Yahoo Tuning Groups Ultimate Backup tuning New Pages: MegaScore Tour

Hi Aaron,

This is great stuff. Very clever how you've made a
41-position-per-octave staff manageable. And extended it to 205-ET
with accidentals for quarter commas.

My only suggestion, and I feel very strongly about this, is that it
would be much better to use symbols other than conventional sharps and
flats and their doubles and triples for the quarter comma inflections.
The maning of those symbols is so ingrained for most musicians.

May I suggest sagittal symbols for these inflections. For example the
first three symbols (apart from natural) in the 217-EDO notation in
figure 9 on page 16 of
http://dkeenan.com/sagittal/Sagittal.pdf
and their inversions.

And while we're at it, why not use the sagittal symbols for the comma
and semisharp/semiflat. /| and /|\ and their inversions. What you call
sub/super and grave/acute, although I understand that these only
appear in text and not on the staff. See the first two symbols (apart
from natural) in the 41-EDO notation in figure 8 on page 15 of the
above paper.

We've always said (in footnote 2 on page 2), "The Sagittal accidentals
may also be used in a consistent manner with systems that do not use a
conventional staff, ..."

And the Sagittal font's free and compatible with commercial music
fonts, so there's no need to overload the conventional symbols with
multiple new and very different meaqnings.

-- Dave Keenan

--- In tuning@yahoogroups.com, Aaron Andrew Hunt <aahunt@...> wrote:
>
> The H-Pi website has been updated with a set of explanatory pages
> about the MegaScore notation system. Some of you may have previously
> seen earlier versions of these pages which were up on my former
> faculty space several years ago. In that case you will be happy to
> know that all the graphics have been updated. The relatively small
> amount of text remains almost the same. Loading of these pages may be
> slow, as there are lots of graphics on some of them. Feedback and
> suggestions welcome as always. See the grey menubar for the new pages:
>
> http://www.h-pi.com/MSCintro.html
>
> Cheers,
> Aaron Hunt
> H-Pi Instruments
>

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

Hi Dave!

Thanks for the feedback. As you know I have watched the sagittal
project from its inception on the tuning-math list. I even joined
in on the discussion now and then. I greatly admire what you and
George have done, and I find sagittal to be remarkably clever, logical
and thorough. It is also a very different approach to the whole
problem of microtonal notation than the one I have taken.

While sagittal is based on comma relations, the megastaff is
based on average perceptual limits. While I'm certainly not
going to stop anyone from using sagittal symbols on a megastaff,
it doesn't make sense to me to make this the default standard for
the system, as the two ways of thinking are very different in
my opinion.

Part of my goal in creating the system was to use existing nomenclature
and include as few foreign symbols and terminology as possible.
Another goal was to make small pitch differences as intuitive and as
simple as possible to notate and read. The only things anyone using
the megastaff has to understand are a circle of 41 fifths, comma shifting,
and JND fine tuning. The comma is a step of 41ET, which is adjusted
by JNDs. Anyone can see which pitches are higher and lower at sight,
without having to think about this or that comma shift, or even this or
that accidental, since accidentals are now part of the position. The
position + the inflection gives the pitch, tuned within 1/2 JND
accuracy, so notes on the same position are easily differentiated by
the small JND shifts. Position naming is totally flexible, since accidentals
are not written, so correct spelling of harmonies is not even a notational
issue anymore; it is a matter left only to theory, where it belongs.

Regarding the use of the sharp and flat symbols for JND tuning,
these symbols are not being given new meanings which are contrary
to the ingrained thinking of trained musicians, as you suggest. The
terms "sharp" and "flat" do not conventionally only refer to symbols;
they are also used simply to mean "a little higher" and "a little lower"
in pitch, as in "that was a bit sharp". I simply took this existing usage
and turned it into something useful for music notation. Trained
musicians can easily see the logic, as there is already presently a
distinction between "accidental" and "inflection". Existing usage
of the term accidental remains essentially the same, and the term
inflection (presently having no precise meaning) is clarified with
a precise meaning, making it useful. Positions are defined by
accidentals; inflections fine tune positions in JNDs.

The system also provides a 1 to 1 correspondence with the keys of a
Tonal Plexus keyboard, and the shapes and sizes of the keys are
directly related to the system of JND inflections in the notation.

In sum, the megastaff is staying the way it is for good reasons.
The only thing I have yet to explain is the notation of pure JI on
the megastaff, which I have also fully developed. All in due time...

Cheers,
Aaron Hunt
H-Pi Instruments

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> Hi Aaron,
>
> This is great stuff. Very clever how you've made a
> 41-position-per-octave staff manageable. And extended it to 205-ET
> with accidentals for quarter commas.
>
> My only suggestion, and I feel very strongly about this, is that it
> would be much better to use symbols other than conventional sharps and
> flats and their doubles and triples for the quarter comma inflections.
> The maning of those symbols is so ingrained for most musicians.
>
> May I suggest sagittal symbols for these inflections. For example the
> first three symbols (apart from natural) in the 217-EDO notation in
> figure 9 on page 16 of
> http://dkeenan.com/sagittal/Sagittal.pdf
> and their inversions.
>
> And while we're at it, why not use the sagittal symbols for the comma
> and semisharp/semiflat. /| and /|\ and their inversions. What you call
> sub/super and grave/acute, although I understand that these only
> appear in text and not on the staff. See the first two symbols (apart
> from natural) in the 41-EDO notation in figure 8 on page 15 of the
> above paper.
>
> We've always said (in footnote 2 on page 2), "The Sagittal accidentals
> may also be used in a consistent manner with systems that do not use a
> conventional staff, ..."
>
> And the Sagittal font's free and compatible with commercial music
> fonts, so there's no need to overload the conventional symbols with
> multiple new and very different meaqnings.
>
> -- Dave Keenan
>
>
> --- In tuning@yahoogroups.com, Aaron Andrew Hunt <aahunt@> wrote:
> >
> > The H-Pi website has been updated with a set of explanatory pages
> > about the MegaScore notation system. Some of you may have previously
> > seen earlier versions of these pages which were up on my former
> > faculty space several years ago. In that case you will be happy to
> > know that all the graphics have been updated. The relatively small
> > amount of text remains almost the same. Loading of these pages may be
> > slow, as there are lots of graphics on some of them. Feedback and
> > suggestions welcome as always. See the grey menubar for the new pages:
> >
> > http://www.h-pi.com/MSCintro.html
> >
> > Cheers,
> > Aaron Hunt
> > H-Pi Instruments
> >
>

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

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@> wrote:
> > Regarding the use of the sharp and flat symbols for JND tuning,
> > these symbols are not being given new meanings which are contrary
> > to the ingrained thinking of trained musicians, as you suggest.
>
> No, I wouldn't say "contrary to". But certainly _very_ different in
> size. In fact only one sixteenth of the size. I would say that
> disagrees with the ingrained thinking of trained musicians.

But please follow the logic all the way through. A sharp
written on the megastaff is an inflection, not an accidental.
Any given note can have both. For example, a note on the
E-flat position notated with a sharp is :

"sharp E flat"

"sharp" is the inflection, as in "it's a bit sharp", and "flat" is the
accidental, as in "it's in the flat part of the fifths chain". If anything
this makes more sense to anyone learning the system than
conventional notation, since the language follows the notation
from left to right instead of backwards. The paradigm shift
is that the accidentals are not written; they are in the positions
themselves, which have to be memorized, and this, believe it or
not, is not as hard as it may at first appear.

> > The
> > terms "sharp" and "flat" do not conventionally only refer to symbols;
> > they are also used simply to mean "a little higher" and "a little
> lower"
> > in pitch, as in "that was a bit sharp".
>
> That's certainly true of the _terms_ "sharp" and "flat", but not the
> sharp and flat _symbols_, which is what I'm referring to.

If you follow the logic, you'll see I call these things - flats and
sharps - "signs" which are used in two distinct ways, as
demonstrated in the example above and in examples on
the website.

It's all very simple, really. To use the megastaff you hardly have to
know anything. Just put notes in higher or lower positions and
use your ear to fine tune them with inflections. It doesn't really
require much knowledge of music theory either. I wanted
something simple = high and low, tune it by ear, then ask the
question: what did I do there? Then that analysis leads to a
composition. This is an intuitive way of working. All the patterns
of music theory can follow from something which was conceived
without consulting theory at all. The theory is all there if I want it,
but it isn't necessary to write the music. I can just draw pictures
with notes and in the megastaff system, the notes actually sound
the way they look. If that is appealing enough, then I think people
will get past the accidental / inflection issue if it bothers them.

Yours,
Aaron Hunt
H-Pi Instruments

🔗Graham Breed <gbreed@gmail.com>

Aaron Andrew Hunt wrote:

> But please follow the logic all the way through. A sharp > written on the megastaff is an inflection, not an accidental. > Any given note can have both. For example, a note on the
> E-flat position notated with a sharp is :
> > "sharp E flat"

This is fine as logic, but intuitively it's scary. Overloading a symbol with contradictory meanings is generally not a good idea. Why not bring in some new symbols like Dave suggests?

> "sharp" is the inflection, as in "it's a bit sharp", and "flat" is the > accidental, as in "it's in the flat part of the fifths chain". If anything
> this makes more sense to anyone learning the system than > conventional notation, since the language follows the notation > from left to right instead of backwards. The paradigm shift
> is that the accidentals are not written; they are in the positions
> themselves, which have to be memorized, and this, believe it or
> not, is not as hard as it may at first appear.

Sure, it follows the language ... if you speak English. Are you confident that the system won't catch on enough that you'll need to worry about speakers of languages that do things differently? Or should the order depend on the language to keep translators on their tones? (Like with B in German, *blech*) What about languages that don't even have a consistent word order?

> If you follow the logic, you'll see I call these things - flats and > sharps - "signs" which are used in two distinct ways, as > demonstrated in the example above and in examples on
> the website.
> > It's all very simple, really. To use the megastaff you hardly have to > know anything. Just put notes in higher or lower positions and > use your ear to fine tune them with inflections. It doesn't really > require much knowledge of music theory either. I wanted > something simple = high and low, tune it by ear, then ask the > question: what did I do there? Then that analysis leads to a > composition. This is an intuitive way of working. All the patterns > of music theory can follow from something which was conceived > without consulting theory at all. The theory is all there if I want it, > but it isn't necessary to write the music. I can just draw pictures > with notes and in the megastaff system, the notes actually sound > the way they look. If that is appealing enough, then I think people
> will get past the accidental / inflection issue if it bothers them.

All that's true whatever symbols you use. Yes people will get used to the same symbols meaning different things in different contexts. Wouldn't it be easier to learn new symbols?

I think the basic idea behind sagittal -- to coordinate the symbols used for accidentals between notation systems -- is a good one. They may not have the details right (who would expect it first time?) but nobody else has tried. And yet those of you developing new notations are ignoring it rather than suggesting changes. This is not only on the staff but with your note names ("shifts"). Maybe notating each of the 205 notes with only one accidental would be too difficult to remember. But sagittal has symbols for any of the shifts you need. It wouldn't hurt your system at all to use them.

If musicians ever start moving between systems (and don't we all hope they will?) it'll be a lot easier if the symbols are used consistently. It's such a shame the microtonal community is too splintered to agree on this.

Graham

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Aaron Andrew Hunt wrote:
>
> > But please follow the logic all the way through. A sharp
> > written on the megastaff is an inflection, not an accidental.
> > Any given note can have both. For example, a note on the
> > E-flat position notated with a sharp is :
> >
> > "sharp E flat"
>
> This is fine as logic, but intuitively it's scary.
> Overloading a symbol with contradictory meanings is
> generally not a good idea. Why not bring in some new
> symbols like Dave suggests?

Sharp and flat = higher and lower. Place them left and right,
they still mean higher and lower. On the left it is a smaller
change and the right is a larger one. It is very simple and
absolutely *not* contradictory, and new symbols are not
needed.

> Sure, it follows the language ... if you speak English.

Fair enough.

> > It's all very simple, really. ... I can just draw pictures
> > with notes and in the megastaff system, the notes actually sound
> > the way they look. If that is appealing enough, then I think people
> > will get past the accidental / inflection issue if it bothers them.
>
> All that's true whatever symbols you use. Yes people will
> get used to the same symbols meaning different things in
> different contexts. Wouldn't it be easier to learn new symbols?

I think not.

> I think the basic idea behind sagittal -- to coordinate the
> symbols used for accidentals between notation systems -- is
> a good one. They may not have the details right (who
> would expect it first time?) but nobody else has tried. And
> yet those of you developing new notations are ignoring it
> rather than suggesting changes. This is not only on the
> staff but with your note names ("shifts"). Maybe notating
> each of the 205 notes with only one accidental would be too
> difficult to remember. But sagittal has symbols for any of
> the shifts you need. It wouldn't hurt your system at all to
> use them.

I already said if someone wants to use sagittals, great. I don't
think it makes sense as a default standard for the megastaff.
A person looking at the megastaff sees familiar symbols.
It still looks like music.

Originally I had different clef symbols. Comparing this with
standrad clefs over a few years convinced me that standard clefs
make it look more like music. Replace the clefs with new symbols,
replace the sharps and flats with new symbols, and you have
something which doesn't resemble standard notation enough
in my opinion...

> If musicians ever start moving between systems (and don't we
> all hope they will?) it'll be a lot easier if the symbols
> are used consistently. It's such a shame the microtonal
> community is too splintered to agree on this.

Sagittal requires too much knowledge in my opinion.

The symbols I use are all in a standard font set, plus
standard musical symbols. The only symbols which are slightly
different are triple sharp and triple flat. An asterisk can be used
as the triple sharp (as it is a stylized asterisk), and the triple
flat can be made from a double and single in a standard
music font set. The shifts are standard characters in standard
font sets, they are + and html codes b for positive
shifts and ~ (b<) and &conj; for the
negatives. These resemble plus, double plus, minus and
double minus (I could have used - and = for the negatives, but
a wavy line is better since = means equals). I know the
negatiives have other meanings, but most people aren't
bothered by that since those symbols aren't used as often
and they probably don't know what they mean anyway.
The doubles are singles stacked vertically. This makes
more sense than using sagittal symbols which are not in a
standard font set and have too specific a meaning to use
for my purposes. A shifted note is fine tuned by a JND
inflection, so the shift can't be a sagittal
symbol anyway since the size of the shift would require a
different sagittal symbol to be correct.

The system is staying as it is, as I said, for good reasons.
Anyone who wants to use sagittal on it is welcome to it.

Yours,
Aaron Hunt
H-Pi Instruments

🔗Klaus Schmirler <KSchmir@online.de>

Aaron Andrew Hunt schrieb:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>> Aaron Andrew Hunt wrote:
>>
>>> But please follow the logic all the way through. A sharp
>>> written on the megastaff is an inflection, not an accidental.
>>> Any given note can have both. For example, a note on the
>>> E-flat position notated with a sharp is :
>>>
>>> "sharp E flat"
>> This is fine as logic, but intuitively it's scary.
>> Overloading a symbol with contradictory meanings is
>> generally not a good idea. Why not bring in some new
>> symbols like Dave suggests?
> > > > Sharp and flat = higher and lower. Place them left and right,
> they still mean higher and lower. On the left it is a smaller
> change and the right is a larger one. It is very simple and
> absolutely *not* contradictory, and new symbols are not
> needed.

Sharp and flat = between this note (nominal) and the next named note above/below. And most people off this list have trouble conceptualizing that there's space for an F# _and_ a Gb between G and F. The "flat gee flat" stuff in English only works because these are set phrases with the adjective last (like "obvious heir apparent"). But admittedly, the distinction can be made in other languages I know and is even easier (Maybe I'm just lucky with my selection of languages!): "sol diese acut", "tiefes Ges". But I couldn't say "erniedrigtes Ges", because "erniedrigt" implies "by a Pythagorean comma" - and "doppeltief" or "doppelt tief" sounds just as absurd as "double deep".

In principle, I'm all for sneaking in the Sagittal symbols. But is it even possible when it is not apparent any more which nominal a note is derived from? And if it is (was), to situate myself completely on the geeky side: Whouldn't a composer want a myriad of symbols for any commas available between 41-ET and 205-ET to remind themself (does that form exist?) of its actual harmonic meaning?

klaus

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

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

--- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@...> wrote:
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> > No, I wouldn't say "contrary to". But certainly _very_ different in
> > size. In fact only one sixteenth of the size. I would say that
> > disagrees with the ingrained thinking of trained musicians.
>
>
> But please follow the logic all the way through. A sharp
> written on the megastaff is an inflection, not an accidental.
> Any given note can have both. For example, a note on the
> E-flat position notated with a sharp is :
>
> "sharp E flat"
>
> "sharp" is the inflection, as in "it's a bit sharp", and "flat" is the
> accidental, as in "it's in the flat part of the fifths chain".

Hi Aaron,

Yes, I understand all that. Your web pages are very clear. (I wish we
had educational material as good as that for Sagittal). But you seem
to be missing the point that several people now are trying to make.

The symbols on the staff don't _look_ like inflections. They _look_
like accidentals.

Logic isn't everything, as was pointed out to us quite forcefully by
Joseph Pehrson in regard to Sagittal, and for which we will be
eternally grateful.

> If anything
> this makes more sense to anyone learning the system than
> conventional notation, since the language follows the notation
> from left to right instead of backwards. The paradigm shift
> is that the accidentals are not written; they are in the positions
> themselves, which have to be memorized, and this, believe it or
> not, is not as hard as it may at first appear.

I don't have a problem with this aspect of it. I think your semantics
(meanings) are just fine. It's only the choice of symbols or "signs"
for the inflections that I find jarring, and I think many others will too.

> It's all very simple, really. To use the megastaff you hardly have to
> know anything. Just put notes in higher or lower positions and
> use your ear to fine tune them with inflections. It doesn't really
> require much knowledge of music theory either. I wanted
> something simple = high and low, tune it by ear, then ask the
> question: what did I do there? Then that analysis leads to a
> composition. This is an intuitive way of working. All the patterns
> of music theory can follow from something which was conceived
> without consulting theory at all. The theory is all there if I want it,
> but it isn't necessary to write the music. I can just draw pictures
> with notes and in the megastaff system, the notes actually sound
> the way they look. If that is appealing enough,
...

I think the linear graphical representation of pitch is very
appealing. The biggest problem with the standard staff, for
microtonality is that it has those dreadful hiccups where some steps
are about twice as big as others. I recall some group trying to agree
on a staff that represented 12-equal linearly. They hadn't made much
progress in many years. You have neatly stepped over the top of that
issue by going to 41-equal. This, you must feel, gives the right
balance between indicating larger pitch changes by position, and
smaller ones by symbols adjacent to the notehead.

I would probably tend to put that figure closer to 24-equal. I'd love
to see you and Herman Miller pool ideas and develop a staff, or system
of related staffs, based on Herman's notation system for linear
temperaments which uses a natural set of nominals for a given
temperament, taken from a superset of 24.

> ... then I think people
> will get past the accidental / inflection issue if it bothers them.

They may, or they may not, but why should they be presented with such
a cognitive dissonance at all?

-- Dave Keenan

🔗Herman Miller <hmiller@IO.COM>

Dave Keenan wrote:

> I would probably tend to put that figure closer to 24-equal. I'd love
> to see you and Herman Miller pool ideas and develop a staff, or system
> of related staffs, based on Herman's notation system for linear
> temperaments which uses a natural set of nominals for a given
> temperament, taken from a superset of 24.

We already have Joe Monzo's quarter-tone staff, and I've considered using that for the 24-nominal notation system:

http://tonalsoft.com/enc/q/qt-staff.aspx

On the other hand, over the last couple of years I've been shifting more in the direction of pure Sagittal notation based on chain-of-fifth nominals. The main thing this doesn't work for is any scale that isn't a consistent temperament, like many of the MOS from the Golden Horograms. There are specific difficulties with a few temperaments, but those are mainly ones that no one as far as I know has actually used (e.g., vishnu, luna). Most of the difficulties have been cleared up with the introduction of new flag combinations, so I'm hoping that the latest updates will fix any remaining issues.

There are still reasons to prefer a specific notation for some tuning systems, as with Graham Breed's decimal notation for miracle temperament. It seems as if practically every note has a different accidental when miracle is written in Sagittal notation. But I think that if you work with numerous tuning systems, there's a distinct advantage to the idea of keeping the notation as consistent as possible. Sagittal is one system that seems to work, and it's possible that a system like MegaScore based on 41 notes (a good landmark ET associated with temperaments like schismatic, magic, and miracle) could also be adaptable.

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
> Yes, I understand all that. Your web pages are very clear. (I wish we
> had educational material as good as that for Sagittal). But you seem
> to be missing the point that several people now are trying to make.
>
> The symbols on the staff don't _look_ like inflections. They _look_
> like accidentals.

