14th Century Harmony in 17 EDO – by Margo Schulter

1211m1
Above is the scordatura notation of Margo’s examples
Example 1
Text and examples by Margo Schulter: Here’s a curious sketch for another side of 17-ed2, (17 edo) or a 17-WT also, that starts with some 14th-century European common practice, and then gets a bit more uncommon with thirdtone shifts.

A---G---F---E---F..|.F--G---A.|
E---D---C---B---C....C--D---E.|
C---Bb--A---G---F....F--Bb--A.|

Here’s what I hope is a clearer notation of my idea for 17-ed2 or a 17-note well-temperament (17-WT) like George Secor’s, showing the voices using scale steps as well as Pythagorean note names.

A---G---F---E---F..|.F--G---A.|
E---D---C---B---C....C--D---E.|
C---Bb--A---G---F....F--Bb--A.|

23--20--17--16--17.|.17-20--23|
16--13--10--9---10...10-13--16|
10--7---6---3----0...0--7---6.|

Notice how cadences with ascending semitones tend to be more conclusive that those with descending semitones, and the way that the wide major third and sixth expand efficiently to the fifth and octave respectively.

1211m2
Above is the scordatura notation of Margo’s examples
Example 2

A---G---F-------G..|.A--G---F-------Gb.|
E---D---C-------D....E--D---C-------Db.|
C---Bb--A---Ab--G....C--Bb--A---Ab--Gb.|

23--20--17------20.|.23-20--17------18.|
16--13--10------13...16-13--10------11.|
10--7---6---4---3....10--7--6---4---1..|

Here the lower F is step “0,” on which we cadence in the fifth sonority, F-C-F or 0-10-17 steps.

Note that in the first eight sonorities, all melodic steps are either regular tones (3 steps) or regular diatonic semitones (1 step).

In the lower system, however, the lowest voice moves through scale steps 10-7-6-4-3 (descending 3-1-2-1 steps) or C-Bb-A-Ab-G, with Ab-A a chromatic semitone or 2 steps; and then 10-7-6-4-1 (desecnding 3-1-2-3 steps, or a 9-step tritone in all at 635.3 cents, close to 13/9), C-Bb-A-Ab-Gb.

Here it may also be helpful that 10 steps is a perfect fifth, 7 steps a perfect fourth; 4 steps, a minor third, and 6 steps a major third; 11 steps, a minor sixth, and 13 steps a major sixth. There are no vertical neutral or middle intervals used here, although that would open lots and lots of other possibilities. However, the melodic middle seconds or chromatic semitones A-Ab in the lowest voice (2 steps) may give a hint.

Again, what the numbers count is thirdtone steps in 17-ed2 (or some 17-WT), which I’m hoping will clarify the notation.

Margo requested an organ version – I broke up the examples into four phrases.
Scott Dakota requested a choir version – as above this is in four phrases.

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