Yahoo Tuning Groups Ultimate Backup tuning The New Notation

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> I'm sure with our preeminent tunesters George Secor and Dave Keenan
> that we're going to be getting a notation that will set an
important
> new standard.
>
> I would just want to make sure that it's really *tested* enough and
> enough people have looked at it and thought about it as a standard
> before I would switch from my beloved (well I hate the
quartertones)
> Sims 72-tET notation...
>
> I would also need to design, or have a font designed in PostScript,
> so it could be used the way I use the Sims accidentals with the
font
> designed by Ted Mook.
>
> So, I'm not saying I'm not going to do it. I probably can be
> convinced, but I'll need these practicalities.
>
> Additionally, I will need a thorough explanation, a dummies manual
> that doesn't assume that one has been following Tuning Math for the
> last three years or whatever...
>
> Thanks!
>
> Joseph P.

if you're using sagittal for 72-equal, all you have to do is replace
the sims accidentals with a different set, most of which look
like "arrows" . . . and that's it, that's all that *you'll* ever have
to understand (unless george secor's dream of 31-equal and 41-equal
instruments comes true, in which case you might become interested in
some of the compatibilities that the system offers between different
tuning systems) . . .

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_47435.html#47436

>>
> if you're using sagittal for 72-equal, all you have to do is
replace
> the sims accidentals with a different set, most of which look
> like "arrows" . . . and that's it, that's all that *you'll* ever
have
> to understand (unless george secor's dream of 31-equal and 41-equal
> instruments comes true, in which case you might become interested
in
> some of the compatibilities that the system offers between
different
> tuning systems) . . .

***Well, that's great, Paul, since, as you gather, I will only be
using the 72-tET set for the time being (maybe just for a little
while, like the rest of my lifetime... :)

However, of course, I will have to like the way the symbols *look.*
I'm pretty happy with the Sims for the 12th tones and 6th tones. The
quartertones "suck" to use the vernacular... I certainly wouldn't
mind replacing *those...*

But, I like the idea that these progressive ideas are happening and
people are seriously trying to find a "generalized" solution for
microtonality... so I'll try to be as supportive as possible...

[Of course my friend Johnny Reinhard already believes there *is* such
a generalized system with *cents* notation, so all of this is, of
course, somewhat open for debate...]

Joseph

🔗Paul Erlich <paul@stretch-music.com>

🔗Jon Szanto <JSZANTO@ADNC.COM>

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> they still look the same as
> when george presented them here last year. for example, you can
> go to message 39833 and find the following link:

That is still a very intriguing and lovely graphic to look at; I also remember that, IIRC, George indicated he would make some examples of 'music' in the notation - at some point.

My perspective, as both a composer but primarily a performer, is that until someone can present a *number* of example pages, scores, and performance parts - so that one can have a rough idea of what it will entail to visually parse such a system - this is still very much in the infancy.

I do recall that George has more than a passing experience with reading/performing notated music; I don't believe Dave K. is in this same category. But *unless* this universal notation exist simply for the presentation and analysis of scores _sans_ performance, then before things get cast in concrete or bit, someone needs to spend some time preparing music in this notation (and it doesn't matter if it is good music or not, just something representative of reading the notation).

I don't imply that this isn't one of the steps coming up, but only that it is all so highly speculative in the 'practical' realm that I need to see more before I could ever consider moving to it. Which, of course, is by virtue of having to encourage *others* to use it, to play my music.

Cheers,
Jon

🔗Paul Erlich <paul@stretch-music.com>

🔗Joseph Pehrson <jpehrson@rcn.com>

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

🔗monz <monz@attglobal.net>

hi Jon,

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
>
> > they still look the same as
> > when george presented them here last year. for example, you can
> > go to message 39833 and find the following link:
>
> That is still a very intriguing and lovely graphic to look
> at; I also remember that, IIRC, George indicated he would
> make some examples of 'music' in the notation - at some point.
>
> My perspective, as both a composer but primarily a performer,
> is that until someone can present a *number* of example pages,
> scores, and performance parts - so that one can have a rough
> idea of what it will entail to visually parse such a system
> - this is still very much in the infancy.

