Music creation based on the golden ratio: a theoretical and practical approach to the 34-tone equal-tempered scale - Marco Franco, Julio Emilio (2021)
The sensory phenomena of music perception are considered to be highly non-linear. The golden ratio plays a key role in nonlinear dynamic systems and has been recognized as an aesthetic element in many places over time. This research develops the 34-note equal tempered scale (34-TET). A microtonal model based on the golden ratio, containing the harmonic musical intervals, and permitting a consistent approach that embraces the different temperaments throughout history, as well as other music cultures. These theoretical properties are practically exposed in two portfolios, including compositional samples of art music with European roots (from the Renaissance to the twentieth century), popular music (bossa nova, tango, swing), maqãm, and Indian music. The second portfolio, created within the scope of this thesis, contains the artistic work “The Asian Garden” combining the equal tempered scales of 34 and 12 notes (12-TET), and provides additional cultural references from China and Japan. The 34-TET scale offers an overall approach to just intonation scale more than twice as good as that of 12-TET, with all consonant intervals well below the differential threshold. If a maximum impurity value was accepted, not appreciably different from that agreed upon when the equal-tempered 12- tone scale was standardized (17.65 cents vs. 15.67 cents), then the 34-TET scale would become, additionally, a useful tool for approaching different cultures.