Names for 26 EDO Intervals

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William Lynch
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Names for 26 EDO Intervals

Post by William Lynch » Sun May 15, 2016 5:33 am

These are my proposed names for 26 EDO intervals. Sagittal uses normal accidentals for 26 so these names are extremely intuitive. I didn't use any of my usual artsy jargon but made them as clear and simple as possible. I would note that I have eliminated augmented and diminished entirely as I think they cause annoying confusion. I could be doing a bad thing here so let me know if you think we should keep augmented and diminished for certain intervals.

1/26 C C Perfect First
2/26 C C#, C Dbb Sharp-First, Flat Minor Second (Flat Second)
3/26 C Db Minor Second
4/26 C D Major Second
5/26 C D# Sharp-Major Second (Sharp Second)
6/26 C Dx, Super Sharp Major Second, C Ebb, Flat Minor Third (Flat third)
7/26 C Eb Minor Third
8/26 C E Major Third
9/26 C E# Sharp-Major Third (Sharp Third)
10/26 C Ex Super-Sharp Major Third, C Fb Flat Fourth
11/26 C F Perfect Fourth
12/26 C F# Sharp-Fourth
13/26 C Fx Super-Sharp Fourth, C Gbb Super-Flat Fifth
14/26 C Gb Flat-Fifth
15/26 C G Perfect Fifth
16/26 C G# Sharp-Fifth
17/26 C Gx Super Sharp Fifth, C Abb Super-Flat Minor Sixth
18/26 C Ab Minor Sixth
19/26 C A Major Sixth
20/26 C A# Sharp-Major Sixth
21/26 C Ax Super-Sharp Major Sixth C Bbb Super-Flat Minor Seventh
22/26 C Bb Minor Seventh
23/26 C B Major Seventh
24/26 C B# Sharp Major Seventh
25/26 C Cb Flat Octave, C Bx Super Sharp Major Seventh
26/26 C C Perfect Octave

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Dave Keenan
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Re: Names for 26 EDO Intervals

Post by Dave Keenan » Sun May 15, 2016 11:39 am

Hi William. I figure you'd want to get the pitch notation correct before we bother looking at your interval nomenclature. I think your mistakes were (a) to begin numbering from zero, and (b) to omit Cx, Dbb. The second mistake cancels out the first, so your list is correct from Db onward. And I note that you've used slashes for your octave fractions thereby risking confusion with frequency ratios. The convention is to use either backslashes or degree symbols e.g. 1\26 or 1°26. The pitch notation for 26 edo is:
 0°26	C
 1°26	C#
 2°26	Cx, Dbb
 3°26	Db
 4°26	D
 5°26	D#
 6°26	Dx, Ebb
 7°26	Eb
 8°26	E
 9°26	E#
10°26	Fb
11°26	F
12°26	F#
13°26	Fx, Gbb
14°26	Gb
15°26	G
16°26	G#
17°26	Gx, Abb
18°26	Ab
19°26	A
20°26	A#
21°26	Ax, Bbb
22°26	Bb
23°26	B
24°26	B#
25°26	Cb

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Dave Keenan
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Re: Names for 26 EDO Intervals

Post by Dave Keenan » Sun May 15, 2016 1:02 pm

Here are my usual two preferences, which can be used simultaneously without ambiguity:
 
		By pitch notation		By sound
		-------------------		----------
 0°26	C:C	1	one			P1	perfect unison
 1°26	C:C#	#1	sharp one		S1	super unison
 2°26	C:Dbb	bb2	double flat two		sm2	subminor second
 3°26	C:Db	b2	flat two		m2	minor second
 4°26	C:D	2	two			M2	major second
 5°26	C:D#	#2	sharp two		SM2	supermajor second
 6°26	C:Ebb	bb3	double flat three	sm3	subminor third
 7°26	C:Eb	b3	flat three		m3	minor third
 8°26	C:E	3	three			M3	major third
 9°26	C:E#	#3	sharp three		SM3	supermajor third
10°26	C:Fb	b4	flat four		s4	sub fourth
11°26	C:F	4	four			P4	perfect fourth
12°26	C:F#	#4	sharp four		S4	super fourth
13°26	C:Fx	x4	double sharp four	Aug4	augmented fourth
14°26	C:Gb	b5	flat five		s5	sub fifth
15°26	C:G	5	five			P5	perfect fifth
16°26	C:G#	#5	sharp five		S5	super fifth
17°26	C:Abb	bb6	double flat six		sm6	subminor sixth
18°26	C:Ab	b6	flat six		m6	minor sixth
19°26	C:A	6	six			M6	major sixth
20°26	C:A#	#6	sharp six		SM6	supermajor sixth
21°26	C:Bbb	bb7	double flat seven	sm7	subminor seventh
22°26	C:Bb	b7	flat seven		m7	minor seventh
23°26	C:B	7	seven			M7	major seventh
24°26	C:B#	#7	sharp seven		SM7	supermajor seventh
25°26	C:Cb	b8	flat eight		s8	sub octave
26°26	C:C	8	eight			P8	perfect octave
Of course alternative names are possible for many intervals, in what is hopefully an obvious manner. The system used to derive the "by sound" names is described in http://dkeenan.com/Music/EdoIntervalNames.pdf.

