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 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 is an isoharmonic sequence consisting of the following frequencies (in Hz): 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, and their octave equivalents. This sequence forms an arithmetic progression with a constant difference of 9, which gives rise to the name "Factor 9 grid". It hence is identical to the [[14ado]] scale spanning the 14th through 28th harmonics, and since 14ado is a [[23-limit]] just intonation system, Factor 9 grid correspondingly is a part of 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~~.

More precisely, the "Factor 9 grid" refers to a specific mode of [[14ado]] whose tonic is placed on the step corresponding to 432 Hz and its octave equivalents, such as 216 Hz or 864 Hz, which is the 11th step of 14ado itself. It is this particular modal alignment that is commonly associated with "A = 432 Hz" conspiracy theories, where the emphasis is placed on organizing the scale around 432 Hz as a tonic.

~~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~~.

Proponents of the "Factor 9 grid" manly present it as the more consonant or acoustically "healthier" alternative to the prevailing [[12edo|12-tone equal temperament]], often accompanied by references to the symbolic or "sacred” significance of the number 12. However, descriptions of the scale, as they are presented in the video, contain several internal inconsistencies. The underlying structure of the grid, as mentioned above, corresponds to [[14ado]], which by definition contains 14 distinct steps per octave rather than 12, thus conflicting with the initial claims that the scale is 12-note or is a replacement for 12edo.

Furthermore, in the cited material, the sequence appears to omit the frequency 243 Hz (and its octave equivalents), despite it being a member of arithmetic progression that constitutes the scale. This omission appears to be motivated by an attempt to align the number of pitches with the 12-note framework of standard Western notation, as the presentation maps the resulting tones onto conventional note names. However, the rationale for excluding specifically 243 Hz and its octave displacement, as opposed to any other member of the sequence, is not explicitly addressed. No criteria are provided for why this particular step is removed while the remaining tones are retained, leaving the adjustment unexplained within the context of the scale’s stated arithmetic construction.

Additionally, the accompanying table distinguishes between G♯ and A♭ as separate pitches, resulting in a 13-note scale rather than either 12 or 14. This is not explained in the video as well, and further complicates the stated aim of aligning the system with a 12-note framework, particularly in light of the emphasis placed on the number 12 in the associated commentary.

== 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 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 is an isoharmonic sequence consisting of the following frequencies (in Hz): 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, and their octave equivalents. This sequence forms an arithmetic progression with a constant difference of 9, which gives rise to the name "Factor 9 grid". It hence is identical to the [[14ado]] scale spanning the 14th through 28th harmonics, and since 14ado is a [[23-limit]] just intonation system, Factor 9 grid correspondingly is a part of 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.
+More precisely, the "Factor 9 grid" refers to a specific mode of [[14ado]] whose tonic is placed on the step corresponding to 432 Hz and its octave equivalents, such as 216 Hz or 864 Hz, which is the 11th step of 14ado itself. It is this particular modal alignment that is commonly associated with "A = 432 Hz" conspiracy theories, where the emphasis is placed on organizing the scale around 432 Hz as a tonic.
-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.
+Proponents of the "Factor 9 grid" manly present it as the more consonant or acoustically "healthier" alternative to the prevailing [[12edo|12-tone equal temperament]], often accompanied by references to the symbolic or "sacred” significance of the number 12. However, descriptions of the scale, as they are presented in the video, contain several internal inconsistencies. The underlying structure of the grid, as mentioned above, corresponds to [[14ado]], which by definition contains 14 distinct steps per octave rather than 12, thus conflicting with the initial claims that the scale is 12-note or is a replacement for 12edo.
+Furthermore, in the cited material, the sequence appears to omit the frequency 243 Hz (and its octave equivalents), despite it being a member of arithmetic progression that constitutes the scale. This omission appears to be motivated by an attempt to align the number of pitches with the 12-note framework of standard Western notation, as the presentation maps the resulting tones onto conventional note names. However, the rationale for excluding specifically 243 Hz and its octave displacement, as opposed to any other member of the sequence, is not explicitly addressed. No criteria are provided for why this particular step is removed while the remaining tones are retained, leaving the adjustment unexplained within the context of the scale’s stated arithmetic construction.
+Additionally, the accompanying table distinguishes between G♯ and A♭ as separate pitches, resulting in a 13-note scale rather than either 12 or 14. This is not explained in the video as well, and further complicates the stated aim of aligning the system with a 12-note framework, particularly in light of the emphasis placed on the number 12 in the associated commentary.
 == Intervals ==