Introduction to Pitch Systems in Tonal Music Part 09: A 12-Tone Pythagorean Set (English)
Recorded: Fall 2012
Description: This presentation uses 3:2 ratios to create a 12-tone set very much like the twelve tone chromatic system in common use today. Despite its out-of-tune triads, this scale seems very functional but suffers from a gap in its frequencies, another comma, meaning it is not circular. Since the tonal pitch system relies on circularity (the ability to modulate from any key center to another without adjusting the tuning system), it becomes clear that although fifths and triads sound best when tuned to simple ratios some adjustment will have to be made to these pure ratios to make a truly circular pitch system.
Required attribution: Crooks, John. Introduction to Pitch Systems in Tonal Music (UCI OpenCourseWare: University of California, Irvine), http://ocw.uci.edu/courses/introduction_to_pitch_systems_in_tonal_music.html [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License.
- John Crooks
Introduction to Pitch by John Crooks is licensed under a Creative Commons Attribution-ShareAlike 3.0 United States License.