Dave, I'm not missing the point; I just disagree. Sure, they look like
accidentals. That's what most people call them. I explained my
point of view a few times to try to make myself as clear as possible.
Sorry this sounded like I was ignoring you or anyone else; this was
not my intent.

I think anyone who wants to use the system would
investigate it enough to find out how the symbols are used, and
and at that point find logic is persuasive enough that the whole
issue you've raised is not a big deal.

> ...I think your semantics
> (meanings) are just fine. It's only the choice of symbols or "signs"
> for the inflections that I find jarring, and I think many others will too.

At first glance, maybe. This is why I kept saying follow the logic
through. If someone takes the time to do that, it makes sense. I
understand a few of you are telling me you took the time to
do that and you still don't like it. Is it possible that you
may be reacting very strongly to this because you have an
unusually well developed preference for alternate symbols,
especially those of you who developed the whole sagittal system?
The fact is that most people will find a lot of new symbols a
lot more jarring and confusing than the familiar symbols.
Most people do not want to learn new symbols. This has always
been a problem for microtonality, and it's also part of the reason
I reject the idea of using new symbols in this basic way.

> I recall some group trying to agree
> on a staff that represented 12-equal linearly. They hadn't made much
> progress in many years. You have neatly stepped over the top of that
> issue by going to 41-equal. This, you must feel, gives the right
> balance between indicating larger pitch changes by position, and
> smaller ones by symbols adjacent to the notehead.

41ET is special for notation and for theory. It's the only small numberd
ET having an almost perfect 2:3 which spans an even number of steps
that is rich in divisors and can be shown on a complex (nested) staff
from a line to a line the same way it is shown in standard notation.
I wrote a paper in 2001 about the concept of complex staves which I
could post if you like.

My initial interest in 41 came from Patrick Ozzard-Low's work, but
my choosing it for theory and notation came about through quite
unrelated investigations. Suffice it to say 41 is not a system chosen
at random. Rather it is part of a comprehensive recasting of standard
Western music theory which has been worked out in detail over a
number of years.

Complex staves could be used in any number of ways. Yasser used
a two-level complex staff for 19ET. The megastaff is the best of them.

> > ... then I think people
> > will get past the accidental / inflection issue if it bothers them.
>
> They may, or they may not, but why should they be presented with such
> a cognitive dissonance at all?

I feel that different symbols would create more of a barrier.
Please consider that if these symbols would change, it would mean
that writing music using my system would not entail using the
standard symbols known to musicians world-wide, that is, sharps
and flats, double sharps and double-flats, in the notation. You
suggest some new symbols will be more appropriate. I strongly
disagree. For trained musicians, using other symbols will not feel
like writing and reading music. While the familiar symbols are there,
it feels like music on the page when you write it, and it looks like
music on the page when you read it. I don't think this is just because
I learned to write music with sharps and flats. It's because the
vast corpus of Western music has those symbols, and in my view
that is a very important fact to consider. That that the symbols
mean something differnt on a megastaff than they do on a traditional
staff is in my opinion not as big a cognative dissonance as results
from a whole new set of symbols. Other symbols just make the
whole thing look too foreign and disconnected from history in my
opinion, and I think any system requiring them has less of a chance
of succeeding than a system which sticks to the traditional symbols,
even using them in a new way, particularly when this new way makes
sense according to existing musical semantics.

Yours,
Aaron Hunt
H-Pi Instruments

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

--- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@...> wrote:
> Sharp and flat = higher and lower. Place them left and right,
> they still mean higher and lower. On the left it is a smaller
> change and the right is a larger one. It is very simple and
> absolutely *not* contradictory, and new symbols are not
> needed.

Hi Aaron,

Again, it isn't so much this textual usage I have a problem with, but
the usage on the staff, where the symbols only appear in one position
relative to the notehead and indicate a pitch change which is only
about a twentieth (not a sixteenth as I wrote earlier) of that which
they have indicated for over a thousand years (?), namely a chromatic
semitone or apotome.

> I already said if someone wants to use sagittals, great. I don't
> think it makes sense as a default standard for the megastaff.
> A person looking at the megastaff sees familiar symbols.
> It still looks like music.
>
> Originally I had different clef symbols. Comparing this with
> standrad clefs over a few years convinced me that standard clefs
> make it look more like music. Replace the clefs with new symbols,
> replace the sharps and flats with new symbols, and you have
> something which doesn't resemble standard notation enough
> in my opinion...

Aha! This really helps me understand your thinking. Thanks.

And I can tell you exactly the effect this had on me. I felt I'd been
tricked! (Now this may well serve me right, given the trick I helped
perpetrate recently, but it doesn't serve _everyone_ right. ;-)

I saw the familiar clefs and familiar accidentals and assumed they had
the familiar meanings, or at least _some_ obvious generalisation from
their conventional meanings.

In the case of the clefs this is so. But when I got to the part about
the JND inflections and found that _that_ is what the conventional
sharp and flat symbols were being used for. I thought, "No! How could
you do this to us". Force us to have to _unlearn_ something we've
spent many valuable hours learning.

I note that this objection is entirely independent of any suggestions
to use sagittal symbols. It's just about _not_ using symbols which
already have a well established meaning as a pitch alteration, but of
a very different magnitude. More like a GPD (greatest possible
difference) than an JND.

> Sagittal requires too much knowledge in my opinion.

You don't have to memorise it all. You can usually just look up the
notation for whatever tuning you need it for. In this case you would
only need the symbols for 1, 2 and 3 degrees of 205-ET. Admittedly not
an EDO we have published a proposed standard for yet. These three
could be )| )|( ~|( or the second one could be ~| instead of )|( .
[Of course I mean the actual symbols in the sagittal font not these
multi-character plain-text representations.] In either case, the
number of JNDs corresponds to the number of curves in the arrow head
and these symbols are visually smaller than conventional sharps and
flats, while still being in the same "style". Being up and down
arrows, their direction of pitch alteration is obvious.

The symbols can be seen in a PDF of the character map spreadsheet here
http://dkeenan.com/sagittal/Sagittal2_character_map.pdf
Scroll down to symbol 144 on page 5, the (conventional) natural, and
you'll find the relevant symbols a little above and below it.

To _determine_ valid sagittal symbols for the degrees of an EDO
requires a knowledge of the comma "primary roles" of the symbols and
their relative popularity, as given in the spreadsheet. But this only
has to be done once, and once it is done they just _become_ the
symbols for those EDO degrees and the comma meanings can be forgotten,
as we point out in the analogous case of the "Trojan" notation for
fractional-step inflections from 12-equal, on page 16 of
http://dkeenan.com/sagittal/Sagittal.pdf

> The symbols I use are all in a standard font set, plus
> standard musical symbols.

Good point. But I expect you could find some symbols that _look_ more
like JND inflection symbols (by being small) even without going
outside these sets.

I should also mention that you are also welcome to copy only those
glyphs you need, from the sagittal font, and add them to your own
font, or another font, as Oz has done. Or Oz or I could do it for you.

> The only symbols which are slightly
> different are triple sharp and triple flat. An asterisk can be used
> as the triple sharp (as it is a stylized asterisk), and the triple
> flat can be made from a double and single in a standard
> music font set. The shifts are standard characters in standard
> font sets, they are + and html codes b for positive
> shifts and ~ (b<) and &conj; for the
> negatives. These resemble plus, double plus, minus and
> double minus (I could have used - and = for the negatives, but
> a wavy line is better since = means equals). I know the
> negatiives have other meanings, but most people aren't
> bothered by that since those symbols aren't used as often
> and they probably don't know what they mean anyway.
> The doubles are singles stacked vertically.

I have no great problem with any of those. Certainly none of them
produce the cognitive dissonance produced by your current use of the
conventional sharp and flat symbols.

> This makes
> more sense than using sagittal symbols which are not in a
> standard font set and have too specific a meaning to use
> for my purposes.

I don't understand what you mean by "too specific a meaning to use for
[your] purposes". Please explain. I seem to remember someone once
criticising it for being too flexible. This was based on a
misunderstanding, which is of course our fault for not explaining it
better.

> A shifted note is fine tuned by a JND
> inflection, so the shift can't be a sagittal
> symbol anyway since the size of the shift would require a
> different sagittal symbol to be correct.

I'm sorry, I'm having trouble finding a reading of that sentence that
makes sense to me. I understand that you have "shifts" of -2 -1 +1 +2
degrees of 41-EDO and "inflections" of -3 -2 -1 +1 +2 +3 degrees of
205-EDO (205 = 5 * 41). So the sagittal symbols for those numbers of
degrees of those EDOs would be valid, wouldn't they?

Oh, wait a minute.

I just figured out that the sagittal symbols for 5 and 10 degrees of
205-EDO could not be the same as those given in the sagittal paper for
1 and 2 degrees of 41-EDO, since 205's best approximations of the
5-comma and 11-diesis are 4 and 9 degrees respectively.

Is that what you are referring to?

So this _does_ make an interesting problem for sagittal notation of
your shifts, which do not appear on the staff in any case, but it does
not alter the validity of the proposed sagittal symbols for your
inflections, which do appear on the staff.

> The system is staying as it is, as I said, for good reasons.

You haven't yet convinced me (for one) that you have a good reason for
expecting users to unlearn the standard meaning of the conventional
sharp and flat. Not that you have to convince me of course.

> Anyone who wants to use sagittal on it is welcome to it.

Thanks. But I'm concerned that we may have given you some wrong idea
about sagittal, and if so, I hope we can figure out what it is.

Regards,
-- Dave Keenan

🔗J.A.Martin Salinas <tony@tonysalinas.com>

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

Hi Tony!

I welcome anyone to use whatever symbols on the megastaff they want;
using quartertone symbols could give you twice the precision... but
it misses the whole point of the megastaff, which is that practically
speaking there is no need to do that. Psychoacoustic research has
shown that on average around 200 pitches can be perceived within
one octave. That is an *average*, the same way the smallest step in
the system is an *average* JND. Electronics can produce pitches with
greater tuning accuracy, but acoustic instruments and human beings
cannot. The whole megastaff system is based on these psychoacoustic
averages and basic human limitations, and is intended as a
*practical superstructure*. Other systems like sagittal have other
uses which I see as being geared more towards the strictly theoretical.

I strongly disagree that Tartini accidentals are a standard.
If they were a standard, then Wyschnegradsky, Haba, Carrillo, and
the hundred or so composers from the 20th century and beyond
would have used them. Check out Gardner Read's book 20th Century
Microtonal Notation and you don't ifind Tartini as a standard, although
almost everything in there is about quartertones. You find a myriad
of systems, almost none of which agree, just about all of which were
capricious, used for one composition, and promptly abandoned by
their creators.

I'm glad you like the megastaff in terms of picture contours : ) For me,
this quality of the system makes playing around with melodic shapes
a lot of fun and it feels very childlike, while the results can be very
sophisticated. Larger complex staves are certainly possible, but the
next smallest staff which maintains the 2:3 mapping property, which
I consider crucial, has over 300 lines (383 to be exact, a staff for
653ET).

Yours,
Aaron Hunt
H-Pi Instruments

--- In tuning@yahoogroups.com, "J.A.Martin Salinas" <tony@...> wrote:
>
> Dear Aaron and list,
>
> You said:
>
> I feel that different symbols create more of a barrier.
>
> My opinion is what I think and not what you should do!
>
> Couper/Tartini quatertone notation is already a standard for Western
> music.
> Yes indeed for advance students, but who are more likely to move on into
> microtonality than the advance students, and even if the beginners want
> to get initiated too the would not mind to use the advance quatertone
> symbols
> that they will have to study soon or later anyhow.
>
> A quarter sharp would be a half step of the 205th divisions of the
> octave.
> Maybe one day you can use the quartertones once you enhance the system
> to 410 notes! I would buy that for sure!
>
> I think there is no problem to understand this augmentation process when
> you play in real quartertones at all.
>
> On the other hand if the system you are proposing is intending to be
> pictographic,
> I would buy a non accidental version with more lines since that is a
> very
> intuitive way to compose music with dynamic pitch.
>
> Tony Salinas
>

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

--- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@...> wrote:
> I understand a few of you are telling me you took the time to
> do that and you still don't like it.

Right.

> Is it possible that you
> may be reacting very strongly to this because you have an
> unusually well developed preference for alternate symbols,
> especially those of you who developed the whole sagittal system?

Of course that's possible and obviously I'm in no position to judge
that. We'd have to do some kind of survey. But we'd have to have a
well developed alternative before such a survey would be valid.

> The fact is that most people will find a lot of new symbols a
> lot more jarring and confusing than the familiar symbols.

But you don't need a lot. Only 6. And if they are up and down arrows
their direction is obvious and so there are only really 3. And if the
magnitude is indicated by some countable graphical property of the
symbol, there is really nothing to learn at all, and just as
importantly nothing to _un_learn either.

Forget Sagittal for now. The Symbol font is a standard. It contains up
and down arrows with zero one and two shafts. This is not as good as
1, 2 and 3 shafts would be, but a user could be told to think of the
arrowhead as a single bent stroke and count strokes.

> Most people do not want to learn new symbols.

That's true, but compared to learning a new complex staff, learning
that some arrows indicate JND inflections in proportion to the number
of strokes in the arrow (or curves, in the case of sagittals) would
seem no big deal to me. Particularly since a player could completely
ignore these JND symbols and few listeners would be any the wiser in
most cases.

Imagine telling someone, "For a first pass, just ignore the sharps and
flats". :-)

> My initial interest in 41 came from Patrick Ozzard-Low's work, but
> my choosing it for theory and notation came about through quite
> unrelated investigations. Suffice it to say 41 is not a system chosen
> at random.

Certainly not random. I well understand its attractions.

> I feel that different symbols would create more of a barrier.

Clearly this is the core of our disagreement.

> Please consider that if these symbols would change, it would mean
> that writing music using my system would not entail using the
> standard symbols known to musicians world-wide, that is, sharps
> and flats, double sharps and double-flats, in the notation.

Obviously. But why is that a problem? Many pieces of conventional
sheetmusic do not include them either, except perhaps in the key
signature. Do you think composers worry about this and think, "I must
get at least one accidental on every page or it won't _look_ like
music"? ;-)

> You
> suggest some new symbols will be more appropriate. I strongly
> disagree. For trained musicians, using other symbols will not feel
> like writing and reading music. While the familiar symbols are there,
> it feels like music on the page when you write it, and it looks like
> music on the page when you read it.

So are you saying that although it will have conventional clefs and
bar lines and noteheads and notestems and flags and ties and rests and
expression symbols and all the other paraphernalia of standard written
music, it won't look like music unless it has some conventional sharp
or flat symbols? Even though those symbols have been rendered
unnecessary by the staff and it's just a kind of a trick putting them
there because they don't mean what you think they mean?

> Other symbols just make the
> whole thing look too foreign and disconnected from history in my
> opinion,

So you don't think the megastaff itself looks very foreign and scary?

> and I think any system requiring them has less of a chance
> of succeeding than a system which sticks to the traditional symbols,
> even using them in a new way,

Does this still apply if the meaning of the new symbols is incredibly
easy to remember because of the form of the symbols (a real
no-brainer), and the visual style of the symbols is reminiscent of
conventional sharps and flats?

> particularly when this new way makes
> sense according to existing musical semantics.

But it doesn't make sense to me (or apparently Graham or Klaus). The
magnitude disparity is simply too great.

-- Dave

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

Dear Dave,

My, you are persistent! ... Not sure what else to say
except that I'm not really interested in debating this further,
and I am not changing it. I see no good reason to do so.
Try giving the work I've done a chance as it is, as I created it.

But please don't get the impression I'm not interested
in what anybody else has to say. I'm open to feature
requests for all software, and have set up a forum for
encouraging folks to discuss what they want. The way this
works is, you join the discussion forum, present your feature
request to the members of the forum, discuss it with them,
get as many people on board as you can, come up with the
best description of the functionality you can, and then
notify me with the description and a list of the folks who
want the feature. If I see enough people want the feature
and it is described clearly enough for me to figure out
how to implement it, then it could become a new feature.

Right now the forum doesn't have many members. I'm
hoping more people will join.

http://www.h-pi.com/phpBB2/

Yours,
Aaron Hunt
H-Pi Instruments

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
> > The fact is that most people will find a lot of new symbols a
> > lot more jarring and confusing than the familiar symbols.
>
> But you don't need a lot. Only 6. And if they are up and down arrows
> their direction is obvious and so there are only really 3. And if the
> magnitude is indicated by some countable graphical property of the
> symbol, there is really nothing to learn at all, and just as
> importantly nothing to _un_learn either.
>
> Forget Sagittal for now. The Symbol font is a standard. It contains up
> and down arrows with zero one and two shafts. This is not as good as
> 1, 2 and 3 shafts would be, but a user could be told to think of the
> arrowhead as a single bent stroke and count strokes.
>
> > Most people do not want to learn new symbols.
>
> That's true, but compared to learning a new complex staff, learning
> that some arrows indicate JND inflections in proportion to the number
> of strokes in the arrow (or curves, in the case of sagittals) would
> seem no big deal to me. Particularly since a player could completely
> ignore these JND symbols and few listeners would be any the wiser in
> most cases.
>
> Imagine telling someone, "For a first pass, just ignore the sharps and
> flats". :-)
>
> > My initial interest in 41 came from Patrick Ozzard-Low's work, but
> > my choosing it for theory and notation came about through quite
> > unrelated investigations. Suffice it to say 41 is not a system chosen
> > at random.
>
> Certainly not random. I well understand its attractions.
>
> > I feel that different symbols would create more of a barrier.
>
> Clearly this is the core of our disagreement.
>
> > Please consider that if these symbols would change, it would mean
> > that writing music using my system would not entail using the
> > standard symbols known to musicians world-wide, that is, sharps
> > and flats, double sharps and double-flats, in the notation.
>
> Obviously. But why is that a problem? Many pieces of conventional
> sheetmusic do not include them either, except perhaps in the key
> signature. Do you think composers worry about this and think, "I must
> get at least one accidental on every page or it won't _look_ like
> music"? ;-)
>
> > You
> > suggest some new symbols will be more appropriate. I strongly
> > disagree. For trained musicians, using other symbols will not feel
> > like writing and reading music. While the familiar symbols are there,
> > it feels like music on the page when you write it, and it looks like
> > music on the page when you read it.
>
> So are you saying that although it will have conventional clefs and
> bar lines and noteheads and notestems and flags and ties and rests and
> expression symbols and all the other paraphernalia of standard written
> music, it won't look like music unless it has some conventional sharp
> or flat symbols? Even though those symbols have been rendered
> unnecessary by the staff and it's just a kind of a trick putting them
> there because they don't mean what you think they mean?
>
> > Other symbols just make the
> > whole thing look too foreign and disconnected from history in my
> > opinion,
>
> So you don't think the megastaff itself looks very foreign and scary?
>
> > and I think any system requiring them has less of a chance
> > of succeeding than a system which sticks to the traditional symbols,
> > even using them in a new way,
>
> Does this still apply if the meaning of the new symbols is incredibly
> easy to remember because of the form of the symbols (a real
> no-brainer), and the visual style of the symbols is reminiscent of
> conventional sharps and flats?
>
> > particularly when this new way makes
> > sense according to existing musical semantics.
>
> But it doesn't make sense to me (or apparently Graham or Klaus). The
> magnitude disparity is simply too great.
>
> -- Dave
>

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

🔗J.A.Martin Salinas <tony@tonysalinas.com>

Hi Aaron and list members!

Yes the pitch contours is the fascinating part of megastaff. It is very close
to millimetric paper which is what I like to use to compose. I guess, if you
did happen to place also some kind of shaded vertical lines for placing the
note in time you will end up with 'millimetric notation' to map time and rhythm,
and you would still miss a third dimension for the volume which is also great
fun when you can make it dynamic.

I have been after that notation book for ages with no success so far...and even though
I am aware of many notations for quartertones I thought it was a broad standard
in music conservatoires and academies in the 21st century to use Tartini/Couper
notation....I would like to know what other people with experience (from different
parts of the world) from the list have to say to this!!!

Aaron, I know that you have explained this nicely on your page, but I am still
not 100% sure what you mean by 2:3 mapping property and also about 653ET.
Would you kindly explain us with some more detail. Thanks in advance for that!

As for my opinion, in order to achieve polymicrotonality and be as partial as possible
to different tuning systems I would stick to Johnny Reinhard's notation for practice and rehearsals.
I will have to train myself or take masterclases on-line if available since I am here in Japan,
and I woul also love to provide training to musicians in a future here in Japan.