this is only one very small example, but i think it's a
good one: a notation and MIDI-file of Dave Keenan's
adaptive-JI I-VI-II-V-I "comma-pump" chord progression,
written in the "sagittal" notation and tuned by me in 217edo:

http://sonic-arts.org/dict/adaptiveji.htm

(about 3/4 of the way down the page)

-monz

🔗Jon Szanto <JSZANTO@ADNC.COM>

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Jon,
>
> --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
>
> > --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> >
> > > they still look the same as
> > > when george presented them here last year. for example, you can
> > > go to message 39833 and find the following link:
> >
> > That is still a very intriguing and lovely graphic to look
> > at; I also remember that, IIRC, George indicated he would
> > make some examples of 'music' in the notation - at some point.
> >
> > My perspective, as both a composer but primarily a performer,
> > is that until someone can present a *number* of example pages,
> > scores, and performance parts - so that one can have a rough
> > idea of what it will entail to visually parse such a system
> > - this is still very much in the infancy.
>
> this is only one very small example, but i think it's a
> good one: a notation and MIDI-file of Dave Keenan's
> adaptive-JI I-VI-II-V-I "comma-pump" chord progression,
> written in the "sagittal" notation and tuned by me in 217edo:
>
> http://sonic-arts.org/dict/adaptiveji.htm
>
> (about 3/4 of the way down the page)
>
> -monz

Monz,

These changes are starting to get a little embarrassing, but I think
you will understand why Dave and I have taken so long to release the
details of the notation. Since we have made sagittal JI notation
completely independent of *any* ET, the reference to 217-ET in the
diagram is inappropriate, so that *both* the diagram and your midi
file are now out of date.

I will send you a new graphic for the diagram off-list. Your midi
file should now have pitches that are actual n/4-comma alterations to
tones in a pythagorean sequence, where n corresponds to degrees in
the athenian symbol sequence given in the new diagram.

--George

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > However, of course, I will have to like the way the symbols
> >*look.*
>
> unless dave and george changed something, they still look the same
as
> when george presented them here last year. for example, you can go
to
> message 39833 and find the following link:
>
> /tuning-
math/files/secor/kbds/KbDec72.gif

The appearance of the symbols has changed somewhat since I put that
graphic out there, but this involves only a cosmetic makeover
(particularly for those symbols that have X's instead of arrow
shafts). I have therefore deleted the graphic and have replaced it
with an updated version, in which:

1) The symbols shown on the keytops are now the latest version (sized
for staff lines 6 pixels apart, identical to the sagittal graphics in
Scala 2.2);
2) There is a full sequence of sagittal symbols for 72-ET at the
bottom (in a larger size, for staff lines 8 pixels apart);
3) The key colors can be more easily identified if the figure is
printed in black and white.

As Dave Keenan also explained in msg. #47451, these symbols are for
the "pure" version of the sagittal notation, which eliminates
conventional sharp and flat (single and double) symbols, thus
requiring only a single symbol for each notehead. This results in a
relatively uncluttered appearance for notating chords on a
manuscript, something that can be a problem with a notation that
requires multiple symbols for each notehead.

Since Sibelius will not presently handle the number of new symbols
for 72-ET required with the pure version of sagittal, Joseph will
have to use the "mixed" version of the notation, which uses single-
shaft sagittal symbols in combination with conventional sharp and
flat symbols. Since the mixed version uses fewer new symbols, it has
a gentler learning curve, and clutter is not an issue for parts
written for instruments that play only one note at a time.

--George

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> > they still look the same as
> > when george presented them here last year. for example, you can
> > go to message 39833 and find the following link:
>
> That is still a very intriguing and lovely graphic to look at; I
also remember that, IIRC, George indicated he would make some
examples of 'music' in the notation - at some point.
>
> My perspective, as both a composer but primarily a performer, is
that until someone can present a *number* of example pages, scores,
and performance parts - so that one can have a rough idea of what it
will entail to visually parse such a system - this is still very much
in the infancy.
>
> I do recall that George has more than a passing experience with
reading/performing notated music; I don't believe Dave K. is in this
same category. But *unless* this universal notation exist simply for
the presentation and analysis of scores _sans_ performance, then
before things get cast in concrete or bit, someone needs to spend
some time preparing music in this notation (and it doesn't matter if
it is good music or not, just something representative of reading the
notation).
>
> I don't imply that this isn't one of the steps coming up, but only
that it is all so highly speculative in the 'practical' realm that I
need to see more before I could ever consider moving to it. Which, of
course, is by virtue of having to encourage *others* to use it, to
play my music.
>
> Cheers,
> Jon

