16-tone equal temperament
16-tone Guitar theory
The first 9-string I ever made was a 16-tone. Gary Kahler made me the bridge after years of a painful non locking system, and the instrument plays much better and sounds much better now. It used to be much more haggard looking (not that it still isn't) as it was a learning experience.
In 16-tone guitar, each fret is 75 cents, and because of the 25 cents difference (or difference of 1/4 a fret) from 100 cents in 12-tone, after 4 steps are stacked, we get a 'new' step. Each Minor third contains 4 steps, meaning m3's can now be directly divided. In addition, we have a new tetrachords- with 5/4 on the outside: LLs, LsL, & sLL. These divide the minor third equally in half and allow us to arrive melodically on the 5/4, something totally melodically new from 12-tone. For this reason 16-tone as well as 15 and 17 fall into a "Xenmelodic" category, as they use have these tetrachords as well as interesting pentachords. In 16-tone these tetrachords and pentachords are found in Mavila.
Below are the Mavila [9] modes:
16-tET is a very "Xenharmonic" system, as it contains the inclusion of intervals which approximate mathematical ratios found in the harmonic series dealing with the number 7, 11 and 13, as well as new categories of intervals found in the 9-note Mavila Super-diatonic scale. The smaller whole tone in 16 divides the minor third directly in half, like a whole tone in 12-tET divides a major third. This 150-cent interval has a very ethnomusical "middle eastern" quality to it. This narrow whole tone can be a tempered 10:9 but closely resemble 8:7 and 12:11 as well.
16-tET keyboard:
Youtube Demonstration:
16-tone Piano converted from wurlitzer 12-tone in 2011: 
The first proposed 16-tone keyboards include 3 and 4 black "sharp keys" repeating among 9 "notes". The system of harmony found on the white keys has been named Mavila [9], which is a rank 2 Moment of Symmetry scale (scale with 2 step sizes), based on a very flat fifth generating interval. Ervin Wilson was the first to name this temperament and reportedly would show the 7-note subset ssLsssL to the 7-note LLsLLLs found in 12-tone on either side of 7-equal division, showing the inverse/inside out properties of Mavila and teaching at the same time a beautiful philosophical multiplicity.
Subminor and Supermajor are two new categories found in 16-tone which do not exist in conventional music. If one were to write a well-tempered series of compositions ala Bach, there would be 32 major and minor pieces, and an additional 32 subminor and supermajor pieces.
The 3rd interval in Mavila[9] is a minor third, the 4th is categorically a Super-major third. The 8th and 9th categorically are harmonic seventh and a major seventh/diminished octave. In the 9-note system it makes sense to no longer refer to 3/2 as the fifth, but as a 6th degree of the scale- also it is no longer a "Perfect fifth", but a highly tempered one.
A Little Math for a Middle Path
In 16-tone because of the 25 cent sharp 4/3 in conjunction with the 25 cent flat 3/2, the cycle of narrow fifths produces "minor" while the sharp fourths produce "major", reversing the traditional western functions of these intervals. Ther are many new intervallic resources which can be used to generate scales in 16-tone including Slendric, Lemba, Mavila/Pelogic, Magic and Vishnu.
Like the conventional 12-tet diatonic and pentatonic (Meantone) scales, these arise from tempering out 135:128 (difference of 16/15 and 9/8), instead of 81:80 (10/9 and 9/8).
The narrow fifths of 675 cents have an exotic, pelog-like sound. These take the player and listener to new places and well within a managable number of tones.
More soon!
In 16-tone guitar, each fret is 75 cents, and because of the 25 cents difference (or difference of 1/4 a fret) from 100 cents in 12-tone, after 4 steps are stacked, we get a 'new' step. Each Minor third contains 4 steps, meaning m3's can now be directly divided. In addition, we have a new tetrachords- with 5/4 on the outside: LLs, LsL, & sLL. These divide the minor third equally in half and allow us to arrive melodically on the 5/4, something totally melodically new from 12-tone. For this reason 16-tone as well as 15 and 17 fall into a "Xenmelodic" category, as they use have these tetrachords as well as interesting pentachords. In 16-tone these tetrachords and pentachords are found in Mavila.
16-tET keyboard:
The first proposed 16-tone keyboards include 3 and 4 black "sharp keys" repeating among 9 "notes". The system of harmony found on the white keys has been named Mavila [9], which is a rank 2 Moment of Symmetry scale (scale with 2 step sizes), based on a very flat fifth generating interval. Ervin Wilson was the first to name this temperament and reportedly would show the 7-note subset ssLsssL to the 7-note LLsLLLs found in 12-tone on either side of 7-equal division, showing the inverse/inside out properties of Mavila and teaching at the same time a beautiful philosophical multiplicity.
The 3rd interval in Mavila[9] is a minor third, the 4th is categorically a Super-major third. The 8th and 9th categorically are harmonic seventh and a major seventh/diminished octave. In the 9-note system it makes sense to no longer refer to 3/2 as the fifth, but as a 6th degree of the scale- also it is no longer a "Perfect fifth", but a highly tempered one.
A Little Math for a Middle Path
In 16-tone because of the 25 cent sharp 4/3 in conjunction with the 25 cent flat 3/2, the cycle of narrow fifths produces "minor" while the sharp fourths produce "major", reversing the traditional western functions of these intervals. Ther are many new intervallic resources which can be used to generate scales in 16-tone including Slendric, Lemba, Mavila/Pelogic, Magic and Vishnu.
Like the conventional 12-tet diatonic and pentatonic (Meantone) scales, these arise from tempering out 135:128 (difference of 16/15 and 9/8), instead of 81:80 (10/9 and 9/8).
The narrow fifths of 675 cents have an exotic, pelog-like sound. These take the player and listener to new places and well within a managable number of tones.