127834/1: Difference between revisions

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127834/1, the '''127834th harmonic''', or '''29-wood supermajor 119th''', is 16 octaves above [[63917/32768]]. It is a part of 397-limit harmony, the 78th prime number.

The number appears in a sequence of fractional part of <math>1.5^n</math> decreasing monotonically to zero, meaning the sequence offers progressively closer approximations to repeated stacks of [[3/2]]. Indeed, this interval is close to a stack of perfect fifths by two parameters - both its fractional part decreases progressively, and it is also better than all the <math>1.5^k</math> for <math>0<k<29</math>. The difference between the ~~two~~ is 0.534 millicents, or 1 in 2.24 million parts of an octave.

The number appears in a sequence of fractional part of <math>1.5^n</math> decreasing monotonically to zero, meaning the sequence offers progressively closer approximations to repeated stacks of [[3/2]]. Indeed, this interval is close to a stack of perfect fifths by two parameters - both its fractional part decreases progressively, and it is also better than all the <math>1.5^k</math> for <math>0<k<29</math>. The difference between the stack of 29 perfect fifths and 127834/1, which is the [[68630377364883/68630356164608]] comma is 0.534 millicents, or 1 in 2.24 million parts of an octave.

== Equal divisions of the 127834/1 ==

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 /1, the '''127834th harmonic''', or '''29-wood supermajor 119th''', is 16 octaves above [[63917/32768]]. It is a part of 397-limit harmony, the 78th prime number.
-The number appears in a sequence of fractional part of <math>1.5^n</math> decreasing monotonically to zero, meaning the sequence offers progressively closer approximations to repeated stacks of [[3/2]]. Indeed, this interval is close to a stack of perfect fifths by two parameters - both its fractional part decreases progressively, and it is also better than all the <math>1.5^k</math> for <math>0<k<29</math>. The difference between the two is 0.534 millicents, or 1 in 2.24 million parts of an octave.
+The number appears in a sequence of fractional part of <math>1.5^n</math> decreasing monotonically to zero, meaning the sequence offers progressively closer approximations to repeated stacks of [[3/2]]. Indeed, this interval is close to a stack of perfect fifths by two parameters - both its fractional part decreases progressively, and it is also better than all the <math>1.5^k</math> for <math>0<k<29</math>. The difference between the stack of 29 perfect fifths and 127834/1, which is the [[68630377364883/68630356164608]] comma is 0.534 millicents, or 1 in 2.24 million parts of an octave.
 == Equal divisions of the 127834/1 ==