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
Names for 26 EDO Intervals
- Dave Keenan
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Re: Names for 26 EDO Intervals
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
- Dave Keenan
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Re: Names for 26 EDO Intervals
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 octaveOf 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.
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Re: Names for 26 EDO Intervals
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
.....
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
.....
- Dave Keenan
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Re: Names for 26 EDO Intervals
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.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 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".
Reason: Corrected "narrow subminor third" to "narrow minor third".