Okay, Jon, I'll toss you a bone (actually a figure from an article I
was working on):

/tuning-
math/files/secor/notation/SagJI.gif

This is just 6 measures of something to illustrate a few simple
things in JI -- at the top the mixed-symbol version of sagittal,
below that the pure sagittal version, and below that the ratios for
each note. The article that contains this figure will have a blow-by-
blow explanation of what the symbols mean, but you should be able to
figure out a lot of this (i.e., the symbols for 80:81, 63:64, 32:33,
and 26:27) from the ratios. Here's a tip: For symbols containing
straight-line half-arrowheads (or "barbs", which appear in the 1st,
2nd, and 4th chords), pay particular attention to the *slope* of the
barbs, which is an indication of the direction of the 5-comma (80:81)
alteration to that note (in both the pure and mixed-symbol
versions). For single-shaft symbols altering by a 5-comma, the half-
arrow also points in the same direction that the barb slopes, giving
another indication of the direction of pitch alteration.

When I put this file out there, I noticed that there was an old
version of the sagittal adaptive JI (comma pump) example, so I
replaced that:

/tuning-
math/files/secor/notation/AdaptJI.gif

No time to do any full scores yet, but I hope that this gives you
some idea of what the notation looks like.

--George

🔗monz <monz@attglobal.net>

hi George,

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

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> >
> > this is only one very small example, but i think it's a
> > good one: a notation and MIDI-file of Dave Keenan's
> > adaptive-JI I-VI-II-V-I "comma-pump" chord progression,
> > written in the "sagittal" notation and tuned by me in 217edo:
> >
> > http://sonic-arts.org/dict/adaptiveji.htm
> >
> > (about 3/4 of the way down the page)
> >
> > -monz
>
> Monz,
>
> These changes are starting to get a little embarrassing,
> but I think you will understand why Dave and I have taken
> so long to release the details of the notation. Since we
> have made sagittal JI notation completely independent of
> *any* ET, the reference to 217-ET in the diagram is
> inappropriate, so that *both* the diagram and your midi
> file are now out of date.
>
> I will send you a new graphic for the diagram off-list.
> Your midi file should now have pitches that are actual
> n/4-comma alterations to tones in a pythagorean sequence,
> where n corresponds to degrees in the athenian symbol
> sequence given in the new diagram.

thanks for making the new graphic!

but does this new "athenian" version really supercede
the 217edo version? isn't it simply another variant?

it seems to me that my "Adaptive-JI" Dictionary page
could illustrate both approaches to adaptive-JI, no?

... and if i *can* keep the 217edo example, how does
sagittal notation now fit into that?

-monz

🔗monz <monz@attglobal.net>

hi George,

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

> > http://sonic-arts.org/dict/adaptiveji.htm
>
> I will send you a new graphic for the diagram off-list.
> Your midi file should now have pitches that are actual
> n/4-comma alterations to tones in a pythagorean sequence,
> where n corresponds to degrees in the athenian symbol
> sequence given in the new diagram.

by "comma", you do mean "syntonic comma", correct?

that seems obvious to me because the first and last chords
have an "E" which is the "major-3rd", and the accidental
shows it to be a Pythagorean "major-3rd" narrowed by
1/4-comma -- so if that's 1/4 of a syntonic comma, then
it's a perfectly tuned 5:4 JI "major-3rd". so far so good.

but the # and b symbols represent 21/4 = 5 & 1/4 commas.

if those are syntonic commas, then that interval is
~112.9080204 cents.

of course, because of the incommensurability of the prime-factors,
that cents-value does not correspond to the Pythagorean
"chromatic semitone" (also called "apotome") with the
ratio 2187:2048, which has the [2,3] monzo [-11 7],
and the cents-value ~113.6850061. this is ~0.776985675
of a cent larger than 21/4 syntonic commas.

can you explain further how this fits into the adaptive-JI
scheme?

(i asked this question because it concerns the retuning
of the MIDI-file.)