As for megastaff for composition at home and also planning now to prepare an interface
for a mechanism to play 'conic bells' and other ultramicrotonal percussion instruments

As for sagittal, I think my would love to have a tuning meter attached to instrument
or maybe to the music stand, that gives me the note name with the symbol in order
to start making sense of the symbols with my ears. Maybe a software could be developed
to start with among members, and I do not even mind to invest money (not a programmer)
on this idea if other members are prepare to do so ... I cannot way to see the new set of 2460 symbols,
and I am sure you guys will be planning to move on to the 4296 notes system in a future, even
though there will be very few players and instruments that would allow you to keep a digital
meter fixed to one single symbol without jumping to the one next door haha!

I also mentioned on the h-pi list about my interest to invest money and ideas into a
custom development of the h-pi keyboards in in order to have 256 notes per octave
even though I would love to try 612, 1420 or 4296. I am sure that megastaff will be adapted
as the keyboards developed further into the ultramicrotonal wonders.

Now that we have a team developing microtonal music technology it is a great chance
for all of us to invest ideas and money in order to complement the theory with some
serious practice.

Please do get in touch with me or Aaron if interested.

Tony Salinas
tony@tonysalinas.com

On 2007/11/17, at 12:42, Aaron Andrew Hunt wrote:

> Hi Tony!
>
> I welcome anyone to use whatever symbols on the megastaff they want;
> using quartertone symbols could give you twice the precision... but
> it misses the whole point of the megastaff, which is that practically
> speaking there is no need to do that. Psychoacoustic research has
> shown that on average around 200 pitches can be perceived within
> one octave. That is an *average*, the same way the smallest step in
> the system is an *average* JND. Electronics can produce pitches with
> greater tuning accuracy, but acoustic instruments and human beings
> cannot. The whole megastaff system is based on these psychoacoustic
> averages and basic human limitations, and is intended as a
> *practical superstructure*. Other systems like sagittal have other
> uses which I see as being geared more towards the strictly > theoretical.
>
> I strongly disagree that Tartini accidentals are a standard.
> If they were a standard, then Wyschnegradsky, Haba, Carrillo, and
> the hundred or so composers from the 20th century and beyond
> would have used them. Check out Gardner Read's book 20th Century
> Microtonal Notation and you don't ifind Tartini as a standard, > although
> almost everything in there is about quartertones. You find a myriad
> of systems, almost none of which agree, just about all of which were
> capricious, used for one composition, and promptly abandoned by
> their creators.
>
> I'm glad you like the megastaff in terms of picture contours : ) > For me,
> this quality of the system makes playing around with melodic shapes
> a lot of fun and it feels very childlike, while the results can be > very
> sophisticated. Larger complex staves are certainly possible, but the
> next smallest staff which maintains the 2:3 mapping property, which
> I consider crucial, has over 300 lines (383 to be exact, a staff for
> 653ET).
>
> Yours,
> Aaron Hunt
> H-Pi Instruments
>
> --- In tuning@yahoogroups.com, "J.A.Martin Salinas" <tony@...> wrote:
> >
> > Dear Aaron and list,
> >
> > You said:
> >
> > I feel that different symbols create more of a barrier.
> >
> > My opinion is what I think and not what you should do!
> >
> > Couper/Tartini quatertone notation is already a standard for Western
> > music.
> > Yes indeed for advance students, but who are more likely to move > on into
> > microtonality than the advance students, and even if the > beginners want
> > to get initiated too the would not mind to use the advance > quatertone
> > symbols
> > that they will have to study soon or later anyhow.
> >
> > A quarter sharp would be a half step of the 205th divisions of the
> > octave.
> > Maybe one day you can use the quartertones once you enhance the > system
> > to 410 notes! I would buy that for sure!
> >
> > I think there is no problem to understand this augmentation > process when
> > you play in real quartertones at all.
> >
> > On the other hand if the system you are proposing is intending to be
> > pictographic,
> > I would buy a non accidental version with more lines since that is a
> > very
> > intuitive way to compose music with dynamic pitch.
> >
> > Tony Salinas
> >
>
>
>

🔗Graham Breed <gbreed@gmail.com>

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

Thanks and no hard feelings, Dave. Thanks also for your email
about the mistakes on the accidentals page, which have now been
fixed.

Everyone, I should have been much more clear about what I
meant by "feedback and suggestions". I'm not looking for advice
about how the notation should work. It is finished for you to
accept or not. I'm looking for feedback on how well the website
is working, if something isn't clear, if you'd like to see something
covered that isn't there, if you find typos, errors - that sort of
thing.

Kraig, very true, the staff requires a lot more space; US Tabloid in
landscape, or A3 in landscape I find works best at 100% size. These
larger papers in portrait allow more staves on a page. A score can
become pretty huge. The staff can also be reduced to about 65% and
work well with plenty more space for ledgers and margins, although
the notes do become small, they are still legible. The staff paper is
presently not as good as it could be; it is converted from a postscript
based graphics program to pdf, and the spacing of the lines prints
wrong at some resolutions. There are improvements to be made.

Thanks everyone for your support. Please if you are interested in
making feature requests for the software, join the forum. You can
see how requests and bug reports work for the software that
has been released on these pages:

http://www.h-pi.com/TPXEreports.html
http://www.h-pi.com/TBXEreports.html

I hope to release MegaScore as a free public beta within the next
year. I may release just a working interface sooner than that if there
is enough interest. It is still in its infancy in terms of development,
as all attention has been going to the tuning box and the keyboards
so far. Only recently has there been much interest in MegaScore, so
I finally got around to adding the new (old updated) webpages.

Cheers,
Aaron Hunt
H-Pi Instruments

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> Sorry Aaron,
>
> for giving you such a hard time. I must repeat that I find your
> notation system in general to be quite brilliant, and your educational
> material to be exceptionally clear.
>
> -- Dave Keenan
>

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

To Dave, Graham, and anyone else who might be bothered
by the use of sharps and flats and their additives as JND
inflections on the megastaff...

No composers or performers who have seen the megastaff
notation have ever raised your objection; the symbols have
appeared appropriate and intuitively correct to them. There
is a simple explanation which should explain as to why
this has been so. Thinking in terms of staff *positions* is
the key, which is an orientation that is more practical than
it is theoretical, but it stands up to both kinds of tests.

On a regular 5 line staff, a sharp, flat, double sharp or
double flat shows that a given note is shifted in pitch up or
down from its diatonic natural position. A note is not shifted
in pitch into an adjacent position without a double inflection
in most cases and a single inflection in some. While an
inflected note might match the pitch of an inflected note
in an adjacent position, an inflected note never shifts
*past* an adjacent position.

Knowing that this how standard notation works in practice,
intuition would suggest that a note written with an inflection
in front of it on any musical staff of whatever
size should not be shifted from its position past the next
adjacent position, whatever the position means in terms
of pitch; the furthest an inflected note could be expected
to shift is into an adjacent position above or below it. It
also stands to reason that an inflected note might reach the
same pitch as another inflected note in an adjacent position,
but it should never move past it.

This is exactly how things work on the megastaff.
There are 6 times as many positions on a megastaff as
on a traditional staff, since the megastaff does not show
only positions for diatonic naturals, but shows positions for
41ET. The positions also have no particular attachment to the
diatonic naturals; that is, differences in pitch by position are
uniform across the entire range of the staff. So it makes sense
that an inflection should work relative to adjacent staff positions,
shifting notes in pitch by small amounts.

The only differences are the size of the shifting, and the
degree of inflecting required to shift a note into an adjacent
position. On the megastaff, it is always a triple inflection
which moves into the adjacent position and overlaps
with the corresponding opposite double inflection,
while on a traditional staff, the degree of infelction required
changes with the letter name due to the diatonic framework
of the staff. In either case, the size and degree of the shift is
a direct reflection of the underlying structure of the staff,
the traditional being diatonic, and the megastaff being 41ET.

In closing, let me thank you for raising the objection, as it
has helped me to formulate an explanation which I believe
will improve the general disclosure of the system. I will at
some point rework the text on the website to make these
things more clear.

Yours,
Aaron Hunt
H-Pi Instruments

P.S. If you still object on grounds as previously stated,
please consider your objection duly noted, but the case
is closed.

--- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@...> wrote:
>
> Dear Dave,
>
> My, you are persistent! ... Not sure what else to say
> except that I'm not really interested in debating this further,
> and I am not changing it. I see no good reason to do so.
> Try giving the work I've done a chance as it is, as I created it.
>
> But please don't get the impression I'm not interested
> in what anybody else has to say. I'm open to feature
> requests for all software, and have set up a forum for
> encouraging folks to discuss what they want. The way this
> works is, you join the discussion forum, present your feature
> request to the members of the forum, discuss it with them,
> get as many people on board as you can, come up with the
> best description of the functionality you can, and then
> notify me with the description and a list of the folks who
> want the feature. If I see enough people want the feature
> and it is described clearly enough for me to figure out
> how to implement it, then it could become a new feature.
>
> Right now the forum doesn't have many members. I'm
> hoping more people will join.
>
> http://www.h-pi.com/phpBB2/
>
> Yours,
> Aaron Hunt
> H-Pi Instruments
>
>
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> > > The fact is that most people will find a lot of new symbols a
> > > lot more jarring and confusing than the familiar symbols.
> >
> > But you don't need a lot. Only 6. And if they are up and down arrows
> > their direction is obvious and so there are only really 3. And if the
> > magnitude is indicated by some countable graphical property of the
> > symbol, there is really nothing to learn at all, and just as
> > importantly nothing to _un_learn either.
> >
> > Forget Sagittal for now. The Symbol font is a standard. It contains up
> > and down arrows with zero one and two shafts. This is not as good as
> > 1, 2 and 3 shafts would be, but a user could be told to think of the
> > arrowhead as a single bent stroke and count strokes.
> >
> > > Most people do not want to learn new symbols.
> >
> > That's true, but compared to learning a new complex staff, learning
> > that some arrows indicate JND inflections in proportion to the number
> > of strokes in the arrow (or curves, in the case of sagittals) would
> > seem no big deal to me. Particularly since a player could completely
> > ignore these JND symbols and few listeners would be any the wiser in
> > most cases.
> >
> > Imagine telling someone, "For a first pass, just ignore the sharps and
> > flats". :-)
> >
> > > My initial interest in 41 came from Patrick Ozzard-Low's work, but
> > > my choosing it for theory and notation came about through quite
> > > unrelated investigations. Suffice it to say 41 is not a system chosen
> > > at random.
> >
> > Certainly not random. I well understand its attractions.
> >
> > > I feel that different symbols would create more of a barrier.
> >
> > Clearly this is the core of our disagreement.
> >
> > > Please consider that if these symbols would change, it would mean
> > > that writing music using my system would not entail using the
> > > standard symbols known to musicians world-wide, that is, sharps
> > > and flats, double sharps and double-flats, in the notation.
> >
> > Obviously. But why is that a problem? Many pieces of conventional
> > sheetmusic do not include them either, except perhaps in the key
> > signature. Do you think composers worry about this and think, "I must
> > get at least one accidental on every page or it won't _look_ like
> > music"? ;-)
> >
> > > You
> > > suggest some new symbols will be more appropriate. I strongly
> > > disagree. For trained musicians, using other symbols will not feel
> > > like writing and reading music. While the familiar symbols are there,
> > > it feels like music on the page when you write it, and it looks like
> > > music on the page when you read it.
> >
> > So are you saying that although it will have conventional clefs and
> > bar lines and noteheads and notestems and flags and ties and rests and
> > expression symbols and all the other paraphernalia of standard written
> > music, it won't look like music unless it has some conventional sharp
> > or flat symbols? Even though those symbols have been rendered
> > unnecessary by the staff and it's just a kind of a trick putting them
> > there because they don't mean what you think they mean?
> >
> > > Other symbols just make the
> > > whole thing look too foreign and disconnected from history in my
> > > opinion,
> >
> > So you don't think the megastaff itself looks very foreign and scary?
> >
> > > and I think any system requiring them has less of a chance
> > > of succeeding than a system which sticks to the traditional symbols,
> > > even using them in a new way,
> >
> > Does this still apply if the meaning of the new symbols is incredibly
> > easy to remember because of the form of the symbols (a real
> > no-brainer), and the visual style of the symbols is reminiscent of
> > conventional sharps and flats?
> >
> > > particularly when this new way makes
> > > sense according to existing musical semantics.
> >
> > But it doesn't make sense to me (or apparently Graham or Klaus). The
> > magnitude disparity is simply too great.
> >
> > -- Dave
> >
>

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

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Dave Keenan wrote:
>
> > But it doesn't make sense to me (or apparently Graham or Klaus). The
> > magnitude disparity is simply too great.
>
> It isn't the size of the difference as I see as the problem,
> but the fact that the same symbols are being used in
> confusingly similar contexts with meanings that are supposed
> to be distinguished.

Right.

The same problem occurs with using
> identical notation for both Pythagorean and meantone
> tunings. And if anything it's worse there because the
> smaller the difference between two systems the harder it is
> to remember intuitively. The Megastaff at least gives you a
> whopping great clue that you're in a different context.

Yes. And I'm keen to learn what meantones look like on the Megastaff.

> Following this logic, I humbly suggest you standardize on
> the 25:24 symbol for sharps and flats in meantones (13, 19,
> etc). In the paper I have to hand you don't do that.

Hi Graham,

This is problematic. A single symbol for 24:25 only exists in the pure
Sagittal )||( and while this is certainly a valid accidental for the
job and would be the most logical for Herman Miller's style of linear
temperament notations using sagittal, there are reasons why it
probably should not be the "standard" sagittal notation for meantones.

I agree with Aaron Hunt that in general people don't want to have to
learn new symbols (we just disagree about the relative weighting of
cognitive dissonance versus perceptual overload). And since meantones
have historically been notated with conventional sharps and flats we
see no reason to change that.

But we do suggest (and maybe we should insist, or more realistically
beg) that sagittal users indicate in some way at the start of their
score what the size of the notational octave and fifth are, in much
the same way as a Tempo indication. e.g

Octave = 1200 cents
Fifth = 696.5 cents

Or for EDOs and JI simply describe them as say "19-EDO" or "JI" (or
"Pythagorean").

I believe Hudson Lacerda has implemented the above in the MicroABC
notation software, which uses Sagittal. I understand MicroABC also
uses the information in generating the correct MIDI playback of the
Sagittal. Please correct me if I'm wrong, Hudson, or MicroABC users.

> If you're using standard notation there are reasons for
> being conservative and keeping the old sharps and flats.
> But if you're going to bring in a load of new symbols they
> should resolve these ambiguities.

Weeell, I guess this just lets me empathiose more with Aaron. There
are so many tradeoffs. You're always going to upset someone.

Does the fifth size-spec on the score resolve it sufficiently well to
your mind?

-- Dave Keenan

🔗Graham Breed <gbreed@gmail.com>

Dave Keenan wrote:

>>Following this logic, I humbly suggest you standardize on >>the 25:24 symbol for sharps and flats in meantones (13, 19, >>etc). In the paper I have to hand you don't do that.
>
> > Hi Graham,
> > This is problematic. A single symbol for 24:25 only exists in the pure
> Sagittal )||( and while this is certainly a valid accidental for the
> job and would be the most logical for Herman Miller's style of linear
> temperament notations using sagittal, there are reasons why it
> probably should not be the "standard" sagittal notation for meantones.

It's rightbarbdoubleup ||\ #\ I was thinking of.

> I agree with Aaron Hunt that in general people don't want to have to
> learn new symbols (we just disagree about the relative weighting of
> cognitive dissonance versus perceptual overload). And since meantones
> have historically been notated with conventional sharps and flats we
> see no reason to change that.

Well, maybe we agree about what people want to do, but reading music's a sufficiently difficult task that I prefer to think of what they're capable of doing. The human brain has a vast capacity for learning symbols. It has more difficulty attaching conflicting meanings to existing symbols. Learning both meantone and pythagorean tunings is a difficult enough task that two extra symbols should be neither here nor there. (Unless you use a keyboard where the fingering's the same.)

If they don't want to learn new symbols, you can always tell them it's the same symbol, but written differently! They're both two shaft arrows, after all, by design. And if they really don't want to learn new symbols they'll be using mixed sagittal anyway. Or staying away from microtonality completely.

> But we do suggest (and maybe we should insist, or more realistically
> beg) that sagittal users indicate in some way at the start of their
> score what the size of the notational octave and fifth are, in much
> the same way as a Tempo indication. e.g
> > Octave = 1200 cents
> Fifth = 696.5 cents
> > Or for EDOs and JI simply describe them as say "19-EDO" or "JI" (or
> "Pythagorean").

That's good.

>>If you're using standard notation there are reasons for >>being conservative and keeping the old sharps and flats. >>But if you're going to bring in a load of new symbols they >>should resolve these ambiguities.
> > Weeell, I guess this just lets me empathiose more with Aaron. There
> are so many tradeoffs. You're always going to upset someone.

There has to be a compromise somewhere. Ultimately, you've provided the symbol set, and it's up to musicians how they use it. When they start giving you feedback I'm sure you'll need to revise the system, probably in ways we didn't think of.

I thought the consensus was that musicians who think in Pythagorean terms have difficulty adapting to meantone notation. It was why extended meantone was less successful in practice (despite its obvious theoretical simplicity) than divisions of 12-equal. Is that still the case?

I'll go as far as suggesting comma shifts of some kind for the more distant fifths in the flatter meantones. Performers who don't need them can ignore them. Whether they help will have to be determined by experience.

> Does the fifth size-spec on the score resolve it sufficiently well to
> your mind?

Unfortunately, no. It works for theoretical purposes but it doesn't really help performers. The tuning needs to reside constantly in their short term memory for them to interpret the symbols correctly. If there's a near-diatonic passage the audible context will be enough for them to get it right without thinking of the tuning, and then they encounter a microtonal passage that depends on the relative pitch of C# and Db (however written) they'll have to think "what was the tuning again"? And that's fatal because it means they've stopped concentrating on the score (or maybe focused on the start where you specified the fifth size).

Pythagorean and meantone having a different appearance because of the shape of the accidentals will do a lot more to reinforce the tuning context. And in a homogeneous way, throughout the score, so the cue's there wherever their attention's focused.

I've changed the subject because I do have some other thoughts on this matter and maybe I'll set them out later. My own decimal notation is obviously an accident waiting to happen.

Graham

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

🔗Carl Lumma <carl@lumma.org>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> The human brain
> has a vast capacity for learning symbols. It has more
> difficulty attaching conflicting meanings to existing
> symbols.

It also has a vast capacity for learning contexts, and
placing symbols within them. We don't have a base 60
counting system, we use place-value. I can't remember
getting confused by numbers like 11.

> Learning both meantone and pythagorean tunings is
> a difficult enough task that two extra symbols should be
> neither here nor there.

Yes, it probably isn't a big deal either way in that case.
But if we're talking about 200 new symbols, we might have
an argument.

> There has to be a compromise somewhere. Ultimately, you've
> provided the symbol set, and it's up to musicians how they
> use it. When they start giving you feedback I'm sure you'll
> need to revise the system, probably in ways we didn't think of.

On the contrary, learning something like reading is so
difficult, as you rightly point out, that learners aren't
in a position to criticize (everything just seems hard).
There are lots of fairly convincing arguments that standard
music notation is non-optimal, but it flourished anyway.
Any optimizations pale in comparison to the overall size of
the task (probably Jim Plamondon would disagree).

At any rate, it sounds like Aaron has shown it to musicians
over the years he's spent developing it.

> I've changed the subject because I do have some other
> thoughts on this matter and maybe I'll set them out later.
> My own decimal notation is obviously an accident waiting to
> happen.

I think your decimal notation was very much headed in the
right direction.

-Carl

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

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> It's rightbarbdoubleup ||\ #\ I was thinking of.

OK. Well that's valid too, but it's actually 128:135. An apotome less
a 5-comma.

> Well, maybe we agree about what people want to do, but
> reading music's a sufficiently difficult task that I prefer
> to think of what they're capable of doing. The human brain
> has a vast capacity for learning symbols. It has more
> difficulty attaching conflicting meanings to existing
> symbols. Learning both meantone and pythagorean tunings is
> a difficult enough task that two extra symbols should be
> neither here nor there. (Unless you use a keyboard where
> the fingering's the same.)

Aha! Yes. That's the thing. If it's a pretty much fixed pitch
instrument that has been retuned, whether it be a keyboard or a
refretted guitar or a re-tubed/valved brass instrument or a woodwind
with different hole placements, you will want a different notation
than you will if it's a flexible pitch instrument or you are otherwise
bending the notes away from some underlying tuning.

In both cases it is the underlying tuning of the instrument whose
chain of fifths (assuming it has one) you want represented by naturals
or nominals.