William Lynch
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Re: Names for 26 EDO Intervals

Post by William Lynch » Sun May 15, 2016 10:05 pm

Oh yeah thanks for the pitch correction. I wanted to entirely get rid of augmented and diminished as I think they do nothing but cause confusion in microtonal systems. I propose either Wide/Narrow or Super/Sub but not use Aug/dim at all. Paul Erlich's suggestion was Wide and Narrow for +1 and -1 and Superwide and Sub-Narrow for +2, -2. In other words why is 11/8 an aug4 but 9/7 a supermajor? Why not just have 11/8 as super fourth and 9/7 a supermajor third? It's less confusing to have only one term meaning +1 or -1.

But I prefer Wide and Narrow for 1, and Super Sub for 2 thus we have

C C Perfect First
C C# Wide First, C Dbbb Super-Narrow (Minor) Second
C Cx Super-wide First, C Dbb Narrow (Minor) Second
C Db Minor Second
C D Major Second
C D# Wide (Major) Second
C Dx Superwide (Major) Second, C Ebbb Super-Narrow (Minor) Third
C Ebb Narrow (Minor) Third
C Eb Minor Third
C E Major Third
C E# Wide (Major) Third
C Ex Super-wide (Major) Third, C Fb Narrow Fourth
C F Perfect Fourth
C F# Wide Fourth
C Fx Superwide Fourth, C Gbb Super Narrow Fifth
C Gb Narrow Fifth
C G Perfect Fifth
C G Super Fifth
.....

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Dave Keenan
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Re: Names for 26 EDO Intervals

Post by Dave Keenan » Sun May 15, 2016 11:51 pm

William Lynch wrote:In other words why is 11/8 an aug4 but 9/7 a supermajor? Why not just have 11/8 as super fourth and 9/7 a supermajor third? It's less confusing to have only one term meaning +1 or -1.
I think you may not have read my list correctly. In my 26 edo naming scheme above, super is always +1, sub is always -1, augmented is always +2 (from the major or the perfect), diminished is always -2 (from the minor or the perfect). The 7:9 approximation is the supermajor third (9°26), the 8:11 is the super fourth (12°26) and the 5:7 is the augmented fourth (13°26). These names have been assigned to these just intervals since time immemorial.

I prefer to use "wide" and "narrow" in a way that corresponds, at least approximately, with the following names for rational or just intervals:
Interval
symbol	Ratio	Interval name
------------------------------------
P1	1:1	perfect unison
m2	15:16	minor second
N2	11:12	neutral second
WN2	10:11	wide neutral second
M2	9:10	major second
WM2	8:9	wide major second
SM2	7:8	supermajor second
sm3	6:7	subminor third
nm3	27:32	narrow minor third
m3	5:6	minor third
N3	9:11	neutral third
WN3	13:16	wide neutral third
M3	4:5	major third
nSM3	11:14	narrow supermajor third
SM3	7:9	supermajor third
P4	3:4	perfect fourth
S4	8:11	super fourth
A4	5:7	augmented fourth
d5	7:10	diminished fifth
s5	11:16	sub fifth
P5	2:3	perfect fifth
sm6	9:14	subminor sixth
Wsm6	7:11	wide subminor sixth
m6	5:8	minor sixth
nN6	8:13	narrow neutral sixth
N6	11:18	neutral sixth
M6	3:5	major sixth
WM6	16:27	wide major sixth
SM6	7:12	supermajor sixth
sm7	4:7	subminor seventh
nm7	9:16	narrow minor seventh
m7	5:9	minor seventh
nN7	11:20	narrow neutral seventh
N7	6:11	neutral seventh
M7	8:15	major seventh
P8	1:2	perfect octave
Last edited by Dave Keenan on Mon May 16, 2016 11:37 am, edited 1 time in total.
Reason: Corrected "narrow subminor third" to "narrow minor third".

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