441-et in ennealimmal notation

I'm not getting much feedback, so I presume I can do whatever I like.
I used the following symbol set:

#, b 36/35
), ( 50/49-49/48
^, v 126/125
>, < 225/224
}, { 32805/32768

to notate 441 steps of 441 equal, which should be this unless I've
made an unfortunate mistake:

0: C
1: C}
2: C^<
3: C>
4: C>}
5: C^
6: C>>
7: C^^<
8: C)v
9: C>>>
10: C^^
11: C^>>
12: C){
13: C)
14: C)}
15: C#<
16: C)>
17: C#{
18: C#
19: C#}
20: D((<
21: C#>
22: D(({
23: D((
24: C#>>
25: Db<<
26: C))
27: C))}
28: Db<
29: C))>
30: Db{
31: Db
32: Db}
33: D(<
34: Db>
35: D({
36: D(
37: D(}
38: Dv<<
39: Dvv
40: D<<<
41: D(^
42: Dvv>
43: D<<
44: Dv
45: D<{
46: D<
47: Dv>
48: D{
49: D
50: D}
51: D^<
52: D>
53: D>}
54: D^
55: D>>
56: D^^<
57: D)v
58: D>>>
59: D^^
60: D^>>
61: D){
62: D)
63: D)}
64: D#<
65: D)>
66: D#{
67: D#
68: D#}
69: E((<
70: D#>
71: E(({
72: E((
73: D#>>
74: Eb<<
75: D))
76: D))}
77: Eb<
78: D))>
79: Eb{
80: Eb
81: Eb}
82: E(<
83: Eb>
84: E({
85: E(
86: E(}
87: Ev<<
88: Evv
89: E<<<
90: E(^
91: Evv>
92: E<<
93: Ev
94: E<{
95: E<
96: Ev>
97: E{
98: E
99: E}
100: E^<
101: E>
102: E>}
103: E^
104: E>>
105: E^^<
106: E)v
107: E>>>
108: E^^
109: E^>>
110: E){
111: E)
112: E)}
113: E#<
114: E)>
115: E#{
116: E#
117: E#}
118: F((<
119: E#>
120: F(({
121: F((
122: E#>>
123: Fb<<
124: E))
125: E))}
126: Fb<
127: E))>
128: Fb{
129: Fb
130: Fb}
131: F(<
132: Fb>
133: F({
134: F(
135: F(}
136: Fv<<
137: Fvv
138: F<<<
139: F(^
140: Fvv>
141: F<<
142: Fv
143: F<{
144: F<
145: Fv>
146: F{
147: F
148: F}
149: F^<
150: F>
151: F>}
152: F^
153: F>>
154: F^^<
155: F)v
156: F>>>
157: F^^
158: F^>>
159: F){
160: F)
161: F)}
162: F#<
163: F)>
164: F#{
165: F#
166: F#}
167: G((<
168: F#>
169: G(({
170: G((
171: F#>>
172: Gb<<
173: F))
174: F))}
175: Gb<
176: F))>
177: Gb{
178: Gb
179: Gb}
180: G(<
181: Gb>
182: G({
183: G(
184: G(}
185: Gv<<
186: Gvv
187: G<<<
188: G(^
189: Gvv>
190: G<<
191: Gv
192: G<{
193: G<
194: Gv>
195: G{
196: G
197: G}
198: G^<
199: G>
200: G>}
201: G^
202: G>>
203: G^^<
204: G)v
205: G>>>
206: G^^
207: G^>>
208: G){
209: G)
210: G)}
211: G#<
212: G)>
213: G#{
214: G#
215: G#}
216: H((<
217: G#>
218: H(({
219: H((
220: G#>>
221: Hb<<
222: G))
223: G))}
224: Hb<
225: G))>
226: Hb{
227: Hb
228: Hb}
229: H(<
230: Hb>
231: H({
232: H(
233: H(}
234: Hv<<
235: Hvv
236: H<<<
237: H(^
238: Hvv>
239: H<<
240: Hv
241: H<{
242: H<
243: Hv>
244: H{
245: H
246: H}
247: H^<
248: H>
249: H>}
250: H^
251: H>>
252: H^^<
253: H)v
254: H>>>
255: H^^
256: H^>>
257: H){
258: H)
259: H)}
260: H#<
261: H)>
262: H#{
263: H#
264: H#}
265: I((<
266: H#>
267: I(({
268: I((
269: H#>>
270: Ib<<
271: H))
272: H))}
273: Ib<
274: H))>
275: Ib{
276: Ib
277: Ib}
278: I(<
279: Ib>
280: I({
281: I(
282: I(}
283: Iv<<
284: Ivv
285: I<<<
286: I(^
287: Ivv>
288: I<<
289: Iv
290: I<{
291: I<
292: Iv>
293: I{
294: I
295: I}
296: I^<
297: I>
298: I>}
299: I^
300: I>>
301: I^^<
302: I)v
303: I>>>
304: I^^
305: I^>>
306: I){
307: I)
308: I)}
309: I#<
310: I)>
311: I#{
312: I#
313: I#}
314: A((<
315: I#>
316: A(({
317: A((
318: I#>>
319: Ab<<
320: I))
321: I))}
322: Ab<
323: I))>
324: Ab{
325: Ab
326: Ab}
327: A(<
328: Ab>
329: A({
330: A(
331: A(}
332: Av<<
333: Avv
334: A<<<
335: A(^
336: Avv>
337: A<<
338: Av
339: A<{
340: A<
341: Av>
342: A{
343: A
344: A}
345: A^<
346: A>
347: A>}
348: A^
349: A>>
350: A^^<
351: A)v
352: A>>>
353: A^^
354: A^>>
355: A){
356: A)
357: A)}
358: A#<
359: A)>
360: A#{
361: A#
362: A#}
363: B((<
364: A#>
365: B(({
366: B((
367: A#>>
368: Bb<<
369: A))
370: A))}
371: Bb<
372: A))>
373: Bb{
374: Bb
375: Bb}
376: B(<
377: Bb>
378: B({
379: B(
380: B(}
381: Bv<<
382: Bvv
383: B<<<
384: B(^
385: Bvv>
386: B<<
387: Bv
388: B<{
389: B<
390: Bv>
391: B{
392: B
393: B}
394: B^<
395: B>
396: B>}
397: B^
398: B>>
399: B^^<
400: B)v
401: B>>>
402: B^^
403: B^>>
404: B){
405: B)
406: B)}
407: B#<
408: B)>
409: B#{
410: B#
411: B#}
412: C.1((<
413: B#>
414: C.1(({
415: C.1((
416: B#>>
417: C.1b<<
418: B))
419: B))}
420: C.1b<
421: B))>
422: C.1b{
423: C.1b
424: C.1b}
425: C.1(<
426: C.1b>
427: C.1({
428: C.1(
429: C.1(}
430: C.1v<<
431: C.1vv
432: C.1<<<
433: C.1(^
434: C.1vv>
435: C.1<<
436: C.1v
437: C.1<{
438: C.1<
439: C.1v>
440: C.1{

>I'm not getting much feedback, so I presume I can do whatever I like.
>I used the following symbol set:
>
>#, b 36/35
>), ( 50/49-49/48
>^, v 126/125
>>, < 225/224
>}, { 32805/32768

I thought your earlier post said you didn't need more than
3 accidental pairs.

>to notate 441 steps of 441 equal, which should be this unless I've
>made an unfortunate mistake:

Looks like the way I would do it. Except, what about alternate
spellings? Did you just list the simplest spelling, like you
did for your boneheaded 31-tET notation?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >I'm not getting much feedback, so I presume I can do whatever I like.
> >I used the following symbol set:
> >
> >#, b 36/35
> >), ( 50/49-49/48
> >^, v 126/125
> >>, < 225/224
> >}, { 32805/32768
>
> I thought your earlier post said you didn't need more than
> 3 accidental pairs.

You don't need more than one accidental pair, but what I was talking
about was that no more of three accidentals from the above list are
being used to notate everything in 441 equal.

> Looks like the way I would do it. Except, what about alternate
> spellings? Did you just list the simplest spelling, like you
> did for your boneheaded 31-tET notation?

First I eliminated everything but the smallest number of accidentals.
Then I eliminated everything using smaller accidentals when possible.
Then I eliminated everything with accidentals going both up and down,
if there was an alternative where it was all up or all down. Then I
decided to favor repeating the same accidental over using a larger
number of accidentals, with no repetitions. For smaller sizes I can
make it conform to how 441 does it, so maybe I should have started
from 612. 441 though is the smallest division which gives you the full
tuning power of ennealimmal.

>> >I'm not getting much feedback, so I presume I can do whatever I like.
>> >I used the following symbol set:
>> >
>> >#, b 36/35
>> >), ( 50/49-49/48
>> >^, v 126/125
>> >>, < 225/224
>> >}, { 32805/32768
>>
>> I thought your earlier post said you didn't need more than
>> 3 accidental pairs.
>
>You don't need more than one accidental pair, but what I was talking
>about was that no more of three accidentals from the above list are
>being used to notate everything in 441 equal.

Oh, so that's your master symbol set so far? How did you arrive
at it?

>> Looks like the way I would do it. Except, what about alternate
>> spellings? Did you just list the simplest spelling, like you
>> did for your boneheaded 31-tET notation?
>
>First I eliminated everything but the smallest number of accidentals.
>Then I eliminated everything using smaller accidentals when possible.
>Then I eliminated everything with accidentals going both up and down,
>if there was an alternative where it was all up or all down. Then I
>decided to favor repeating the same accidental over using a larger
>number of accidentals, with no repetitions.

