If the notation of a wide range of non-twelve equidistant divisions of the

octave (n-tET�s) is predominately (though certainly not exclusively) the

concern of those using fixed pitch instruments, exactly specifying pitch on

the manuscript page (i.e., using special �microtonal accidentals� to denote

the specific variance in which a pitch differs from the standard target

pitches of twelve tone equal temperament*) would seem not so much of a

concern�

If there were some sort of a compromise in which the chromatic spelling of

any n-tET could be consistently addressed** (if not �consistently�

rendered***), and then taken to the manuscript without altering the

sequential spelling of keys (or the sequence of diatonic seconds****)�

Perhaps an additional set of two glyphs (some suitable analogue to the sharp

and the flat that alerts one to the �altered� notes � relation to its

correct spelling) could then address the altered scale degrees� This would

seem especially convenient in the case of (�tonal�) music that largely

adheres to a key signature.*****

Dan Stearns

*I personally use a variant of Ezra Sims� notation that crosses the (�arrow�

, �half-arrow�, and �square root�) symbols. This grew out of an attempt to

achieve a �utilitarian� all purpose pitch continuum reference and notation

that required learning one (learnable) main set of multipurpose symbols� The

problems with this are that most any densely voiced single staff writing can

quickly become a rather daunting thicket of �data� - But again, I don�t

believe that fixed pitch instruments need to trouble themselves with this

kind of notation� The other problem is that while I find it very easy to

memorize one main set of three symbols - Learning to navigate (approximate)

eight and a third cent alterations of eighth tones is quite another matter!

**If one assumes that any such process is largely a �utility� of recasting

the heptad� There would seem to be two �ideals� achievable by addressing

fifth size (that also accommodate both an internally consistent fidelity to

the procedure of equally dividing the octave _and_ the �third friendly�

constitution of quarter comma meantone or five limit just intonation). The

first would involve recasting n-"d" in an approximation of quarter comma

meantone. This could be done by recasting "O" as 31, "F" as 18, and "f" as

13. Then d � O � F = the "d" approximation of a quarter comma meantone

fifth. The second would involve a variant of the same process� If "O" = 31

and "d" = 53; 53 is recast in 31, thus allowing "O" to = 53 but "F" to =

30.24/31 (and therefore "f" to = 22.7/31), and functionally recasting n-"d"

in an approximation of five limit just intonation.

***If 22tET is recast in five limit just intonation @:

C

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

F 9 G 13

Bb 18 D 4

Eb 6 A 16

Ab 15 E 7

Db 2 B 20

Gb 11 F# 11

Cb 21 C# 1

Fb 8 G# 14

Bbb 17 D# 5

Ebb 4 A# 18

Abb 13 E# 9

Dbb 1 B# 21

Gbb 10 Fx 12

Cbb 19 Cx 3

Fbb 6 Gx 16

Bbbb 16 Dx 6

D = Ebb... but not CX, F = E#... but not Gbb etc., etc., But as the whole

idea is to circumnavigate an Eb that is Fbb and DX and yet is not DX, E, or

Fb (!)� A major scale in any key (of any utilitarian n-tET) that maintains

both a consistent (having nothing to do with symmetric) array of diatonic

seconds and consecutive note spelling would seem to at least be a desirable

line of inquiry?

****Recasting 16 tET in quarter comma meantone would necessitate the

following alterations:

(Db) 0 [2] 5 [6] 9 [11] 14 16

(D) 0 [2] 5 [6] 9 [11] 14 16

(Eb) 0 3 5 7 9 12 [15] 16

(E) 0 3 5 7 9 12 [15] 16

(Fb) 0 [2] 5 [6] 9 12 14 16

(F) 0 [2] 5 [6] 9 12 14 16

(F#) 0 [2] 5 [6] 9 12 14 16/(Gb) 0 3 5 7 [10] 12 [15] 16

(G) 0 3 5 7 [10] 12 [15] 16

(G#) 0 3 5 7 [10] 12 [15] 16

(Ab) 0 [2] 5 7 9 12 14 16

(A) 0 [2] 5 7 9 12 14 16

(Bb) 0 3 [6] 7 [10] 12 [15] 16

(B) 0 3 [6] 7 [10] 12 [15] 16

*****However when the equidistant division of the octave is large enough

that "appropriately altering the sequence" exceeds the tuning unit (1/n of

an octave), the � glyph would have to indicate this