12-edo-staff (musical notation)
[Joe Monzo]
A form of manuscript paper invented by Joe Monzo, in which each staff represents one octave, beginning on "C". Each semitone of the standard 12-edo scale is represented alternately by a line and a space. The line for "C" is omitted so that staves can be stacked with a space between each one, with "C" represented by a ledger-line where it occurs -- this is a visual representation of the octave periodicity which is a feature of the vast majority of the world's music.
The material presented below was adapted from three A HREF="linkto.aspx?http://groups.yahoo.com/group/tuning/">Yahoo Tuning Group posts:
47732 From: monz
Date: Tue Oct 7, 2003 1:31am
Subject: Re: Polyphonic notation
47733 From: monz
Date: Tue Oct 7, 2003 1:35am
Subject: Re: Polyphonic notation
47734 From: monz
Date: Tue Oct 7, 2003 1:45am
Subject: Re: Polyphonic notation
i never addressed the problem of changing nominals for either 12edo or octatonic. i merely came up with what i think is a better staff notation for it.
Below is an illustration of one "octave" of the 12edo scale on the 12edo-staff, giving both the 12edo degree-numbers and the 12edo-HEWM nominals and accidentals. it's a "quick-and-dirty" ASCII diagram of my 12edo-staff, showing the mapping and two typical scales:
mapping of 12edo to 12edo-staff:
-- -- 0 C --
11 B
-------- 10 A#/Bb ------------------------------------------
9 A
--------- 8 G#/Ab ------------------------------------------
7 G
--------- 6 F#/Gb ------------------------------------------
5 F
--------- 4 E ----------------------------------------------
3 D#/Eb
--------- 2 D ----------------------------------------------
1 C#/Db
-- -- 0 C --
12-edo diatonic C-major scale:
-----------------------------
mapping of nominals:
-- --C--
B
-------------------------------------------------
A
-------------------------------------------------
G
-------------------------------------------------
F
----------------E--------------------------------
-----------D-------------------------------------
-- --C--
simulated appearance of notation in whole-notes:
-- --O--
O
-------------------------------------------------
O
-------------------------------------------------
O
-------------------------------------------------
O
----------------O--------------------------------
-----------O-------------------------------------
-- --O--
my opinion is that the octatonic scale in this notation
is just as "transparent" as the diatonic.
12edo octatonic scale, starting on C:
-------------------------------------
mapping of nominals:
-- --C--
B
--------------------------------------------------
A
-------------------------G#/Ab--------------------
---------------------F#/Gb------------------------
F
--------------------------------------------------
D#/Eb
-----------D--------------------------------------
-- --C--
simulated appearance of notation in whole-notes:
-- --O--
O
---------------------------------------------------
O
----------------------------O----------------------
-----------------------O---------------------------
O
---------------------------------------------------
O
------------O--------------------------------------
-- --O--
and so is
any other 12edo scale, such as the "whole-tone scale":
6edo "whole-tone scale"
-----------------------
mapping of nominals:
-- --C--
---------------------------------A#/Bb--------------
----------------------------G#/Ab-------------------
-----------------------F#/Gb------------------------
------------------E---------------------------------
------------D---------------------------------------
-- --C--
simulated appearance of notation in whole-notes:
-- --O--
---------------------------------O------------------
----------------------------O-----------------------
-----------------------O----------------------------
------------------O---------------------------------
------------O---------------------------------------
-- --O--
Using nominals A...L on 12edo-staff
Yahoo Tuning Group posts:
--- In tuning-math@yahoogroups.com, "monz" wrote:
if one only need keep a 1-dimensional chain of notes in mind as either his set of nominals (i.e., the pythagorean diatonic scale) or his nominals-plus-accidentals (setting an arbitrary limit somewhat based on historical usage, the 35-tone pythagorean chain stretching from Fbb to Bx), matters are greatly simplified.
(they would be simply even further if all nominals could be used for the entire chain, thus giving an absolute consistency to the meaning of the notational symbols.)
so anyway, HEWM and sagittal have a pythagorean basis for this reason, and also because it reflects historical usage. indeed, if they were to ignore historical usage, they *would* employ a larger nominal set to represent a 12-tone pythagorean chain rather than a 7-tone chain, since the pythagorean comma (3^12) is a less-perceptible change in tuning than a 2187/2048 chromatic semitone (3^7).
as an example, one could notate either 12edo or a 12-tone pythagorean chain nicely with the nominals A...L, and put it on my 12edo-staff:
(the numerals at the left are either 12edo degrees or degrees of the pythagorean scale, and can be considered as a kind of clef)
-0- --A--
11 L
10 ----------------------------------K----------------
9 J
8 ----------------------------I----------------------
7 H
6 -----------------------G---------------------------
5 F
4 ------------------E--------------------------------
3 D
2 ------------C--------------------------------------
1 B
-0- --A--
in this convention, if the bottom --A-- is "middle-C",
then the set of diatonic triads in C-major is:
(read vertically for each triad)
-0-
11 L L L
10 --------------------------------------------------
9 J J J
8 --------------------------------------------------
7 H H H
6 --------------------------------------------------
5 F F F
4 -----E------------E-----------------E-------------
3
2 ------------C------------------C-----------C------
1
-0- --A-- --A-- --A--
I ii iii IV V vi vii
Another alternative is to use the regular 7-nominal system (A,B,C,D,E,F,G) and make the bottom note of each staff represent "A", as follows:
-- --A--
--------------------------------G----------------
----------------------------F--------------------
E
-------------------------------------------------
D
-------------------------------------------------
C
-----------B-------------------------------------
-- --A--
Using this convention, here is an example illustrating the first phrase of Für Elise:
. . . . . . . . .
