Yahoo Tuning Groups Ultimate Backup tuning shruti-s and Staff Notation

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
wrote:

> Hello ALL, have the symbols for representing the 22
> shruti-s on the Staff been standardized?
>
> Can you tell me where these symbols are to be found, please?
>
> Regards,
> Haresh.

i don't know about a standardized notation that may
already exist ... but one can be made from sagittal
which perhaps *should* be the standard.

Dave Keenan perhaps can do this?

----

anyway, if one accepts the "traditional" ancient tuning
of the shruti system as a 3-limit Pythagorean chain,
then all the notes may be notated with standard notation.
i can also provide a HEWM notation for the 5-limit version.

about 1/4 of the way down this page:

http://tonalsoft.com/td/erlich/srutipblock.htm

you can see a 5-limit periodicity-block which Paul Erlich
says is the most common interpretation of the shruti
system -- here i add the 5-limit HEWM notation:

(in the Yahoo interface, click the "Reply" link to view properly)

B- F#- C#- G#- D#-
182---884---386---1088--590
/ \ / \ / \ / \ / \
/ \ / \ / \ / \ / \
Bb F C G D A E B F# C# G# D#
90---792---294---996---498----0----702---204---906---408---1110--612
\ / \ / \ / \ / \ /
\ / \ / \ / \ / \ /
Bb+ F+ C+ G+ D+
112---814---316---1018--520

here is a table showing data for these pitches/intervals,
with their HEWM notation, and the 3-limit equivalents:

A = 1/1

/---------- 5-limit version -------------\ /-- 3-limit --\
cents HEWM 2,3,5-monzo ratio HEWM 2,3-monzo

1109.775004 G# [ -7 5, 0 > 243 : 128
1088.268715 G#- [ -3 1, 1 > 15 : 8 Ab [ 12 -7, >
1017.596288 G+ [ 0 2, -1 > 9 : 5 Fx [-15 10, >
996.0899983 G [ 4 -2, 0 > 16 : 9
905.8650026 F# [ -4 3, 0 > 27 : 16
884.358713 F#- [ 0 -1, 1 > 5 : 3 Gb [ 15 -9, >
813.6862861 F+ [ 3 0, -1 > 8 : 5 E# [-12 8, >
792.1799965 F [ 7 -4, 0 > 128 : 81
701.9550009 E [ -1 1, 0 > 3 : 2
611.7300052 D# [ -9 6, 0 > 729 : 512
590.2237156 D#- [ -5 2, 1 > 45 : 32 Eb [ 10 -6, >
519.5512887 D+ [ -2 3, -1 > 27 : 20 Cx [-17 11, >
498.0449991 D [ 2 -1, 0 > 4 : 3
407.8200035 C# [ -6 4, 0 > 81 : 64
386.3137139 C#- [ -2 0, 1 > 5 : 4 Db [ 13 -8, >
315.641287 C+ [ 1 1, -1 > 6 : 5 B# [-14 9, >
294.1349974 C [ 5 -3, 0 > 32 : 27
203.9100017 B [ -3 2, 0 > 9 : 8
182.4037121 B- [ 1 -2, 1 > 10 : 9 Cb [ 16 -10, >
111.7312853 Bb+ [ 4 -1, -1 > 16 : 15 A# [-11 7, >
90.22499567 Bb [ 8 -5, 0 > 256 : 243
0 A [ 0 0, 0 > 1 : 1

