Greetings Gedankenwelt,
I apologize for the month long delay between your post and my response. I am happy to share and do not find your inquiries intrusive in the least bit. I am just very busy. I am not active on any other microtonal site or forum. I appreciate you pointing out that the 12edo major third is nearly identical to a minor whole step(10/9) down from the lesser septimal tritone(7/5). I had never thought of it that way. I have not really explored extendeded harmonies much and my chords don't usual include intervals more complex than a harmonic minor seventh(7/4). I use the higher limit intervals primarily for melodies. The scale of 53 'commas' to the octave works great for the 5 limit, from which the vast majority of my chord tones are drawn. The intervals that are derived from 7/4 are about 5 cents sharp. My approach to guitar playing is based somewhat on the instability of the fretted note. I use finger pressure toward the bridge, just behind the fret to flatten pitches when necessary. I can only flatten a pitch so far, depending on how far up the neck I am playing. 5 cents is no problem. It is even manageable in the midst of a dominant seventh chord. The 11 limit is poorly represented by 53edo. 13 limit intervals are only a few cents off. If one 'splits the comma', giving the octave 106 intervals, the 11 limit intervals are more closely represented. My acoustic eight string accomodates the 106edo in the middle section of the neck. It is difficult to do accurate, subtle pitch bending at high velocity, but I am not much of a shredder. Practice makes it easier. The basic fret work for the 53edo guitar is to place a fret for every third comma. So the frets are about 68 cents apart, a very narrow 'half step', almost identical to 26/25, and a very close approximation of 25/24. Three frets add up to a whole tone 9/8. You could call it a 1/3 tone scale. The first octave on any string contains only a third of the 53 notes, so adjacent strings are tuned to hold the remaining two-thirds.On the electric 8 string,I added a couple of extra frets, commas 5 and 13, to the section of the fingerboard nearest the nut, where things are not to crowded.The acoustic has a very long scale length, so I included all but the first comma in the lowest wholetone of the fingerboard. Although the scale is tempered, I pretty much tune with just intervals. Here is a typical tuning, from low to high-E1/1,G6/5,A4/3,C8/5,D16/9,F32/15,G64/27,Bb128/45. This tuning works well for my musical purposes but many others are surely useful, once discovered and learned.
I came up with this fret work a little over a year ago, and I have really just gotten started. I believe that fretwork/tuning has great potential, and I would love for some other folks to explore the possibilities as well. Thanks for your interest. I will attempt to post a picture in the photo area.
Matt Autry