-monz

🔗Jon Szanto <JSZANTO@ADNC.COM>

Hi George,

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> Okay, Jon, I'll toss you a bone (actually a figure from an article
> I was working on):
>
> /tuning-
> math/files/secor/notation/SagJI.gif

Thanks, George. I downloaded it and appended your explanation in graphic text so the two are always together. I'll do a little study of it, too.

I hope it was clear, and that I soft-pedaled enough: I'm not trying to throw cold water on any of your's and Dave's hard work. But I am painfully aware that notation is for the benefit of human beings, and I am just hoping that the development is continuing beyond deciding on symbols for individual notes and trying to grasp what large amounts of music would be like to *read* in these notations.

Practicality shouldn't stop you, by any means, but it certainly has to be figured into the scenario at some point. Or am I way off base?

> No time to do any full scores yet, but I hope that this gives you
> some idea of what the notation looks like.

That it does, and I thank you for posting the example!

Cheers,
Jon

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi George,
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > >
> > > this is only one very small example, but i think it's a
> > > good one: a notation and MIDI-file of Dave Keenan's
> > > adaptive-JI I-VI-II-V-I "comma-pump" chord progression,
> > > written in the "sagittal" notation and tuned by me in 217edo:
> > >
> > > http://sonic-arts.org/dict/adaptiveji.htm
> > >
> > > (about 3/4 of the way down the page)
> > >
> > > -monz
> >
> > Monz,
> >
> > These changes are starting to get a little embarrassing,
> > but I think you will understand why Dave and I have taken
> > so long to release the details of the notation. Since we
> > have made sagittal JI notation completely independent of
> > *any* ET, the reference to 217-ET in the diagram is
> > inappropriate, so that *both* the diagram and your midi
> > file are now out of date.
> >
> > I will send you a new graphic for the diagram off-list.
> > Your midi file should now have pitches that are actual
> > n/4-comma alterations to tones in a pythagorean sequence,
> > where n corresponds to degrees in the athenian symbol
> > sequence given in the new diagram.
>
> thanks for making the new graphic!
>
> but does this new "athenian" version really supercede
> the 217edo version? isn't it simply another variant?

Well, yes, but it's closer to real JI (as alterations to a
pythagorean sequence of fifths) than is the 217-ET version (which
uses the symbols for a 217 mapping, hence is technically alterations
to a sequence of 217-ET fifths), so the athenian version should be
considered the best sagittal representation of 1/4-comma adaptive JI
and the 217 version the variant. In fact, you could also have a 224-
ET variant based on a 224-ET mapping (which is closer to the athenian
version, since the fifth of 224 has less error than in 217). While
all 3 of these divide the apotome into 21 parts and the 5-comma into
4 parts, the two ETs differ in the number of degrees in a limma
(diatonic semitone) and pythagorean whole tone, and all 3 use a
slightly different sequence of symbols:

JI: |( )|( ~|( /| |) (| (|( //| /|) /|\ (|) (|\
)||( ~||( )||~ ||) ||\ (||( //|| /||) /||\
224: |( )|( ~|( /| |) |\ (|( //| /|) /|\ (|) (|\
)||( ~||( /|| ||) ||\ (||( //|| /||) /||\
217: |( ~| ~|( /| |) |\ (|( //| /|) /|\ (|) (|\
)||( ~||( /|| ||) ||\ (||( ||~) /||) /||\

The single-shaft symbols differ only in the symbols for 2 and 6
degrees (and therefore also for their double-shaft apotome
complements, 15 and 19deg). These symbols have the following primary
comma meanings:

~| 17 kleisma, 2176:2187, ~8.730c
)|( 7:11 kleisma, 891:896, ~9.688c
|\ 55 comma, 54:55, ~31.767c
(| 7:11 comma, 45056:45927, ~33.148c

The reason for the variation in symbols between 217 and 224 is due to
the fact that ~| is valid as 2deg217 but as 1deg224, while )|( is
1deg217 but 2deg224. The athenian JI symbol set could theoretically
use either symbol in either pair, but )|( and (| were chosen because
they are more useful for JI in that they both exactly notate 11-limit
consonances (11/7 and 14/11, in alternate spellings), so that 14/11
may be spelled as either E)|( -- a pythagorean E raised by 891:896,
or Fb(| -- a pythagorean F-flat raised by 45056:45927.