That sounds like a good way for listing the notation, but in practice
the other spellings would probably be useful, no?

-Carl

Gene wrote:
________________________________________________________________________
Date: Mon, 11 Apr 2005 19:14:16 -0000
Subject: Ennealimmal notation

I've worked out 441, which never needs more than three accidentals,
and 612, which never needs more than four. The only problem I see is
that sometimes there are as many as six different ways to write the
same note. It seems to me it might make sense to eliminate all but the
possibilities where the minimum size of accidental is maximized.

Notating 72, 99, 171, 270, 441 and 612 in ennealimmal, and 72, 270,
342 and 612 in hemiennealimmal seems like the thing to do. For
hemiennealimmal, nine nominals A to I (or J) and then nine more AX to
IX makes sense to me.
________________________________________________________________________

Then a little later (while we were sleeping)
________________________________________________________________________
Date: Tue, 12 Apr 2005 04:11:51 -0000
Subject: 441-et in ennealimmal notation

I'm not getting much feedback, so I presume I can do whatever I like.
I used the following symbol set:

#, b 36/35
), ( 50/49-49/48
^, v 126/125
>, < 225/224
}, { 32805/32768

to notate 441 steps of 441 equal, which should be this unless I've
made an unfortunate mistake:

0: C
1: C}
2: C^<
3: C>
4: C>}
5: C^
6: C>>
...
410: B#
411: B#}
412: C.1((<
413: B#>
414: C.1(({
415: C.1((
416: B#>>
417: C.1b<<
418: B))
419: B))}
420: C.1b<
421: B))>
422: C.1b{
423: C.1b
424: C.1b}
425: C.1(<
426: C.1b>
427: C.1({
428: C.1(
429: C.1(}
430: C.1v<<
431: C.1vv
432: C.1<<<
433: C.1(^
434: C.1vv>
435: C.1<<
436: C.1v
437: C.1<{
438: C.1<
439: C.1v>
440: C.1{
________________________________________________________________________

(Patience, Gene, some of us have other things to do, you know!
Like sleeping, eating, ... even working for money. :-) )

But please do tell me how C.1 fits into this notation system - neither
the DOT nor the ONE appeared in your list of apotomes and commas.

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.308 / Virus Database: 266.9.5 - Release Date: 7/4/05

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> I'm not getting much feedback, so I presume I can do whatever I
like.
> I used the following symbol set:
>
> #, b 36/35
> ), ( 50/49-49/48
> ^, v 126/125
> >, < 225/224
> }, { 32805/32768

Gene, of course you can do whatever you like, but I would think that
using character pairs that are already understood to represent
completely different intervals would be confusing to some of us. I'm
thinking particularly of ^ and v, which have been used for 32:33 (not
to mention # and b, which I can't imagine using for anything other
than an apotome).

I don't know how closely you followed Herman Miller's and Dave
Keenan's recent efforts (mid-February; see TM msg. #11629) to notate
temperaments with non-diatonic sets of nominals. I had only a
passing interest in this, since most of their attention was devoted
to notating the nominals. Anyway, they agreed to use pure Sagittal
symbols as accidentals, which would neatly avoid the problem of
having the same symbols representing entirely different intervals in
different temperaments. This follows the Sagittal "learn-as-needed"
philosophy that whatever symbols one learns to notate one tuning will
not have to be unlearned when notating another tuning.

Many Sagittal symbols already have shorthand character-pairs
assigned, including the following (down-character given to the left
of the up-character):

u n 35:36
. ' 32768:32805
h p 4096:4131 (which is within a cent of 125:126)
c r 5103:5120 (difference between 63:64 and 80:81)
.c 'r 224:225 (the above used in combination)
j ? 45056:45927 (7:11-comma)
.j '? 2^27*11:3^16*5*7 (~35.1c; between 49:50 & 48:49)

> to notate 441 steps of 441 equal, which should be this unless I've
> made an unfortunate mistake:
>
> 0: C
> 1: C}
> 2: C^<
> 3: C>
> 4: C>}
> 5: C^
> 6: C>>
> 7: C^^<
> 8: C)v
> 9: C>>>
> 10: C^^
> 11: C^>>
> 12: C){
> 13: C)
> 14: C)}
> 15: C#<
> 16: C)>
> 17: C#{
> 18: C#
> 19: C#}

Another tenet of the Sagittal philosophy is not to use more than one
microtonal accidental for a notehead, with the exception that accent
marks (representing a schisma, 32768:32805) may be used in
combination with any other symbol. This permits the following
combinations:

0: C
1: C'
2: Cr
3: C'r
4: C.p
5: Cp
6: C'p
7: C./
8: C/
9: C'/
10: Cf
11: C.?
12: C?
13: C'?
14:
15:
16:
17: C.n
18: Cn
19: C'n

The combinations you have for 8 and 10 degrees are very close to the
5-comma (80:81) and 7-comma (63:64), respectively, and the symbols
for those intervals were used above. I've left a few positions
blank, because I'm not about to get bogged down in any more of the
details.

I'm not attempting to anticipate what Herman and Dave might come up
with for enealimmal, but I just though I'd put this out here to let
you know about some of the possibilities. I think it was your
intention to use only a few different accidentals to notate this
temperament (with up to 3 in combination), whereas it has been our
objective to have additional (Sagittal) accidentals to take care of
the combinations.

Best,

--George

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> Oh, so that's your master symbol set so far? How did you arrive
> at it?

I looked at what was already apparently being done, and then added a
pair for the schisma.

> That sounds like a good way for listing the notation, but in practice
> the other spellings would probably be useful, no?

They show up in remote keys of ennealimmal, which might not see much
use. I don't know what the limiations on Scala are so far as listing
alternatives goes.

--- In tuning-math@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...> wrote:

> But please do tell me how C.1 fits into this notation system - neither
> the DOT nor the ONE appeared in your list of apotomes and commas.

It doesn't fit into the notation system, and you'd take it out if you
were going to use this as a Scala scale file. I put it in since I
wanted to show an octave starting at C, and near the end we have
modified C.1, not C.

--- In tuning-math@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:

> Gene, of course you can do whatever you like, but I would think that
> using character pairs that are already understood to represent
> completely different intervals would be confusing to some of us.

Perhaps, but I didn't start it. :)

The symbols I used were ones I found in apparent use in scale files on
Scala, aside from the pair for the schisma, which is too small to be
used in the scales Scala has. For instance in both E99 and EL99 (which
I thought you might have done) the single step of 99, which I took to
be 126/125, was a ^, v pair; though in E130 it is >, < which doesn't
help matters. But from E140 and E171 I concluded that 225/224 should
be >, <.

I'm
> thinking particularly of ^ and v, which have been used for 32:33 (not
> to mention # and b, which I can't imagine using for anything other
> than an apotome).
>
> I don't know how closely you followed Herman Miller's and Dave
> Keenan's recent efforts (mid-February; see TM msg. #11629) to notate
> temperaments with non-diatonic sets of nominals. I had only a
> passing interest in this, since most of their attention was devoted
> to notating the nominals. Anyway, they agreed to use pure Sagittal
> symbols as accidentals, which would neatly avoid the problem of
> having the same symbols representing entirely different intervals in
> different temperaments.

I don't think pure Sagittal is a good system for notating acidentals
in a single temperament. The important considerations there are to get
*simple*, one-character, accidentals and to use them consistently for
all equal temperaments being notated in this way. That way a score
notated to start out with in one equal temperament can be used in
another with more notes, and scores are on a more abstract,
temperament-defined, level than simply for a single equal temperament.

> Many Sagittal symbols already have shorthand character-pairs
> assigned, including the following (down-character given to the left
> of the up-character):
>
> u n 35:36

This looks good.

> . ' 32768:32805

This will conflict with the . symbol already in use to define octave
numbers, and is not every clear.

> .c 'r 224:225 (the above used in combination)

Not one-symbol, and so unacceptable for such an important comma.

> j ? 45056:45927 (7:11-comma)
> .j '? 2^27*11:3^16*5*7 (~35.1c; between 49:50 & 48:49)

Again, far too baroque for such an important interval.

> I'm not attempting to anticipate what Herman and Dave might come up
> with for enealimmal, but I just though I'd put this out here to let
> you know about some of the possibilities. I think it was your
> intention to use only a few different accidentals to notate this
> temperament (with up to 3 in combination), whereas it has been our
> objective to have additional (Sagittal) accidentals to take care of
> the combinations.

In terms of a period of 27/25 and generator of 36/35 we have, as
abbreviations, the following:

49/48 = (27/25)/(36/35)^2 ~ 50/49
1728/1715 = (36/35)^3/(27/25) ~ 126/125 ~ 245/243
144120025/143327232 = (27/25)^3/(36/35)^8 ~ 225/224 ~ 1029/1024
(27/25)^7/(36/35)^19 ~ 32805/32768 ~ 65625/65536

It is these I'd propose to find symbols for and use.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
>
> > Gene, of course you can do whatever you like, but I would think
that
> > using character pairs that are already understood to represent
> > completely different intervals would be confusing to some of us.
>
> Perhaps, but I didn't start it. :)
>
> The symbols I used were ones I found in apparent use in scale files
on
> Scala, aside from the pair for the schisma, which is too small to be
> used in the scales Scala has. For instance in both E99 and EL99
(which
> I thought you might have done) the single step of 99, which I took
to
> be 126/125, was a ^, v pair; though in E130 it is >, < which doesn't
> help matters. But from E140 and E171 I concluded that 225/224 should
> be >, <.

