16edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:guest|guest]] and made on <tt>2010-05-05 03:56:28 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2010-05-05 03:58:34 UTC</tt>.

: The original revision id was <tt>~~139570467~~</tt>.

: The original revision id was <tt>139570655</tt>.

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The 25 cent difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic genera.

It can be It can be treated as 4 interwoven diminished seventh arpeggios, or as 2 interwoven 8-edo scales (narrow 11-limit whole tones which when stacked produce traditional 300 cent minor third intervals). 16-tone has the same stacked minor thirds diminished seventh scale/chord available in 12, and It is often cited that the most consonant chords involve the tritone. There are two minor seventh intervals, a harmonic seventh at step 13, a 7/4 ratio approximation, off by 3.5879 cents, followed by an undecimal 11/6 ratio or neutral seventh. The septimal can be the 9/4th tone or septimal semi diminished fourth (35/27 ratio) , semi-augmented fifth (54/35), harmonic seventh (7/4), and septimal whole tone 8/7. The Undecimal intervals are the 3/4 tone or undecimal neutral second (12/11), and the 21/4th tone or undecimal neutral seventh (11/6).

It can be It can be treated as 4 interwoven diminished seventh arpeggios, or as 2 interwoven 8-edo scales (narrow 11-limit whole tones which when stacked produce traditional 300 cent minor third intervals). 16-tone has the same stacked minor thirds diminished seventh scale/chord available in 12, and It is often cited that the most consonant chords involve the tritone. There are two minor seventh intervals, a harmonic seventh at step 13, a 7/4 ratio approximation, off by 3.5879 cents, followed by an undecimal 11/6 ratio or neutral seventh. The septimal intervals can be the 9/4th tone or septimal semi diminished fourth (35/27 ratio) , semi-augmented fifth (54/35), harmonic seventh (7/4), and septimal whole tone 8/7. The Undecimal intervals are the 3/4 tone or undecimal neutral second (12/11), and the 21/4th tone or undecimal neutral seventh (11/6).

One neat xenharmonic aspect of 16-tone is how the 11-limit whole tone scale using the neutral second, interlocks with the diminished scale, similar to the augmented scale and whole tone relationship in 12-tone (the whole tone divides the major third in 12, in 16-it's the minor third).

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The 25 cent difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic genera.

It can be It can be treated as 4 interwoven diminished seventh arpeggios, or as 2 interwoven 8-edo scales (narrow 11-limit whole tones which when stacked produce traditional 300 cent minor third intervals). 16-tone has the same stacked minor thirds diminished seventh scale/chord available in 12, and It is often cited that the most consonant chords involve the tritone. There are two minor seventh intervals, a harmonic seventh at step 13, a 7/4 ratio approximation, off by 3.5879 cents, followed by an undecimal 11/6 ratio or neutral seventh. The septimal can be the 9/4th tone or septimal semi diminished fourth (35/27 ratio) , semi-augmented fifth (54/35), harmonic seventh (7/4), and septimal whole tone 8/7. The Undecimal intervals are the 3/4 tone or undecimal neutral second (12/11), and the 21/4th tone or undecimal neutral seventh (11/6).

It can be It can be treated as 4 interwoven diminished seventh arpeggios, or as 2 interwoven 8-edo scales (narrow 11-limit whole tones which when stacked produce traditional 300 cent minor third intervals). 16-tone has the same stacked minor thirds diminished seventh scale/chord available in 12, and It is often cited that the most consonant chords involve the tritone. There are two minor seventh intervals, a harmonic seventh at step 13, a 7/4 ratio approximation, off by 3.5879 cents, followed by an undecimal 11/6 ratio or neutral seventh. The septimal intervals can be the 9/4th tone or septimal semi diminished fourth (35/27 ratio) , semi-augmented fifth (54/35), harmonic seventh (7/4), and septimal whole tone 8/7. The Undecimal intervals are the 3/4 tone or undecimal neutral second (12/11), and the 21/4th tone or undecimal neutral seventh (11/6).

One neat xenharmonic aspect of 16-tone is how the 11-limit whole tone scale using the neutral second, interlocks with the diminished scale, similar to the augmented scale and whole tone relationship in 12-tone (the whole tone divides the major third in 12, in 16-it's the minor third).

