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>2010-04-12 06:12:03 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2010-04-12 06:14:04 UTC</tt>.

: The original revision id was <tt>~~133667523~~</tt>.

: The original revision id was <tt>133667677</tt>.

: The revision comment was: <tt></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 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. ~~(However with the correct timbre, one can suggest consonance with any tuning.)~~ There are two minor seventh intervals. 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.

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 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. 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 are the 9/4th tone or septimal semi diminished fourth (35/27 ratio) , septimal semi-augmented

fifth (54/35), and the septimal harmonic seventh (7/4).

The Undecimal intervals are the 3/4 tone or undecimal neutral second (12/11), and the 21/4 tone 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 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. ~~(However with the correct timbre, one can suggest consonance with any tuning.)~~ There are two minor seventh intervals. 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.

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 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. 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 are the 9/4th tone or septimal semi diminished fourth (35/27 ratio) , septimal semi-augmented

fifth (54/35), and the septimal harmonic seventh (7/4).

The Undecimal intervals are the 3/4 tone or undecimal neutral second (12/11), and the 21/4 tone 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>2010-04-12 06:12:03 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2010-04-12 06:14:04 UTC</tt>.<br>
-: The original revision id was <tt>133667523</tt>.<br>
+: The original revision id was <tt>133667677</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 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. (However with the correct timbre, one can suggest consonance with any tuning.) There are two minor seventh intervals. 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.
+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 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. 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 are the 9/4th tone or septimal semi diminished fourth (35/27 ratio) , septimal semi-augmented
+fifth (54/35), and the septimal harmonic seventh (7/4).
+The Undecimal intervals are the 3/4 tone or undecimal neutral second (12/11), and the 21/4 tone 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 74: / Line 76: @@
 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 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. (However with the correct timbre, one can suggest consonance with any tuning.) There are two minor seventh intervals. 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.&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 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. 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 are the 9/4th tone or septimal semi diminished fourth (35/27 ratio) , septimal semi-augmented&lt;br /&gt;
+fifth (54/35), and the septimal harmonic seventh (7/4).&lt;br /&gt;
+The Undecimal intervals are the 3/4 tone or undecimal neutral second (12/11), and the 21/4 tone 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;