{"id":2141,"date":"2026-09-02T19:27:08","date_gmt":"2026-09-02T19:27:08","guid":{"rendered":"https:\/\/legatto.space\/?p=2141"},"modified":"2026-09-02T19:38:43","modified_gmt":"2026-09-02T19:38:43","slug":"erv-wilson-teoria","status":"publish","type":"post","link":"https:\/\/legatto.space\/en\/erv-wilson-teoria\/","title":{"rendered":"Ervin Wilson's Musical Theory: Geometry, Sound, and Recursion"},"content":{"rendered":"Ervin M. Wilson (1928-2016) representa una de las figuras m\u00e1s formidables e innovadoras en la historia de la teor\u00eda musical, la ac\u00fastica f\u00edsica y la microtonalidad<\/b><\/a>. While traditional Western music theory has tended to treat tuning systems as static structures derived from historical practice, Wilson's work approached tuning from an integrated mathematical perspective, combining discrete number theory, multidimensional geometry, combinatorics, and physiological psychoacoustics.\n

<\/p>\n\t\t\t\t\t\t\t\t\t\"Ervin\n\t\t\t\t\t\t\t\t\t\t\tErvin Wilson\n\t

<\/p>\n

Introduction and Acoustic Fundamentals: The Tempered System Problem<\/b><\/h2>\n

Para comprender la trascendencia de los sistemas creados por Wilson y la raz\u00f3n psicoac\u00fastica por la cual son percibidos como cualitativamente “m\u00e1s afinados” que las escalas est\u00e1ndar, es necesario analizar primero la estructura del Temperamento Igual de 12 Tonos (12-TET). El sistema 12-TET subdivide el intervalo de octava -cuya raz\u00f3n de frecuencia f\u00edsica en la ac\u00fastica fundamental es 2:1\u00a0 – en doce partes logar\u00edtmicamente id\u00e9nticas. La raz\u00f3n de frecuencia entre cualquier par de semitonos adyacentes viene dada por el valor irracional (2^(1\/12) \u2248 1.059463)<\/b>, which assigns exactly 100 Cents to each semitone within the 1200 Cents spectrum that makes up the octave.<\/p>\n

The functional advantage of the 12-TET lies in its absolute symmetry, which grants unlimited freedom of transposition across the twelve keys without altering the proportions of the intervals. However, this symmetry requires a significant acoustic sacrifice: a systematic deviation from Just Intonation, that is, from the simple whole-number ratios that govern the series of natural harmonics. <\/p>\n

In Just Intonation, the frequencies of the intervals form simple whole-number ratios (2:1 for the octave, 3:2 for the perfect fifth, 5:4 for the major third, and 7:6 for the harmonic seventh). When two tones forming a pure whole-number ratio are played simultaneously, their sound pressure waves align periodically without generating annoying beats or phase interference. In contrast, the intervals of the 12-TET force irrational ratios that distort these harmonic alignments.<\/p>\n\t\n\n\n\n\n\n\n\n\n