Athenian is our name for the sagittal symbol set that notates medium-
precision JI. We call our "bare-bones" or "starter" symbol
set "spartan"; it's capable of notating 7-limit consonances and 16
harmonics in JI, plus most of the more popular ETs under 100, and a
lot of folks might not need anything more than that. We thought
that, since we were naming one symbol set after Sparta, we should
also honor the other pre-eminent ancient Greek city-state with a
symbol set name.

We have 2 or 3 other JI symbols sets still to be finalized (all
higher-precision than athenian) that, since they contain both pairs
of symbols, are able to distinguish between the above pairs of
commas. Athenian JI does not make the distinction of the 5-schisma
(~1.954c), but the higher-precision symbol sets do. The choice of
which particular set to use will come down to a trade-off between
simplicity and precision.

> it seems to me that my "Adaptive-JI" Dictionary page
> could illustrate both approaches to adaptive-JI, no?

Yes, it could, and the 224 approach could also be included. The 224
symbol set is easier to remember in the pure sagittal version,
because the entire sequence of double-shaft symbols has flags that
match a portion of the single-shaft symbol sequence. Athenian JI
notation in the pure sagittal version would also be simpler if the
224 symbol set were used, but this would be at the expense of
substituting an inexact symbol |\ for an exact one (| for the 7:11
comma, and in deciding that (| should be in the athenian set we chose
precision over simplicity.

> ... and if i *can* keep the 217edo example, how does
> sagittal notation now fit into that?

The figure that you have is still valid, since the 217-ET notation
depicted therein has not changed, but as a 217 mapping it must be
identified as based on a specific ET. It's a couple of steps removed
from athenian adaptive JI (with a 224 mapping being one step
removed). You could note, however, that the 217 approach might be a
bit more practical with acoustic instruments, since flexible-pitch
instruments specially built for 31-ET could be employed to bend tones
by +-3 degrees of 217 (in steps of ~5.5c with a max. alteration <17
cents) to produce any pitch of 217-ET.

--George

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi George,
>
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > > http://sonic-arts.org/dict/adaptiveji.htm
> >
> > I will send you a new graphic for the diagram off-list.
> > Your midi file should now have pitches that are actual
> > n/4-comma alterations to tones in a pythagorean sequence,
> > where n corresponds to degrees in the athenian symbol
> > sequence given in the new diagram.
>
>
>
> by "comma", you do mean "syntonic comma", correct?
>
> that seems obvious to me because the first and last chords
> have an "E" which is the "major-3rd", and the accidental
> shows it to be a Pythagorean "major-3rd" narrowed by
> 1/4-comma -- so if that's 1/4 of a syntonic comma, then
> it's a perfectly tuned 5:4 JI "major-3rd". so far so good.
>
>
> but the # and b symbols represent 21/4 = 5 & 1/4 commas.

no (why would you think so), and actually they don't represent
anything, because they're absent from the example in question.

> (i asked this question because it concerns the retuning
> of the MIDI-file.)

you must mean a different midi file, then? which one? the lasso? you
did that in 217-equal??

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi George,
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > > http://sonic-arts.org/dict/adaptiveji.htm
> >
> > I will send you a new graphic for the diagram off-list.
> > Your midi file should now have pitches that are actual
> > n/4-comma alterations to tones in a pythagorean sequence,
> > where n corresponds to degrees in the athenian symbol
> > sequence given in the new diagram.
>
> by "comma", you do mean "syntonic comma", correct?

Yes. Dave and I call it a 5 comma.

> that seems obvious to me because the first and last chords
> have an "E" which is the "major-3rd", and the accidental
> shows it to be a Pythagorean "major-3rd" narrowed by
> 1/4-comma -- so if that's 1/4 of a syntonic comma, then
> it's a perfectly tuned 5:4 JI "major-3rd". so far so good.
>
> but the # and b symbols represent 21/4 = 5 & 1/4 commas.
>
> if those are syntonic commas, then that interval is
> ~112.9080204 cents.
>
> of course, because of the incommensurability of the prime-factors,
> that cents-value does not correspond to the Pythagorean
> "chromatic semitone" (also called "apotome") with the
> ratio 2187:2048, which has the [2,3] monzo [-11 7],
> and the cents-value ~113.6850061. this is ~0.776985675
> of a cent larger than 21/4 syntonic commas.
>
> can you explain further how this fits into the adaptive-JI
> scheme?
>
> (i asked this question because it concerns the retuning
> of the MIDI-file.)