-monz

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> --- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
> wrote:
>
> > Hello ALL, have the symbols for representing the 22
> > shruti-s on the Staff been standardized?
> >
> > Can you tell me where these symbols are to be found, please?
> >
> > Regards,
> > Haresh.
>
> i don't know about a standardized notation that may
> already exist ... but one can be made from sagittal
> which perhaps *should* be the standard.
>
> Dave Keenan perhaps can do this?
>
> ----
>
> anyway, if one accepts the "traditional" ancient tuning
> of the shruti system as a 3-limit Pythagorean chain,
> then all the notes may be notated with standard notation.
> i can also provide a HEWM notation for the 5-limit version.
>
> about 1/4 of the way down this page:
>
> http://tonalsoft.com/td/erlich/srutipblock.htm
>
> you can see a 5-limit periodicity-block which Paul Erlich
> says is the most common interpretation of the shruti
> system -- here i add the 5-limit HEWM notation:
>
> (in the Yahoo interface, click the "Reply" link to view properly)
>
> B- F#- C#- G#- D#-
> 182---884---386---1088--590
> / \ / \ / \ / \ / \
> / \ / \ / \ / \ / \
> Bb F C G D A E B F# C# G#
D#
> 90---792---294---996---498----0----702---204---906---408---1110--
612
> \ / \ / \ / \ / \ /
> \ / \ / \ / \ / \ /
> Bb+ F+ C+ G+ D+
> 112---814---316---1018--520
>
>
> here is a table showing data for these pitches/intervals,
> with their HEWM notation, and the 3-limit equivalents:
>
> A = 1/1
>
> /---------- 5-limit version -------------\ /-- 3-limit --\
> cents HEWM 2,3,5-monzo ratio HEWM 2,3-monzo
>
> 1109.775004 G# [ -7 5, 0 > 243 : 128
> 1088.268715 G#- [ -3 1, 1 > 15 : 8 Ab [ 12 -7, >
> 1017.596288 G+ [ 0 2, -1 > 9 : 5 Fx [-15 10, >
> 996.0899983 G [ 4 -2, 0 > 16 : 9
> 905.8650026 F# [ -4 3, 0 > 27 : 16
> 884.358713 F#- [ 0 -1, 1 > 5 : 3 Gb [ 15 -9, >
> 813.6862861 F+ [ 3 0, -1 > 8 : 5 E# [-12 8, >
> 792.1799965 F [ 7 -4, 0 > 128 : 81
> 701.9550009 E [ -1 1, 0 > 3 : 2
> 611.7300052 D# [ -9 6, 0 > 729 : 512
> 590.2237156 D#- [ -5 2, 1 > 45 : 32 Eb [ 10 -6, >
> 519.5512887 D+ [ -2 3, -1 > 27 : 20 Cx [-17 11, >
> 498.0449991 D [ 2 -1, 0 > 4 : 3
> 407.8200035 C# [ -6 4, 0 > 81 : 64
> 386.3137139 C#- [ -2 0, 1 > 5 : 4 Db [ 13 -8, >
> 315.641287 C+ [ 1 1, -1 > 6 : 5 B# [-14 9, >
> 294.1349974 C [ 5 -3, 0 > 32 : 27
> 203.9100017 B [ -3 2, 0 > 9 : 8
> 182.4037121 B- [ 1 -2, 1 > 10 : 9 Cb [ 16 -10, >
> 111.7312853 Bb+ [ 4 -1, -1 > 16 : 15 A# [-11 7, >
> 90.22499567 Bb [ 8 -5, 0 > 256 : 243
> 0 A [ 0 0, 0 > 1 : 1
>
> -monz

When I saw Haresh's message, I had a few questions, but it appears
that you've answered all of them, Monz!

Since this involves only 5-limit intervals, conversion of the above
to Sagittal (JI) is extremely simple. All of the ratios can be
represented *exactly* with Sagittal symbols if, in the above table,
you replace each occurrence #, b, +, and - as follows:

Pure Sagittal:

Replace with
------- ----
# /||\
b \!!/
+ /|
- \!
#- ||\
b+ !!/

Mixed Sagittal:

Replace with
------- ----
+ /|
- \!

Please bear in mind that the combinations of characters in the second
column are only ascii simulations of Sagittal symbols and that the
actual symbols are much more compact in appearance.

You can get a better idea of how these look by loading a file of
these ratios into Scala, resetting your 1/1 to A (I don't remember
how this is done -- Manuel?), and entering the command "set nota
saji1". For mixed-symbol Sagittal enter "set sagi mixed", and to
revert back to the pure version enter "set sagi pure".

--George

🔗Haresh BAKSHI <hareshbakshi@hotmail.com>

Thanks, Monz and George.

Regards,
Haresh.