As I understand it, any notation in Scala with a name in the form E-
integer is based on Paul Rapaport's system, in which the accidentals
are all 5-limit (including half-commas!). That explains why you're
getting different symbols in different divisions for intervals having
a 7 factor.

> I don't think pure Sagittal is a good system for notating acidentals
> in a single temperament. The important considerations there are to
get
> *simple*, one-character, accidentals and to use them consistently
for
> all equal temperaments being notated in this way. ...
>
> > Many Sagittal symbols already have shorthand character-pairs
> > assigned, including the following (down-character given to the
left
> > of the up-character):
> > ...
> > . ' 32768:32805
>
> This will conflict with the . symbol already in use to define octave
> numbers, and is not every clear.

We originally had ` instead of the period to represent the schisma-
down alteration, but we concluded that it was too easy to confuse
with the apostrophe ' (schisma-up). I suppose you could use a comma
character "," instead (although it slopes in the wrong direction). I
believe that we were going to try to iron out the syntax problem with
Manuel but haven't gotten around to it yet, since it wasn't
particularly pressing that the schisma accent marks be implemented in
Scala.

> > .c 'r 224:225 (the above used in combination)
>
> Not one-symbol, and so unacceptable for such an important comma.

These are, in fact, single symbols, just as "a", "á", and "à" are all
single characters in written language to indicate variations in
spoken sound. In Sagittal we have accent marks in some of the
symbols to indicate subtle (schismatic) variations in pitch. The
problem is that the ASCII character set doesn't permit us to display
those accents as they would appear in printed music, so we have to
use two characters to simulate that.

> > j ? 45056:45927 (7:11-comma)
> > .j '? 2^27*11:3^16*5*7 (~35.1c; between 49:50 & 48:49)
>
> Again, far too baroque for such an important interval.

Yes, I agree that 48:49 is an important interval, and we do have a
Sagittal symbol pair for it:
~!) down, ~|) up
Dave Keenan assigned extended ASCII characters to the following
Sagittal symbols (some of which may not display properly in email):

long short short
up up down description
--------------------------------------------------------------------
)~| ¡ ¦ inverted exclamation mark, broken bar
~~| § paragraph sign, section sign
)|~ ¯ ÷ macron, divide sign
)|) þ ß lowercase thorn (iceland), lowercase sz
ligature
~|) ç ¿ lowercase c cedilla, inverted question mark
/|~ ø ð lowercase o slash, lowercase eth (iceland)
~|\ µ £ lowercase mu, pound sterling
|~) ¢ not sign, cents
|~\ ¥ ± yen, plus or minus
(|~ ª æ female ordinal, lowercase ae ligature
|\) ° ¤ degree sign, general currency sign
|\\ » « right angle-quote, left angle-quote
((| ® © registered, copyright

The characters are entered by holding down the <Alt> key, entering
the following 3-digit number on the numeric keypad, then releasing
the <Alt> key to get the characters representing the following ratios:

As decimal character codes:
long short short
up up down ratio(s)
--------------------------------------------------------------------
)~| 161 166 143:144
~~| 182 167 99:100, 98:99
)|~ 175 247 19456:19683
)|) 254 223 56:57
~|) 231 191 48:49
/|~ 248 240 45:46
~|\ 181 163 16384:16767
|~) 172 162 45927:47104
|~\ 165 177 36:37 (?)
(|~ 170 230 171:176
|\) 176 164 1701:1760 or 2^23:3^11*7^2
|\\ 187 171 2^15*11:3^9*19
((| 174 169 2^24*11^2:3^16*7^2

This is in addition to our regular ASCII set:

ASCII shorthand
long down up Comma
----- ---- -- -----------------------
)| ; " 19-schisma, 512:513
|( c r 5:7-kleisma, 5103:5120
~| s $ 17-kleisma, 2176:2187
)|( i * 7:11 kleisma, 891:896
~|( h p 17-comma, 4096:4131
|~ z ~ 23-comma, 729:736
/| \ / 5-comma, 80:81
)/| & % 5:19-comma, 40960:41553
|) t f 7-comma, 63:64
|\ k y 55-comma, 54:55
(| j ? 7:11-comma, 45056:45927
(|( d q 5:11S-diesis, 44:45
//| _ = 25S-diesis, 6400:6561
/|) u n 35M (or 13M)-diesis, 35:36 (or 1024:1053)
/|\ v ^ 11M-diesis, 32:33
(/| a g 49M-diesis, 3969:4096
(|) o @ 11L-diesis, 704:729
(|\ w m 35L (or 13L-diesis), 8192:8505 (or 26:27)

Any or all of the above may be modified with accent marks:

ASCII shorthand
long down up Schisma/schismina
----- ---- -- -----------------------
'| . ' 32768:32805, placed to the left of a character
|' . ' 4095:4096, placed to right of a character
|'' .. '' 2079:2080, placed to right of a character

These particular ratios were selected according to which ones would
be needed as accidentals modifying tones in an extended Pythagorean
sequence to notate the most popular pitches in the Scala tuning files
(.scl) archives. With the above there are more than enough
combinations to notate 2460-ET (for example), with alternate
spellings for most of the tones, and I'm sure that there are also
enough combinations to notate practically any interval you'd want to
use as an accidental.

The real problem is that we're limited to relatively few character
pairs with ASCII and that we would prefer to be using a font
containing the actual symbols as single characters.

Anyway, here are the character pairs that are not used in Sagittal
character shorthand, which we've set aside for user-defined purposes
(such as yours):

down up
---- --
, `
- +
< >
[ ]
{ }

Also, the letters "e" and "l" and the characters "(" and ")" are not
used in Sagittal shorthand, so you could also use those without
conflicting with Sagittal shorthand.

--George

--- In tuning-math@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> I don't know how closely you followed Herman Miller's and Dave
> Keenan's recent efforts (mid-February; see TM msg. #11629) to notate
> temperaments with non-diatonic sets of nominals. I had only a
> passing interest in this, since most of their attention was devoted
> to notating the nominals. Anyway, they agreed to use pure Sagittal
> symbols as accidentals, which would neatly avoid the problem of
> having the same symbols representing entirely different intervals in
> different temperaments. This follows the Sagittal "learn-as-needed"
> philosophy that whatever symbols one learns to notate one tuning will
> not have to be unlearned when notating another tuning.
...
> I'm not attempting to anticipate what Herman and Dave might come up
> with for enealimmal, but I just though I'd put this out here to let
> you know about some of the possibilities. I think it was your
> intention to use only a few different accidentals to notate this
> temperament (with up to 3 in combination), whereas it has been our
> objective to have additional (Sagittal) accidentals to take care of
> the combinations.

In the(multi-)linear temperament notation system that Herman and I
(and occasional others) have been talking about, the nominals
correspond to a set of around 5 to 12 pitch-classes contiguous on the
chain(s) of generators and equally distributed between chains.

Since ennealimmal has 9 chains (a period of 1/9 octave) I imagine we
would use 9 nominals. These would effectively be notating 9-ET and the
(compound) nominals would be
D vE ^E #F ^G vA bB vC ^C D
pronounced "D", down-"E", up-"E", sharp-"F", etc.,
where "^" and "v" to the left of a letter are to be understood as the
Tartini-Couper half-sharp and half-flat (backwards narrow flat)
respectively.

The sagittal accidental for a shift of one 49 cent generator would be
Athene's helmet /|), the symbol for 35:36, which in the ASCII
shorthand is "n" for up and "u" for down.

You could simply use multiples of these for multiple generator shifts,
or ...

For two ennealimmal generators we have the accented symbol for
189:200, /||~'' from which the double-right accent can be dropped
without ambiguity in this application. In ASCII shorthand this is "#z"
for up and "b~" for down.

For three gens we have (|||, in shorthand "#?" for up, "bj" for down.

For four gens we have /X' from which the right accent can be dropped
without ambiguity in this application. In shorthand "xk" for up, "bby"
for down.

For more than four gens there is no single sagittal symbol.

You can see the True-type symbols at
http://dkeenan.com/sagittal/map/index.htm

This sort of 9-nominals notation probably makes sense for up to 45
notes of Ennealimmal, if the piece used 9-ET as the melodic scale and
the others as variations on it (or something like that). However for
notating random pitches of 441-ET, a notation based on nominals in a
chain-of-best-fifths, with appropriate sagittals, make more sense to
me, due to their greater familiarity.

-- Dave Keenan

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> Since ennealimmal has 9 chains (a period of 1/9 octave) I imagine we
> would use 9 nominals. These would effectively be notating 9-ET and the
> (compound) nominals would be
> D vE ^E #F ^G vA bB vC ^C D
> pronounced "D", down-"E", up-"E", sharp-"F", etc.,
> where "^" and "v" to the left of a letter are to be understood as the
> Tartini-Couper half-sharp and half-flat (backwards narrow flat)
> respectively.

Why so complicated? What is wrong with A through I?

Any notation system will have to be practical for the purpose in
question, which is producing a simple ascii notation to use in
conjunction with Scala.

> The sagittal accidental for a shift of one 49 cent generator would be
> Athene's helmet /|), the symbol for 35:36, which in the ASCII
> shorthand is "n" for up and "u" for down.

"n" and "u" will work, and George apparently gave his blessing to
">" and "<" for 225/224. He also suggested we are free to use

down up
---- --
, `
- +
< >
[ ]
{ }

Hence if > and < go to 225/224, and 36/35 is taken care of, we have
four remaining pairs for the three remaining commas, 49/48, 126/125,
and 32805/32768. I suppose , ` makes sense for 32805/32768 if people
can actually read it. What about the other two?

