic semilimma, is notable for being one of only two quartertone intervals in the 2.3.11 subgroup 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 being some sort of second. It is of further note that this interval is only just shy of being half of 256/243- the Pythagorean limma- being separated from the interval forming the other part of the Pythagorean limma by the nearby 1331/1296 by the nexus comma.
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.