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > --- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
> > wrote:
> >
> > > Hello ALL, have the symbols for representing the 22
> > > shruti-s on the Staff been standardized?
> > >
> > > Can you tell me where these symbols are to be found, please?
> > >
> > > Regards,
> > > Haresh.
> >
> > i don't know about a standardized notation that may
> > already exist ... but one can be made from sagittal
> > which perhaps *should* be the standard.
> >
> > Dave Keenan perhaps can do this?
> >
> > ----
> >
> > anyway, if one accepts the "traditional" ancient tuning
> > of the shruti system as a 3-limit Pythagorean chain,
> > then all the notes may be notated with standard notation.
> > i can also provide a HEWM notation for the 5-limit version.
> >
> > about 1/4 of the way down this page:
> >
> > http://tonalsoft.com/td/erlich/srutipblock.htm
> >
> > you can see a 5-limit periodicity-block which Paul Erlich
> > says is the most common interpretation of the shruti
> > system -- here i add the 5-limit HEWM notation:
> >
> > (in the Yahoo interface, click the "Reply" link to view properly)
> >
> > B- F#- C#- G#- D#-
> > 182---884---386---1088--590
> > / \ / \ / \ / \ / \
> > / \ / \ / \ / \ / \
> > Bb F C G D A E B F# C# G#
> D#
> > 90---792---294---996---498----0----702---204---906---408---1110--
> 612
> > \ / \ / \ / \ / \ /
> > \ / \ / \ / \ / \ /
> > Bb+ F+ C+ G+ D+
> > 112---814---316---1018--520
> >
> >
> > here is a table showing data for these pitches/intervals,
> > with their HEWM notation, and the 3-limit equivalents:
> >
> > A = 1/1
> >
> > /---------- 5-limit version -------------\ /-- 3-limit --\
> > cents HEWM 2,3,5-monzo ratio HEWM 2,3-monzo
> >
> > 1109.775004 G# [ -7 5, 0 > 243 : 128
> > 1088.268715 G#- [ -3 1, 1 > 15 : 8 Ab [ 12 -7, >
> > 1017.596288 G+ [ 0 2, -1 > 9 : 5 Fx [-15 10, >
> > 996.0899983 G [ 4 -2, 0 > 16 : 9
> > 905.8650026 F# [ -4 3, 0 > 27 : 16
> > 884.358713 F#- [ 0 -1, 1 > 5 : 3 Gb [ 15 -9, >
> > 813.6862861 F+ [ 3 0, -1 > 8 : 5 E# [-12 8, >
> > 792.1799965 F [ 7 -4, 0 > 128 : 81
> > 701.9550009 E [ -1 1, 0 > 3 : 2
> > 611.7300052 D# [ -9 6, 0 > 729 : 512
> > 590.2237156 D#- [ -5 2, 1 > 45 : 32 Eb [ 10 -6, >
> > 519.5512887 D+ [ -2 3, -1 > 27 : 20 Cx [-17 11, >
> > 498.0449991 D [ 2 -1, 0 > 4 : 3
> > 407.8200035 C# [ -6 4, 0 > 81 : 64
> > 386.3137139 C#- [ -2 0, 1 > 5 : 4 Db [ 13 -8, >
> > 315.641287 C+ [ 1 1, -1 > 6 : 5 B# [-14 9, >
> > 294.1349974 C [ 5 -3, 0 > 32 : 27
> > 203.9100017 B [ -3 2, 0 > 9 : 8
> > 182.4037121 B- [ 1 -2, 1 > 10 : 9 Cb [ 16 -10, >
> > 111.7312853 Bb+ [ 4 -1, -1 > 16 : 15 A# [-11 7, >
> > 90.22499567 Bb [ 8 -5, 0 > 256 : 243
> > 0 A [ 0 0, 0 > 1 : 1
> >
> > -monz
>
> When I saw Haresh's message, I had a few questions, but it appears
> that you've answered all of them, Monz!
>
> Since this involves only 5-limit intervals, conversion of the above
> to Sagittal (JI) is extremely simple. All of the ratios can be
> represented *exactly* with Sagittal symbols if, in the above table,
> you replace each occurrence #, b, +, and - as follows:
>
> Pure Sagittal:
>
> Replace with
> ------- ----
> # /||\
> b \!!/
> + /|
> - \!
> #- ||\
> b+ !!/
>
> Mixed Sagittal:
>
> Replace with
> ------- ----
> + /|
> - \!
>
> Please bear in mind that the combinations of characters in the second
> column are only ascii simulations of Sagittal symbols and that the
> actual symbols are much more compact in appearance.
>
> You can get a better idea of how these look by loading a file of
> these ratios into Scala, resetting your 1/1 to A (I don't remember
> how this is done -- Manuel?), and entering the command "set nota
> saji1". For mixed-symbol Sagittal enter "set sagi mixed", and to
> revert back to the pure version enter "set sagi pure".
>
> --George

