

A229943


Decimal expansion of 256/243, the Pythagorean semitone.


3



1, 0, 5, 3, 4, 9, 7, 9, 4, 2, 3, 8, 6, 8, 3, 1, 2, 7, 5, 7, 2, 0, 1, 6, 4, 6, 0, 9, 0, 5, 3, 4, 9, 7, 9, 4, 2, 3, 8, 6, 8, 3, 1, 2, 7, 5, 7, 2, 0, 1, 6, 4, 6, 0, 9, 0, 5, 3, 4, 9, 7, 9, 4, 2, 3, 8, 6, 8, 3, 1, 2, 7, 5, 7, 2, 0, 1, 6, 4, 6, 0, 9, 0, 5, 3, 4, 9, 7, 9, 4, 2, 3, 8, 6, 8, 3, 1, 2, 7, 5, 7, 2, 0, 1, 6, 4, 6, 0, 9
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

The Pythagorean diatonic semitone is one of the musical intervals. Has a ratio of 256/243, and is often called the Pythagorean limma. It is also sometimes called the Pythagorean minor semitone.
After the initial term the sequence has period 27, repeat: 0, 5, 3, 4, 9, 7, 9, 4, 2, 3, 8, 6, 8, 3, 1, 2, 7, 5, 7, 2, 0, 1, 6, 4, 6, 0, 9.


REFERENCES

J. M. Merino de la Fuente, Las vibraciones de la música, Editorial Club Universitario (2006), 133.
Alberto Rojo, La física en la vida cotidiana, Siglo Veintiuno Editores (2011), 137.


LINKS

Table of n, a(n) for n=1..109.
Wikipedia, Semitone
OEIS index entry for music
The multifaceted reach of the OEIS: Music


FORMULA

A229948/A221363 = (3^7/2^11)/(3^12/2^19) = 2^8/3^5 = 256/243.


EXAMPLE

1.053497942386831275720164609...


MATHEMATICA

RealDigits[256/243, 10, 120][[1]] (* Harvey P. Dale, Jul 17 2019 *)


CROSSREFS

Cf. A010774, A221363, A229948, A230437.
Sequence in context: A196406 A070367 A086308 * A198132 A117967 A068116
Adjacent sequences: A229940 A229941 A229942 * A229944 A229945 A229946


KEYWORD

nonn,cons


AUTHOR

Omar E. Pol, Oct 25 2013


STATUS

approved



