Archive for the ‘Music Theory’ Category

Melodyne Deep Dive in an Aeolian Harp Sound Sample

Saturday, August 27th, 2016

00_cents
The above aeolian harp sample (from 2014-11-07 21:12:51 pm) had an interesting sonority to my ears. I wanted to find out what the chord was so that I could reproduce it. So I put it into Melodyne to analyze the chord. As I listened to the file and looked at the display there seemed to be a bit of a disconnect. So I dissected the sample (Sections labeled A through H by ear – there are two disjunct groups) into individual files. Then I normalized them and ran them through Melodyne once more. The resulting sound files and analysis are below. You will notice that in some cases what was a single tone in the original now breaks into more than one note. In other cases more than one note is heard but Melodyne doesn’t show them as separate – I think in these cases the program analysis is tagging them as part of the harmonics which is shown below the main window of the program. Since an aeolian harp is a special case where the harmonics of this is a special case, interesting though it may be. Most of the dead air was removed from the A through H audio samples.

The labeled file below is in Hz. You can download the audio and graphics here as a zip file.
00_Hz
Full file (click on any graphic to enlarge / download)

Section A
0a_

Section B
0b_

Section C
0c_

Section D
0d_

Section E
0e_

Section F
0f_

Section G
0g_

Section H
0h_

Comparing 22 edo Superpyth Modes

Sunday, July 17th, 2016

Example music is Debussy’s Arabesque No. 2 from a performed midi file.

Arabesque no. 2 click to see piano roll

mode 1

mode 2

mode 3

mode 4

mode 5

mode 6

mode 7

mode 8

mode 9

mode 10

mode 11

mode 12

The original as played by Debussy (youtube)

SP22_modes all of the modes – click to enlarge
scala files of all 12 modes
score from midi file used

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.

Some I-IV-V Progressions in 16 equal

Sunday, August 4th, 2013

To avoid confusion
1. All of the notation is in scordatura. If your regular midi controller is tuned to play 16 edo you will get the sound of the chord progressions if you play the 12 equal notation. Consider it a transformation in tuning.
2. When I talk about scale degrees, such as referring to I, IV, or V, or a fifth or third, I am relating the structure in 16 edo to the function in 12 equal for the sake of being able to discuss something which does not have a widely know naming conventions. When, as I plan, start using progressions ambivalent or foreign to 12 equal this naming convention will have to be expanded. For now just consider it a way to get ideas across.

Tonic in root, 1st inversion V, I root


Cadence 1


Tonic root, IV 2nd inversion with open voicing, V in 1st inversion with open voicing, tonic in root with double root.


Cadence 2


Tonic I7 in root, IV7 in 2nd inversion, V7 in 1st inversion, tonic in 2nd inversion with 5th doubled.


Cadence 3


Tonic root I7, IV7 in 4th inversion, V7 in 1st inversion, tonic in root with doubled tonic.


Cadence 4


Tonic in 1st inversion, IV in root, V in 1st inversion, tonic in root with 3rd doubled.


Cadence 5


Tonic in root, 3rd doubled, IV7 in 2nd inversion and open voicing, V7 in 2nd inversion (note the “incorrect” parallel “5ths”), tonic I with doubled root.


Cadence 6


Tonic I7 in 1st inversion, IV7 in root, V in 1st inversion, tonic with doubled 3rd.


Cadence 7


Tonic in 2nd inversion, IV7 in root, Tonic I7 in root, root doubled.


Cadence 8


Tonic I7 in 2nd inversion, IV7 in root, V7 in 1st inversion, tonic I in root


Cadence 9


Some Plagal Cadences in 16 edo

Saturday, July 27th, 2013

Note: all of the music is presented as scordatura – if you tune your midi controller to 16 notes per octave and play the notes shown you will hear the example progressions.

Tonic in root, 2nd inversion functional IV, tonic in root


Major Cadence 1


Tonic in root, functional IV in 2nd inversion, tonic in 1st inversion


Major Cadence 2


Tonic in root, functional IV in root, tonic in 1st inversion


Major Cadence 3


Tonic in 1st inversion, functional IV in root, tonic in root


Major Cadence 4


Tonic in root (doubled “M3rd”), functional IV7 in 2nd inversion, tonic in root


Major Cadence 5


Tonic 1st inversion 7th, IV7 root, tonic root doubled “M3”


Major Cadence 6


Tonic in 2nd inversion, IV in root, open voicing, tonic in root doubled tonic


Major Cadence 7


Tonic I7 in 1st inversion, IV7 in root, tonic in root


Major Cadence 8



Below this point the “IV” chord is a minor “iv” chord – making for a minor plagal cadence – see Plagal Cadence

Tonic in root, functional iv in 2nd inversion, tonic in root


Minor iv Cadence 1


Tonic in root, functional iv in 2nd inversion, tonic in 1st inversion


Minor iv Cadence 2


Tonic in root, functional iv in root, tonic in 1st inversion


Minor iv Cadence 3


Tonic in 1st inversion, functional iv in root, Tonic in root


Minor iv Cadence 4


Tonic in root, functional iv7 in 2nd inversion, tonic in root


Minor iv Cadence 5


Tonic 7 in 1st inversion, functional iv7 in root, tonic in root


Minor iv Cadence 6


Tonic in 2nd inversion, functional iv in root open voicing, tonic in root


Minor iv Cadence 7


Tonic 7 in 1st inversion, functional iv7 in root, tonic in root


Minor iv Cadence 8


Note: all of the music is presented as scordatura – if you tune your midi controller to 16 notes per octave and play the notes shown you will hear the example progressions.