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗monz <monz@attglobal.net>

hi Gene, George, Haresh,

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

> It's possible to look on this as a detempered schismic;
> it is very similar to a chain of fifths from -10 to +11
> fifths. Tuning in 53-equal would be logical; it has 19 pure
> fifths, and two fifths flat by a schisma, whereas 53 would
> give 21 fifths, each flat by 1/29 of a schisma. The three
> step sizes of 81/80, 25/24 and 256/243 would be converted
> by 53-et to 1, 3 and 4 steps, as compared to ratios to
> the Didymus comma of 1, 3.286 and 4.195. In 118-equal that
> would be instead 1, 3.5 and 4, and in 94-et (for the 7-limit)
> it would be 1, 2.5 and 3.

it's almost certain that this tuning had its origin as
an extended chain of pythagorean pitches. i don't have
real evidence ... just my speculations that what Partch
called poly-pythagoreanism, goes all the way back to
the Sumerians c.3000 BC.

Danielou, one of the big Western authorities on Indian
music, described it in terms of 53edo.

-monz

🔗Petr Parízek <p.parizek@worldonline.cz>

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > http://tonalsoft.com/td/erlich/srutipblock.htm
> >
> > you can see a 5-limit periodicity-block which Paul Erlich
> > says is the most common interpretation of the shruti
> > system -- here i add the 5-limit HEWM notation:
> >
> > (in the Yahoo interface, click the "Reply" link to view properly)
> >
> > B- F#- C#- G#- D#-
> > 182---884---386---1088--590
> > / \ / \ / \ / \ / \
> > / \ / \ / \ / \ / \
> > Bb F C G D A E B F# C# G#
> D#
> > 90---792---294---996---498----0----702---204---906---408---1110--
> 612
> > \ / \ / \ / \ / \ /
> > \ / \ / \ / \ / \ /
> > Bb+ F+ C+ G+ D+
> > 112---814---316---1018--520
> >
> > -monz

I saw more than one version of the Shruti scale some time ago and I think it
would be useful to make some sort of comparison here. To be able to do this,
I'm gonna use the symbol "P" for the pure fifth (3/2) and "S" for the fifth
which is a schisma smaller (16384/10935). For those who are interested in
tuning the Shrutis, please understand that all the versions are essentially
the same as the pitches never differ more than by a single schisma (only
about 2 cents) so they are more or less inaudible.
The first version that I've met is the same as Monz has listed. Its
chain of fifths looks like this:

P P P P S P P P P P P P P P P P S P P P P

The "disadvantage" of this scale is that the two smaller fifths are too far
from each other in the chain and tuning the pure fifths in-between (there
are 11 of them) is not so easy as the only way to check the interval quality
is to play the fifths themselves. Well, next comes the version which, as I
managed to find out (in Manuel's scale archive), Firoze Framjee describes in
his "Text book of Indian music". It looks like this:

P P P P P P P S P P P P P P S P P P P P P

The good thing about this scale is that the two smaller fifths are not so
far from each other as in the previous example. On the other side, the
previous factors of 128/81 and 32/27 now became 405/256 and 1215/1024. It's
really not good to have such complex ratios in the scale if there are less
complex ones which can easily replace them. So the best way I think it
should be done is a compromise. The two complex ratios will be replaced with
the simpler ones (they will be the same as in the first version) and the
rest is left as above (like the second version). The resulting scale looks
like this:

P P P P P S P P P P P P P P S P P P P P P

I believe I've also seen this interpretation somewhere, but I don't know who
it was who made it this way (perhaps some of you know?). Though, this is the
version I always use if I need to analyze the Shruti scale in some way.
Petr

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@w...> wrote:

> P P P P P S P P P P P P P P S P P P P P P
>
> I believe I've also seen this interpretation somewhere, but I don't
know who
> it was who made it this way (perhaps some of you know?). Though,
this is the
> version I always use if I need to analyze the Shruti scale in some way.

Scala doesn't know about this one, so I've put a version of it below
(the mode was chosen to minimize Tenney height.) Of course with 21
fifths and two schismas, one could simply make all the fifths flat by
2/21 of a shisma, pretty close to what 171-equal would give you. The
only virtue I can see in this exact tuning is that it keeps the final
400/243 which completes the circle of 19 P and 2 S fifths; one could
instead choose (34816/7)^21, which is 0.12 schismas flat, and has a
pure 17/14 third. Fans of the 10:12:14:17 diminished seventh chord
could try to discover if it is ever used in Indian music tuned to
shruti scales; if it is, this would be one way to tune them. The comma
involved here incidentally is (243/200)/(17/14) = 1701/1700.

! indpar.scl
Parizek shruti scale
22
!
25/24
135/128
10/9
9/8
75/64
32/27
5/4
320/243
4/3
25/18
45/32
40/27
3/2
25/16
128/81
5/3
225/128
16/9
50/27
15/8
160/81
2

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
wrote:
> Hello ALL, have the symbols for representing the 22 shruti-s on
the Staff been standardized?
>
> Can you tell me where these symbols are to be found, please?
>
> Regards,
> Haresh.

Hi Haresh,

I know I'm rather late answering this. But your request send me on
an odyssey lasting several days, to try to understand what the 22
shruti-s actually are! I expect you are well aware of what a fools
errand that is.

I admit defeat! It seems there is no end of controversy, not only
about what the shruti-s are, but which shruti-s correspond to the 7
notes of sa-gramma or the 7 of ma-gramma, and which correspond to a
larger set of 12, or indeed whether there is anything useful at all
in the notion of 22 shruti-s. There's Carnatic (Southern) versus
Hindustani (Northern) and ancient versus modern.

Some particularly interesting papers in English, on ancient shruti
systems were these by Chris Forster:
http://www.chrysalis-foundation.org/Bharata's_Vina.htm
http://www.chrysalis-foundation.org/Ramamatya's_Vina.htm

and of course the "History of 22 tone tunings" section in Paul
Erlich's paper:
http://lumma.org/tuning/erlich/erlich-decatonic.pdf

But the good news is, because of the way the Sagittal notation
system works, all but the most extreme interpretations of the 22
shruti-s end up being notated in the same way, including most
alternative spellings (enharmonic spellings). Alternative spellings
should of course be chosen so that no two notes in a raga have the
same letter or staff position, unless they are variations of a note
between ascending and descending.

The only requirement is a single accidental that represents the
comma of Didymus (syntonic comma), and by approximation also
represents the comma of Pythagoras, only a schisma (about 2 cents)
larger. And in the pure Sagittal notation (at most one symbol per
note) we also need symbols that represent its combinations with the
apotome.

Others gave suggestions which had Sa (1/1) as A. I don't see the
sense in this. It makes more sense to me, and seemed more common in
my reading, to notate Sa as C (irrespective of its actual
frequency). This is the default in Scala, and I understand that
typical frequencies for Sa are somewhere between the B and D of
western concert pitch.

I assume you know where to find Scala (with Sagittal implemented),
but I don't think anyone told you where to find the Sagittal
accidentals font, and explanations of how the system works.
http://dkeenan.com/sagittal
There's a link to Scala from the above site too, just in case.

