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).
| Semitone | Equal temperament approximation (2^(n/12)) | Interval | Just intonation (5-limit diatonic major scale) (a/b) | Angular Separation (360*(1 – b/a)) | Alignment |
| 0 | 1 | Perfect Unison | 1/1 | 0 | Conjunction |
| 1 | 1.06 | Minor 2nd | |||
| 2 | 1.12 | Major 2nd | 9/8 | 40 | Novile |
| 3 | 1.19 | Minor 3rd | |||
| 4 | 1.26 | Major 3rd | 5/4 | 72 | Quintile |
| 5 | 1.33 | Perfect 4th | 4/3 | 90 | Square |
| 6 | 1.41 | Tritone | 10/7 | 108 | SesquiQuintile |
| 7 | 1.5 | Perfect 5th | 3/2 | 120 | Trine |
| 8 | 1.59 | Minor 6th | |||
| 9 | 1.68 | Major 6th | 5/3 | 144 | BiQuintile |
| 10 | 1.78 | Minor 7th | |||
| 11 | 1.89 | Major 7th | 15/8 | 168 | ? |
| 12 | 2 | Perfect Octave | 2/1 | 180 | Opposition |
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.
- Klocek, D 2011, Climate: soul of the earth, Lindisfarne Books, Great Barrington MA. âŠī¸