Erisian Modes - org-page

A quick bit about intervals

If I really wanted to harp on about the arbitrariness of musical theory, then I would give these intervals some kind of name. The problem is that we have chafed under the iron fist of the Bean Haters (Pythagorean) and we must suffer with letter note names, and piano-rolls rather than the austere purity of numbers.

I toyed with the idea of naming them after astrological signs, but that is a rabbit hole I am not prepared to go down.

Anyhoo, here is a list of intervals and their "Musical Quality". Keep in mind this is a gradient in terms of it's effect on human perception; Unisons, Octaves and Perfect intervals tend to sound more cross culturally musically pleasing, but after that, all bets are off.

Distance	Western	Abbrev	"Quality"
From	Name		"Character"
Root			"Sound"
0	Unison	P1	Itself
1	Minor 2nd	m2	Harsh
2	Major 2nd	M2	Dense
3	Minor 3rd	m3	Mellow, Melancolic
4	Major 3rd	M3	Happy
5	Perfect 4th	P4	Pure
6	TriTone	TT	HAIL SATAN
7	Perfect 5th	P5	Pure
8	Minor 6th	m6	Mellow, Distant
9	Major 6th	M6	Optimistic, Distant
10	Minor 7th	m7	Tension
11	Major 7th	M7	Hash, Discordant
12	Octave	P8	Itself but higher

Erisian Scales

Okay, just to be clear, I didn't make these. I just decided to name them. The whole point of this is to explore intervals and to show the arbitrary nature of Western Musical Scales and Theory.

They are called Erisian because each Mode is composed of 5 notes, with 2 intervals of 3 semitones, and 3 intervals of 2 semitones in sequence. Lots of Law of Fives action going on here.

Element	Note	Interval Seq	Visual	"Western" Scale	Western Interval Name
Sweet	Db	2 3 2 2 3	.X..X	Blues Major	P1, M2, P4, P5, M6
Boom	Eb	3 2 2 3 2	X..X.	Minor Pent	P1, m3, P4, P5, m7
Prickle	Gb	2 2 3 2 3	..X.X	Major Pent	P1, M2, M3, P5, M6
Pungent	Ab	2 3 2 3 2	.X.X.	Egyptian	P1, M2, P4, P5, m7
Orange	Bb	3 2 3 2 2	X.X..	Blues Minor	P1, m3, P4, m6, m7
Kallisti	??	2 2 3 3 2	..XX.		P1, M2, M3, P5, m7

So a "Erisian Sweet" in "A" would be A B D E Gb

Intervals from within the scales

Perhaps one of the more interesting explorations was to examine all possible intervals from within a particular scale. So for the "Sweet (Blues Major Pentatonic)" scale, what is the interval between the 1st note and the 3rd? How about the 4th note and the 2nd?

Knowing these intervals will actually tell you a whole lot about the scale itself, and what kind of tone that scale will have.

Sweet (Blues Major Pentatonic)

To	1st	2nd	3rd	4th	5th
From
1st	P	M2	P4	P5	M6
2nd	(m7)	P	m3	P4	P5
3rd	(P5)	(M6)	P	M2	M3
4th	(P4)	(P5)	(m7)	P	M2
5th	(m3)	(P4)	(m6)	(m7)	P

Okay, so just a few things to note here:

Intervals in Parenthesis represent wrapping around to the octave.
there is not a single Tritone, Major 7th, or Minor 2nd. Which is to say notes right beside the Unison or Perfects. In fact, the interval palette is quite limited.
Each Erisian scale is encoded in the intervals between the notes. This is not true of the C Major scale, where the distance between F and B is a Tritone, but the tritone interval isn't itself part of the scale.

We can then count the number of times a given interval shows up in this scale:

Interval	Occurances
M2	2
m3	2
M3	1
P4	3
P5	3
m6	1
M6	1
m7	3

Boom

Here are Booms intervals

To	1st	2nd	3rd	4th	5th
From
1st	P	m3	P4	P5	m7
2nd	(M6)	P	M2	M3	P5
3rd	(P5)	(m7)	P	M2	P4
4th	(P4)	(m6)	(m7)	P	m3
5th	(M2)	(P4)	(P5)	(M6)	P

And the number of times each one occurs. Notice the pattern?

Interval	Occurrences
M2	3
m3	1
M3	1
P4	3
P5	3
m6	1
M6	2
m7	2

Prickle

From	1st	2nd	3rd	4th	5th
To
1st	P	M2	M3	P5	M6
2nd	(m7)	P	M2	P4	P5
3rd	(m6)	(m7)	P	m3	P4
4th	(P4)	(P5)	(m6)	P	M2
5th	(m3)	(P4)	(P5)	(m7)	P

Interval	Occurances
M2	2
m3	2
M3	0
P4	4
P5	3
m6	1
M6	1
m7	3

So here we have a departure in the pattern of interval occurrences. Notice how there are 4 Perfect 4ths.

Pungent

From	1st	2nd	3rd	4th	5th
To
1st	P	M2	P4	P5	m7
2nd	(m7)	P	m3	P4	m6
3rd	(P5)	(M6)	P	M2	P4
4th	(P4)	(P5)	(m7)	P	m3
5th	(M2)	(M3)	(P5)	(M6)	P

Interval	Occurrence
M2	2
m3	2
M3	1
P4	3
P5	3
m6	1
M6	2
m7	2

There is a nice internal symmetry here.

Orange

From	1st	2nd	3rd	4th	5th
To
1st	P	m3	P4	m6	m7
2nd	(M6)	P	M2	P4	P5
3rd	(P5)	(m7)	P	m3	P4
4th	(M3)	(P5)	(M6)	P	M2
5th	(M2)	(P4)	(P5)	(m7)	P

Interval	Occurrence
M2	2
m3	2
M3	0
P4	4
P5	3
m6	1
M6	1
m7	3

And this guy is a mirror image of Prickle!

Kallisti - The Prettiest one

So as I alluded to in my video, I mathed wrong, and ended up making this scale by raising he interval of the last note by one.

From	1st	2nd	3rd	4th	5th
To
1st	P	M2	M3	P5	m7
2nd	(m7)	P	M2	P4	m6
3rd	(m6)	(m7)	P	m3	TT
4th	(P4)	(P5)	(M6)	P	m3
5th	(M2)	(M3)	(TT)	(M6)	P

The distribution here is radically different though

Interval	Occurrence
M2	2
m3	2
M3	1
P4	2
TT	2
P5	1
m6	2
M6	2
m7	2

For Ableton Push

If you want, here is the python chunk to add the Erisian modes to Pushes scales.

'Erisian Sweet',
[0, 
 2, 
 5,
 7,
 9],
'Erisian Boom',
[0,
 3,
 5,
 7,
 10],
'Erisian Prickle',
[0,
 2,
 4,
 7,
 9],
'Erisian Pungent',
[0,
 2,
 5,
 7,
 10],
'Erisian Orange',
[0,
 3,
 5,
 8,
 10],
'Erisian Kallisti',
[0,
 2,
 4,
 7,
 10],