127834/1: Difference between revisions

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{{Infobox Interval

| Name = 127834th harmonic, 29-wood major 119th

| Color name = c<sup>16</sup>397o23oz9

}}

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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* 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.

== References ==

* ~~https://oeis.org/~~A081464

* {{OEIS|A081464}}

* ~~https://oeis.org/~~A267122

* {{OEIS|A267122}}

~~[[Category:Extreme]]~~

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+{{Novelty}}
 {{Infobox Interval
 | Name = 127834th harmonic, 29-wood major 119th
+| Color name = c<sup>16</sup>397o23oz9
 }}
 /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 ==
@@ Line 11: / Line 13: @@
 * 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.
 == References ==
-* https://oeis.org/A081464
+* {{OEIS|A081464}}
-* https://oeis.org/A267122
+* {{OEIS|A267122}}
-[[Category:Extreme]]