If the underlying tuning is either pythagorean or 12-equal we have
standard sagittal solutions for those, to represent any tuning to the
same kind of accuracy as Aaron's megastaff, namely to within about +-3
cents. In the sagittal paper these are called Athenian (pythag-based)
and Trojan (12-based).

If you want to see what these notations for 19-EDO or 31-EDO look like
you can use Scala. Simply generate the appropriate tuning wit EQUAL
then SET NOTA SAJI1 or SET NOTA SA12R and take a look at the staff
view. You may also want to SET SAG MIXED or SET SAG PURE.

Let us know what you think of them. Too many different accidentals I'm
thinking.

> If they don't want to learn new symbols, you can always tell
> them it's the same symbol, but written differently!

Good one.

> They're
> both two shaft arrows, after all, by design.

Yes.

> And if they
> really don't want to learn new symbols they'll be using
> mixed sagittal anyway. Or staying away from microtonality
> completely.

Yes.

> There has to be a compromise somewhere. Ultimately, you've
> provided the symbol set, and it's up to musicians how they
> use it.

Right. Perhaps it isn't right to speak of there being a standard
sagittal notation for say 19 or 31-EDO. There are at least 3 standard
sagittal notations for it. One using native-fifth nominals, one using
12-EDO nominals and one using pythagorean nominals.

The _core_ sagittal standard is the list of (possibly tempered) comma
definitions of the symbols.

> When they start giving you feedback I'm sure you'll
> need to revise the system, probably in ways we didn't think of.

Yes. And we've already done that in several cases.

> I thought the consensus was that musicians who think in
> Pythagorean terms have difficulty adapting to meantone
> notation. It was why extended meantone was less successful
> in practice (despite its obvious theoretical simplicity)
> than divisions of 12-equal. Is that still the case?

I don't know. But the so-called SAJI1 or "Athenian" notation will give
you such a pythagorean based notation for meantones.

> I've changed the subject because I do have some other
> thoughts on this matter and maybe I'll set them out later.
> My own decimal notation is obviously an accident waiting to
> happen.

Why do you say that? It seems the optimal notation for miracle
temperaments.

-- Dave Keenan

🔗Aaron Wolf <backfromthesilo@yahoo.com>

I must chime in to say that while I don't agree with every single
justification Aaron has made for MegaScore or his instruments, the end
result seems far superior to everything else I've seen.

As a trained musician and as a teacher trying to bridge the gap
between presenting traditional theory and music and the possibilities
beyond that, I really appreciate the goal of connecting to traditional
visual representations.

I see absolutely no problem with the sharp and flat accidental symbols
being used as Aaron has them. I think it is like learning a language
that pronounces known symbols differently. I was recently on my
honeymoon in Slovenia, where the letter C is pronounced like "ts" and
I was COMPLETELY comfortable with that concept before we even arrived.
I shifted that in my head and that was that. I read "Mercator" as
sounding like mertsator. It just made sense. The important thing is
that everything within the context is consistent. Having C always be
ts in Slovene is not confusing. I just have to note whether I'm
reading Slovene or another language. The real confusion is C not
always being the same all in English - though as a native speaker,
I've gotten used to that.

I really think this is a fine analogy. It will be no problem for any
musician to shift back and forth between the meaning of these same
symbols as long as there is no doubt about context, meaning whether we
are in MegaScore or in regular staff. Everything within MegaScore is
totally consistent, and there is relatively little to memorize or
adapt to.

I am at this point most interested in seeing Aaron's JI notation
system within this. If it is as intuitive as what he's presented so
far, I'll be extremely pleased.

At the risk of being a little judgmental, I wonder if the
disagreements and criticism is coming not mainly from musicians
anticipating confusion, but rather from those here who are defensive
about other notation concepts they've already invented and are biased
toward for personal reasons and are trying to defend the decisions
they made in their work...

Best,
Aaron Wolf

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

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@> wrote:
> > At the risk of being a little judgmental, I wonder if the
> > disagreements and criticism is coming not mainly from musicians
> > anticipating confusion, but rather from those here who are defensive
> > about other notation concepts they've already invented and are biased
> > toward for personal reasons and are trying to defend the decisions
> > they made in their work...
>
>
> Hi other other Aaron,
>
> You might be interested to know that Aaron Hunt and I made our peace
> some days ago, via email. I genuinely thought that Aaron was asking
> for criticism of the Megascore notation system, not merely the new
> educational resources for it. I assumed that would be the case because
> George and I welcome well-informed and constructive criticism of
> Sagittal (although I admit it can be hard to hear sometimes). And who
> better to give it than someone else who has also thought deep and long
> about the issues involved in notating microtonal scales and tunings in
> all their bewildering variety.
>
> I'm not sure how anyone _could_ defend themselves against the charge
> you have made. I think we should try to assume that people are
> honourably motivated until it is proven otherwise.
>
> -- Dave Keenan
>

Dave,

I don't mean to charge that you are acting on bad intentions! I'm
glad to hear you have settled your concerns. I only meant that
perhaps you were biased by your defense of your work - and in a
subconscious way. Let me put it this way: it didn't appear that you
admitted any bias yourself, and it was clear that the strongest
critique was coming from those with their own notation systems. I
don't mean to invalidate you from sharing your criticisms, but it
would be only honest to admit at least the potential for bias.

Put simply, the insistence of your criticism and the way you presented
it didn't sound like "perhaps this will be confusing to some people"
but more like "this is bad and confusing." I know you said positive
things as well.

For another analogy, it's kind of like Ford talking about why General
Motors made the wrong decision when they did something the alternative
way to Ford's decisions. It may be valid criticism or not, but Ford
cannot possibly claim to be objective. If someone said that Ford
wasn't objective, you are right that they would have no real possible
defense. Same in your case. You have no way to eliminate my
accusation of bias or to claim pure objectivity here, but you can
admit your potential bias and claim to be attempting to be as
objective as possible.

I think it is impossible in your case to be free of bias, but unlike
Ford, you have no financial motive, and I trust your good intentions
absolutely. I don't mean any offense.

Peace,
Aaron

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

There was an initial misunderstanding about what kind of
"feedback and suggestions" I was looking for, because I was
not clear about this in my original message, and that was
completely my fault. At one point I did suggest that
the objections being raised could be borne of some
subconscious sagittal predisposition, and Dave admitted
it could very well be but this would be nearly impossible to
prove. We all have our personal biases. At any rate, I think
the exchanges have been to everyone's benefit.

Aaron Wolf thanks also for the nice words. BTW, I will always
use your full name to avoid confusion. Too bad we don't have
other versions of our first name to differentiate us. Since
a friend of mine told me there is an Aaron Hunt football player
on Wikipedia, I have started using my middle name more
often.

<http://en.wikipedia.org/wiki/Aaron_Hunt>

Curiously, as many of you already know, the football player
internet pantheon also includes an honorable Keenan and
Secor...

<http://dkeenan.com/sagittal/Keenan%20and%20Secor%20Honored.ht
m>

Yours,
Aaron (hasn't played football since his teens) Andrew Hunt
H-Pi Instruments

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

🔗Aaron Wolf <backfromthesilo@yahoo.com>

Well, Aaron Andrew Hunt, and others,

I hope I did not offend anyone. I was more interested in sharing my
language analogy as far as letters and symbols go than in criticizing
anyone. I do think it is a good analogy.

While my thoughts aren't really biased by anything particular I can
identify, my certainly *subjective* opinion clearly influences my
views, like anyone. My opinion is that sagittal is well-intentioned
but overbearing and I was genuinely concerned that the suggestions
might be actually considered. And I for one would be quite
disappointed to see MegaScore adopt sagittal notation. I'm glad it
will remain only a non-standard option for those who really want to
use it. I like MegaScore as is, from what I've seen so far.

Best,
The Wolf

--- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@...> wrote:
>
> There was an initial misunderstanding about what kind of
> "feedback and suggestions" I was looking for, because I was
> not clear about this in my original message, and that was
> completely my fault. At one point I did suggest that
> the objections being raised could be borne of some
> subconscious sagittal predisposition, and Dave admitted
> it could very well be but this would be nearly impossible to
> prove. We all have our personal biases. At any rate, I think
> the exchanges have been to everyone's benefit.
>
> Aaron Wolf thanks also for the nice words. BTW, I will always
> use your full name to avoid confusion. Too bad we don't have
> other versions of our first name to differentiate us. Since
> a friend of mine told me there is an Aaron Hunt football player
> on Wikipedia, I have started using my middle name more
> often.
>
> <http://en.wikipedia.org/wiki/Aaron_Hunt>
>
> Curiously, as many of you already know, the football player
> internet pantheon also includes an honorable Keenan and
> Secor...
>
>
<http://dkeenan.com/sagittal/Keenan%20and%20Secor%20Honored.ht
> m>
>
> Yours,
> Aaron (hasn't played football since his teens) Andrew Hunt
> H-Pi Instruments
>
>
>
>
>
>
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> >
> > --- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@> wrote:
> > > At the risk of being a little judgmental, I wonder if the
> > > disagreements and criticism is coming not mainly from musicians
> > > anticipating confusion, but rather from those here who are defensive
> > > about other notation concepts they've already invented and are
biased
> > > toward for personal reasons and are trying to defend the decisions
> > > they made in their work...
> >
> >
> > Hi other other Aaron,
> >
> > You might be interested to know that Aaron Hunt and I made our peace
> > some days ago, via email. I genuinely thought that Aaron was asking
> > for criticism of the Megascore notation system, not merely the new
> > educational resources for it. I assumed that would be the case because
> > George and I welcome well-informed and constructive criticism of
> > Sagittal (although I admit it can be hard to hear sometimes). And who
> > better to give it than someone else who has also thought deep and long
> > about the issues involved in notating microtonal scales and tunings in
> > all their bewildering variety.
> >
> > I'm not sure how anyone _could_ defend themselves against the charge
> > you have made. I think we should try to assume that people are
> > honourably motivated until it is proven otherwise.
> >
> > -- Dave Keenan
> >
>

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

--- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@...> wrote:
> Hi Dave. That's an interesting idea. If I was calling positions quarter
> this and that, then it would make sense, but since I have not used
> either the quartertone terminology or the quartertone symbols as
> accidentals, it doesn't seem necessary or logical to me to introduce
> them in the inflections. The way it is, the only new symbols needed
> for accidentals and inflections are the triples, and in both cases they
> serve as enharmonics, albeit in slightly different ways.

Hi Aaron H.,

I hope we agree that you did invite _this_ discussion. And I hope
readers note that the Tartini/Couper symbols were not invented by me
or any of my friends, and nor are they part of Sagittal. :-)

But wait! We did include them in the sagittal version 2 font along
with some other non-sagittal symbols due to Erv Wilson, so I could be
biased. ;-)

Or then again, maybe I'm suggesting them here for the same reason we
included them in the font, because they are easily understood symbols
compatible with conventional sharps and flats, provided you don't want
to divide the apotome or chromatic semitone into more than four parts.

I fully expect it is way too late to make any such changes to
MegaScore, however I must correct your misperception that I was
suggesting the use of _quarter_-anything terminology for your inflections.

I put "quartertone" in scare-quotes precisely because I do not
consider them so (and nor, I think, did their creators), although that
is what they are popularly known as.

These symbols are properly called "semisharp" and "semiflat" and don't
really represent a quarter of anything (except relative to 12-EDO),
but rather a half of whatever the sharp and flat symbols represent.

They are very well known and are used in commercial notation software
such as Sibelius and Finale. They even appear on
http://en.wikipedia.org/wiki/Accidental_(music)
which contains no other microtonal accidentals. So they wouldn't
exactly be _new_ symbols.

So I'm suggesting that it would make a lot more sense from the
fraction-of-a-staff-position view that you espoused, to call an
inflection by 1 degree of 205-EDO "semisharp" or "half sharp", and 2
degrees "sharp", and 3 degrees (which as you point out is enharmonic
and so doesn't really need to be used) "sesquisharp or "sharp and a half".

By the way, if you think musicians are such neophobes, why did you
feel the need for totally new symbols for your "shifts", when the
existing Wilson slanted plus and minus symbols and the Tartini/Couper
semisharp and semiflat symbols would have served admirably -- call
them what you will?

Again by the way, given your knowledge of perceptual issues, don't you
think the double-dagger is a poor substitute for the Tartini
semisharp, since it was not designed to avoid interference with staff
lines or ledger lines?

-- Dave Keenan

🔗Graham Breed <gbreed@gmail.com>

Dave Keenan wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

>>Well, maybe we agree about what people want to do, but >>reading music's a sufficiently difficult task that I prefer >>to think of what they're capable of doing. The human brain >>has a vast capacity for learning symbols. It has more >>difficulty attaching conflicting meanings to existing >>symbols. Learning both meantone and pythagorean tunings is >>a difficult enough task that two extra symbols should be >>neither here nor there. (Unless you use a keyboard where >>the fingering's the same.)
> > Aha! Yes. That's the thing. If it's a pretty much fixed pitch
> instrument that has been retuned, whether it be a keyboard or a
> refretted guitar or a re-tubed/valved brass instrument or a woodwind
> with different hole placements, you will want a different notation
> than you will if it's a flexible pitch instrument or you are otherwise
> bending the notes away from some underlying tuning.

Ideally we'd use the same notation regardless of the instrument.

> In both cases it is the underlying tuning of the instrument whose
> chain of fifths (assuming it has one) you want represented by naturals
> or nominals.

There are more cases than two. For woodwinds I know (penny whistle, dizi, bawu?) I'd want the nominals (maybe as a transposing instrument, maybe with numerical notation) to follow the chain of fifths and the accidentals to follow pitch size. That's because the hole placement will sort out one diatonic scale but for accidentals I need to cover extra holes. And more holes covered for a higher pitch. Is there another way you can see this working?

For a refretted guitar as well, the physical design of the instrument biases towards pitch size for accidentals. The important thing is to know which order C# and Db should be.

For a generalized keyboard I don't see it would do any harm to use the accidentals to remind the performer of the coarse tuning.

> If the underlying tuning is either pythagorean or 12-equal we have
> standard sagittal solutions for those, to represent any tuning to the
> same kind of accuracy as Aaron's megastaff, namely to within about +-3
> cents. In the sagittal paper these are called Athenian (pythag-based)
> and Trojan (12-based).
> > If you want to see what these notations for 19-EDO or 31-EDO look like
> you can use Scala. Simply generate the appropriate tuning wit EQUAL
> then SET NOTA SAJI1 or SET NOTA SA12R and take a look at the staff
> view. You may also want to SET SAG MIXED or SET SAG PURE.
> > Let us know what you think of them. Too many different accidentals I'm
> thinking.

I don't have Scala installed I'm afraid. But generally I think if you're going to notate pitch to that much precision it's better to use the megastaff or AFMM cents notation. If the number of shafts is consistent I expect people can get used to it. If musicians could train specifically in Sagittal for a number of years I expect they could handle all kinds of things and you'd really better take the comments from them.

>>I've changed the subject because I do have some other >>thoughts on this matter and maybe I'll set them out later. >>My own decimal notation is obviously an accident waiting to >>happen.
> > Why do you say that? It seems the optimal notation for miracle
> temperaments.

It works for me for composition. But then I always have the pitch structure in my head when I write. There's a bit of confusion with 5-limit harmonies, because I know what they should look like on a normal staff. With higher limits I only map them to the decimal staff so there's no problem.

The problem for musicians would be that, in detail, it looks confusingly similar to a normal staff. As I write it the accidentals are different, but if you used sagittal for both cases that wouldn't be true any more. I don't like Monz's 4 line staff because it doesn't work with normal manuscript paper (not such a big deal) and I'm not a fan of leger lines.

My original solution was to make the first line bold. I'm thinking of different colours now, following the elements of the heavenly stems corresponding to each note:

1 wood, 3 fire, 5 earth, 7 metal, 9 water

There may even be a standard colour scheme. This would mean the decimal staff would look distinctive in high-quality printing for musicians, but would still be readable in black and white. It'd also be easier to navigate leger lines.

A similar scheme would work for the traditional staff. The obvious extention to an elements+2 scheme is

C moon, D fire, E water, F wood, G metal, A earth, B sun

The natural look for the treble clef would be

water, metal, sun, fire, wood

and the bass clef

metal, sun, fire, wood, earth

You can then vary the pattern for different key signatures (if you use them). Maybe use plain black and white for Pythagorean tuning and colours for meantone.

I know that some colored staves have been suggested and didn't catch on. Maybe this would work because the colours only add redundancy.

Graham

🔗Graham Breed <gbreed@gmail.com>

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

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Aaron Wolf wrote:
> > Well, Aaron Andrew Hunt, and others,
> >
> > I hope I did not offend anyone. I was more interested in sharing my
> > language analogy as far as letters and symbols go than in criticizing
> > anyone. I do think it is a good analogy.
>
> Here's a language analogy for you. I tried to write a reply
> to Dave in Commonwealth English but I thought "is there a
> 'u' in 'coloured'"? And, in fact, there should be, although
> not in "coloration" of course.
>
> The moral: the more similar the context the more cause of
> confusion.
>
>
> Graham
>

A fair point, however, I think the possibility to confuse whether we
are reading British English versus American English is much more
likely than whether you are reading any English versus reading
Slovene, even though Slovene basically uses the same alphabet and the
same format.

I other words, I would agree with your concerns completely if I
thought there was any chance that I'd confuse MegaScore with regular
staff notation. If someone was using a 5-line staff for microtonal
notation and using a different meaning of known symbols, it would be
more of an issue because harder to tell which system we're in.

To continue with the language analogy, I believe confidently for
myself and others that I've observed that there is less resistance to
learning to read Slovene (ignoring meaning, I just mean pronounce the
words) than to reading Korean. Korean is extremely logical and
consistent a written language, but it uses a whole new set of symbols
than English. I think most English speakers more quickly learn
Slovene, which uses mostly the same symbols, even though some change
meaning, versus learning Korean which is a whole new set of symbols.

I think that is basically our argument here. You seem to suggest that
the new symbols way is better than any change to known symbols. But
I'm arguing, with this analogy, that in fact new context and meaning
of the same symbols is more easily received than new sets of symbols.
I too, would love to see actual studies on this of course. But just
ask yourself, if you went on a long trip to Slovenia or to Korea,
which one do you think you'd more quickly and comfortably learn to
pronounce by reading?

Best,
The Wolf

🔗Carl Lumma <carl@lumma.org>

🔗Aaron Wolf <backfromthesilo@yahoo.com>

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

Hi Dave.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
> These symbols are properly called "semisharp" and "semiflat"

Of course.

> They are very well known and are used in commercial notation software
> such as Sibelius and Finale. They even appear on
> http://en.wikipedia.org/wiki/Accidental_(music)
> which contains no other microtonal accidentals. So they wouldn't
> exactly be _new_ symbols.

No, but despite their inclusion in these notation programs and
their appearance on Wikipedia, they are absolutely not a standard
for educated musicians, as I've said before...

> So I'm suggesting that it would make a lot more sense from the
> fraction-of-a-staff-position view that you espoused, to call an
> inflection by 1 degree of 205-EDO "semisharp" or "half sharp", and 2
> degrees "sharp", and 3 degrees (which as you point out is enharmonic
> and so doesn't really need to be used) "sesquisharp or "sharp and a half".

I disagree, for reasons already stated.

> By the way, if you think musicians are such neophobes, why did you
> feel the need for totally new symbols for your "shifts", when the
> existing Wilson slanted plus and minus symbols and the Tartini/Couper
> semisharp and semiflat symbols would have served admirably -- call
> them what you will?

Using the Tartini symbols would mean getting rid of the idea of an
additional and to-the-left-of-the-letter shift, and go right back to
the idea of introducing new symbols for accidentals, which is what I
am avoiding, saying things like C-sharp and C-semisharp for a C#
that is shifted down by a comma. That simply does not work for
cases such as a double flat shifted down by a comma, and you end
up using sandwiched symbols anyway. More importantly, what do
you call the intervals? Once you start changing accidentals, you
screw up intervals, and musicians trained to know standard
intervals in music theory will not easily be able to to make sense
of anything intervallic. Using shifts, this problem is avoided.

Shifts do not change the spelling of an interval, as Tartini
accidentals would. Shifts provide consistent names for all intervals,
which make logical sense to musicians who already know standard
intervals with standard spellings which they learn to recognize
through standard ear training. With the addition of shifts, the
intervals now have families of interval "type":

Wide (W)
Large (L)
(normal Pythagorean - no prefix needed)
Small (S)
Narrow (N)

For example, the m3, you have the following "type" family:

Wm3
Lm3
m3
Sm3
Nm3

32:27 is a m3. 5:6 is a Lm3, a comma larger, and using an inflection
sharp on the upper note this interval is also called a "Perfect Large
Minor Third" PLm3 because it can be made beatless. The JND
inflections have an expanded set of qualities using all the standard
terms applied to interval quality, from doubly diminished to
doubly augmented, and including Perfect for a beatless tuning.
This system allows all kinds of useful observations, such as Wide
minors and Narrow majors overlap and are enharmonic, such
as a NM3 and a Wm3, which makes perfect sense, since thse intervals
sound neither M nor m, but in fact can sound like either M or m
depending on the context ...