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:guest|guest]] and made on <tt>2010-05-05 03:56:28 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2010-05-05 03:58:34 UTC</tt>.<br>
-: The original revision id was <tt>139570467</tt>.<br>
+: The original revision id was <tt>139570655</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 12: / Line 12: @@
 The 25 cent difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic genera.
-It can be It can be treated as 4 interwoven diminished seventh arpeggios, or as 2 interwoven 8-edo scales (narrow 11-limit whole tones which when stacked produce traditional 300 cent minor third intervals). 16-tone has the same stacked minor thirds diminished seventh scale/chord available in 12, and It is often cited that the most consonant chords involve the tritone. There are two minor seventh intervals, a harmonic seventh at step 13, a 7/4 ratio approximation, off by 3.5879 cents, followed by an undecimal 11/6 ratio or neutral seventh. The septimal can be the 9/4th tone or septimal semi diminished fourth (35/27 ratio) , semi-augmented fifth (54/35), harmonic seventh (7/4), and septimal whole tone 8/7. The Undecimal intervals are the 3/4 tone or undecimal neutral second (12/11), and the 21/4th tone or undecimal neutral seventh (11/6).
+It can be It can be treated as 4 interwoven diminished seventh arpeggios, or as 2 interwoven 8-edo scales (narrow 11-limit whole tones which when stacked produce traditional 300 cent minor third intervals). 16-tone has the same stacked minor thirds diminished seventh scale/chord available in 12, and It is often cited that the most consonant chords involve the tritone. There are two minor seventh intervals, a harmonic seventh at step 13, a 7/4 ratio approximation, off by 3.5879 cents, followed by an undecimal 11/6 ratio or neutral seventh. The septimal intervals can be the 9/4th tone or septimal semi diminished fourth (35/27 ratio) , semi-augmented fifth (54/35), harmonic seventh (7/4), and septimal whole tone 8/7. The Undecimal intervals are the 3/4 tone or undecimal neutral second (12/11), and the 21/4th tone or undecimal neutral seventh (11/6).
 One neat xenharmonic aspect of 16-tone is how the 11-limit whole tone scale using the neutral second, interlocks with the diminished scale, similar to the augmented scale and whole tone relationship in 12-tone (the whole tone divides the major third in 12, in 16-it's the minor third).
@@ Line 85: / Line 85: @@
 The 25 cent difference in the steps can have a similar effect the scales of Olympos have with buried enharmonic genera.&lt;br /&gt;
 &lt;br /&gt;
-It can be It can be treated as 4 interwoven diminished seventh arpeggios, or as 2 interwoven 8-edo scales (narrow 11-limit whole tones which when stacked produce traditional 300 cent minor third intervals). 16-tone has the same stacked minor thirds diminished seventh scale/chord available in 12, and It is often cited that the most consonant chords involve the tritone. There are two minor seventh intervals, a harmonic seventh at step 13, a 7/4 ratio approximation, off by 3.5879 cents, followed by an undecimal 11/6 ratio or neutral seventh. The septimal can be the 9/4th tone or septimal semi diminished fourth (35/27 ratio) , semi-augmented fifth (54/35), harmonic seventh (7/4), and septimal whole tone 8/7. The Undecimal intervals are the 3/4 tone or undecimal neutral second (12/11), and the 21/4th tone or undecimal neutral seventh (11/6).&lt;br /&gt;
+It can be It can be treated as 4 interwoven diminished seventh arpeggios, or as 2 interwoven 8-edo scales (narrow 11-limit whole tones which when stacked produce traditional 300 cent minor third intervals). 16-tone has the same stacked minor thirds diminished seventh scale/chord available in 12, and It is often cited that the most consonant chords involve the tritone. There are two minor seventh intervals, a harmonic seventh at step 13, a 7/4 ratio approximation, off by 3.5879 cents, followed by an undecimal 11/6 ratio or neutral seventh. The septimal intervals can be the 9/4th tone or septimal semi diminished fourth (35/27 ratio) , semi-augmented fifth (54/35), harmonic seventh (7/4), and septimal whole tone 8/7. The Undecimal intervals are the 3/4 tone or undecimal neutral second (12/11), and the 21/4th tone or undecimal neutral seventh (11/6).&lt;br /&gt;
 &lt;br /&gt;
 One neat xenharmonic aspect of 16-tone is how the 11-limit whole tone scale using the neutral second, interlocks with the diminished scale, similar to the augmented scale and whole tone relationship in 12-tone (the whole tone divides the major third in 12, in 16-it's the minor third).&lt;br /&gt;