> For two ennealimmal generators we have the accented symbol for
> 189:200, /||~'' from which the double-right accent can be dropped
> without ambiguity in this application. In ASCII shorthand this is "#z"
> for up and "b~" for down.
>
> For three gens we have (|||, in shorthand "#?" for up, "bj" for down.

But why do we want two and three generator symbols?

> This sort of 9-nominals notation probably makes sense for up to 45
> notes of Ennealimmal, if the piece used 9-ET as the melodic scale and
> the others as variations on it (or something like that). However for
> notating random pitches of 441-ET, a notation based on nominals in a
> chain-of-best-fifths, with appropriate sagittals, make more sense to
> me, due to their greater familiarity.

Chain of fifths is completely useless for the purpose I have in mind,
and since I have two scores I want to to notate and so far as I know
no one else has any, that should be a consideration. I've got the
experience. Moreover, the gcd of 258, which is the fifth in 441-et,
and 441, is 3; hence chains of fifths not only give bad temperaments,
they require nonoctave periods anyway. As the size of an et increases,
the chances that a fifth will be any good as a generator drops towards
zero. In the case of 441, the most efficient way to organize its notes
is ennealimmal. Other possibiities are to use an approximate
(8/3)^(1/3) or (5/4)^(1/2) as a generator.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > Since ennealimmal has 9 chains (a period of 1/9 octave) I imagine we
> > would use 9 nominals. These would effectively be notating 9-ET and the
> > (compound) nominals would be
> > D vE ^E #F ^G vA bB vC ^C D
> > pronounced "D", down-"E", up-"E", sharp-"F", etc.,
> > where "^" and "v" to the left of a letter are to be understood as the
> > Tartini-Couper half-sharp and half-flat (backwards narrow flat)
> > respectively.
>
> Why so complicated? What is wrong with A through I?

Well we do also have corresponding alphabetic-only nominals, but they
arent as simple as A to I in this case because we are trying to
preserve the existing meaning of A thru G being in a chain of fiftha
(whenever that's relevant) and giving consistent nominals for lots of
different (multi-)linear temperaments, so switching between them is
not too hard.

Of course you can always make a simpler notation for one specific
temperament, as long as that's the only one you'll ever want or need
to use.

>
> Any notation system will have to be practical for the purpose in
> question, which is producing a simple ascii notation to use in
> conjunction with Scala.
>
> > The sagittal accidental for a shift of one 49 cent generator would be
> > Athene's helmet /|), the symbol for 35:36, which in the ASCII
> > shorthand is "n" for up and "u" for down.
>
> "n" and "u" will work, and George apparently gave his blessing to
> ">" and "<" for 225/224. He also suggested we are free to use
>
> down up
> ---- --
> , `
> - +
> < >
> [ ]
> { }

Agreed.

> Hence if > and < go to 225/224, and 36/35 is taken care of, we have
> four remaining pairs for the three remaining commas, 49/48, 126/125,
> and 32805/32768. I suppose , ` makes sense for 32805/32768 if people
> can actually read it. What about the other two?

We already allocated . and ' for 32805/32768, but you can use , and `
if you prefer.

I think we agreed on some "8-bit-ASCII" unicode symbols for 49/48 at
Robert Walkers request, for his upcoming FTS implementation of
Sagittal. I'll have to look them up. And we'll have to figure out what
126/125 should be. So little time and so few helpers ...

-- Dave

>Of course you can always make a simpler notation for one specific
>temperament, as long as that's the only one you'll ever want or need
>to use.

The same symbols can have different meanings in different
scores.

-Carl

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
>
> > Since ennealimmal has 9 chains (a period of 1/9 octave)
> > I imagine we would use 9 nominals. These would effectively
> > be notating 9-ET and the (compound) nominals would be
> > D vE ^E #F ^G vA bB vC ^C D
>
> <snip>
>
> In the case of 441, the most efficient way to organize
> its notes is ennealimmal. Other possibiities are to use
> an approximate (8/3)^(1/3) or (5/4)^(1/2) as a generator.

/tuning-math/files/monz/441edo_2-
good-generators-compared.gif

(delete line break), OR

http://tinyurl.com/49hdk

Gene or Herman or anyone, can you fill out the "tuning family"
template for ennealimmal? if i knew more about it, i'd make
graphs for that too.

-monz

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Of course you can always make a simpler notation for one specific
> >temperament, as long as that's the only one you'll ever want or need
> >to use.
>
> The same symbols can have different meanings in different
> scores.

That's the sort of schizophrenia that motivated Dave and me to
persevere with Sagittal. We insist that a symbol should retain its
meaning, regardless of the tuning. (Is it any wonder that we came up
with so many symbols?)

--George

--- In tuning-math@yahoogroups.com, "monz" <monz@t...> wrote:

> /tuning-math/files/monz/441edo_2-
> good-generators-compared.gif
>
> (delete line break), OR
>
> http://tinyurl.com/49hdk

These are not the next two in Graham complexity for 441 after
ennealimmal, but are interesting because they have a 5-limit
consonance to a low complexity.

The (8/3)^(1/3) system is 53&441, or you could call it 441&494. As
53&441 suggest, it also works as a 5-limit system, with comma
|39 -29 3>. Hence organizing 441 this way starts you off with lots of
triads. The wedgie is <<3 29 -95 39 -159 -302|| for a Graham complexity of
124 in the 7 or 9 limits. This temperament also allows for filddling
with the tuning, in case that still matters by the time we reach 441,
and as 441&494 suggests, is extendible to higher limits.

The (5/4)^(1/2) system belongs to the hemithirds family, so a family
tree with it in it would be nice, I guess. It can be called 118&441,
and again we see we start off with a ton of triads, because we have a
hemithirds temperament in the 5-limit, with comma |38 -2 -15>; 441 is
very close to being 5-limit poptimal for hemithirds, if in fact it
isn't. Again, moving to the 7-limit boosts the complexity a ton, with
the wedgie being <<15 -2 113 -38 137 268||.

The lowest 7-limit complexity for 441 systems by a considerable margin
is ennealimmal; the runner-up is <<60 -8 11 -152 -151 48||. This has
a tempered 57344/46875 as a generator, which especially after tuning
it flattens it a smidgen is pretty much an 11/9. Two of these quasi
neutral third generators produce a meantone fifth, so you get a whole
lot of meantone harmonies to use before the much more nearly JI
7-limit stuff arrives. You might call this the 31&441 system.

The sagittal symbol for 48:49 is a boathook and arc on a single shaft.
~|) in long ASCII. For the short ASCII, George Secor, Robert Walker
and I agreed on the "8-bit-unicode" or "extended ASCII" characters "ç"
lowercase c cedilla) for up, and "¿" (inverted question mark) for
down. The decimal character codes for these are 231 and 191.

I don't know whether Scala can use these, or whether it might be
easier for Manuel to make it do so, than to implement full unicode,
since these are at least only 8 bits.

The sagittal symbol for 125:126 has not previously been given much
attention. It is certainly important as a vanishing comma, but not
often required for notating pitches or intervals since the simplest
ratio it notates is 125/7 and its transpositions by octaves or fifths,
and their inversions.

Given the number of people that have been totally freaked out by Table
3 of
http://dkeenan.com/sagittal/Sagittal.pdf
and George's and my subsequent agreement to drop most of the
non-Athenian symbols from this table, it seems to me that 125:126 must
be notated as an accented version of the symbol called "Hephaestus'
axe". In ASCII longhand it is "~|(". In ASCII shorthand it is "h" for
down and "p" for up. Just think of hewlett packard or hp-sauce, or
indeed HePhaestus.

[ By the way, I mentioned the pair "k" (down) and "y" (up) in a
previous message. For these just think of ky-jelly.]

The details of the accents don't really matter for now, since they can
be dropped in notating ennealimmal, but the primary comma for
Hephaestus axe is 4096:4131 (14.73c) and 125:126 is 0.94 cents smaller
at 13.79c. So I guess it has to be double right accents in the
opposite direction to the main symbol. So h'' and p.. (or h`` and p,,).

To summarise:

comma down up
---------------
35:36 u n
48:49 ¿ ç
49:50 j. ?'
125:126 h'' p..
224:225 c. r'

Can you confirm these George?

And feel free to drop the accents ' and . when it is known to be a
notation for ennealimmal (or any other tuning that doesn't use any
other accented or unaccented form of these symbols).

-- Dave

I'd like to point out a possible difference in our approaches to
choosing which commas (and hence which symbols) to use in notating
steps of an ET (or LT) relative to a chosen set of nominals. Take an
example of choosing the comma to represent a single step of an ET.

One method is to find the simplest comma that corresponds to 1 step of
the ET (by any reasonable measure of comma complexity). That seems to
be what you are doing.

Our method is (in effect) to go through the ratios corresponding to
each combination of nominal plus or minus one step and find the
simplest ratio (not usually a comma) that is approximated, relative to
the chosen 1/1. We then use the comma that is implied by that simplest
notated ratio. This is not necessarily the simplest comma. We do this
because we are trying to consistently notate the simplest harmonies
across multiple tunings.

In the case where the nominals are in a chain of fifths there is a
shortcut to our approach and that is to simply ignore all factors of 2
and 3 when calculating a comma's complexity and then apply the first
method above.

However this shortcut won't work when the nominals are not in a chain
of fifths.

-- Dave

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> One method is to find the simplest comma that corresponds to 1 step of
> the ET (by any reasonable measure of comma complexity). That seems to
> be what you are doing.

