Factor 9 grid
Factor 9 grid is a type of musical scale which was first proposed for esoteric reasons, as a supposed replacement to 12edo.
Theory
The scale is an isoharmonic sequence that consists of the following notes, in Hertz: 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 252 (octave), and their octave displacements. However, since the esoteric affliction towards the note A being 432 Hz is usually considered, the scale is supposed to be played starting with A, which leaves a wide semitone inside the octave. The scale contains one major inconsistency - it has 13 notes (G sharp and A flat are not enharmonic), while it claims to be supposedly a better replacement towards the current 12-note system and makes references towards the sacrality of the number 12.
The motivation behind the scale, or any kind of esoteric just intonation proposal, is that the irrational pitch standard of equal temperament has an acoustically unpleasant effect, that subsequently allegedly spreads to the subconscious part of the mind. The irrationality of equal temperament has been known since ancient times by various names, the most common being the proof by infinite descent of the square root of two. Another way to look at this is that if a stack of fifths (3/2) were to close at the octave, it would imply the existence of an even power of 3, which is nonsense.
As a whole, Factor 9 Grid is a part of 23-limit just intonation.
Intervals
| Frequency (Hz) | Note | Interval |
|---|---|---|
| 432 | A | 1/1 |
| 450 | A#/Bb | 25/24 |
| 468 | B | 13/12 |
| 504 | C | 7/6 |
| 540 | C#/Db | 5/4 |
| 576 | D | 4/3 |
| 612 | D#/Eb | 17/12 |
| 648 | E | 3/2 |
| 684 | F | 19/12 |
| 720 | F#/Gb | 5/3 |
| 756 | G | 7/4 |
| 792 | G# | 11/6 |
| 828 | Ab | 23/12 |
| 864 | A | 2/1 |
Factor 9 Grid temperament (495 & 666)
In an extremely ironic twist, this allegedly divine and enlightening scale is well-approximated by an evil satanic temperament of 666 equal divisions of the octave. If performed using general temperament theory, it results in the following 23-limit temperament: Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 442/441, 715/714, 2300/2299, 3060/3059, 3179/3174, 9025/9009, 57375/57344
POTE Generator: 63.0631c (~27/26)
Vals: 171f, 495, 666