A112732 Denominators of the convergents to the continued fraction for log_2(5)/4.

1, 2, 5, 7, 12, 19, 31, 174, 205, 789, 2572, 3361, 9294, 12655, 97879, 7647217, 15392313, 207747286, 1054128743, 2316004772, 24214176463, 74958534161, 174131244785, 3557583429861, 3731714674646, 14752727453799, 77495351943641

Offset: 0

Author

Gene Ward Smith, Dec 31 2005

Keywords

• nonn

Comments

This is the fifth of 1/4-comma meantone temperament and hence of significance in music theory, as these represent equal divisions of the octave in which the circle of fifths nearly closes. The sequence is therefore closely related to A005664.

Links

• Tonalsoft Encyclopedia, Quarter-comma meantone
• Wikipedia, Quarter-comma meantone

Crossrefs

Cf. A005664.

Programs

Mathematica

Rest[Denominator[Convergents[(Log[5]/(4 Log[2])),50]]] (* Peter J. C. Moses, Oct 05 2014 *)
Rest[Convergents[Log2[5]/4,50]//Denominator] (* Harvey P. Dale, May 12 2025 *)