So the answer to all of these suggested changes is NO, NO, and NO.
The system, as it is, is worked out in extreme detail to be completely
comprehensive and consistent as an expansion of the simple logic
of standard music theory, which I know well and have considered
deeply over many years.

Cheers,
Aaron Hunt
H-Pi Instruments

>
> Again by the way, given your knowledge of perceptual issues, don't you
> think the double-dagger is a poor substitute for the Tartini
> semisharp, since it was not designed to avoid interference with staff
> lines or ledger lines?
>
> -- Dave Keenan
>

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

🔗Aaron Wolf <backfromthesilo@yahoo.com>

Thank you Mr. Hunt for your insistence. I could not agree more.

I really believe that I am no neophobe at all! And yet, I simply
can't see getting used to all these systems that try to focus on
combinations of different shifts and different commas etc etc. I
understand completely the origin of different commas, kleismas,
schismas, etc etc, but I simply do not think about those things when
I'm dealing with MUSIC.

Pitch in music, the way I think of it, has two aspects that interact:
melodic and harmonic. Melodic pitch is based on two factors, 1.
movement and by how much, and 2. memory (does this remind me of
something I heard earlier?).

Neither of those two factors really needs the specificity of these
complex new symbols. I simply need to know if the pitch is raising or
lowering and whether a little or a lot (and 20 cents and 22 cents are
melodically identical). And then I need to know if something is
within a JND of a previous or otherwise specified pitch (the memory
aspect). That's it.

Now, harmonically, there is basically one main factor: how much does
the partials of this sound match up with versus beat against the
partials of another concurrent sound?

It IS relevant whether it is off by 2 cents or no cents. So in this
case, more specificity is useful. That's why I'm interested in seeing
MegaScore's JI adaptation. But at any rate, the important thing
harmonically is not exactly how far a pitch is from the previous or
from the "scale" note, but how far from the other concurrent notes.

What is great about MegaScore is that it can clearly show melodic
motion visually, with enough specificity for any melodic function.
The JND concept is truly all that is needed for melodic music. I have
yet to see any notation system besides actual ratio numbers, lattices,
or chord names that really shows harmonic music well. Again, I'm
awaiting Aaron Hunt's explanation of MegaScore's JI aspect. The
reason I am interested in MegaScore anyway is that its JND
specificity, while not enough to be harmonically precise, is close
enough that almost no context will have more than one useful JI ratio
within the range of the JND, so musicians could learn to harmonically
adjust within the JND by ear without any ambiguity.

My point is that these loads of esoteric symbols that may specify
pitch to the degree required by harmonic music are being suggested for
a notation that is more essentially melodic.

I hope this is clear, I'm finding it excessively hard to express these
ideas in this context. Sorry.

Best,
The Wolf

🔗Carl Lumma <carl@lumma.org>

🔗banaphshu <kraiggrady@anaphoria.com>

🔗Mark Rankin <markrankin95511@yahoo.com>

Kraig, et al,

The first sentence below reminds me that Siemen
Terpstra came to the conclusion several years ago that
there *have to be* be at least two different kinds of
generalized keyboards. He named them Male and Female,
and a prototype of one of the genders was built and
shown at Queens College, New York, on July, 17, 2006.

Johnny Reinhard collaborated with Siem and Dylan
Horvath in Canada, and Professor Joel Mandelbaum is
the instrument's custodian.

Mark Rankin

--- banaphshu <kraiggrady@anaphoria.com> wrote:

> It seems impossible ot come up with a notation
> system that will
> satisfy all cases. with generalized keyboards. it
> seems best to base
> the notation on where the notes are in the fashion
> wilson does in the
> early xenharmonikon. omitting possibly those
> documents incorporation
> of yassers note names. with standard instruments,
> there is no way
> hardly to not escape using cents measurements,
> either in the score or
> making the players do this yourself. other
> instruments can call for
> some type of tableture. the very basis of how a
> scale or tuning
> spectrum can call for different methods of
> notation.A system based on
> a series of commas would be little use in scales
> made of recurrent
> sequences.
> the furture may find that scores, where they exist,
> may resemble more
> what we find in early music where there are parts
> more than an
> overlooking master score.
> all in all though i tend to favor notations that
> deals with scale as
> oppsed to interval as being more inclusive. having
> played instruments
> in a variety of generalized layouts, it has never
> bothered me that the
> same symbols will mean different things in different
> tunings. It has
> been more helpful that the notation tells me where
> the pitch is.I see
> no reason not incorporate an interval based system
> when appropiate to
> a generalized pattern when one reaches toward
> extreme limits.
> what instruments we use in the future will have more
> bearing on how
> all this is sorted out and the possibilty that such
> deversity will
> continue to exist for quite a ling time should not
> be very surprising.
>
>
>
>
>
>
> You can configure your subscription by sending an
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🔗Aaron Wolf <backfromthesilo@yahoo.com>

🔗Carl Lumma <carl@lumma.org>

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, "banaphshu" <kraiggrady@...> wrote:
>
> It seems impossible ot come up with a notation system that will
> satisfy all cases. with generalized keyboards. it seems best to base
> the notation on where the notes are in the fashion wilson does in the
> early xenharmonikon. omitting possibly those documents incorporation
> of yassers note names. with standard instruments, there is no way
> hardly to not escape using cents measurements, either in the score or
> making the players do this yourself. other instruments can call for
> some type of tableture. the very basis of how a scale or tuning
> spectrum can call for different methods of notation.A system based on
> a series of commas would be little use in scales made of recurrent
> sequences.
> the furture may find that scores, where they exist, may resemble more
> what we find in early music where there are parts more than an
> overlooking master score.
> all in all though i tend to favor notations that deals with scale as
> oppsed to interval as being more inclusive. having played instruments
> in a variety of generalized layouts, it has never bothered me that the
> same symbols will mean different things in different tunings. It has
> been more helpful that the notation tells me where the pitch is.I see
> no reason not incorporate an interval based system when appropiate to
> a generalized pattern when one reaches toward extreme limits.
> what instruments we use in the future will have more bearing on how
> all this is sorted out and the possibilty that such deversity will
> continue to exist for quite a ling time should not be very surprising.
>

This is all a question of tab vs notation type issues. The question
is, do I tell you what to do, or am I describing the resulting sound.

My understanding is that for the most part composers are not always
the best at writing specific instructions for different instruments.
Composing and orchestrating and arranging and notating are all
different activities to a degree.

It would seem we will always have use both for notations that show the
resulting sound as well as for notations for what to physically do
with an instrument. However, with electronic music being a big part
of our future, the latter will be less primary than it has been
historically. So notations that simply make logical sense of the
basically limitless choices we have will be warranted.

Composers and theorists need a way to make sense of music without
being bogged down by mechanical notations for instrumentalists. And
instrumentalists who are to get to any high degree of musicality need
to understand the music too, not just how to make it.

Anyway, I guess your point is we shouldn't try to have one be-all
system that asks all instrumentalists to play directly off the score
without any specific mechanical notation. And accepting that, we
should be clear which of these is our main goal when discussing any
proposed notation...

Boy, lots of seemingly never-ending issues end up getting brought up
here...

-Aaron Wolf

🔗Aaron Wolf <backfromthesilo@yahoo.com>

🔗Carl Lumma <carl@lumma.org>

🔗Aaron Wolf <backfromthesilo@yahoo.com>

>
> Not confused at all. The overwhelming majority of guitarists
> do not read any notation at all. And the number who read tab
> surpasses the number who read "standard notation". Further,
> aside from "classical guitar" (which is something of an oxymoron),
> no school of guitar playing is based in "standard notation".
> Are you disputing any of this?
>
> -Carl
>

Well, you are diminishing the significance of classical guitar, which
is admittedly a minority of guitarists, but if we consider only
SCHOOLED guitarists, a large portion are classically trained using
standard notation. The rest of the SCHOOLED guitarists are generally
trained in a jazz approach that doesn't emphasize standard notation
but certainly does not ignore it and any graduate from any university
guitar program in the world is able to read standard notation
somewhat, if not particularly well. The vast majority of guitar
methods and instructional material include standard notation, and the
standard tab system for published music includes standard notation
along with tab.

The idea that "classical guitar" as an oxymoron is ridiculous
considering that a substantial amount of music for guitar was written
during the end of what is considered the "classical era" and in the
classical formal style. And if we include the Romantic era within the
broad term, "classical" then we have an absolutely clear tradition of
classical guitar, including some of the most renound classical names,
such as Paganini who was as dedicated and talented on the guitar as he
was on the violin.

I am certainly aware that guitarists are notoriously unskilled as
readers of standard notation, but almost no schools of guitar that I'm
aware of would talk about the significance of standard notation as
being as irrelevant to guitar as you seem to imply.

I happen to currently have 8 guitar method and song books from the
library to evaluate for potential use with students. I mention this
because I didn't select them on personal preference, but just picked
random books to see what's out there. These particular 8 are all
designed specifically for the popular, rock, and folk style student,
and not "classical guitar." Of these, 3 are strictly standard
notation only, and the other 5 include a mix of standard notation and
tab, some of them having notation throughout and tab only for some
selections.

Let me just put it this way, do you think standard notation is less
relevant and less known to guitarists than to singers? Do you think
the fact that most singers cannot read music is any proof of the
applicability of notation to singing or not?

Best,
Aaron Wolf

🔗Aaron Wolf <backfromthesilo@yahoo.com>

🔗Graham Breed <gbreed@gmail.com>

Aaron Wolf wrote:

> A fair point, however, I think the possibility to confuse whether we
> are reading British English versus American English is much more
> likely than whether you are reading any English versus reading
> Slovene, even though Slovene basically uses the same alphabet and the
> same format.

Yes, because the contexts are more similar.

> I other words, I would agree with your concerns completely if I
> thought there was any chance that I'd confuse MegaScore with regular
> staff notation. If someone was using a 5-line staff for microtonal
> notation and using a different meaning of known symbols, it would be
> more of an issue because harder to tell which system we're in.

Right, that's why I'm not much concerned about MegaScore either, and I changed the subject line to reflect this.

> To continue with the language analogy, I believe confidently for
> myself and others that I've observed that there is less resistance to
> learning to read Slovene (ignoring meaning, I just mean pronounce the
> words) than to reading Korean. Korean is extremely logical and
> consistent a written language, but it uses a whole new set of symbols
> than English. I think most English speakers more quickly learn
> Slovene, which uses mostly the same symbols, even though some change
> meaning, versus learning Korean which is a whole new set of symbols.

Ignoring meaning is ignoring precisely the hardest part of a language. And I assume that most letters have very similar pronunciations between English and Slovene which helps for the initial learning. This is for exactly the same reason that it'd be nice to standardize on a set of microtonal accidentals. Would you find it easy to learn a language with the usual 26 letters, but their meanings all jumbled up?

Also, there's a difference between speed of learning and efficiency of using a language. Alphabets are great for fast learning when you already know or don't care about the meanings of words. They're not maximally efficient once you learn them because many words have similar shapes. (Not enough to stop them being used, of course, but enough to make dyslexia a problem.) I also believe (but don't have a reference) that it's easier to forget words you learned with an alphabet compared to other systems.

> I think that is basically our argument here. You seem to suggest that
> the new symbols way is better than any change to known symbols. But
> I'm arguing, with this analogy, that in fact new context and meaning
> of the same symbols is more easily received than new sets of symbols.
> I too, would love to see actual studies on this of course. But just
> ask yourself, if you went on a long trip to Slovenia or to Korea,
> which one do you think you'd more quickly and comfortably learn to
> pronounce by reading?

I'm arguing that the brain finds it easier to learn new symbols than to give conflicting meanings to old symbols. I believe there is a scientific basis for this but, alas, no reference. I am still arguing for retaining existing symbols with their existing meanings. That's why, for the difference it makes, I'd rather uase Megascore with sagittal accidentals. As far as it makes a difference (which is not much) I expect it to be easier to switch between the systems that way.

I'm also arguing that it gets more confusing the more similar the contexts are. The brain is good at distinguishing languages, probably as a direct result of natural selection. The question is how much a new notation system counts as a new language or a variant of an old language.

The analogy here is between sagittal and the International Phonetic Alphabet. The idea is to give each sound a unique symbol, consistent between languages. Although I hope sagittal will be of more everyday use.

Graham

🔗Graham Breed <gbreed@gmail.com>

🔗Carl Lumma <carl@lumma.org>

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> "Aaron Wolf" <backfromthesilo@> wrote:
> > The idea that "classical guitar" as an oxymoron is ridiculous
> > considering that a substantial amount of music for guitar was
> > written during the end of what is considered the "classical era"
> > and in the classical formal style.
>
> I stand corrected:
> http://tinyurl.com/36ecr7
>
> Ok, you win. Classical guitar is a real school of guitar
> playing. I wonder why recordings I've heard have always
> been transcriptions, and why I don't know of any pieces
> by famous composers for guitar.
>
> > I am certainly aware that guitarists are notoriously unskilled as
> > readers of standard notation, but almost no schools of guitar that
> > I'm aware of would talk about the significance of standard
> > notation as being as irrelevant to guitar as you seem to imply.
>
> It's not relevant to the success of the guitar as the primary
> polyphonic instrument of the last 60 years.
>
> -Carl
>

Does the fact that most any musician you possibly meet has NO
familiarity with microtonal music mean that it isn't happening?

Independently of that, if you were to eliminate all non-notation based
guitar playing and composing of the last 60 years, guitar wouldn't be
the number one polyphonic instrument, but there would still be a
MASSIVE amount of guitar music remaining.

I happen to be aware of a compilation of only a portion of the most
popular classical guitar pieces, ranging from lute transcriptions to
20th century, all in standard notation... this compilation is roughly
8,000 pieces, and I recall that a number of pieces off the top of my
head were NOT included in that list.

As for your ignorance of guitar composers, it is certainly unfortunate
that traditional major label industry collections of "classical
guitar" tend to focus on transcriptions, probably because they are
marketing to non-musicians who they think will buy albums with names
they recognize more. However, of many classical guitar albums I have,
I think only a small minority are completely transcriptions. And many
are purely guitar compositions.

A simple random Amazon.com search for recordings of music by Fernando
Sor (just one, but perhaps the most famous and popular of the guitar
composers from around the turn of the 19th century) gave a result of
371 CDs. So, I understand that you haven't been exposed to his or any
of his contemporaries' compositions, or to the VAST number of
compositions in the school of guitar that descended from him,
including 20th century "classical" composers such as Heitor
Villa-Lobos, Leo Brouwer, Jorge Morel, and hundreds of others. As for
not having heard from names you know, such as Paganini, his
guitar-specific compositions are extremely challenging and so much
less recorded and known compared to easier pieces. Your personal
ignorance of this whole world of music is not evidence of its
insignificance. I personally recommend a lot of this music as it
includes some extremely fine composing.

Fact is, a decent portion of all published guitar music is in standard
notation. True, the majority of guitar playing is not notated or
published at all. Still, you wouldn't see huge catalogs of published
standard notation guitar music if it wasn't selling...

I'd really like to get back to the purpose of your original point.
The question is whether it is practical to get an instrument like
guitar to work with standard notation, hence the question of notation
crossing over different instruments.
I'd like to hear your thoughts about my mentioning VOICE. Voice is
just like guitar, it works with notation, has a history of notation,
but most singers do not read and the prominence of singing is not due
to notation. Do you think this shows the inadequacy of notation for
voice or not? Is this comparable to guitar or do you still argue a
distinction?

Best,
Aaron W

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Carl Lumma wrote:
> >>>--- In tuning@yahoogroups.com, Graham Breed <gbreed@> wrote:
> >>>
> >>>>The human brain
> >>>>has a vast capacity for learning symbols. It has more
> >>>>difficulty attaching conflicting meanings to existing
> >>>>symbols.
>
> > But I know something about (and have done) interface design,
> > and what you imply is not right. Successful interfaces depend
> > on the abstraction and reuse of functions in different contexts.
>
> Where do successful interfaces reuse the same symbols with
> different meanings in similar contexts? I'm not talking
> about abstraction or reuse, but consistency.
>
> I have the Apple Human Interface Guidelines here; the page
> is "Human Interface Design Principles". There's a section
> on Consistency, with the rhetorical question "Do icons mean
> the same thing every time they are used?" That's pretty
> much exactly what I'm advocating. Also, under Aesthetic
> Integrity, "Don't change the meaning or behavior of standard
> items."
>
> Right after that is Modelessness. Different meanings of a
> notation count as different modes. I can't interpret any of
> their acceptable uses as covering inconsistent accidentals.
> (But then they don't mention language, and anyway, they'd
> disallow vi so they're obviously fallible.) You could say
> that holding a different instrument counts as a real-life
> situation for a musican though.
>
>
> Graham
>

I'd argue in the case of MegaScore that sharp signs and flat signs
still mean sharp and flat. If they were meaning that the notes should
be shorter or faster or louder or more vibrato, or were backwards from
standard, that would all be HORRID. But to say that the sign only
means an exact amount or even a general amount sharp isn't something
determined. There is clearly no consistent current use of the signs
as meaning an exact amount sharp and not another amount. The # sign
means SHARP, meaning raised pitch. And MegaScore is completely
consistent with that meaning. I would agree with you 100% if a sign
like that were being used to mean something different from standard.

-The Wolf

🔗banaphshu <kraiggrady@anaphoria.com>

🔗Carl Lumma <carl@lumma.org>

--- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@...>
wrote:
> Does the fact that most any musician you possibly meet has NO
> familiarity with microtonal music mean that it isn't happening?

No.

> I happen to be aware of a compilation of only a portion of the most
> popular classical guitar pieces, ranging from lute transcriptions

Transcriptions are not guitar music.

> to 20th century, all in standard notation... this compilation is
> roughly 8,000 pieces, and I recall that a number of pieces off the
> top of my head were NOT included in that list.

8,000 pieces, compared to the roughly 60,000 recordings (each
containing ~ 10 pieces) in an average mom-and-pop record store.

> As for your ignorance of guitar composers, it is certainly
> unfortunate that traditional major label industry collections
> of "classical guitar" tend to focus on transcriptions, probably
> because they are marketing to non-musicians who they think will
> buy albums with names they recognize more.

Understood, but I can't think of another instrument so badly
afflicted thus. I think Albeniz is the only endemic composer
I've ever heard recordings of.

> And many are purely guitar compositions.

Can you recommend anything?

> A simple random Amazon.com search for recordings of music by
> Fernando Sor (just one, but perhaps the most famous and popular
> of the guitar composers from around the turn of the 19th
> century) gave a result of 371 CDs. So, I understand that you
> haven't been exposed to his or any of his contemporaries'
> compositions, or to the VAST number of compositions in the
> school of guitar that descended from him, including 20th
> century "classical" composers such as Heitor Villa-Lobos,
> Leo Brouwer, Jorge Morel, and hundreds of others. As for
> not having heard from names you know, such as Paganini, his
> guitar-specific compositions are extremely challenging and so
> much less recorded and known compared to easier pieces. Your
> personal ignorance of this whole world of music is not evidence
> of its insignificance. I personally recommend a lot of this
> music as it includes some extremely fine composing.

Thanks! I had of course heard of Villa-Lobos and Paganini,
though I wasn't aware of the guitar compositions of the latter.

> I'd like to hear your thoughts about my mentioning VOICE. Voice
> is just like guitar, it works with notation, has a history of
> notation, but most singers do not read and the prominence of
> singing is not due to notation. Do you think this shows the
> inadequacy of notation for voice or not? Is this comparable to
> guitar or do you still argue a distinction?

I'm not sure what you're asking, but I think we should stop
arguing about it now. I could say notation is an insignificant
zit on the face of guitar music, but perhaps a better phrasing
would be:

* If notation is important (we hope you who are designing
notations think it is)

* Then there must be something wrong with using standard
notation on the guitar.

-Carl

🔗Carl Lumma <carl@lumma.org>

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

🔗Carl Lumma <carl@lumma.org>

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Oh, and
>
> --- "Aaron Wolf" <backfromthesilo@> wrote:
> > Fact is, a decent portion of all published guitar music is in
> > standard notation.
>
> Almost all (by sales) are transcriptions of music
> composed on guitars, without notation.
>
> -Carl
>

That's really not what I was talking about, sorry for the confusion,
my fault.

