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Harmonic alignments

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This little piece of work derives from comments in the introduction to Climate: Soul of the Earth by Dennis Klocek, in which he associates certain musical intervals with certain planetary alignments (Klocek 2011 p. vii).1 I was intrigued and demonstrate here the correspondences he notes (4th and tritone).

SemitoneEqual temperament approximation
IntervalJust intonation (5-limit diatonic major scale) (a/b)Angular Separation
(360*(1 – b/a)
01Perfect Unison1/10Conjunction
11.06Minor 2nd
21.12Major 2nd9/840Novile
31.19Minor 3rd
41.26Major 3rd5/472Quintile
51.33Perfect 4th4/390Square
71.5Perfect 5th3/2120Trine
81.59Minor 6th
91.68Major 6th5/3144BiQuintile
101.78Minor 7th
111.89Major 7th15/8168?
122Perfect Octave2/1180Opposition

The just intonation shown was devised by Ptolemy (no less), Ptolemy’s intense diatonic scale. The ratios correspond approximately to the equal temperament scale. There are also other approaches to just intonation. The table above simply demonstrates how musical intervals (ratios between 1 and 2) can be mapped to planetary alignments (angles between 0 and 360), and the curious may wish to tease this out further.

See these Wikipedia articles for more information on intervals and just intonation.

  1. Klocek, D 2011, Climate: soul of the earth, Lindisfarne Books, Great Barrington MA. ↩ī¸Ž