David R Canright - Music of the Spheres

Music of the Spheres -
HD 110067

This piece was inspired by a science article about a star with 6 planets all in orbital resonance. The orbits define a cross-rhythmic groove; then the planets start jamming, each in its own little scale.

I also created an animation (gif) of the orbits (with orbit sizes and speeds to scale), to be watched while listening to the piece.

performed by: my laptop, via MIDI file in Finale
at the MCCF "Emerald Vibes" concert, March 17, 2024 at Hidden Valley.

See the video of the animation and sound track.

Or just listen on SoundCloud.

Program Notes

The star HD 110067, 100 light-years away, was recently found to have 6 planets all in orbital resonance with each other! For every 3 obits of the innermost planet (A), the next planet (B) orbits twice. The same relation 3:2 applies to pairs (B,C) and (C,D), while further out the ratio is 4:3 for pairs (D,E) and (E,F). This "Music of the Spheres" inspired me to write this piece, where each planet is represented with its own rhythm (from period of orbit) and pitch (from frequency of orbit). Then I gave each its own little scale (mostly pentatonic) so they could sing together...

The musical intervals are untempered, with frequency ratios such as 3:2 (perfect fifth) and 4:3 (perfect fourth) as in the planets. The complexity required using a computer to render the music.

Tuning & Timing

The (largest) unit of time that divdes all of the orbital periods was notated as a 1/16 note. Then the (smallest) overall period, divisible by all the planetary periods, is 432 units, and the individual periods, from innermost to outermost, are
8, 12, 18, 27, 36, 48 units, respectively.
I represented the orbits with guitar sounds: each plucks its key note once per orbit, where the frequency ratios of the key notes are the same as those of the planets. This "rhythm section" I call the "groove".

Then the planets start jamming, each in its own little scale, where all intervals are untempered (Just Intonation). Altogether they form a gamut of 23 pitches, octave equivalents of 10 notes. Some of these are noticably not standard, so I use some nonstandard accidentals: + and - . Here are the tunings in the key of A, as frequency ratios and pitch-bend settings relative to a standard reference note. (One half-step = 100 cents.)

Tuning: Spheres pitch bends

note Pb ratio cents ref
A 8192 1/1 0 0
B 8352 9/8 204 200
C# 7631 5/4 386 400
D- 6995 21/16 471 500
D 8112 4/3 498 500
D+ 6198 11/8 551 600
E 8272 3/2 702 700
F# 7551 5/3 884 900
G- 6915 7/4 969 1000
G 8032 16/9 996 1000

Here are the scales each planet uses, again ordered from inner to outer:
Key note, color in animation, instrument sound, measure size (beats x beat length in units),
and scale in frequency ratios, first relative to key note, [then relative to overall key of A].

Planet Scales:
orb key color sound measure
I B4 RED Flute 2x4
1/1 10/9 11/9 4/3 14/9 16/9 2/1
[ 9/8 5/4 11/8 3/2 7/4 1/1 9/8 ]
II E4 GREEN Saxophone 2x6
1/1 7/6 4/3 3/2 7/4 2/1
[ 3/2 7/4 1/1 9/8 21/16 3/2 ]
III A3 BLUE Trombone 3x6
1/1 9/8 5/4 3/2 7/4 2/1
[ 1/1 9/8 5/4 3/2 7/4 1/1 ]
IV D3 ORANGE Accordian 3x9
1/1 9/8 4/3 3/2 27/16 2/1
[ 4/3 3/2 16/9 1/1 9/8 4/3 ]
V A2 CYAN Bassoon 4x9
1/1 5/4 4/3 3/2 5/3 2/1
[ 1/1 5/4 4/3 3/2 5/3 1/1 ]
VI E2 PURPLE Organ 4x12
1/1 4/3 3/2 16/9 2/1
[ 3/2 1/1 9/8 4/3 3/2 ]

Below is a harmonic-melodic diagram of the pitches (planet keys are red).

Music of the Spheres - HD 110067

Program Notes

Tuning & Timing

Music of the Spheres -
HD 110067