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. 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 and results in degradation of the quality of life. The esoteric properties of the scale were subsequently refuted by an infamous YouTuber, bassist, and composer Adam Neely.
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, 243, (octave), and their octave displacements. Therefore this is an otonal scale running from 14th to 28th harmonic.This is an arithmetic progression with the difference of 9, hence why this scale was named, although quite misnomerly, "Factor 9 grid". Since the largest prime is 23, this makes Factor 9 grid a part of 23-limit just intonation.
The scale, as proposed in the video, contains a 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. Also, the scale in the video skips number 243 for an unknown reason, given that 126 = 9 * 14, and you need 14 notes to count to the octave displacement, if you are using an arithmetic difference of 9. This page will consider the full 14:15:...:28 otonal sequence.
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.
Mysticism and reality
However, it is not possible to have both the rationality of just intonation and evenness of equal temperament. 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.
Intervals
The 9/8 interval was skipped by the original video for unknown reasons.
| Frequency (Hz) | Note | Interval |
|---|---|---|
| 432 | A | 1/1 |
| 450 | A#/Bb | 25/24 |
| 468 | B | 13/12 |
| 486 | - | 9/8 |
| 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 (~28/27)
Vals: 171f, 495, 666
References
- Sonic Geometry: The Language of Frequency and Form - the original video
- Testing 432Hz Frequencies and Temperaments - refuting by Adam Neely