For Scala to notate them in Sagittal you can describe your sruti-s
as ratios, either as a 3-limit chain of 22 fifths (extended
Pythagorean), or any 5-limit version where notes differ by at most a
schisma from the extended Pythagorean, such as the one given by
Monz. When you SET NOTATION SAJI1 in Scala, the schismas vanish so
these come out the same.

Or you can describe them as steps of 22-equal and SET NOTATION SA22.
Or you can describe them as 22 notes in a chain of the best fifths
in 29, 34, 41, 46 or 53 equal (in all of which the schisma
vanishes), and use the corresponding SET NOTATION SAxx.

In all cases you should find that you get the chain of fifths
notated as (enharmonic spellings in parenthesis):

D\
A\
E\
B\
F#\ (Gb)
Db (C#\)
Ab (G#\)
Eb (D#\)
Bb (A#\)
F
C = Sa = 1/1
G
D
A
E
B
F# (Gb/)
Db/ (C#)
Ab/ (G#)
Eb/ (D#)
Bb/ (A#)
F/

where the 6 accidental combinations b b/ \ / #\ # are replaced by
the appropriate sagittal symbols.

Note that a 4:5 major third (or its schismic approximation) is found
by stepping backwards 8 places on the chain of fifths, and a 5:6
minor third by stepping forward 9 places.

In pitch order these are:

C = Sa = 1/1
Db (C#\)
Db/ (C#)
D\
D
Eb (D#\)
Eb/ (D#)
E\
E
F
F/
F#\ (Gb)
F# (Gb/)
G
Ab (G#\)
Ab/ (G#)
A\
A
Bb (A#\)
Bb/ (A#)
B\
B

Regards,
-- Dave Keenan

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
wrote:
> > Hello ALL, have the symbols for representing the 22 shruti-s on
> the Staff been standardized?
> >
> > Can you tell me where these symbols are to be found, please?
> >
> > Regards,
> > Haresh.
>
> Hi Haresh,
>
> I know I'm rather late answering this. But your request send me on
> an odyssey lasting several days, to try to understand what the 22
> shruti-s actually are! ...
>
> But the good news is, because of the way the Sagittal notation
> system works, all but the most extreme interpretations of the 22
> shruti-s end up being notated in the same way, including most
> alternative spellings (enharmonic spellings). Alternative spellings
> should of course be chosen so that no two notes in a raga have the
> same letter or staff position, unless they are variations of a note
> between ascending and descending.
>
> The only requirement is a single accidental that represents the
> comma of Didymus (syntonic comma), and by approximation also
> represents the comma of Pythagoras, only a schisma (about 2 cents)
> larger. And in the pure Sagittal notation (at most one symbol per
> note) we also need symbols that represent its combinations with the
> apotome.
> ...
> For Scala to notate them in Sagittal you can describe your sruti-s
> as ratios, either as a 3-limit chain of 22 fifths (extended
> Pythagorean), or any 5-limit version where notes differ by at most
a
> schisma from the extended Pythagorean, such as the one given by
> Monz. When you SET NOTATION SAJI1 in Scala, the schismas vanish so
> these come out the same.
>
> Or you can describe them as steps of 22-equal and SET NOTATION
SA22.
> Or you can describe them as 22 notes in a chain of the best fifths
> in 29, 34, 41, 46 or 53 equal (in all of which the schisma
> vanishes), and use the corresponding SET NOTATION SAxx.
>
> In all cases you should find that you get the chain of fifths
> notated as (enharmonic spellings in parenthesis):
>
> D\
> A\
> E\
> B\
> F#\ (Gb) ...
>
> Regards,
> -- Dave Keenan

Haresh,

I am in complete agreement with Dave.

If you wish Scala to display the 5-comma symbols as Dave has them in
his lists (using the single characters "/" and "\" instead of "/|"
and "\!", which is less cumbersome), then you should also enter the
commands SET SAGITTAL MIXED and SET SAGITTAL SHORT.

Something that we have not mentioned in our documentation is that we
have single-character symbols for all of the most common Sagittal
symbols.

