A229943 Decimal expansion of 256/243, the Pythagorean semitone.

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

Offset: 1

Author

Omar E. Pol, Oct 25 2013

Keywords

• nonn
• cons

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.

Examples

			1.053497942386831275720164609...
		

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

• Wikipedia, Semitone
• OEIS index entry for music
• The multi-faceted reach of the OEIS: Music

Crossrefs

Cf. A010774, A221363, A229948, A230437.

Programs

Mathematica

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

Formula

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