Let me clarify this way: there exists a large number, in absolute
terms, of published guitar music in notation that is NOT
transcriptions of recordings or of music for other instruments.
Regardless of its proportion, this simply would not be the case if
there were not a real market for this.

Anyway, I really don't have time to do much for an organized
introduction to composed guitar, but here is a few selections from
YouTube of great performances of pieces by composers who wrote
specifically for guitar and composed in standard notation:

Barrios, 20th century composer, challenging piece:
http://www.youtube.com/watch?v=8YcrGUkdD1I

Sor, greatest of the classical era composers, one of his simple
studies that is nevertheless artistic and well written:
http://www.youtube.com/watch?v=rIwyqHv_XfY

Another Sor study, happened to be played by someone currently in the
university program I graduated from:
http://www.youtube.com/watch?v=DsCyshHZMt8

Paganini, again very technically challenging:
http://www.youtube.com/watch?v=w-ycSroNG_Q

Tarrega, the most famous Romantic era guitar composer:
http://www.youtube.com/watch?v=ThruwvV25nc

All of these link to a seemingly endless list of related videos, all
of which are connected to guitarists who use standard notation.

Really, it is ridiculous for me to try to select things like this.
The world of classical guitar is truly vast and includes thousands of
formal schools around the world, including many of the most respected
music conservatories. Everyone is expected to read standard notation.
Players like the world-renound John Williams emphasizes reading,
which he claims to often do even while recording, rather than
memorizing everything.

I have the feeling that you'll find a way to disregard whatever
evidence I bring up. I thought it was made clear that you aren't that
knowledgeable about the world of guitar, being totally ignorant of
some basic facts about guitar composition and history, and yet
admitting ignorance, you seem still totally confident that standard
notation for guitar is minimal to the point of disregard. I'm not
arguing that every guitarist does in fact read, but that in fact a
LARGE portion of dedicated players are familiar with notation and
numerous schools in fact emphasize it along with composers who use it.
There ARE issues about guitar notation, but they are not enough to
make it unusable. All the pieces I linked to above are presented in
standard notation, and players all over the world aspire to play these
and learn to read notation. I'm obviously a bit bullheaded but I'll
just quit this argument at this point.

Carl, I really respect your views in many areas. Particularly in
barbershop, you have helped promote clear understanding. When others
say ignorant things about barbershop such as "nobody can tune a 4:7 by
ear consistently" you help correct them. I'm just trying to do the
same here. Please consider that if you really are ignorant of
something, you should be a little more humble. At any rate, I take no
personal offense, and please do not take any yourself, I really hope I
do not seem disrespectful.

Back to the tuning discussions...

Peace,
Aaron Wolf

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@> wrote:
> > There is clearly no consistent current use of the signs
> > as meaning an exact amount sharp and not another amount.
>
> Hi Aaron W.,
>
> What are the most extreme examples you can find of different amounts
> of sharpening and flattening represented by conventional sharps and
> flats on an ordinary staff in common use? I don't mind whether you
> describe that amount in cents or as a fraction of a staff position.
>
> I find that they are quite consistent in one particular way:
> B:F# and Bb:F are always recognisable perfect fifths.
>
> -- Dave Keenan
>

Very interesting point! Hmm... how DOES MegaScore deal with this?

Waitaminit! I was a little rash all along...

I went through the MegaScore stuff and got the idea that # vs + were
for different degrees of sharping, comma level and JND level...
But I got them mixed up. I thought # was for COMMA level, and + was
JND level! That way makes more sense to me. But Aaron Hunt did it
the other way around. So now # isn't for the more substantial shift,
but for the more subtle and the + is for the more substantial...

That IS backwards from what I'm used to! Sorry for my confusion. I
need to clarify some things.

First off, I don't tend to like the entire alphabetical system, and
I'd rather think in terms of ratio and interval. The MegaScore
concept specifies those clearly enough and there is no inherent need
for translating the notation into alphabetic names, so I was ignoring
the #/b NAMING issues. I guess they are still valid concerns, but I
don't care personally much.

Then, the #/b symbols being used on the score for smaller intervals
than usual made perfect sense to me because the staff itself shows
smaller intervals than we're used to, so I thought it was sort of
proportional.

I was a little wrong, because while the regular system # symbol means
either up to the next position or half-way to the next position, in
MegaScore, it take a double-# to get to half-way.

Still, it isn't THAT bad. Basically here's what we have, roughly:

Regular system # = half-way to next position, except the odd diatonic
half-step issue.

MegaScore, # = 1/4 way to next position, x = 1/2 way to next position,
* = 3/4 to next position.

So, it isn't as comfortable an adjustment as I thought originally, but
still, look at it the RELATIVE way, instead of an absolute number of
cents and you can see that it isn't that confusing. The way to think
is that #/b means approaching the next staff position.

Sorry for my confusion, but does this make sense now?

It still does not address the alphabetic name issue, but what I like
best about MegaScore is that Aaron Hunt can quote alphabetic names and
pythagorean theory all day and I can still use MegaScore ignoring all
of that. MegaScore itself doesn't show alphabetic names, so I don't
need to bother with them. I think they are the source of the confusion.

Best,
Aaron

🔗Aaron Wolf <backfromthesilo@yahoo.com>

> > --- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@>
>
> Regular system # = half-way to next position, except the odd diatonic
> half-step issue.
>
> MegaScore, # = 1/4 way to next position, x = 1/2 way to next position,
> * = 3/4 to next position.
>

Ok, I'd like to clarify since I was still a little wrong...

In regular notation, there is ONE specified note between two staff
positions, with the exception of diatonic half-steps. That means
enharmonic sharp or flat to reach that in-between position.

In MegaScore, there are FOUR notes possible between each staff
position, hence specified by #, X, bb, b in order of raising pitch.
The triples are unnecessary because they are enharmonic with the other
symbol's doubles.

At any rate, now that I think about it this way, I still like it and
think there is no problem.

The #/b symbols are consistent because in BOTH traditional and
MegaStaff they indicate the pitch going into a range between two
un-marked staff positions. Again, think of them that way and it
doesn't seem so inconsistent.

The presentation by Aaron Hunt as these symbols representing an amount
of cents change is confusing I think.

Ok, Aaron Hunt - I have some feedback along the lines of what you
actually requested! Not a change to the system, but feedback about
your explanation web pages:

I personally feel that emphasizing the letter names and emphasizing
the amount of cents that symbols mean is confusing. I think if the
explanation first made clear the relationships between staff positions
WITHOUT the letter names, and THEN mentioned the inflections, and THEN
mentioned the shifts, that would make the visual aspect of the system
clear. All the possible positions and pitches would be clear. Then
LATER you can explain the origin and how it relates to letter names
and such, because that stuff is important of course.

In other words, instead of presenting issues of accidentals, letter
names, and triple sharps from chains of fifths - that stuff makes the
system seem confusing and complex - present the FINAL resulting way of
working FIRST, therefore showing the logic and simplicity of the
system. Then explain the complex origins and stuff later to answer
those readers who want to know how that fits in.

Hope this feedback is helpful! I'm loving the system and look forward
to the software and keyboard!

Best,
Aaron Wolf

🔗Aaron Andrew Hunt <aahunt@h-pi.com>

Hello Aaron Wolf!

I hesitate to respond as these lengthy messages begin to
create an unneccessary impression of general confusion
surrounding the notation and how it works.

I think whatever points of confusion there are can be easily
cleared up via a perusal of the web pages. The most basic
of these is that there are:

41 positions x 5 inflections (not 4) = 205 pitches.

I appreciate that it would be simpler to see the notation in
action and then then have its inner workings revealed. I've
been testing out some full-screen recording software to make
video demos of MegaScore. I also have a shockwave web
plugin of the system, but it is using the old clef symbols
so I have not included it in the website yet.

There is room for improvement in terms of exactly how the
presentation is done and I'll certainly keep your comments
in mind when I am able to make some revisions.

Thanks,
Aaron Hunt
H-Pi instruments

--- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@...> wrote:
>
>
> > > --- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@>
> >
> > Regular system # = half-way to next position, except the odd diatonic
> > half-step issue.
> >
> > MegaScore, # = 1/4 way to next position, x = 1/2 way to next position,
> > * = 3/4 to next position.
> >
>
> Ok, I'd like to clarify since I was still a little wrong...
>
> In regular notation, there is ONE specified note between two staff
> positions, with the exception of diatonic half-steps. That means
> enharmonic sharp or flat to reach that in-between position.
>
> In MegaScore, there are FOUR notes possible between each staff
> position, hence specified by #, X, bb, b in order of raising pitch.
> The triples are unnecessary because they are enharmonic with the other
> symbol's doubles.
>
> At any rate, now that I think about it this way, I still like it and
> think there is no problem.
>
> The #/b symbols are consistent because in BOTH traditional and
> MegaStaff they indicate the pitch going into a range between two
> un-marked staff positions. Again, think of them that way and it
> doesn't seem so inconsistent.
>
> The presentation by Aaron Hunt as these symbols representing an amount
> of cents change is confusing I think.
>
> Ok, Aaron Hunt - I have some feedback along the lines of what you
> actually requested! Not a change to the system, but feedback about
> your explanation web pages:
>
> I personally feel that emphasizing the letter names and emphasizing
> the amount of cents that symbols mean is confusing. I think if the
> explanation first made clear the relationships between staff positions
> WITHOUT the letter names, and THEN mentioned the inflections, and THEN
> mentioned the shifts, that would make the visual aspect of the system
> clear. All the possible positions and pitches would be clear. Then
> LATER you can explain the origin and how it relates to letter names
> and such, because that stuff is important of course.
>
> In other words, instead of presenting issues of accidentals, letter
> names, and triple sharps from chains of fifths - that stuff makes the
> system seem confusing and complex - present the FINAL resulting way of
> working FIRST, therefore showing the logic and simplicity of the
> system. Then explain the complex origins and stuff later to answer
> those readers who want to know how that fits in.
>
> Hope this feedback is helpful! I'm loving the system and look forward
> to the software and keyboard!
>
> Best,
> Aaron Wolf
>

🔗Klaus Schmirler <KSchmir@online.de>

Aaron Wolf schrieb:
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>> Oh, and
>>
>> --- "Aaron Wolf" <backfromthesilo@> wrote:
>>> Fact is, a decent portion of all published guitar music is in
>>> standard notation. >> Almost all (by sales) are transcriptions of music
>> composed on guitars, without notation.
>>
>> -Carl
>>
> > That's really not what I was talking about, sorry for the confusion,
> my fault.
> > Let me clarify this way: there exists a large number, in absolute
> terms, of published guitar music in notation that is NOT
> transcriptions of recordings or of music for other instruments. > Regardless of its proportion, this simply would not be the case if
> there were not a real market for this.

It's still different: There are vast amounts of guitar and lute pieces that weren't published in "standard notation" originally, but are now, "in transcription". One reason is that the guitar has aquired a fifth and sixth string, so the tablature has become obsolete (and I can't quite make myself say that "lute" and "present time" is an oxymoron, so ...). And maybe, for mass produced editions, the publishers don't trust their customers to check their string tunings before tackling a piece in tablature.

Another thing is that tablature doesn't indicate duration. Which means all the modern editions had to come up with plausible note values and pauses; however, this is more of a problem with organ literature.

The biggest microtonal project has of course been done in an easy and obvious mix of instrument specific tablature, color codes and approximate staff notation, plus fractions instead of note names (I'm counting the AFMM as many little projects, obviously). Proof that nobody needs neither megastaves nor sagittals nor anything else relating to post-Guidonean notation.

I was going to hold back until the Megastaff JI extensions were published, but here it is anyway: Here's one system that can depict melodic contour in an obvious way down to steps of 30 cents and there's another, nominal- and harmony-oriented one, that tries to do everything and is therefore a little complicated. Megastaff loses its visual advantage beyond 41-ET; Sagittal using the Megastaff can get rid of its coarser accidentals. The obvious idea is to combine the two.

Reintroducing these "coarse accidentals" can give you intermediate staff sizes. i.e. you may save on paper if have to learn more sagittal - and I'm sure real life will have to settle on a comprise, maybe several, between ease of reading sizewise (and not gettign distracted turning pages) and ease of reading comprehensionwise. Sagittal can make the megastaff idea so much more flexible, and megastaff can put training wheels on sagittal (an image of Hermes on a monocycle comes to mind). I know if I have to notate something microtonal again, I'll use some mix.

klaus

🔗Aaron Wolf <backfromthesilo@yahoo.com>

Sorry for all my confusion, what I was saying is that there is one
"natural" staff position, and 4 in-between positions that require
extra symbols.

Sorry I got it confused at first though. I think I've got it now...

Hope my suggestions about simply showing the working system first and
explanation afterwards prove useful.

Furthermore, feel free to use my explanation of # and b symbols as
meaning to move sharp or flat between the "natural" positions. That
explanation shouldn't actually be necessary, but obviously some people
here had an immediate negative reaction to being told immediately that
# was to mean a very small number of cents. Maybe my explanation
would've made them initially more comfortable. At any rate, it makes
sense to me!

Best,
Aaron

--- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@...> wrote:
>
> Hello Aaron Wolf!
>
> I hesitate to respond as these lengthy messages begin to
> create an unneccessary impression of general confusion
> surrounding the notation and how it works.
>
> I think whatever points of confusion there are can be easily
> cleared up via a perusal of the web pages. The most basic
> of these is that there are:
>
> 41 positions x 5 inflections (not 4) = 205 pitches.
>
> I appreciate that it would be simpler to see the notation in
> action and then then have its inner workings revealed. I've
> been testing out some full-screen recording software to make
> video demos of MegaScore. I also have a shockwave web
> plugin of the system, but it is using the old clef symbols
> so I have not included it in the website yet.
>
> There is room for improvement in terms of exactly how the
> presentation is done and I'll certainly keep your comments
> in mind when I am able to make some revisions.
>
> Thanks,
> Aaron Hunt
> H-Pi instruments
>
>
>
>
>
>
> --- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@> wrote:
> >
> >
> > > > --- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@>
> > >
> > > Regular system # = half-way to next position, except the odd
diatonic
> > > half-step issue.
> > >
> > > MegaScore, # = 1/4 way to next position, x = 1/2 way to next
position,
> > > * = 3/4 to next position.
> > >
> >
> > Ok, I'd like to clarify since I was still a little wrong...
> >
> > In regular notation, there is ONE specified note between two staff
> > positions, with the exception of diatonic half-steps. That means
> > enharmonic sharp or flat to reach that in-between position.
> >
> > In MegaScore, there are FOUR notes possible between each staff
> > position, hence specified by #, X, bb, b in order of raising pitch.
> > The triples are unnecessary because they are enharmonic with the other
> > symbol's doubles.
> >
> > At any rate, now that I think about it this way, I still like it and
> > think there is no problem.
> >
> > The #/b symbols are consistent because in BOTH traditional and
> > MegaStaff they indicate the pitch going into a range between two
> > un-marked staff positions. Again, think of them that way and it
> > doesn't seem so inconsistent.
> >
> > The presentation by Aaron Hunt as these symbols representing an amount
> > of cents change is confusing I think.
> >
> > Ok, Aaron Hunt - I have some feedback along the lines of what you
> > actually requested! Not a change to the system, but feedback about
> > your explanation web pages:
> >
> > I personally feel that emphasizing the letter names and emphasizing
> > the amount of cents that symbols mean is confusing. I think if the
> > explanation first made clear the relationships between staff positions
> > WITHOUT the letter names, and THEN mentioned the inflections, and THEN
> > mentioned the shifts, that would make the visual aspect of the system
> > clear. All the possible positions and pitches would be clear. Then
> > LATER you can explain the origin and how it relates to letter names
> > and such, because that stuff is important of course.
> >
> > In other words, instead of presenting issues of accidentals, letter
> > names, and triple sharps from chains of fifths - that stuff makes the
> > system seem confusing and complex - present the FINAL resulting way of
> > working FIRST, therefore showing the logic and simplicity of the
> > system. Then explain the complex origins and stuff later to answer
> > those readers who want to know how that fits in.
> >
> > Hope this feedback is helpful! I'm loving the system and look forward
> > to the software and keyboard!
> >
> > Best,
> > Aaron Wolf
> >
>

🔗Carl Lumma <carl@lumma.org>

🔗Graham Breed <gbreed@gmail.com>

Carl Lumma wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
> >>>>I'd argue in the case of MegaScore that sharp signs and
>>>>flat signs still mean sharp and flat.
>>>
>>>Thank you. And I'm still waiting for Dave and Graham to explain
>>>how the decimal number system isn't broken.
> > //
> >>Roman numerals make arithmetic hard.
> > > If that's true, it must be because context-switching is cheaper
> than not.

There are different levels of context switch. I'll put them in a hierarchy:

1) Unconscious pattern matching

2) Different languages

3) Different modes of operation

4) Different tasks

In order to recognize symbols you need to do (1). In many cases strings of digits are recognized this way. As are words, of course, and you could have asked how we could possibly read English fluently. It's a very difficult task after all and not one we've had time to evolve for.

Ideally, when you become expert in a notation it should all be handled by level (1). That's why I'm suggesting accidental symbols shouldn't be re-used to identify different sizes. Also why I'm trying to make different staves look different -- so that a given note at a given position on a given staff has a unique appearance.

Shifts between languages are clearly done very quickly. Bilingual people will naturally switch between languages mid-sentence, with correct pronunciation even where the two language use different sounds. If it's possible for different notations and tunings to be recognized as different languages then I'd expect that to be very efficient. Maybe Megascore versus a normal staff will do this. I don't expect it to work for different Sagittal subsets because there are too many of them.

Modes of operation are generally artificial. They can be confusing and are discouraged in interface design. It's probably inevitable that different microtonal notations will fall into this region. Hence we need to follow interface design rules and provide a clear visual clue that you're in a different mode, and make sure that mistakes caused by applying rules to the wrong mode are not fatal.

Switching between tasks is expensive, but focusing attention on a specific task is efficient. Playing different pieces or different instruments fall into this category. So musicians can be expected to use different notations for different pieces. However, certain abstractions will be shared between tasks. Switching to an obviously different notation will work but re-interpreting symbols in a subtly different way will be difficult. I'd also expect switching notations within a piece to be very difficult, unless they're recognized as distinct languages.

Now, you say you really want to know about decimal place notation, so I'll try and explain that.

Firstly, as Dave says, place arithmetic is very efficient. That works because operations on digits are the same regardless of their position. You learn arithmetic by learning rules of operations on digits, and then applying rules on combining digits.

Learning these rules is harder with Roman numerals because you have to keep learning the same rules for different symbols. Sexagesimal is good for fractions but means you have to learn a lot more rules for operating on digits (100 for pairs of decimal digits, 3600 for pairs of sexagesimal digits, ignoring symmetry). In both cases the cost is in the number of rules you have to remember, not the number of symbols. Decimal place notation gives the best mapping between symbols and concepts.

The second way we can understand decimal numbers is that we remember basic patterns, which is very similar to remembering new symbols. (And complex symbol sets are usually built out of smaller symbols anyway.) Your example of 11 is clearly in this category. I sound it out as "eleven" without a moment's thought. So it's recognized as a word. I know that 十一 refers to the same number but I have to consciously translate it into English.

Other patterns like small numbers, round numbers, "10\d" as "hundred and \d" and so on are recognized a basic patterns. Reading arbitrary large numbers is difficult and often avoided. How often to you skip over numbers when reading a text? Often the alternative is to stop and transate it into words. That requires a context shift from your usual, intuitive recognition of words.

We separate digits into groups of 3 to help pattern recognition (and provide a link to spoken language). Large numbers are often written with "m" for million, or equivalents in other languages. SI units come with standard prefixes so that you don't need numbers over a thousand. Scientific notation places only one digit to the left of the decimal point. (Digits to the right of the decimal point are easier to ignore.) Phone numbers and the like are read as a string of digits, not a big number.

I have a copy of the "Primary Framework for literacy and mathamatics" published by some branch of the UK government and available on the web somewhere. (Sorry for not being more specific -- I downloaded the PDF a few weeks back.) So I can outline the way they expect children to learn mathematics. (Note that the page numbers are off by one between the document and the PDF so I'll probably mix them up.)

There's a brief overview pp.40-41. That includes the telling sentence "A good knowledge of numbers or a 'feel' for numbers is the product of structured practice and repetition." That tells you that it's being pushed into unconscious pattern recognition, and that it isn't an easy skill to learn.

There's then a three point list. The first is very relevant:

"- recall key number facts instantly for example, all addition and subtraction facts for
each number to at least 10 (Year 2), sums and differences of multiples of 10 (Year 3) and
multiplication facts up to 10 × 10 (Year 4);"

So the first thing is to work on individual digits, then the "\d0" pattern, then multiplication of individual digits. (10 here qualifies as an honorary single digit.) They're also expected to add single digits to multiples of 10 at Year 1 and "partition two-digit numbers in different ways including into multiples of ten and one and add the tens and ones separately and then recombine (Year 2)". So they learn the place context in Year 2 so that they can work with one and two digit numbers in Year 3. At this point they still haven't progressed to three digits!