No, what I'm doing is quite different, and is more like the system of
sharps and flats. In both cases, we start out expressing everything in
terms of two generators, and then introduce what you might call
abbreviations. All the nominals, sharps, and flats of standard
notation reduce to fifths and octaves, or tempered versions therreof.
In the same way, the symbols I want reduce to products of 27/25 and
36/35, or tempered versions thereof. In other words, I want to notate
a rank two ("linear") temperament, and then apply that system to
various equal temperaments. It seems to me this is the obvious way to
proceed, and in most circumtances it strikes me as more likely to be
useful that the method you describe, because very often we approach an
equal (rank one) temperament with the idea of organizing it in terms
of some rank two temperament.

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
>
> The sagittal symbol for 48:49 is a boathook and arc on a single
shaft.
> ~|) in long ASCII. For the short ASCII, George Secor, Robert Walker
> and I agreed on the "8-bit-unicode" or "extended ASCII"
characters "ç"
> lowercase c cedilla) for up, and "¿" (inverted question mark) for
> down. The decimal character codes for these are 231 and 191.

Dave, I gave Gene the complete set here:
/tuning-math/message/11955
beginning about halfway down.

I believe that we noticed before that one of the characters won't
display, but I also seem to recall that you said that there wasn't
anything else you could use; is that correct? In that message I see
two that don't show:

the paragraph sign, up-character for ~~|
the not sign, up-character for |~)

Any ideas? For one, I know we're not presently using either "e"
or "l"; the latter, (small L) looks like a "1" (one), but for
something rarely used, in a pinch?

> I don't know whether Scala can use these, or whether it might be
> easier for Manuel to make it do so, than to implement full unicode,
> since these are at least only 8 bits.

Another thing about Scala is that I don't think we ever resolved the
problem that the 5-schisma-down shorthand symbol "." (period)
conflicts with the delimiter for the octave number. Gene's submitted
his "version 0.5 beta":
/tuning-math/message/11976
where he uses "`" for up and "," for down. We didn't like those
characters, because they slope in the wrong direction. Should we
avoid the comma "," as a shorthand character and allow "`" as an
alternative to "." for a schisma-down?

> The sagittal symbol for 125:126 has not previously been given much
> attention. It is certainly important as a vanishing comma, but not
> often required for notating pitches or intervals since the simplest
> ratio it notates is 125/7 and its transpositions by octaves or
fifths,
> and their inversions.
>
> Given the number of people that have been totally freaked out by
Table
> 3 of
> http://dkeenan.com/sagittal/Sagittal.pdf
> and George's and my subsequent agreement to drop most of the
> non-Athenian symbols from this table, it seems to me that 125:126
must
> be notated as an accented version of the symbol called "Hephaestus'
> axe". In ASCII longhand it is "~|(". In ASCII shorthand it is "h"
for
> down and "p" for up. Just think of hewlett packard or hp-sauce, or
> indeed HePhaestus.
>
> [ By the way, I mentioned the pair "k" (down) and "y" (up) in a
> previous message. For these just think of ky-jelly.]
>
> The details of the accents don't really matter for now, since they
can
> be dropped in notating ennealimmal, but the primary comma for
> Hephaestus axe is 4096:4131 (14.73c) and 125:126 is 0.94 cents
smaller
> at 13.79c. So I guess it has to be double right accents in the
> opposite direction to the main symbol. So h'' and p.. (or h`` and
p,,).
>
> To summarise:
>
> comma down up
> ---------------
> 35:36 u n
> 48:49 ¿ ç
> 49:50 j. ?'
> 125:126 h'' p..
> 224:225 c. r'
>
> Can you confirm these George?

49:50 should be .j and '? ; the rest look okay.

> And feel free to drop the accents ' and . when it is known to be a
> notation for ennealimmal (or any other tuning that doesn't use any
> other accented or unaccented form of these symbols).

Gene won't be able to do that if he's notating 441-ET. He needs both
the c-r and .-' character pairs, and he wants 224:225 for 3deg to be
the single-character symbol and 2deg to be the 3deg symbol combined
with a down-schisma. It looks as if the u-n and ¿-ç character pairs
would be the only ones he could use, since they're the only ones that
are unaccented. He would then have to use a couple of user-defined
character pairs for 125:126 and 224:225. (He doesn't need a separate
pair for 49:50, because it's the same number of degrees as 48:49 in
441-ET.)

Another possibility that just occurred to me for 224:225 (not only as
3deg441, but also 2deg270, 1deg171, and 1deg99) would be ~|.. (double
right-accented 17-kleisma). Dropping the double-right accent in 441
is completely okay because it vanishes (both as 2079:2080 and
255879:256000) in 441, 270, 171, and 99. So the (17-kleisma)
character pair "s" (down) and "$" (up) could be used consistently as
224:225 for enneallimal with 9 nominals. Dave and I consider this a
secondary role for the 17-kleisma symbol, but in the context of a 7-
limit temperament that symbol would obviously be interpreted as
something other than a 17-kleisma (2176:2187), even though it's
perfectly valid as either one.

Oh, one more thing! Gene, I just noticed two things about your
symbol sequence:

> 12: C)`
> 13: C)
> 14: C),
...
> 17: Cn`
> 18: Cn
> 19: Cn,

1) If "`" is supposed to be up and "," is down, then you have the up
and down symbols reversed. I apologize that the tables I gave in
yesterday's message weren't consistent in having the up and down
symbols always in the same (right vs. left) columns from one table to
another. I simply pasted them into the message in the form they were
already in. The column headings and entries are all correct, but you
just have to be careful when reading them.

2) You have the accent marks to the right of the larger accidental.
In Sagittal the relative position has significance: an accent mark to
the right alters by a schismina (~0.4c), whereas to the left alters
by a schisma (~2c). In Sagittal shorthand we would write the above
as:

12: C.ç
13: Cç
14: C'ç
...
17: C.n
18: Cn
19: C'n

If you're combining other characters, then there's no problem in what
order they appear -- only that accent marks representing a schisma
should appear to the left of the other accidentals and those
representing a schismina appear to the right.

Gene, I appreciate the fact that you're making an effort to use
character pairs in a way that won't conflict with the way Dave and I
have assigned them for Sagittal shorthand, and I hope that the above
suggestions will work out for you. We have our different ways of
doing things, and in the process I hope that in using the same
symbols for the same things we might be able to avoid a lot of
confusion in this one area.

Best,

--George

--- In tuning-math@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:

> Another thing about Scala is that I don't think we ever resolved the
> problem that the 5-schisma-down shorthand symbol "." (period)
> conflicts with the delimiter for the octave number. Gene's submitted
> his "version 0.5 beta":
> /tuning-math/message/11976
> where he uses "`" for up and "," for down.

Actually, I used "`" for a schisma down, and a "," for a schisma up.

> 49:50 should be .j and '? ; the rest look okay.

I'm not too enthralled over using a 17-limit symbol for a 7-limit
comma. The symbol in question is not welded to 126/125 in any case;
it could be 245/243, 1728/1715, 4000/3969, or 78732/78125, the last
being a 5-limit comma which may or may not help. This means we really
only need something in the 13-14 cent range.
So the (17-kleisma)
> character pair "s" (down) and "$" (up) could be used consistently as
> 224:225 for enneallimal with 9 nominals.

Is this better than < and >?

Dave and I consider this a
> secondary role for the 17-kleisma symbol, but in the context of a 7-
> limit temperament that symbol would obviously be interpreted as
> something other than a 17-kleisma (2176:2187), even though it's
> perfectly valid as either one.

My own view is that until you can do a really good job on 5 and 7
limit temperaments you've not managed yet to create a generic system;
the 5 and 7 limits being far more basic an important than 17 and beyond.

> 1) If "`" is supposed to be up and "," is down, then you have the up
> and down symbols reversed. I apologize that the tables I gave in
> yesterday's message weren't consistent in having the up and down
> symbols always in the same (right vs. left) columns from one table to
> another.

As I said above, that's how I did up and down. Visually, it makes more
sense to me.

> 2) You have the accent marks to the right of the larger accidental.
> In Sagittal the relative position has significance: an accent mark to
> the right alters by a schismina (~0.4c), whereas to the left alters
> by a schisma (~2c). In Sagittal shorthand we would write the above
> as:

I don't have any accent marks, I have combinations of characters.

> Gene, I appreciate the fact that you're making an effort to use
> character pairs in a way that won't conflict with the way Dave and I
> have assigned them for Sagittal shorthand, and I hope that the above
> suggestions will work out for you.

It should be a priority with you two too in my opinion; you need to be
able to handle temperaments better than notating equal temperaments in
an ad hoc way.

--- In tuning-math@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
> wrote:
> >
> > The sagittal symbol for 48:49 is a boathook and arc on a single
> shaft.
> > ~|) in long ASCII. For the short ASCII, George Secor, Robert Walker
> > and I agreed on the "8-bit-unicode" or "extended ASCII"
> characters "ç"
> > lowercase c cedilla) for up, and "¿" (inverted question mark) for
> > down. The decimal character codes for these are 231 and 191.
>
> Dave, I gave Gene the complete set here:
> /tuning-math/message/11955
> beginning about halfway down.
>
> I believe that we noticed before that one of the characters won't
> display, but I also seem to recall that you said that there wasn't
> anything else you could use; is that correct? In that message I see
> two that don't show:
>
> the paragraph sign, up-character for ~~|
> the not sign, up-character for |~)

There wasn't really anything else usable in the supposed "safe" range.
It was quite an effort to arrange the few available characters as
anything like up/down pairs, let alone matching them up with sagittals
that they were supposed to resemble. These are all supposed to be
available on Mac/PC/Nix. I suspect they only didn't appear in your
post because they disappeared from the email I sent you. Remember,
Robert got them all OK in email but those two got lost for you. I'll
try posting those two pairs here and you can see if they work for you
via Yahoo's web interface.

long short short
up up down description
--------------------------------------------------------------------
~~| ¶ § paragraph sign, section sign
|~) ¬ ¢ not sign, cents

But anyway, aren't they irrelevant now, since we've agreed to avoid
using non-Athenian symbols unless we're really desperate, and go for
double right accents instead. I think it's time we came up with a
preferred symbol for every degree of 233-EDA (2460-ET) and assigned a
primary comma (and maybe some secondaries) to every one, and put the
list up on the website for comment.

