16edo: Difference between revisions

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Hexadecaphonic Octave Theory

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).

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).

In 16-tone, because of the 25 cent difference in the steps from 100 in 12-tone, a western

"twelve tone ear" hears dissonance with more complexity and less familiarity than even 24-tone,

yet within a more manageable number of tones and a strange familiarity - the diminished family

- which is why 16-tone is a truly Xenharmonic system to my ears.

In 16-edo Diatonic scales played are dissonant because of the 25 cent raised superfourth in

conjunction with the 25 cent subtracted fifth / poor 3/2 approximation. The septimal semi

diminished fourth can be more desirable. Perhaps using Moment of Symmetry Scales an

alternative temperament families like the "Anti-Diatonic" Mavila (which reverses step sizes of

diatonic), Diminished, Happy, Rice, Grumpy, Mosh, Magic, Lemba, Cynder, and Decatonic can be

more interesting and suitable:

(meantone) scales, these arise from tempering out a unison vector from Fokker periodicity

blocks. Only in 16-EDO, that unison vector is 135:128, instead of 81:80."

Mavila (1 2 2 2 1 2 2 2 2, 3 2 2 3 2 2 2, 5 2 5 2 2)

Igliashon Jones futher writes, "The trouble (in 16-EDO) has ... to do with the fact that the

distance between the major third and the "fourth" is the same as the distance between the

"fourth" and the "fifth" (i.e. near a 12/11)...This mean(s) that 135/128 (the difference between

16/15 and 9/8) is tempered out...."

Hexadecaphonic Octave Theory&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;

One neat xenharmonic aspect of 16-tone is how the 11-limit whole tone scale using the&lt;br /&gt;

neutral second, interlocks with the diminished scale, similar to the augmented scale and whole&lt;br /&gt;

tone relationship in 12-tone (the whole tone divides the major third in 12, in 16-it's the minor&lt;br /&gt;

third).&lt;br /&gt;

In 16-tone, because of the 25 cent difference in the steps from 100 in 12-tone, a western&lt;br /&gt;

&amp;quot;twelve tone ear&amp;quot; hears dissonance with more complexity and less familiarity than even 24-tone,&lt;br /&gt;

yet within a more manageable number of tones and a strange familiarity - the diminished family&lt;br /&gt;

- which is why 16-tone is a truly Xenharmonic system to my ears.&lt;br /&gt;

In 16-edo Diatonic scales played are dissonant because of the 25 cent raised superfourth in&lt;br /&gt;

conjunction with the 25 cent subtracted fifth / poor 3/2 approximation. The septimal semi&lt;br /&gt;

diminished fourth can be more desirable. Perhaps using Moment of Symmetry Scales an&lt;br /&gt;

alternative temperament families like the &amp;quot;Anti-Diatonic&amp;quot; Mavila (which reverses step sizes of&lt;br /&gt;

diatonic), Diminished, Happy, Rice, Grumpy, Mosh, Magic, Lemba, Cynder, and Decatonic can be&lt;br /&gt;

more interesting and suitable:&lt;br /&gt;

About Mavila Paul Erlich writes, &amp;quot;Like the conventional 12-tet diatonic and pentatonic&lt;br /&gt;

(meantone) scales, these arise from tempering out a unison vector from Fokker periodicity&lt;br /&gt;

blocks. Only in 16-EDO, that unison vector is 135:128, instead of 81:80.&amp;quot;&lt;br /&gt;

Mavila (1 2 2 2 1 2 2 2 2, 3 2 2 3 2 2 2, 5 2 5 2 2)&lt;br /&gt;

Igliashon Jones futher writes, &amp;quot;The trouble (in 16-EDO) has ... to do with the fact that the&lt;br /&gt;

distance between the major third and the &amp;quot;fourth&amp;quot; is the same as the distance between the&lt;br /&gt;

&amp;quot;fourth&amp;quot; and the &amp;quot;fifth&amp;quot; (i.e. near a 12/11)...This mean(s) that 135/128 (the difference between&lt;br /&gt;

16/15 and 9/8) is tempered out....&amp;quot;&lt;br /&gt;

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