There's a table on pp.42-43 showing goals for each year. Year 1 is all 2 digits (usually starting with single digits or multiples of 10). Year 2 introduces more operations, but nothing about the sizes of the numbers. Year 3 expects multiplication and division of 2 digit numbers as well as introducing addition and subtraction of 3 digit numbers. So it takes three years to get to three digits! Year 4 is still 2 and 3 digits for whole numbers, but also introduces two decimal places for currency. It's only at Year 5 that they're expected to efficiently multiply and divide by powers of 10. Also in Year 5 they add and subtract with up to two decimal places. Much of this requires written methods, of course.

Summarizing this, it takes about five years for children to understand the subtlety of decimal place arithmetic. And along the way they learn rules for single digit operations and learn simple patterns for small and round numbers.

At the bottom of page 43 it explicitly says that you have to learn rules for single digits to "add successfully".

On page 45 it says you need to remember facts for numbers up to 20 to do efficient subtraction. Probably this means all numbers up to 20 are recognized as words.

Page 48 talks about facts for numbers up to 10 and rules for multiples of 10 for successful multiplication.

The rules for division are more complicated. They're on pp.51-52 and rely more on explicit knowledge of the place system.

I hope that answers your question :-)

>>Sure humans can extract context-dependent meaning, but it isn't cost
>>free and has to be weighed against lots of other perceptual and
>>cognitive costs.
> > Context switching is fundamental to human memory, in the way
> cortex works (see for instance Jeff Hawkins). There's nothing
> cheaper.

I belive switching between complex tasks takes around 10 seconds. Resolving ambiguous contexts within a task may be faster, but if it requires any conscious intervention it's too slow for reading music.

Graham

🔗Graham Breed <gbreed@gmail.com>

🔗Carl Lumma <carl@lumma.org>

Graham wrote...
> >>Roman numerals make arithmetic hard.
> >
> > If that's true, it must be because context-switching is cheaper
> > than not.
>
> There are different levels of context switch. I'll put them
> in a hierarchy:
>
> 1) Unconscious pattern matching
> 2) Different languages
> 3) Different modes of operation
> 4) Different tasks
>
> In order to recognize symbols you need to do (1).

According to Hawkins, you can't separate context from (1).
V1 neurons are only sensitive to things like an edge of
a particular angle in a particular minute arc of the
visual field, but the pattern of coactivation with other
neurons (a context) makes it meaningful, and so on up
the hierarchy of neurons and representations.

> Modes of operation are generally artificial. They can be
> confusing and are discouraged in interface design.

Tell it to vi users.

> I'd also expect switching
> notations within a piece to be very difficult, unless
> they're recognized as distinct languages.

What do you think about key changes? Notation stays the
same, meanings change. Right in the middle of pieces.
All the time. Truth be told, I've made plenty of mistakes
on this account.

> Firstly, as Dave says, place arithmetic is very efficient.
> That works because operations on digits are the same
> regardless of their position.

A system like Roman numerals (but really without place
value) would be even easier to add and subtract in, I
should think. The only disadvantage is it doesn't scale
well to large numbers.

> Learning these rules is harder with Roman numerals because
> you have to keep learning the same rules for different
> symbols.

The abacus is often said to be superior for arithmetic
(whether or not a physical device is used!). Perhaps you
can tell us how they are notated (if at all). It's
identical to a symbol-value system (Roman numerals without
any place cues) if each class of bead had its own symbol.

> Sexagesimal is good for fractions but means you
> have to learn a lot more rules for operating on digits (100
> for pairs of decimal digits, 3600 for pairs of sexagesimal
> digits, ignoring symmetry). In both cases the cost is in
> the number of rules you have to remember, not the number of
> symbols. Decimal place notation gives the best mapping
> between symbols and concepts.

Actually base-3 is the most efficient base in terms of
average length of numbers * distinct symbols you need to
known.

> The second way we can understand decimal numbers is that we
> remember basic patterns, which is very similar to
> remembering new symbols. (And complex symbol sets are
> usually built out of smaller symbols anyway.) Your example
> of 11 is clearly in this category. I sound it out as
> "eleven" without a moment's thought. So it's recognized as
> a word.

Ok, that stops after 19.

> Scientific notation places only one digit to the left of the
> decimal point.

It's the best way to write decimal numbers, for sure.

> I belive switching between complex tasks takes around 10
> seconds.

Switching between pattern-recognition contexts is notoriously
instantaneous for humans. It's only structured linguistic
stuff (long arguments, stories, etc.) where switching gets
hard. In fact, if you're in the middle of programming and
someone comes into your cube with a stupid question, the
disruption can be pretty serious.

> if it requires any conscious intervention it's
> too slow for reading music.

Agree. Most things that can be called a reading task can
be made unconsious with enough training. It's very poorly
understood what can make this training easier or harder (if
anything).

-Carl

🔗Graham Breed <gbreed@gmail.com>

Carl Lumma wrote:
> Graham wrote...

>>There are different levels of context switch. I'll put them >>in a hierarchy:
>>
>>1) Unconscious pattern matching
>>2) Different languages
>>3) Different modes of operation
>>4) Different tasks
>>
>>In order to recognize symbols you need to do (1).
> > According to Hawkins, you can't separate context from (1).
> V1 neurons are only sensitive to things like an edge of
> a particular angle in a particular minute arc of the
> visual field, but the pattern of coactivation with other
> neurons (a context) makes it meaningful, and so on up
> the hierarchy of neurons and representations.

Makes sense. That's why I put it in a list of context switches.

>>Modes of operation are generally artificial. They can be >>confusing and are discouraged in interface design.
> > Tell it to vi users.

I mentioned that as an exception before. It'd be a hard sell if it were a new application. I count it as an illustration of how interface guidelines focus on ease of learning rather than efficiency of use. Probably it works anyway because whether you're typing text or not sits in your short term memory. My strategy is to leave it in command mode by default and switch to insert mode for only as long as it takes to change something. I do make mistakes.

Another thing vi may be an example of is how you overvalue a skill that's difficult to acquire ;-) I honestly haven't seen any data on efficiency of different text editors but I'd be interested to.

>>I'd also expect switching >>notations within a piece to be very difficult, unless >>they're recognized as distinct languages.
> > What do you think about key changes? Notation stays the
> same, meanings change. Right in the middle of pieces.
> All the time. Truth be told, I've made plenty of mistakes
> on this account.

As regards key signatures, I probably think what you think. They're difficult to learn, disruptive, and a classic cause of errors. But they're not a critical flaw in the system and musicians have to get used to them. I hope they're forbidden in microtonal contexts.

>>Firstly, as Dave says, place arithmetic is very efficient. >>That works because operations on digits are the same >>regardless of their position.
> > A system like Roman numerals (but really without place
> value) would be even easier to add and subtract in, I
> should think. The only disadvantage is it doesn't scale
> well to large numbers.

Roman numerals can't be that bad or they wouldn't have lasted as long. But how about multiplication? Division? "Decimal" fractions?

>>Learning these rules is harder with Roman numerals because >>you have to keep learning the same rules for different >>symbols.
> > The abacus is often said to be superior for arithmetic
> (whether or not a physical device is used!). Perhaps you
> can tell us how they are notated (if at all). It's
> identical to a symbol-value system (Roman numerals without
> any place cues) if each class of bead had its own symbol.

I could probably find some books if you're really interested. I think there is a notation.

>>Sexagesimal is good for fractions but means you >>have to learn a lot more rules for operating on digits (100 >>for pairs of decimal digits, 3600 for pairs of sexagesimal >>digits, ignoring symmetry). In both cases the cost is in >>the number of rules you have to remember, not the number of >>symbols. Decimal place notation gives the best mapping >>between symbols and concepts.
> > Actually base-3 is the most efficient base in terms of
> average length of numbers * distinct symbols you need to
> known.

In an abstract, mathematical sense that assumes distinct symbols are a bad thing.

>>The second way we can understand decimal numbers is that we >>remember basic patterns, which is very similar to >>remembering new symbols. (And complex symbol sets are >>usually built out of smaller symbols anyway.) Your example >>of 11 is clearly in this category. I sound it out as >>"eleven" without a moment's thought. So it's recognized as >>a word.
> > Ok, that stops after 19.

Not immediately. How far it goes depends on the individual. AFMM performers will probably recognize patterns for numbers up to 50. Various larger numbers, like 2008, will be recognized as well.

> Switching between pattern-recognition contexts is notoriously
> instantaneous for humans. It's only structured linguistic
> stuff (long arguments, stories, etc.) where switching gets
> hard. In fact, if you're in the middle of programming and
> someone comes into your cube with a stupid question, the
> disruption can be pretty serious.

Right. That's why I want notation to be pure pattern recognition rather than task-based context. Sharing symbols between Pythagorean and meantone suggests the latter.

>>if it requires any conscious intervention it's >>too slow for reading music.
> > Agree. Most things that can be called a reading task can
> be made unconsious with enough training. It's very poorly
> understood what can make this training easier or harder (if
> anything).

I certainly don't want to dictate anything. I'll bow to the experience of musicians who learn these systems.

Graham

🔗Carl Lumma <carl@lumma.org>

> >>Modes of operation are generally artificial. They can be
> >>confusing and are discouraged in interface design.
> >
> > Tell it to vi users.
>
> I mentioned that as an exception before. It'd be a hard
> sell if it were a new application. I count it as an
> illustration of how interface guidelines focus on ease of
> learning rather than efficiency of use. Probably it works
> anyway because whether you're typing text or not sits in
> your short term memory. My strategy is to leave it in
> command mode by default and switch to insert mode for only
> as long as it takes to change something. I do make mistakes.
>
> Another thing vi may be an example of is how you overvalue a
> skill that's difficult to acquire ;-)

That is a real effect. :)
I'm not a vi user, though I can get by with it.

> > A system like Roman numerals (but really without place
> > value) would be even easier to add and subtract in, I
> > should think. The only disadvantage is it doesn't scale
> > well to large numbers.
>
> Roman numerals can't be that bad or they wouldn't have
> lasted as long. But how about multiplication? Division?

There are apparently very good algorithms to do these on
an abacus, and I assume they would translate to a Roman
numeral -like number system. Multiplication isn't easy
in decimal -- you memorize at least 45 "facts". I assume
there are similar facts for Roman numerals.

> "Decimal" fractions?

Don't know what these are.

> >>Sexagesimal is good for fractions but means you
> >>have to learn a lot more rules for operating on digits (100
> >>for pairs of decimal digits, 3600 for pairs of sexagesimal
> >>digits, ignoring symmetry). In both cases the cost is in
> >>the number of rules you have to remember, not the number of
> >>symbols. Decimal place notation gives the best mapping
> >>between symbols and concepts.
> >
> > Actually base-3 is the most efficient base in terms of
> > average length of numbers * distinct symbols you need to
> > known.
>
> In an abstract, mathematical sense that assumes distinct
> symbols are a bad thing.

It's optimal for radix * base, or no weighting. Plug in
some weights from some old cog psych papers and away you go.

-Carl

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

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@> wrote:
> > Well, nobody said you *have* to use the doubles, and the triples are
> > there only for enharmonic flexibility. Intervals in the 13-limit
from a
> > natural inflected root require only sharp and flat inflections.
>
> Hey that's neat!
>
> > > And the fact that these doubles
> > > do not move you to (anywhere near) the next staff position as
they do
> > > in conventional notation.
> >
> >
> > One JND away from the next position nowhere near?
>
> I'm confused now. I thought a double-sharp or double-flat moved you
> only 2 JND's and I thought there were 5 JND's between staff positions.
>
> That they _should_ move you 4 JND's is exactly what I've been
suggesting.
>
> -- Dave
>

My way of explaining now is this:

Double-sharps and double-flats do, as you originally thought, move
only 2 JNDs. But there are not 5 JNDs between positions, there are 5
TOTAL. Hence 4 that are between positions. What is new is the
elimination of enharmonic symbols, something that is a major
improvement in my mind. So instead of sharps and flats overlapping,
the sharps are raising up from the lower note, and the flats come down
from the upper one.

Think about it this way, let's say you took regular staff and said
that you simply wanted to split C to D to have two in-betweens instead
of one, you make the lower one C# and the upper one Db, any complaints
about that? Then say you wanted another two notes, each between C and
C# and between Db and D. At that point if we treat the symbols as a
generally absolute amount, you might want to say C-half-#, and C#.
But if we treat the symbols as moving to the next degree, then we have
as Aaron Hunt chose, C# and CX, Dbb, Db. As much as this isn't the
way you were used to thinking, double-sharps and double-flats are so
rare in standard notation that I don't think there's comfort with them
among most musicians really. I think it is just as likely for a
musician reading standard notation to see C# and think "the next note
just after C" as to think "in between C and D."

In the end, of course it is a departure from standard, but clearly the
whole thing is. Nobody would see MegaScore and think that they don't
have to learn anything new. The important thing is that within
MegaScore, everything is consistent.

-The Wolf

🔗Graham Breed <gbreed@gmail.com>

🔗Klaus Schmirler <KSchmir@online.de>

Aaron Wolf schrieb:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>> --- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@> wrote:
>>> Well, nobody said you *have* to use the doubles, and the triples are
>>> there only for enharmonic flexibility. Intervals in the 13-limit
> from a >>> natural inflected root require only sharp and flat inflections.
>> Hey that's neat!
>>
>>>> And the fact that these doubles
>>>> do not move you to (anywhere near) the next staff position as
> they do
>>>> in conventional notation.
>>>
>>> One JND away from the next position nowhere near?
>> I'm confused now. I thought a double-sharp or double-flat moved you
>> only 2 JND's and I thought there were 5 JND's between staff positions.
>>
>> That they _should_ move you 4 JND's is exactly what I've been
> suggesting.
>> -- Dave
>>
> > My way of explaining now is this:
> > Double-sharps and double-flats do, as you originally thought, move
> only 2 JNDs. But there are not 5 JNDs between positions, there are 5
> TOTAL. Hence 4 that are between positions. What is new is the
> elimination of enharmonic symbols, something that is a major
> improvement in my mind. So instead of sharps and flats overlapping,
> the sharps are raising up from the lower note, and the flats come down
> from the upper one.
> > Think about it this way, let's say you took regular staff and said
> that you simply wanted to split C to D to have two in-betweens instead
> of one, you make the lower one C# and the upper one Db, any complaints
> about that? Then say you wanted another two notes, each between C and
> C# and between Db and D. At that point if we treat the symbols as a
> generally absolute amount, you might want to say C-half-#, and C#. > But if we treat the symbols as moving to the next degree, then we have
> as Aaron Hunt chose, C# and CX, Dbb, Db. As much as this isn't the
> way you were used to thinking, double-sharps and double-flats are so
> rare in standard notation that I don't think there's comfort with them
> among most musicians really. I think it is just as likely for a
> musician reading standard notation to see C# and think "the next note
> just after C" as to think "in between C and D."
> > In the end, of course it is a departure from standard, but clearly the
> whole thing is. Nobody would see MegaScore and think that they don't
> have to learn anything new. The important thing is that within
> MegaScore, everything is consistent.
> > -The Wolf

Something must be very wrong with the description.

The way I understood it,

- a single accidental takes you 1 JND away _from the note it is attached to_

- triple accidentals are enharmonic and take you halfway to the next note.

Waiting for the official solution ... and more interpretations.

klaus

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Carl Lumma wrote:
>
> > I still don't think we're communicating. I was trying to
> > make a point about notation, which I tried again to state
> > at the bottom of the message prior to the one you're replying
> > to here. If anything, it is made stronger by the earlier
> > existence of a notation-based guitar school -- the guitar
> > only rose to prominence after a new school, which disregarded
> > the previous one, came about.
>
> It rose to prominence in the world as a whole because it was
> an established folk instrument in the USA, and the USA
> became the world's cultural center (especially for popular
> culture). It's long been popular in the folk and classical
> music of Spain. The USA happens to be on the fringe of the
> Hispanic world, but strongly influenced by the core European
> tradition for classical music.
>
> Amplification also helps.
>
>
> Graham
>

Right, my point all along is that, Carl, you have been too swift to
make conclusions about notation and its place or lack thereof in the
prominence of the guitar. There are so many other social factors at
work. Technology, recording, those are the main killers of notation,
because we now have other ways to remember or learn music. Nearly all
instruments have had a degree of decrease in notation use thanks to
recording and other technology.
My point in proving substantial notation use in the guitar world was
to show that, acknowledging issues about guitar notation, we cannot
assume that standard notation is guitar incompatible. It simply isn't
true. And no percent, including 100, of guitarist playing being
non-notation based proves that completely, it is only one piece of
evidence.

The fact that I can pick up all sorts of standard notation and play it
on my guitar is proof enough that it IS compatible.

Carl, you still never addressed my voice analogy really. Most singers
do not read. That does not prove incompatibility with notation.

The real point is that we're trying to identify the purpose or
supposed need of notation, and these examples DO prove that notation
is not absolutely necessary for performance or for composition. So
the question is, what DO we need notation for? OR even do we at all?
Answering this question allows us to evaluate the importance of
notational decisions. If we decide that notation isn't needed for
performers, because we can present them some instrument specific notes
and recorded audio to study by ear, then we can forget any concerns
about performance reading when discussing a notation system. So,
let's answer that question: what are we notating for? What's the point?

I'll say in my case that the biggest interest for me is for composing,
not for scoring for instruments.

Best,
The Wolf

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Aaron Wolf wrote:
>
> > Think about it this way, let's say you took regular staff and said
> > that you simply wanted to split C to D to have two in-betweens instead
> > of one, you make the lower one C# and the upper one Db, any complaints
> > about that? Then say you wanted another two notes, each between C and
> > C# and between Db and D. At that point if we treat the symbols as a
> > generally absolute amount, you might want to say C-half-#, and C#.
> <snip>
>
> Well, that's how the regular staff works out in meantone --
> and therefore how it worked for a significant part of music
> history. I believe there's evidence that it confuses
> musicians to switch between different interpretations, which
> is why I suggested distinct symbols for different cases in
> sagittal. (The half-sharps give 31-equal.)
>
>
> Graham
>

First, are you saying that there exists a history of real use of
half-sharp during times when meantone was popular?

Anyway, with half and full instead of single and double... then we are
specifying sharp as a certain amount and saying you can be double or
half or even other proportions of that. Melodically, there is no
reason to specify that way. Within the comma distance of MegaScore's
staff positions there is absolutely *nothing* that will make the ear
feel like "ah, here we are at exactly the sharp" vs "sounds like we're
approaching the sharp position." These movements are ALL too small
for that, so there is no perceptual reason to specify an amount in
between a comma as the WHOLE unit to which other amounts are compared.

Instead, having sharp mean the next higher possible tone is logical
and consistent.

In other words, half-sharp implies a half-way to something we'd
recognize as fully arrived. None of the JND positions between commas
in MegaScore have the potential to be so clearly perceived the way
entire traditional half-steps can. So, I'm suggesting that this rules
out the idea of specifying sharp by a certain amount.

Returning to my original idea, think of sharp as an ORDINAL symbol,
not an absolute one.

