127834/1: Difference between revisions

Line 9:

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.

== Equal divisions of the 127834/1 ==

For practical purposes, 127834/1 is too complex and too large to be used as an equivalence interval, being over 100 times larger than the human hearing range.

* 29ed127834 - corresponds to [[Pythagorean tuning]]

* 261ed127834 - equivalent to [[Carlos Alpha]]

* 348ed127834 - equivalent to [[12edo]]

== Trivia ==

Prime numbers 23 and 397, having indices 9 and 78, are 69 prime numbers apart. Nice.

@@ Line 9: / Line 9: @@
 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.
+== Equal divisions of the 127834/1 ==
 For practical purposes, 127834/1 is too complex and too large to be used as an equivalence interval, being over 100 times larger than the human hearing range.
+* 29ed127834 - corresponds to [[Pythagorean tuning]]
+* 261ed127834 - equivalent to [[Carlos Alpha]]
+* 348ed127834 - equivalent to [[12edo]]
 == Trivia ==
 Prime numbers 23 and 397, having indices 9 and 78, are 69 prime numbers apart. Nice.