Factor 9 grid: Difference between revisions
Style, rewrote some text, clarified |
mNo edit summary |
||
| (10 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
'''Factor 9 grid''' is a type of musical scale which was first proposed for esoteric reasons as a supposed replacement to [[12edo]]. The scale also became notable in music theory when esoteric properties of the scale were subsequently refuted by the famous YouTuber, bassist, and composer Adam Neely. | '''Factor 9 grid''' is a type of musical scale which was first proposed for esoteric reasons as a supposed replacement to [[12edo]]. The scale also became notable in music theory when esoteric properties of the scale were subsequently refuted by the famous YouTuber, bassist, and composer [[Adam Neely]]. | ||
== Theory == | == 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 | 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 equivalent to [[14ado]] scale, running from 14th to 28th harmonic. This is an arithmetic progression with the difference of 9, hence why this scale was named "Factor 9 grid". Since the largest prime present in the intervals 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 14 notes, 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. In addition, the table presented features a 13-note scale where G# and Ab are not enharmonic. 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. | The scale, as proposed in the video, contains a major inconsistency - it has 14 notes, 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. In addition, the table presented features a 13-note scale where G# and Ab are not enharmonic. 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. | 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. | ||
== Intervals == | == Intervals == | ||
| Line 46: | Line 46: | ||
|} | |} | ||
== | == Attempts at representing the scale through regular temperament theory == | ||
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 15/14 interval. However, Eliora when trying to represent the Factor 9 grid via a rank-2 temperament did not realize that x31eq.com resource takes the first interval in the number series as the equivalence interval, and assumed that it is represented by [[666edo]] instead. "q666" in the temperament finder, when 14:15:16:... typed out, stands for 666ed15/14 as opposed to 666ed2. | 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 15/14 interval. However, [[Eliora]] when trying to represent the Factor 9 grid via a rank-2 temperament did not realize that x31eq.com resource takes the first interval in the number series as the equivalence interval, and assumed that it is represented by [[666edo]] instead. "q666" in the temperament finder, when 14:15:16:... typed out, stands for 666ed15/14 as opposed to 666ed2. | ||
This being said, | This being said, this temperament preserves more properties of the "Factor 9 Grid" than the corrected version, since it's period-9 and its period minus reduced generator interval also maps to the smallest interval in the Factor 9 Grid system, [[28/27]]. So in the end, 666edo does ironically represent the Factor 9 grid well. The corrected version would be with 495ed15/14 & 666ed15/14, which corresponds to a 4973 & 6691 temperament in the 23-limit, that has no structure resembling the initial factor-9 grid other than being made of two good edos in the 23-limit. | ||
The 495 & 666 temperament is given the name ''enneasoteric'' by Eliora, since music was already composed in the 666edo scale approximating Factor 9 grid, while the name "factor 9 grid" to avoid ambiguity will be retained with the scale only. | |||
=== | === Enneasoteric (495 & 666) === | ||
Subgroup: 2.3.5.7.11.13.17.19.23 | [[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 | [[Comma list]]: 442/441, 715/714, 2300/2299, 3060/3059, 3179/3174, 9025/9009, 57375/57344 | ||
[[Mapping]] [[generators]]: ~250/231, ~336/323 | |||
[[Optimal tuning]] ([[CTE]]): ~336/323 = 70.270 | |||
{{Optimal ET sequence|legend=1|171f, 495, 666}}. | |||
== Mysticism and reality == | == Mysticism and reality == | ||