Factor 9 grid: Difference between revisions

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== 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 "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 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.

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 ==

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 == 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 "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 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.
 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 ==