Searching the frontier of the Pythagorean system

Rok, strany: 1999, 273 - 282

It is known that the perfect fifth and octave can be expressed as $X⁴Y³$ and $x⁷Y⁵$ respectively, where $X= 256/243$ is the minor and $Y = 9/8 : X = 3⁷/2¹1$ the major Pythagorean semitone. In this this paper, Pythagorean system is studied when couples of semitones need not be considered in rational numbers; we deal with semitone couples $(X, Y)$ in algebraic numbers expressed by $dth$ roots, $d=1,2,3,…$.

ISO 690:

Haluška, J. 1999. Searching the frontier of the Pythagorean system. In Tatra Mountains Mathematical Publications, vol. 16, no.2, pp. 273-282. 1210-3195.

APA:

Haluška, J. (1999). Searching the frontier of the Pythagorean system. Tatra Mountains Mathematical Publications, 16(2), 273-282. 1210-3195.