4096/3993: Difference between revisions

Line 3:

| Monzo = 12 -1 0 0 -3

| Cents = 44.09117

| Name = Alpharabian paralimma, <br> Alpharabian ~~subminor second~~

| Name = Alpharabian paralimma, <br> Alpharabian paradiatonic semilimma

| Color name = Satrilu 2nd

| FJS name = M2<sub>11,11,11</sub>

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}}

'''4096/3993''', the '''Alpharabian paralimma''' or '''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 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.

@@ Line 3: / Line 3: @@
 | Monzo = 12 -1 0 0 -3
 | Cents = 44.09117
-| Name = Alpharabian paralimma, <br> Alpharabian subminor second
+| Name = Alpharabian paralimma, <br> Alpharabian paradiatonic semilimma
 | Color name = Satrilu 2nd
 | FJS name = M2<sub>11,11,11</sub>
@@ Line 9: / Line 9: @@
 }}
-'''4096/3993''', the '''Alpharabian paralimma''' or '''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 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.