In athenian JI the # and b symbols have exact meanings as apotome
alterations (as their primary interpretation), but 21/4 of a 5 comma
would be a secondary interpretation of those symbols, hence an
approximation at the athenian (medium-precision) JI level.

The symbols used for n/4 commas (where n<>4) would therefore also be
approximations of those (irrational) ratios. So only the 5 comma and
apotome are exact symbols in 1/4-comma adaptive JI. In a score it
would be necessary to specify in the performance notes the intervals
that you intend these symbols to represent. In this case that would
be pythagorean nominals altered by exact quarter-commas, so that is
how you should tune your midi file.

In a 217 symbol-mapping, it would also be possible to specify exact
apotomes, 5-commas, and fractions of 5-commas in the performance
directions, in which case the midi file would be the same as for
athenian adaptive JI. (Or you might elect to specify the tones as
degrees of 217-ET, in which case the precision in a performance might
be no better than that.) You, the composer, would thus have some
flexibility in the way you decide to use the notation.

--George

🔗Paul Erlich <paul@stretch-music.com>

🔗monz <monz@attglobal.net>

hi paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > hi George,
> >
> >
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
> >
> > > > http://sonic-arts.org/dict/adaptiveji.htm
> > >
> > > I will send you a new graphic for the diagram off-list.
> > > Your midi file should now have pitches that are actual
> > > n/4-comma alterations to tones in a pythagorean sequence,
> > > where n corresponds to degrees in the athenian symbol
> > > sequence given in the new diagram.
> >
> >
> >
> > by "comma", you do mean "syntonic comma", correct?
> >
> > that seems obvious to me because the first and last chords
> > have an "E" which is the "major-3rd", and the accidental
> > shows it to be a Pythagorean "major-3rd" narrowed by
> > 1/4-comma -- so if that's 1/4 of a syntonic comma, then
> > it's a perfectly tuned 5:4 JI "major-3rd". so far so good.
> >
> >
> > but the # and b symbols represent 21/4 = 5 & 1/4 commas.
>
> no (why would you think so), and actually they don't represent
> anything, because they're absent from the example in question.

they're in the list George put on the graphic,
and defined there as 21 quarter-commas.

> > (i asked this question because it concerns the retuning
> > of the MIDI-file.)
>
> you must mean a different midi file, then? which one?
> the lasso? you did that in 217-equal??

no, i mean the Dave Keenan comma-pump MIDI-file.
the one i had there before was tuned in 217edo, the new one
is tuned in 1/4-syntonic-comma deviations from Pythagorean.

the Lasso example is tuned in Vicentino's tuning, two
chains of 1/4-comma meantone a quarter-comma apart, as
i describe here:

http://sonic-arts.org/monzo/vicentino/vicentino.htm

-monz

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> Hi George,
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> > Okay, Jon, I'll toss you a bone (actually a figure from an
article
> > I was working on):
> >
> > /tuning-
> > math/files/secor/notation/SagJI.gif
>
> Thanks, George. I downloaded it and appended your explanation in
graphic text so the two are always together. I'll do a little study
of it, too.
>
> I hope it was clear, and that I soft-pedaled enough: I'm not trying
to throw cold water on any of your's and Dave's hard work. But I am
painfully aware that notation is for the benefit of human beings, and
I am just hoping that the development is continuing beyond deciding
on symbols for individual notes and trying to grasp what large
amounts of music would be like to *read* in these notations.
>
> Practicality shouldn't stop you, by any means, but it certainly has
to be figured into the scenario at some point. Or am I way off base?

Jon, thank you for the wisdom so thoughtfully expressed in your
comments, which are "right on".

As you've probably noticed, Dave and I have recently gotten a rather
bad review, and we'd very be grateful for at least a second opinion
(but do take your time). I hope that you will also read the comments
I gave here:

/tuning/topicId_47488.html#47508

Most appreciatively,

--George