--- In tuning@yahoogroups.com, "Robert Walker" <robertwalker@n...>
wrote:
[at /tuning/topicId_54823.html#54823]

> Accidental:
> Symbol used to modify pitch such as # or b.
> Two versions of sixth tone notation are in use:
> + - ++ -- +++ ---
> Maneri / Sims: ^ v > < ] [
> HEWM (newest): - + < > v ^

To these (s/b "twelfth-tone notation") we could then add:

+ - ++ -- +++ ---
Sagittal: / \ f t v ^

For anyone who is interested, here is a complete list of the
shorthand symbols, opposite the longer ascii symbol simulations:

Symbol pairs that do not appear in the above list are allowed for
user-defined applications (in order of recommended size):

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

--George

🔗George D. Secor <gdsecor@yahoo.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> Something that we have not mentioned in our documentation is that
> we have single-character symbols for all of the most common
> Sagittal symbols.

Of course, what George means here is that we have defined single-
ASCII-character equivalents for the most common (single-shaft)
Sagittal symbols, in such a way that there is some resemblance where
possible.

>
> --- In tuning@yahoogroups.com, "Robert Walker" <robertwalker@n...>
> wrote:
> [at /tuning/topicId_54823.html#54823]
>
> > Accidental:
> > Symbol used to modify pitch such as # or b.
> > Two versions of sixth tone notation are in use:
> > + - ++ -- +++ ---
> > Maneri / Sims: ^ v > < ] [
> > HEWM (newest): - + < > v ^
>
> To these (s/b "twelfth-tone notation") we could then add:
>
> + - ++ -- +++ ---
> Sagittal: / \ f t v ^

Of course, these should be

- + -- ++ --- +++
Maneri / Sims: v ^ < > [ ]
HEWM (newest): - + < > v ^
Sagittal: \ / t f v ^

Note that we did not use the characters - + < > [ ] in the single-
character ASCII equivalents for Sagittal, so as to minimise clashes
with these existing ASCII notations. But v and ^ as representing
full arrows, were just too good to pass up.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@w...> wrote:
The resulting scale looks
> like this:
>
> P P P P P S P P P P P P P P S P P P P P P
>
> I believe I've also seen this interpretation somewhere, but I don't
know who
> it was who made it this way (perhaps some of you know?). Though,
this is the
> version I always use if I need to analyze the Shruti scale in some way.

I found an interesting property of this scale. If we take the
Pythagorean scale on 22 notes, and Hahn reduce it via the schisma, we
get a scale where the maximum Hahn distance is 4 from the 1/1, which
is simply a transposition of this scale. I was going to call it
indian-hahn, but Paul Hahn already has his version of shrutis in the
Scala archive! If we replace the 256/135 with something a schisma
higher, 243/128, we get the Tenney-reduced shruti scale; but this has
Hahn size 5 and the other choice seems better.

! indianred.scl
32805/32768 Hahn-reduced
22
!
135/128
16/15
10/9
9/8
32/27
6/5
5/4
81/64
4/3
27/20
45/32
64/45
3/2
128/81
8/5
5/3
27/16
16/9
9/5
15/8
256/135
2

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > For anyone who is interested, here is a complete list of the
> > shorthand symbols, opposite the longer ascii symbol simulations:
>
> Were you going to or did you add a lynchpin symbol for the lynchpin
> comma, 4096/4095; or alternatively for the ennealimmal commas,
> 2401/2400 or 4375/4374?

The tridecimal schismina, 4095:4096, which I referred to as
the "linchpin" (after Dave first called it that in a private email to
me; however, no "lynch"ing, please) of Sagittal has never been
symbolized, since it vanishes, even in high-precision JI. We had no
intention of (reason for) having a symbol for it in extreme-precision
JI, although we did (tentatively) devise *exact* symbols, |~\ and
|)), for the 13M (1024:1053) and 13L (26:27) dieses, which would
differ by that amount from /|) and (|\, which are exactly defined as
the 35M (35:36) and 35L (8192:8505) dieses, respectively.

At present the smallest comma that we notate is the 5-schisma,
32768:32805. If there are any plans afoot to notate anything
smaller, then that is something that you and Dave can work out, and
which I will be happy to review or be available for comment as needed.

--George