Michael Harrison - Tone Cloud II, from Revelation for Piano

(Yes, the gentleman in the first row with the cane is La Monte Young.)

From Michael Harrison's website, the composer describes the concept of "just intonation" (a system of tuning which is subtly different from the standard equal temperament of modern Western instruments):


“ 'Just intonation,' or 'pure' tuning, is the universal foundation for harmony which is constructed from musical intervals of perfect mathematical proportions.  Pythagoras and other ancient Greek philosophers and mathematicians discovered that musical harmonies arise from mathematical relationships based on whole numbers.  The most consonant harmonies are created when two strings or other musical bodies vibrate in simple musical proportions. For example, the two notes comprising an octave have a 2:1 relationship, where the higher note is vibrating exactly twice as fast as the lower note.  A perfect 5th is a 3:2 relationship, a perfect 4th is 4:3, a major 3rd is 5:4, a minor 3rd is 6:5, a “septimal” minor 3rd is 7:6, a whole step is 9:8, and so on.  Every different set of whole numbers corresponds to a different set of musical intervals.  My music uses many of these simple combinations, as well as more complex relationships such as the “celestial comma,” or extremely minute interval of 64:63, which forms the nucleus of my work Revelation..."




Mr. Harrison makes use of an extensively modified grand piano to realize his compositions.