> Another thing about Scala is that I don't think we ever resolved the
> problem that the 5-schisma-down shorthand symbol "." (period)
> conflicts with the delimiter for the octave number. Gene's submitted
> his "version 0.5 beta":
> /tuning-math/message/11976
> where he uses "`" for up and "," for down. We didn't like those
> characters, because they slope in the wrong direction. Should we
> avoid the comma "," as a shorthand character and allow "`" as an
> alternative to "." for a schisma-down?

Definitely not. I think we both agreed long ago that the vertical
position is a far stronger cue than the slope when the glyphs are so
tiny. If we're forced to use them then the backquote ` should
definitely be up and the (punctuation) comma , should be down
irrespective of any other consideration.

We're not forced to use backquote ` here at all, and at least in the
courier font I'm reading this in, it occupies so few pixels it is hard
to tell if there's anything there at all. The backquote is way harder
to see than the apostrophe or the comma or the full-stop (period).

Most people are aware that many European countries use the comma , as
the decimal point where English-speaking countries use the period . I
think we should keep the apostrophe as the up accent and 5-schisma
symbol, and simply allow either the period or the (punctuation) comma
to stand for the down accent and 5-schisma symbol, with the period
being preferred. I think we should throw the backquote in the sagittal
trash can.

> > To summarise:
> >
> > comma down up
> > ---------------
> > 35:36 u n
> > 48:49 ¿ ç
> > 49:50 j. ?'
> > 125:126 h'' p..
> > 224:225 c. r'
> >
> > Can you confirm these George?
>
> 49:50 should be .j and '? ; the rest look okay.

Oops! Yes.

> > And feel free to drop the accents ' and . when it is known to be a
> > notation for ennealimmal (or any other tuning that doesn't use any
> > other accented or unaccented form of these symbols).
>
> Gene won't be able to do that if he's notating 441-ET. He needs both
> the c-r and .-' character pairs, and he wants 224:225 for 3deg to be
> the single-character symbol and 2deg to be the 3deg symbol combined
> with a down-schisma. It looks as if the u-n and ¿-ç character pairs
> would be the only ones he could use, since they're the only ones that
> are unaccented. He would then have to use a couple of user-defined
> character pairs for 125:126 and 224:225. (He doesn't need a separate
> pair for 49:50, because it's the same number of degrees as 48:49 in
> 441-ET.)

OK. I'm sorry I hadn't spent the time to understand his system properly.

> Another possibility that just occurred to me for 224:225 (not only as
> 3deg441, but also 2deg270, 1deg171, and 1deg99) would be ~|.. (double
> right-accented 17-kleisma). Dropping the double-right accent in 441
> is completely okay because it vanishes (both as 2079:2080 and
> 255879:256000) in 441, 270, 171, and 99. So the (17-kleisma)
> character pair "s" (down) and "$" (up) could be used consistently as
> 224:225 for enneallimal with 9 nominals. Dave and I consider this a
> secondary role for the 17-kleisma symbol, but in the context of a 7-
> limit temperament that symbol would obviously be interpreted as
> something other than a 17-kleisma (2176:2187), even though it's
> perfectly valid as either one.

Oh yes! That's definitely the way to go in this case. So in 441-ET
that's "s" for -3 and "$" for +3 degrees instead of "<" and ">". And I
expect Monz will be happier if "<" and ">" are not used for this,
since that was incompatible with how they are used in HEWM.

And I see that you can't just drop the double right accents from the
125:126 symbol because the primary comma for plain h and p is actually
6deg441. There's nothing for 5-degrees but to use some user-definables
as Gene has done. However, if he isn't using "<" and ">" for 3deg441
then they might be more appropriate than "[" and "]" for 5 deg441.
Still incompatiple with HEWM but not as far off.

And yes, he could use the 48:49 symbols ¿ and ç for 13deg441. I see
now that you can't just drop the right accents from the 49:50 symbols
since the primary comma of j and ? alone is 12deg441 not 13.

To summarise:

deg comma down up
441
--------------------------------
1 32768:32805 . or , ' or `
3 224:225 s $ (using a secondary comma role,
but the primary role is valid too)
5 125:126 < > (user defined instead of h'' and p..)
13 48:49 ¿ ç
18 35:36 u n

> Oh, one more thing! Gene, I just noticed two things about your
> symbol sequence:
>
> > 12: C)`
> > 13: C)
> > 14: C),
> ...
> > 17: Cn`
> > 18: Cn
> > 19: Cn,
>
> 1) If "`" is supposed to be up and "," is down, then you have the up
> and down symbols reversed. I apologize that the tables I gave in
> yesterday's message weren't consistent in having the up and down
> symbols always in the same (right vs. left) columns from one table to
> another.

Oh yes. The comma (punctuation mark) definitely should be a down
symbol and the backquote an up symbol. I think Gene commented on the
near invisibility of some of these symbols too and so might prefer to
use the apostrophe instead of the backquote.

> 2) You have the accent marks to the right of the larger accidental.
> In Sagittal the relative position has significance: an accent mark to
> the right alters by a schismina (~0.4c), whereas to the left alters
> by a schisma (~2c).

This brings up the point that in the ASCII shorthand, once you allow
multiple accidentals there is no way to distinguish an accent mark '
from a full 5-schisma symbol '| or a full schismina symbol |' i.e.
those with bare shafts next to them when in True-type symbols.

My feeling is that if Gene's system were expressed in the sagittal
True-type font he would always be using the full 5-schisma symbol with
its own shaft and never applying it as an accent to another symbol, in
which case there would be no problem in having the 5-shisma symbol to
the right. How to deal with this in single-character-ASCII I don't
know, unless we say that in Gene's case he is defining the comma
(punctuation mark) and backquote to stand for a full 5-shisma symbol
while the period and apostrophe still stand for the accents (and are
not used). In that case, what he has is unambiguous.

But of course that conflicts with my earlier suggestion not to use the
backquote at all.

> Gene, I appreciate the fact that you're making an effort to use
> character pairs in a way that won't conflict with the way Dave and I
> have assigned them for Sagittal shorthand, and I hope that the above
> suggestions will work out for you. We have our different ways of
> doing things, and in the process I hope that in using the same
> symbols for the same things we might be able to avoid a lot of
> confusion in this one area.

Yes. I must thank you for that too Gene.

-- Dave Keenan

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> I'm not too enthralled over using a 17-limit symbol for a 7-limit
> comma. The symbol in question is not welded to 126/125 in any case;
> it could be 245/243, 1728/1715, 4000/3969, or 78732/78125, the last
> being a 5-limit comma which may or may not help. This means we really
> only need something in the 13-14 cent range.

That's how sagittal works. In JI (and ennealimmal is so close it
doesn't matter) "s" and "$" are (ASCII for) the unaccented symbols in
the 13 to 14 cent range. You can't expect to distinguish too many
close commas when only using a single ASCII character. So it isn't
really a "17-limit symbol".

We simply found that the 17-comma would notate far more ratio
ocurrences in the Scala archive than any of the other commas you list
above, when the nominals are in a chain of fifths, so we called that
its "primary comma role". That just means that in the absence of any
other information that's what you should assume it means. But the fact
that it's in ennealimmal is sufficient other information.

> My own view is that until you can do a really good job on 5 and 7
> limit temperaments you've not managed yet to create a generic system;
> the 5 and 7 limits being far more basic an important than 17 and beyond.

We think we have done a really good job on the 5 and 7 limits, when
the nominals are in a chian of fifths. It's still very early days for
these (multi-)linear temperament notations with natural nominals, but
we're determined to support them.

But this brings up a point that seemed to get lost in an earlier post
because I chose ETs as my example instead of LTs. You need to consider
the difference between:
(a) notating using the simplest commas and
(b) notating using the commas that notate the simplest ratios.

We would tend to support (b) over (a) where they differ.

>
> > 1) If "`" is supposed to be up and "," is down, then you have the up
> > and down symbols reversed. I apologize that the tables I gave in
> > yesterday's message weren't consistent in having the up and down
> > symbols always in the same (right vs. left) columns from one table to
> > another.
>
> As I said above, that's how I did up and down. Visually, it makes more
> sense to me.

Oh dear. That's why we avoided them in the first place. Because
there's this conflict between the cue given by the slope and the one
given by the vertical position relative to the other chartacters on
the same line.

Can we maybe just go back to . and ' and agree to substitute , for .
only when this is absolutely necessary for Scala.

> I don't have any accent marks, I have combinations of characters.

Yes. That's what I figured. The problem for Sagittal is explained in
more detail in my previous post.

