The Impossibility of a Pythagorean Scale and Square Root of 2 in Music Theory

Explore the mathematical challenges in creating a "perfect" musical scale using the cycle of fifths and the 12-tone chromatic scale. Discover how the same arithmetical issue encountered in geometry manifests in music theory, particularly in the relationship between a note and the interval halfway to the octave. Examine the symmetrical role of the "6-step" interval and its connection to the arithmetic conundrum surrounding the non-existent "square root of 2". Investigate the cycle of fourths and its importance in modern music, classical music, jazz, pop, and rock'n roll. Gain insights into the fascinating intersection of mathematics and music theory, revealing the Pythagoreans' encounter with the same arithmetical problem in two distinct contexts.