Archive for the ‘17 edo’ Category

Drilling on Ceres (17 edo soundscape)

Friday, January 29th, 2016

Occator_PIA19889

Drilling on Ceres – building star ships by mining asteroids – a soundscape in 17 edo using Aalto and the Linnstrument.

17 edo major – minor mode comparison and V of V

Sunday, December 13th, 2015

1212a
NOTE: Above is the scordatura notation. If you use a synthsizer tuned to 17 edo and play these notes on a “normal” keyboard you will reproduce the examples
Example of alternating 10ths and 5ths in major mode (with coda)
I V vi iii IV I V IV I
Piano
Choir
1212b
Example of alternating 10ths and 5ths in minor mode (with coda)
i v VI III iv i V(neutral 3rd) i
Piano
Choir
1212c
Tonicization in minor mode https://en.wikipedia.org/wiki/Tonicization
i II VI V/V V
Piano
Choir
1212d
Tonicization in major mode
I V vi V/V V
Piano
Choir
1212e
The natural minor mode of 17 edo used
Piano
Choir

Complete set of examples in one file Piano Choir

14th Century Harmony in 17 EDO – by Margo Schulter

Friday, December 11th, 2015

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.

17 edo chord progressions and cadences

Wednesday, December 9th, 2015

129a
I – IV 2nd inversion ii V 2nd I The word inversion will be considered understood going forward and see note at bottom for score notation information.
129b
I 2nd inv IV 1st ii 2nd V 1st
129c
I IV 2nd ii V 2nd iii vi 2nd IV vii°7 2nd I 1st
129d
I IV 2nd ii V 2nd iii vi 2nd IV V°7 2nd I 1st
129e
I IV neutral 3 V7 I
129f
I IV neutral 3 V7 no third 2nd I
129g
I7 IV 2nd V 3rd I
129h
I7 IV7 2nd V7 2nd I

NOTE: all examples are scordatura – if you have software in 17 notes per octave and play these notes on a regular keyboard you will get these progressions.
The trade off is one of sacrificing clear notation for playability

the full set of examples

17 edo I-IV-V Cadences

Tuesday, December 8th, 2015

17triads
17 edo triads – framed in a perfect fifth are sus2 (212 cents), minor (282 cents), neutral (353 cents), major (424 cents), sus4 (494 cents) and then walked back down ending on a resolution of the sus4 – more on 17 edo
NOTE: all examples are scordatura – if you have software in 17 notes per octave and play these notes on a regular keyboard you will get these progressions.
The trade off is one of sacrificing clear notation for playability
145a
I root -IV 2nd inversion – V 1st inversion – I root
145b
I root -IV 2nd inversion – V7 1st inversion – I root
145c
I 1st -IV root – V 1st – I 2nd – IV 1st – V 1st (sorry for the missed F# – should be Gb)
145d
I 2nd -IV 1st – V7 1st inversion – I root
145e
i root -iv 2nd inversion – V 1st inversion – i root
145f
i root -iv 2nd inversion – V7 3rd inversion – i root
145g
i root -iv st inversion – V7 2nd inversion – i root

every example in one file

Discussion: The above illustrates the use of 17 edo within the context of common practice as developed for 12 notes per octave tuning. 17 works acceptably in this context. Adding a seventh or using inversions tends to soften the very sharp 423 cent major thirds. In the context of a minor key with the only major third being in the V to i the sharpness becomes an asset as a leading tone.