-- Dave

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> > For two ennealimmal generators we have the accented symbol for
> > 189:200, /||~'' from which the double-right accent can be dropped
> > without ambiguity in this application. In ASCII shorthand this is "#z"
> > for up and "b~" for down.
> >
> > For three gens we have (|||, in shorthand "#?" for up, "bj" for down.
>
> But why do we want two and three generator symbols?

Sorry. You're right of course. We don't. I've been away from this
stuff for too long. I agree we need symbols for 2 and 3 generators
_modulo_ the period, or more correctly we need 2 and 3 generators plus
half a period, modulo the period, minus half a period. Is there a name
for that function? "Balanced modulo"?

1 gen -> 18deg441
2 gens -> -13deg441
3 gens -> 5deg441

So for up to 45 notes of ennealimmal we only need at most one
accidental per note. And then you have

8 gens -> -3deg441
19 gens -> -1deg441

Which let you get to +-24 gens with at most 3 accidentals. Makes sense
to me.

-- Dave

I wrote:
> So for up to 45 notes of ennealimmal we only need at most one
> accidental per note.

That should of course have been "for up to 63 notes of ennealimmal" (9
chains of 7 notes a generator apart).

That sounds like it will be plenty for any practical purpose, given
that it has a complexity of around 36.

By the way:

Regarding the idea of a universal superset of nominals, that Herman
and I have been working on: After trying many variations, we have
settled on a superset of 24 nominals. For any given (multi-)linear
temperament you make D the center of one chain (or next-to-center) and
choose the names of the other nominals according to the nearest degree
of 24-ET.

[Yes Herman, I now agree with you, that equally-spaced boundaries are
the only ones that are workable.]

These 24 nominals can be written in pitch order as either:

vA A ^A bB vB B vC C ^C #C vD D ^D bE vE E ^E F ^F #F vG G ^G G#

or

H A P W I B J C R X K D S Y L E T F U Z N G V O

Here's a table that shows the method in the apparent madness of the
full-alphabetical sequence above.

flat up natural down sharp
------------------------------------------
O bA H vA A A P ^A W #A
W bB I vB B B Q ^B
J vC C C R ^C X #C
X bD K vD D D S ^D Y #D
Y bE L vE E E T ^E
M vF F F U ^F Z #F
Z bG N vG G G V ^G O #G

These are listed so that normal reading order corresponds to pitch
order, but note that the rightmost pitch of each row is the same as
the leftmost pitch of the row below it, and the rightmost of the last
row is the same as the leftmost of the first row. So there are only
24 distinct nominals.

By looking down the columns you can see the logic behind this way of
assigning the alphabet. A-G keep their conventional diatonic
positions. H-N are parallel to A-G but a quartertone lower. "O" is a
kind of zero, half an octave fom D. P-V are parallel to A-G but a
quartertone higher. WXYZO is a parallel pentatonic (the black keys).

That's the full 26 letters of the alphabet, but M covers the same
pitch range as T, and Q is the same as J. So M and Q are not required,
can be used when spelling words in melodies. :-)

So in this scheme the ennealimmal nominals (9-ET) would be

H W J R D L T Z V

If ennealimmal were the only LT you wanted to use then there would be
no point to this. You could just use A to I (or H to P).

But if you're using multiple temperaments, whether in different pieces
or one, having a single universal superset of nominals means you only
have to learn their relationships once. And nearly everyone already
uses meantone, so it makes sense not to have to relearn the meaning of
A-G.

-- Dave Keenan

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
> >
> > --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
> > wrote:
> > >
> > > The sagittal symbol for 48:49 is a boathook and arc on a single
> > shaft.
> > > ~|) in long ASCII. For the short ASCII, George Secor, Robert
Walker
> > > and I agreed on the "8-bit-unicode" or "extended ASCII"
> > characters "ç"
> > > lowercase c cedilla) for up, and "¿" (inverted question mark)
for
> > > down. The decimal character codes for these are 231 and 191.
> >
> > Dave, I gave Gene the complete set here:
> > /tuning-math/message/11955
> > beginning about halfway down.
> >
> > I believe that we noticed before that one of the characters won't
> > display, but I also seem to recall that you said that there
wasn't
> > anything else you could use; is that correct? In that message I
see
> > two that don't show:
> >
> > the paragraph sign, up-character for ~~|
> > the not sign, up-character for |~)
>
> There wasn't really anything else usable in the supposed "safe"
range.
> It was quite an effort to arrange the few available characters as
> anything like up/down pairs, let alone matching them up with
sagittals
> that they were supposed to resemble. These are all supposed to be
> available on Mac/PC/Nix. I suspect they only didn't appear in your
> post because they disappeared from the email I sent you. Remember,
> Robert got them all OK in email but those two got lost for you. I'll
> try posting those two pairs here and you can see if they work for
you
> via Yahoo's web interface.
>
> long short short
> up up down description
> --------------------------------------------------------------------
> ~~| ¶ § paragraph sign, section sign
> |~) ¬ ¢ not sign, cents

These all show up okay.

> But anyway, aren't they irrelevant now, since we've agreed to avoid
> using non-Athenian symbols unless we're really desperate, and go for
> double right accents instead. I think it's time we came up with a
> preferred symbol for every degree of 233-EDA (2460-ET) and assigned
a
> primary comma (and maybe some secondaries) to every one, and put the
> list up on the website for comment.

That's something that we still need to discuss. There may be
applications that we haven't yet anticipated in which we get a much
better result with a non-athenian symbol here and there. It all
comes down to works best or is easiest to understand. With 224:225,
below, I showed that s'' and $.. work better than than .c and 'r for
Gene's one-character-per-comma enealimmal requirements (achieved by
dropping the accent marks).

> > Another thing about Scala is that I don't think we ever resolved
the
> > problem that the 5-schisma-down shorthand symbol "." (period)
> > conflicts with the delimiter for the octave number. Gene's
>
> ... I
> think we should keep the apostrophe as the up accent and 5-schisma
> symbol, and simply allow either the period or the (punctuation)
comma
> to stand for the down accent and 5-schisma symbol, with the period
> being preferred. I think we should throw the backquote in the
sagittal
> trash can.

Yes, I agree!

> ...
> To summarise:
>
> deg comma down up
> 441
> --------------------------------
> 1 32768:32805 . or , ' [dump this: `]
> 3 224:225 s $ (using a secondary comma role,
> but the primary role is valid too)
> 5 125:126 < > (user defined instead of h'' and
p..)
> 13 48:49 ¿ ç
> 18 35:36 u n

Dumping the ` character would do the trick!

Gene, if you put the characters for 32768:32805 to the left of the
others, you'll be completely consistent with Sagittal shorthand.
Otherwise, there's the potential for misinterpretation amounting to
~1.6 cents.

--George

I'm finally replying to a conversation involving 5 people that took
place off-list last week. Evidently Manuel has released something in
Scala regarding this, but I'm in the dark about the details and
haven't had time to install this and have a look for myself. Anyway,
those details are probably irrelevant, because I expect that what I'm
about to propose involves somewhat different issues.

--- Dave Keenan <d.keenan@bigpond.net.au> wrote:

> At 05:22 AM 20/04/2005, George Secor wrote:
> >Gene, I've copied Dave Keenan, since he's been taking primary
> >responsibility for symbol-element left-to-right protocol in our
> >notation project.
> >
> >The order in which symbols actually appear on the musical staff has
> >almost without exception been with the largest to the right:
> >(microtonal accidental) (sharp/flat) (notehead-nominal)
> >e.g.: \! # O (F notehead)
> >to indicate F# lowered by a 5-comma,
>
> I don't recall _any_ exceptions.

I don't either, but then I figured that someone would take issue with
me if I didn't add "almost", claiming that there just might be some
instance that I wasn't aware of.

> >But in ASCII this has often been completely reversed:
> >F#\ or F#\!
> >since the # or b character is written to the right of the nominal
> >letter.
>
> Why only "often"? I thought always.

Not so. Bosanquet did 53-ET this way in ASCII:
\E for 5/4 of C
\F# for 5/4 of D
/Eb for 6/5 of C
\\G# for 5/4 of \E
etc.

You might interpret this as treating a Pythagorean sequence as an
open-ended set of nominals and putting the (microtonal) accidentals
to the left, just as they appear on the staff.

This is really not a bad way to do it. We rejected this quite some
time ago, but that was before anyone considered how to use Sagittal
accidentals with compound (non-diatonic) nominals.

Dave, you and Herman presently have your non-diatonic compound
shorthand notation in the form #F\, but I think it would be much more
logical to put the Sagittal accidental to the *left* of the capital
letter and put any character that's part of a compound nominal to the
*right* of the capital letter, in the form \F#. This would then
allow you to use "d" for the backwards flat and "db" for a
sesquiflat, if you wished (although "v" and "bv" are quite all right
by me), inasmuch as anything following a capital letter could be
interpreted in a different manner than the Sagittal shorthand
character assignment (which could be restricted
to "#", "b", "x", "bb", "^", "v", "/", and "\" when appearing to the
right of the capital letter nominal). ASCII mixed Sagittal shorthand
could also follow this proposed syntax.

I can also think of a reason for ASCII long Sagittal, both mixed &
pure, to have the nominal at the right. We were having a problem in
Scala with the period character (as schisma-down and schismina-down)
conflicting with the syntax for octave number; putting the microtonal
accidental to the left of the nominal letter neatly solves that.

The only reversal of order between the staff notation and the ASCII
notation would involve the characters in the compound nominal, but
this is already common practice. The goal is to minimize differences
in symbol/character order between staff notation and ASCII.

