notation

Re: maximal evenness and notation

One interesting scheme for notating tunings that I use is this
7-out-of-N based one.

Suppose you allow that a C major scale can be generalized so that the
sequential C through C alphabetized letter names correspond to a -1
through 5 generator chain where the 6th interval in the chain is one
greater than -1st interval in the chain.

This is one way to address many equal tunings that are generally
considered very difficult (if not impossible) to shoehorn into any
sort of a standard notational framework.

Here's a simple example of this idea in eleven equal (the second part
is just the same example carried out to a dual completion of the
chain):

0. C
1. Db
2. D
3. E
4. Fb
5. F
6. Gb
7. G
8. A
9. Bb
10. B
11. C

C
E 3 8 A
Gb 6 5 F
Bb 9 2 D
Db 1 10 B
Fb 4 7 G
Ab 7 4 E#
Cb 10 1 C#
Eb 2 9 A#
Gbb 5 6 F#
Bbb 8 3 D#
Dbb 0 11 B#

Here's another example in twenty:

0. C
1. C#
2. Db
3. D
4. D#
5. Eb
6. E
7. E#
8. Fb
9. F
10. F#,Gbb
11. Gb
12. G
13. Abb
14. Ab
15. A
16. Bb
17. B
18. B#
19. Cb
20. C

C
B 17 3 D
Ab 14 6 E
Gb 11 9 F
Fb 8 12 G
Eb 5 15 A
Db 2 18 B#
Cb 19 1 C#
Bb 16 4 D#
Abb 13 7 E#
Gbb 10 10 F#
Fbb 7 13 G#
Ebb 4 16 A#
Dbb 1 19 Bx
Cbb 18 2 Cx
Bbb 15 5 Dx
Abbb 12 8 Ex
Gbbb 9 11 Fx
Fbbb 6 14 Gx
Ebbb 3 17 Ax
Dbbb 0 20 B###

--Dan Stearns

Different applications of ME notation allow different ways to retain a
self-consistent representation of enharmonics and key signatures on
the traditional five line staff.

7-out-of-N orients everything in the seven note name manner of
traditional notation. But I also use the same basic principles to
either add or subtract alphabetized note names in a much more overtly
xenharmonic manner while retaining the convenience of self-consistency
and the five line staff.

Here's one simple example in thirteen equal based on an eight-tone
22121221 "diatonic" scale, C D E F G H A B C:

C
H 8 5 F
Eb 3 10 A
Bb 11 2 D
Gb 6 7 G
Db 1 12 B
Ab 9 4 E
Fb 4 9 H#
Cb 12 1 C#
Hb 7 6 F#
Ebb 2 11 A#
Bbb 10 3 D#
Gbb 5 8 G#
Dbb 0 13 B#

To accommodate the additional alphabetical note name here I placed a
single ledger line through the new note head. Here's the above 8-tone
13-EDO example:

---------------------------------------

---------------------------------------
C
-----------------------------B---------
-H- A
-----------------G---------------------
F
---------E-----------------------------
D
-C-

--Dan Stearns

I wrote,

The key of Gb major in 11 equal would be 5 7 9 10 0 2 4 5, and would
be notated as:

bG
---------------------------------\F------------
/bE
---------------------\bD-----------------------
bC
-----------bB----------------------------------
bA
-bG--------------------------------------------

-----------------------------------------------

The raised by 1/N glyph is a typo, so that should've read:

b5
---------------------------------\4------------
\b2
---------------------\b0-----------------------
b10
-----------b9----------------------------------
b7
-b5--------------------------------------------

-----------------------------------------------

--Dan Stearns