36-Tone Just Scale
In his book Temperering og renstemning (Temperament and Just Intonation, 1948), Groven describes how he derived the tuning system used for the organ. It is actually a quasi-just intonation that employs pure just major thirds (5:4 frequency ratio) and slightly tempered perfect fifths.
Using strictly pure thirds and fifths, the difference between a just major third (e.g., Eb-G) and a diminished fourth (e.g., D#-G) is a skhisma, or 1.628 millioctaves (1.954 cents). In Groven's organ, this discrepancy is distributed across the span of eight perfect fifths, reducing the difference to .204 mo. (.244 cents) per fifth. In otherwords, each fifth is now 584.759 mo. (701.711 cents) instead of a pure 3:2 ratio with 584.963 mo. (701.955 cents). This slight tempering of the fifths allowed Groven to create a closed pitch system with all like-sized fifths and thirds that still produce essentially just triads. In the figure above, you can see the enharmonic equivalents resulting from the elimination of the skhisma in parentheses on the right, allowing one row of fifths to wrap around to the beginning of the next, a major third below the starting point. This scale should not, however, be confused with 36-tone equal temperament, which comes no closer to using just major thirds or perfect fifths than does 12-tone equal temperament. When rearranged in scalar order, Groven's scale represents an uneven partitioning of the octave.
see Scale Table
Each pitch-class has three versions separated by the interval of a slightly diminished syntonic comma (approximately 17 mo. or 20.5 cents) designated, for example, D1, D2, and D3. Since only one of these three can sound at a time, there are technically no microtonal harmonic intervals to be heard in the music.