Another case in point is ASCII trojan, which can be regarded as a
notation with compound nominals (12 in number). In trojan would we
want to have #F\ or \F#? Remember that with compound nominal
notation (as you and Herman developed it) F#\ isn't an option.

> >So precedence would allow doing it either way in ASCII.
>
> I'm not _totally_ opposed to doing it the other way in ASCII, but I
don't
> know of any precedent and don't see any value in it as yet.

I hope I've made my case. In summary, there are four reasons:
1) It's less disorienting in translating staff notation to ASCII,
because *everything* is smaller-to-greater from left-to-right in both
(except , of course, when >1 character is used for a nominal);
2) It solves the Sagittal-Scala octave-syntax problem;
3) ;yaw that sretcarahc fo sgnirts daer ot gnisufnoc ssel eb dluow tI
4) Assuming that Gene wouldn't use any accidentals smaller than a 5-
schisma (and assuming that we also redo Sagittal shorthand this way),
it makes conversion of Gene's characters to and from Sagittal much
simpler (and in some instances identical, as with C'n).

Reason 3 refers to strings of characters such as Gene is proposing.
I don't know exactly what symbols Gene would use for staff notation,
but keeping the order the same from staff to ASCII would eliminate a
great deal of confusion in reading the strings.

> >In Sagittal we've taken this a couple of steps farther, first by
> >putting the schisma accent mark to the *left* of the Sagittal
> >accidental (both in the staff and ASCII forms, which preserves the
> >right-to-left size order), then by putting schismina accent mark
(s) to
> >the *right* of the Sagittal accidental (both staff & ASCII, which
is an
> >exception to the order),
>
> It isn't an exception at all. Accent marks are only components of
symbols,
> not symbols in their own right. So there is no exception to the
ordering of
> symbols. Whether on the staff or in text, the symbols have always
been
> ordered by decreasing size of alteration as you get further from
the
> notehead or nominal.

The exception is in the ordering of ASCII shorthand characters that,
in combination, represent symbols. In Sagittal ASCII you don't have
symbols, only characters that represent symbols.

> > We keep the same order in both staff & ASCII
> >versions, because we consider the accents to be part of the
Sagittal
> >accidental (rather than a separate accidental), just as the accent
in
> >the character "á" is part of the character (rather than a separate
> >character used in combination with an "a" character), which allows
us
> >to read them as a single unit (or character).
>
> Right. So why say there was any exception?

Because this is the Internet, and we just can't seem to pass up an
opportunity to nitpick over details, can we? 8<D

> I'd prefer to use the word "symbol" where you've used "character"
in the
> above paragraph. Since even in Truetype-sagittal a single symbol is
> sometimes composed of two or three characters, but that's merely a
> practical matter regarding the available space in the font mapping.

Whatever.

> >For your purposes it's probably more meaningful to think of the
> >schisma-characters as separate accidentals, particularly in cases
where
> >there are two other characters modifying the notehead,
>
> Yes. That's clearly how Gene has been thinking of them. And it's
clearly
> the right way to think of them in this (multiple sagittal per note)
> case.
>
> It is not Gene who has a problem here, it's us.

I'm just trying to minimize problems for those of us who might need
to read both Gene's enealimmal notation and Sagittal shorthand. The
less potential for confusion, the better.

> We're trying to use, in the short ASCII, one ASCII character to
stand for
> two different things, which are quite distinct when using the
Truetype font
> or the long ASCII.
>
> Originally, short-ASCII was intended as purely one-ASCII-character
=
> one-sagittal-symbol = one-comma, and it was clear that there would
never be
> complete coverage, since even if there were enough single ASCII
characters
> to cover all the unaccented sagittal symbols, there still wouldn't
be
> enough to cover all the accented ones.
>
> I believe we made it clear to Manuel re the Scala implementation of
> sagittal, that in short-ASCII there was no way to represent
accented
> characters and that multiple ASCII characters would never be used
to
> represent single sagittal symbols (except in long-ASCII). This was
due to
> the ambiguity that would otherwise result if multiple sagittals
were used
> against a single note.
>
> We have never favoured or encouraged the use of multiple sagittals
per
> note, but we have always allowed for it in the past.

But it would be to everyone's advantage if Gene's character
combinations are in a form in which they can most easily be
translated to Sagittal accidentals, which would mandate that the
schisma-characters be at the left end of the string (following the
character identifying the nominal).

Strictly speaking, Gene's characters aren't "Sagittals;" they're
largely a subset of Sagittal shorthand.

> So in short-ASCII the apostrophe always represented the complete 5-
schisma
> symbol with a shaft, and it never represented an accent as a
component of a
> larger symbol.

Right!

> It is true that if one never used more than one sagittal per note
there
> would be no ambiguity in short-ASCII, in also using the apostrophe
as an
> accent. The rule would be: If there are no other characters then it
> represents a full 5-schisma symbol, otherwise it is an accent
> component.

Sounds good. And if you wanted a schismina modifying a nominal (with
or without a schisma), you could revert to the long form, with "|"
or "!" symbolizing zero cents:

|'C |''C !.C !..C '|.C '|''C etc.

> But people are bound to want to sometimes have multiple sagittals
per note
> and they are bound to want to do it in short-ASCII, no matter how
we might
> try to discourage either of these things.
>
> I believe we forgot about this when we were working with Robert on
the FTS
> implementation and agreed to represent accented symbols in short-
ASCII by
> using multiple characters per symbol. I must agree that's a pretty
natural
> thing to want to do, but so is having multiple accidentals per
note, and
> now we find ourselves in a bind.

Robert, you'll have to let me know what you think about this latest
scheme of mine. I didn't think I'd be proposing something like this,
but I found myself strongly disliking the backwards order of #F\ for
non-diatonic nominals. This would take a little getting used to, but
as long as long as Sagittal hasn't been released in FTS and we're
still fairly early in the game with Sagittal in Scala, I don't think
it's too late to consider making the change.

> With multiple accidentals per note and both left and right accents,
we also
> have the problem of determining which symbol an accent belongs to.

Not really. First you interpret the characters apart from the accent
(s), and then you apply the accent(s) to the result. They would
always appear in this order:

(schisma-accent) (shorthand character for smaller ratio) (shorthand
character for larger ratio) (schismina-accent) (capital letter)

For mixed Sagittal or Sagittal with compound nominals, the order
would be:

(schisma-accent) (shorthand character) (schismina-accent) (capital
letter) (# or b) (^ or v) (/ or \)

> Notice
> that this problem exists also in the long-ASCII and the True-type,
whereas
> the above problem (full 5-schisma symbol versus accent) only occurs
in the
> short ASCII.

Put schisma-accents at the left end of the string (excepting the
nominal) and schismina-accents at the right end (immediately to the
left of the nominal letter), and allow for the possibility that
everything in between could be replaced by a single Sagittal symbol.
(Not always possible, but nevertheless desirable.)

> > so a
> >right-to-left greater-to-lesser ASCII order would seem to be "in
order"
> >(pardon the pun). The great advantage to this is that the symbol
order
> >would not differ from what would appear on the staff (except that
the
> >notehead would be at the far right, whereas the ASCII letter
nominal is
> >at the far left)
>
> That's a pretty big "except". The notehead/nominal can be thought
of as the
> biggest alteration of all (from the 1/1 or tonic) and so you would
no
> longer be ordering everything from largest to smallest in any
direction.

Yeah, you're right. That's why I'm proposing this latest change.

> >, allowing you to read the accidentals as a single unit
> >(or "word").
>
> That may be an advantage, but as far as I know it is without
precedent.

Reading strings of characters as words is without precedent? ;-)

> I
> have also explained previously (ad nauseum?) how some people think
of say
> F# as a sort of compound nominal and would therefore be disoriented
by F/#
> instead of F#/ in text even though /#(F-notehead) is just fine on
the
> staff.

But Gene's not using the # and b characters for Enealimmal.

Anyway, now I'm advocating /F# in ASCII in preference to the two
forms you give, and I'm arguing against #F/ for non-diatonic nominals.

You had some remaining questions, but I think I've addressed them all
above.

> ...
> Why are we doing this off-list?

Because Gene replied to me off-list, and I CCed my reply to you.

> It would seem a good idea for at least
> Robert and Manuel to be involved too, so I've CCed them.

The more the merrier. Anyway, I've brought this back on-list.

--George

--- In tuning-math@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:

> But Gene's not using the # and b characters for Enealimmal.

That would presumably change in a system based on nominals separated
by fifths, since I would want Eb-B to start out with. I'd also want a
pair for 126/125 and another for 648/625.

> Because Gene replied to me off-list, and I CCed my reply to you.

That must have been an accident.

George D. Secor wrote:

> Dave, you and Herman presently have your non-diatonic compound > shorthand notation in the form #F\, but I think it would be much more > logical to put the Sagittal accidental to the *left* of the capital > letter and put any character that's part of a compound nominal to the > *right* of the capital letter, in the form \F#. This would then > allow you to use "d" for the backwards flat and "db" for a > sesquiflat, if you wished (although "v" and "bv" are quite all right > by me), inasmuch as anything following a capital letter could be > interpreted in a different manner than the Sagittal shorthand > character assignment (which could be restricted > to "#", "b", "x", "bb", "^", "v", "/", and "\" when appearing to the > right of the capital letter nominal). ASCII mixed Sagittal shorthand > could also follow this proposed syntax.

Well, there wouldn't be a need for a sesquiflat (any sesquiflat-sized modification to a nominal would be represented by an appropriate sagittal; the semiflats are just there to allow the 24 nominals to be notated on a traditional staff). But your suggestion sounds fine to me.