Peace,
The Wolf

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, Klaus Schmirler <KSchmir@...> wrote:
>
> Aaron Wolf schrieb:
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
> >> --- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@> wrote:
> >>> Well, nobody said you *have* to use the doubles, and the triples are
> >>> there only for enharmonic flexibility. Intervals in the 13-limit
> > from a
> >>> natural inflected root require only sharp and flat inflections.
> >> Hey that's neat!
> >>
> >>>> And the fact that these doubles
> >>>> do not move you to (anywhere near) the next staff position as
> > they do
> >>>> in conventional notation.
> >>>
> >>> One JND away from the next position nowhere near?
> >> I'm confused now. I thought a double-sharp or double-flat moved you
> >> only 2 JND's and I thought there were 5 JND's between staff
positions.
> >>
> >> That they _should_ move you 4 JND's is exactly what I've been
> > suggesting.
> >> -- Dave
> >>
> >
> > My way of explaining now is this:
> >
> > Double-sharps and double-flats do, as you originally thought, move
> > only 2 JNDs. But there are not 5 JNDs between positions, there are 5
> > TOTAL. Hence 4 that are between positions. What is new is the
> > elimination of enharmonic symbols, something that is a major
> > improvement in my mind. So instead of sharps and flats overlapping,
> > the sharps are raising up from the lower note, and the flats come down
> > from the upper one.
> >
> > Think about it this way, let's say you took regular staff and said
> > that you simply wanted to split C to D to have two in-betweens instead
> > of one, you make the lower one C# and the upper one Db, any complaints
> > about that? Then say you wanted another two notes, each between C and
> > C# and between Db and D. At that point if we treat the symbols as a
> > generally absolute amount, you might want to say C-half-#, and C#.
> > But if we treat the symbols as moving to the next degree, then we have
> > as Aaron Hunt chose, C# and CX, Dbb, Db. As much as this isn't the
> > way you were used to thinking, double-sharps and double-flats are so
> > rare in standard notation that I don't think there's comfort with them
> > among most musicians really. I think it is just as likely for a
> > musician reading standard notation to see C# and think "the next note
> > just after C" as to think "in between C and D."
> >
> > In the end, of course it is a departure from standard, but clearly the
> > whole thing is. Nobody would see MegaScore and think that they don't
> > have to learn anything new. The important thing is that within
> > MegaScore, everything is consistent.
> >
> > -The Wolf
>
> Something must be very wrong with the description.
>
> The way I understood it,
>
> - a single accidental takes you 1 JND away _from the note it is
> attached to_
>
> - triple accidentals are enharmonic and take you halfway to the next
> note.
>
> Waiting for the official solution ... and more interpretations.
>
> klaus
>

Klaus,

Look it over again. The order is:

Natural
b
bb
##
#
Natural

That gives a total of 5 JNDs if we include the natural. 5x41=205,
that's the whole system. Triples are unnecessary, and are not
enharmonic with each other, but enharmonic with the opposite DOUBLE.

http://www.h-pi.com/megastaff/inflections.html
See the parts marked "Essential Inflections" and "Nonessential
Inflections"

Best,
Wolf

🔗Aaron Wolf <backfromthesilo@yahoo.com>

🔗Carl Lumma <carl@lumma.org>

🔗Aaron Wolf <backfromthesilo@yahoo.com>

🔗Herman Miller <hmiller@IO.COM>

Graham Breed wrote:
> Modes of operation are generally artificial. They can be > confusing and are discouraged in interface design. It's > probably inevitable that different microtonal notations will > fall into this region. Hence we need to follow interface > design rules and provide a clear visual clue that you're in > a different mode, and make sure that mistakes caused by > applying rules to the wrong mode are not fatal.

The idea of having a special notation for each tuning system has some attractive points. You could have the spacing between staff lines based on the intervals in your basic scale. Each notation system would have to be learned individually, but similar problems exist with applying a singla notation system (HEWM, Sagittal, or whatever) to a temperament or to a scale that doesn't correspond with JI. Still, even basic skills such as recognizing intervals would have to be relearned.

One of the things I like about the compound-nominal system, or the equivalent system with differently shaped note heads, is that you can easily see which notes are the basic scale of the tuning system, and thus have a pretty good idea which tuning system you're dealing with. You can get a pretty good idea of the size of intervals, but they still need to be learned for each notation system. A D-major triad in my notation for lemba temperament is D F^ )!!(A^.

With a more standard Sagittal notation, on the other hand, at least some of the basic intervals will be recognizable -- you can write D F||\ A for a D major triad. You do run into comma issues with any temperament, but that's the nature of temperament. Start with a D F||\ A C!) tetrad in lemba -- you can go down a major third from D to B!!/, then down a fifth to E!!/, or you can go up a major third from C!) to E\!). But E!!/ and E\!) are the same pitch in lemba. So you can either pick one and stick with it, or change the spelling of the note based on context.

On the whole, my current thinking is that the advantages of a consistent Sagittal notation for most temperaments outweighs the difficulty of the comma issues. But for a performer, having to learn a different pitch for every note in every different tuning system would be a huge mess. So it'll probably end up being necessary to use cents notation or something similar to remind the performer what pitch to use.

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

--- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@...> wrote:
> Sorry I'm late to this reply, but I just wanted to say I actually
> agree. But the reason I still like MegaScore currently is because I
> don't see the signs as having conflicting meanings. I see # as
> meaning pitch is raised to next note, and because I never learned
> sagital, I never identified a particular amount of raising with the
> symbol #,

Sagittal doesn't fix the amount of raising associated with #. It only
specifies that if # is used at all, then F C G D A E B F# should be a
chain of fifths whose size is within the range of 4/7 to 3/5 of an
octave (686 to 720 cents), and that that fifth size should be given at
the start of the score (or part).

Conventional notation fixes the meaning of # far more narrowly.

> and instead thought of the amount as a result of the tuning
> being used. Hence, when using 205ET, # is a tiny JND, when using
> 41ET, # is a comma, when using 12ET, # is a traditional half-step,
> etc etc. There's no reason in my mind to think of that symbol as a
> particular amount, it just means, going sharp. And so then double-#
> means I did that twice. Isn't that totally logical?
> -Aaron Wolf

It _would_ be logical, i.e. it would be a consistent generalisation.
But I hope you don't think that's what Megascore actually does.

At the 41-ET level, when it uses a sharp to the right of the letter
nominal, (in text or speech, not on the staff), these are worth 4
steps of 41-ET, not 1 step.

So in this case it uses the same generalisation that sagittal uses,
namely that Bb:F and F#:B are perfect fifths. This is the same
generalisation that has been used throughout western history as
tunings changed between Pythagorean, meantone and 12-ET.

Megascore does _not_ use # when the pitch is changed by a comma as you
suggest above. It uses a plus sign + which it calls "super".
See http://www.h-pi.com/megastaff/shifts.html

So we're still struggling to find _any_ kind of consistency between
the common use of sharp and both of its different uses in Megascore,
other than the crude fact that it always refers to some kind of
raising of pitch.

-- Dave Keenan

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

--- In tuning@yahoogroups.com, Klaus Schmirler <KSchmir@...> wrote:
> Something must be very wrong with the description.
>
> The way I understood it,
>
> - a single accidental takes you 1 JND away _from the note it is
> attached to_
>
> - triple accidentals are enharmonic and take you halfway to the next
> note.
>
> Waiting for the official solution ... and more interpretations.

Hi Klaus,

Clearly there are 5 JNDs between staff positions as 205 = 41 * 5. So
your first statement above must be correct, except that Aaron doesn't
call them "accidentals" but "inflections".

Your second statement is only approximately correct. A triple must
take you just past halfway, i.e. 3/5 of the way. So "triple-sharp G"
is enharmonic with "double-flat super G".

I made the same mistake myself earlier. I got mixed up between the
fact that there are 4 staff positions to a sharp "accidental", but
there are 5 "inflection" sharps to a staff position.

I also got confused between the fact that the 5-comma (and the 7-comma
for that matter) is best approximated by 4 JNDs, but the difference
between staff positions is referred to as a comma even though it is 5
JNDs (29.3 cents), quite validly I might add, because it does
correspond to the 3-comma (pythagorean) in this temperament.

What's also confusing is that I recently wrote:
>> And the fact that these doubles
>> do not move you to (anywhere near) the next staff position as they
>> do in conventional notation.

And Aaron H. mysteriously replied:
> One JND away from the next position nowhere near?

before taking his leave from the list.

In fact it would be 3 JNDs away from the next staff position.

The obvious reading of this is that Aaron H. has made the very mistake
that I was claiming (and he was denying) that people would make.

But it is very difficult for me to believe that the notation's
designer could make such a mistake. So Aaron H., please explain.

-- Dave Keenan

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

🔗Aaron Wolf <backfromthesilo@yahoo.com>

Dear Dave,

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "Aaron Wolf" backfromthesilo@ wrote:
> > Sorry I'm late to this reply, but I just wanted to say I actually
> > agree. But the reason I still like MegaScore currently is because I
> > don't see the signs as having conflicting meanings. I see # as
> > meaning pitch is raised to next note, and because I never learned
> > sagital, I never identified a particular amount of raising with the
> > symbol #,
>
> Sagittal doesn't fix the amount of raising associated with #. It only
> specifies that if # is used at all, then F C G D A E B F# should be a
> chain of fifths whose size is within the range of 4/7 to 3/5 of an
> octave (686 to 720 cents), and that that fifth size should be given at
> the start of the score (or part).
>

That's fine, but it is then specified a different way from my statement.
But I still maintain that my view is no more of a departure from
standard notation. The two views we have are each taking a different
aspect of the way the symbol works in standard notation. Anyone who
thinks more in relative terms and less in terms of absolutes like letter
names will relate to my way of seeing the symbol.

> Conventional notation fixes the meaning of # far more narrowly.
>
> > and instead thought of the amount as a result of the tuning
> > being used. Hence, when using 205ET, # is a tiny JND, when using
> > 41ET, # is a comma, when using 12ET, # is a traditional half-step,
> > etc etc. There's no reason in my mind to think of that symbol as a
> > particular amount, it just means, going sharp. And so then double-#
> > means I did that twice. Isn't that totally logical?
> > -Aaron Wolf
>
> It _would_ be logical, i.e. it would be a consistent generalisation.
> But I hope you don't think that's what Megascore actually does.
>

No, I meant that as logically what would happen with different
notations, each based on a different tuning, MegaScore being based on
205ET.

> At the 41-ET level, when it uses a sharp to the right of the letter
> nominal, (in text or speech, not on the staff), these are worth 4
> steps of 41-ET, not 1 step.
>

NOPE, that is why I suggested Aaron Hunt explain things differently.
His THEORY does in fact do that with the right of a letter # issue,
however MegaScore *does not*. Megascore never uses any # symbol to the
right of a note. How one chooses to analysis the notes on staff and
whether you want to write letter names for the notes is up to you and is
not part of MegaScore, just part of Aaron Hunt's theories that led to
developing it. I never intend to use such confusing names, which
inevitably end up with double and triple accidentals and are overall
totally confusing because they emphasize some sort of deference to a
scale of 7, which I don't intend to necessarily relate to.

Again, the use of # and b as note-names only exists in Aaron Hunt's
explanation and his discussion. It is not anywhere on the score itself.
We don't need to use letter names at all to use MegaScore. Hence, the
score itself only uses the symbols for JND movements, and only in the
logical way I describe above.

> So in this case it uses the same generalisation that sagittal uses,
> namely that Bb:F and F#:B are perfect fifths. This is the same
> generalisation that has been used throughout western history as
> tunings changed between Pythagorean, meantone and 12-ET.
>
> Megascore does _not_ use # when the pitch is changed by a comma as you
> suggest above. It uses a plus sign + which it calls "super".
> See http://www.h-pi.com/megastaff/shifts.html
>

Once again, the system does not actually really need or include these AT
ALL. They are included in Aaron Hunt's suggested naming for the symbols
on the staff. I myself, may or may not choose to think about those
names. I could just as easily think in terms of "thirds" or in terms of
ratios or cents. Or I could use a whole new set of names that includes
more letters of the alphabet.

You could go ahead and use whatever names you want. MegaScore itself
does not show these symbols on the score.

> So we're still struggling to find _any_ kind of consistency between
> the common use of sharp and both of its different uses in Megascore,
> other than the crude fact that it always refers to some kind of
> raising of pitch.
>

Again, the score itself uses the symbols only ONE single consistent way,
to show a movement to the very next available notated pitch.
I think a good amount of your confusion (mine too originally) comes from
issues in the way Aaron Hunt explained MegaScore. He was attempting to
justify the system by explaining its pythagorean and alphabetic roots in
theory. He went ahead and showed you where you would put these letter
names on the staff, and he showed a suggested naming for notes in
between. But none of these things are actually on the staff! The
symbols that actually go on the staff are completely logical and
consistent.

I will consider thinking about the names as Aaron H suggests and try not
to be close-minded, but as far as I'm concerned, my desire is to use
MegaScore to completely get away from the confusion of these alphabetic
names. And it should work, because there is no required connection. I
might as well use Do Re Mi and add extra names like Du and Ru instead of
the awful alphabet system. All of that is independent of the MegaScore
staff.

Hope that helps clarify. Do go review his pages again if you doubt what
I'm saying. My position is I have criticism of Aaron Hunt's
explanations and presentation. But MegaScore as I've seen so far is
fine.

In Harmony,
Aaron Wolf

🔗Aaron Wolf <backfromthesilo@yahoo.com>

Dave, I hope I can try to clarify, and I hope my own initial
misunderstanding was not part of the confusion...

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

>
> Clearly there are 5 JNDs between staff positions as 205 = 41 * 5. So
> your first statement above must be correct, except that Aaron doesn't
> call them "accidentals" but "inflections".
>

The FIVE include one natural, so there are only 4 that need inflection
symbols.

> Your second statement is only approximately correct. A triple must
> take you just past halfway, i.e. 3/5 of the way. So "triple-sharp G"
> is enharmonic with "double-flat super G".

That is correct.

> I also got confused between the fact that the 5-comma (and the 7-comma
> for that matter) is best approximated by 4 JNDs, but the difference
> between staff positions is referred to as a comma even though it is 5
> JNDs (29.3 cents), quite validly I might add, because it does
> correspond to the 3-comma (pythagorean) in this temperament.
>

A very good point!

> What's also confusing is that I recently wrote:
> >> And the fact that these doubles
> >> do not move you to (anywhere near) the next staff position as they
> >> do in conventional notation.
>
> And Aaron H. mysteriously replied:
> > One JND away from the next position nowhere near?
>
> before taking his leave from the list.
>
> In fact it would be 3 JNDs away from the next staff position.
>

It would include 3 JNDs to arrive at the next "natural" staff
position, yes. Maybe Mr. Hunt meant that it was one JND right next to
a note that would be ON the next staff position, although with
inflections of a double.
In other words, a X (double-sharp) would be only one JND away from a
note on the next staff position that itself had a bb.

Again, I don't think this is an issue with the MegaScore staff system,
but with Aaron Hunt's explanations. Instead of his trying to argue
with you about how close a double inflection gets you, I think my
argument makes more sense. The inflection symbols move you toward the
next position, and a double moves you two steps toward. It happens
there are 5 total steps, including the natural. I don't see a problem
with the double-inflection not being right near the next natural

That make sense?

-The Wolf

🔗Klaus Schmirler <KSchmir@online.de>

🔗Aaron Wolf <backfromthesilo@yahoo.com>

🔗Carl Lumma <carl@lumma.org>

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

--- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@...> wrote:
>
> Dave, I hope I can try to clarify, and I hope my own initial
> misunderstanding was not part of the confusion...

No, it wasn't.

> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@> wrote:
>
> >
> > Clearly there are 5 JNDs between staff positions as 205 = 41 * 5. So
> > your first statement above must be correct, except that Aaron doesn't
> > call them "accidentals" but "inflections".
> >
>
> The FIVE include one natural, so there are only 4 that need inflection
> symbols.

Ah! You're apparently taking a JND to be a pitch, whereas I take it be
a difference between pitches. i.e. The distance between fenceposts,
not the fenceposts themselves. Given that, we are in agreement.

> > What's also confusing is that I recently wrote:
> > >> And the fact that these doubles
> > >> do not move you to (anywhere near) the next staff position as they
> > >> do in conventional notation.
> >
> > And Aaron H. mysteriously replied:
> > > One JND away from the next position nowhere near?
> >
> > before taking his leave from the list.
> >
> > In fact it would be 3 JNDs away from the next staff position.
> >
>
> It would include 3 JNDs to arrive at the next "natural" staff
> position, yes. Maybe Mr. Hunt meant that it was one JND right next to
> a note that would be ON the next staff position, although with
> inflections of a double.
> In other words, a X (double-sharp) would be only one JND away from a
> note on the next staff position that itself had a bb.

That possible reading ocurred to me too and I was about to raise it
myself. One of my favourite philosophers, Daniel Dennet says we should
always try very hard to put the best possible reading on our opponents
statements.

But in this case, my point still stands since we must adopt the same
definition of "next staff position" for both the conventional and
megastaff, for a comparison to be valid.

So by that definition, a single sharp moves us to the "next staff
position" on the conventional staff, while it requires a double-sharp
on the megastaff.

> Again, I don't think this is an issue with the MegaScore staff system,
> but with Aaron Hunt's explanations. Instead of his trying to argue
> with you about how close a double inflection gets you, I think my
> argument makes more sense. The inflection symbols move you toward the
> next position, and a double moves you two steps toward. It happens
> there are 5 total steps, including the natural. I don't see a problem
> with the double-inflection not being right near the next natural

Yes. It can be viewed that way.

But there is nothing visible to remind you that there are 5 steps
between megastaff positions and you have spent most of your musical
education with there being typically two steps between staff positions.

Now you can say that this doesn't matter, and I won't argue further
about that, but Aaron H. seemed to be saying that my conclusion was
not merely immaterial, but wrong -- that I was mathematically in error.

So I remain uncertain about what he really did mean. But hey, I can
live with that.

-- Dave

🔗Aaron Wolf <backfromthesilo@yahoo.com>

🔗Graham Breed <gbreed@gmail.com>

Dave Keenan wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> >>Well, that's how the regular staff works out in meantone -- >>and therefore how it worked for a significant part of music >>history. I believe there's evidence that it confuses >>musicians to switch between different interpretations, which >>is why I suggested distinct symbols for different cases in >>sagittal. (The half-sharps give 31-equal.)
> > Hi Graham,
> > The beauty of it is, this _can_ be done in sagittal, and if it were to
> be clearly preferred by musicians we would be happy to declare it the
> standard. It would be great if you would make up a web page showing
> your proposed alternative sagittal notation for meantones and
> describing its advantages. I'd be happy to link to it from the main
> sagittal website, or even put it there if you prefer.

I would do that, but I don't know how to get the musical examples typeset. I use LaTeX and I know there are ways of using it for music so one day I'll get round to learning them.

My suggestion, anyway, is very simple: change the default # and b symbols for meantones. Let's say ||\ as a compromise between Bb-F as a 3:2 and A-C# as a 5:4.

I'm also thinking about magic, and maybe this colours my reasoning. The 19 note magic scale should be notated consistently with the 19 note meantone scale. But it can't be identical because there's no string of 7 notes separated by perfect fifths to be the nominals. So I want to base magic on a 5-limit notation while having it look as much as possible as meantone. Which by the law of the excluded middle means that meantone has to be consistent with 5-limit JI.

I suppose magic and pythagorean notations should also unify on 41-equal.

Now, the web page *I* would like to see is a comparison of sagittal with the Extended Helmholtz-Ellis JI system. The latter is horribly complex from what I've seen. I want to know if that's a problem with the notation or inherent in high-limit JIs.

Graham

🔗Graham Breed <gbreed@gmail.com>

Herman Miller wrote:
> Graham Breed wrote:
> >>Modes of operation are generally artificial. They can be >>confusing and are discouraged in interface design. It's >>probably inevitable that different microtonal notations will >>fall into this region. Hence we need to follow interface >>design rules and provide a clear visual clue that you're in >>a different mode, and make sure that mistakes caused by >>applying rules to the wrong mode are not fatal.
> > The idea of having a special notation for each tuning system has some > attractive points. You could have the spacing between staff lines based > on the intervals in your basic scale. Each notation system would have to > be learned individually, but similar problems exist with applying a > singla notation system (HEWM, Sagittal, or whatever) to a temperament or > to a scale that doesn't correspond with JI. Still, even basic skills > such as recognizing intervals would have to be relearned.

It's worth having a special notation for a system if you're going to use that system a lot. With sagittal you can make each special notation a special case of a general notation. That should work if the same symbol isn't used in different contexts for confusingly different intervals. (How different is confusing can only be determined by experience, but let's at least preserve pitch contours between different systems.) It needn't mean each individual system is any more complicated than it would have been if designed in isolation (except where it doesn't fit 7 nominals).

<snip>
> On the whole, my current thinking is that the advantages of a consistent > Sagittal notation for most temperaments outweighs the difficulty of the > comma issues. But for a performer, having to learn a different pitch for > every note in every different tuning system would be a huge mess. So > it'll probably end up being necessary to use cents notation or something > similar to remind the performer what pitch to use.

Using cents notation would mean training musicians in cents notation, so why bother with sagittal? I expect the problems can be solved withing sagittal, anyway. Maybe use two accidentals for each note, a big one for the simple meaning and a small one for the precise shift relative to either the simple one or the original natural. Exactly what works, again, to be determined by experience.

Graham

🔗Graham Breed <gbreed@gmail.com>

Aaron Wolf wrote:
>>I'm arguing that the brain finds it easier to learn new >>symbols than to give conflicting meanings to old symbols. I >>believe there is a scientific basis for this but, alas, no >>reference. I am still arguing for retaining existing >>symbols with their existing meanings. > > Sorry I'm late to this reply, but I just wanted to say I actually
> agree. But the reason I still like MegaScore currently is because I
> don't see the signs as having conflicting meanings. I see # as
> meaning pitch is raised to next note, and because I never learned
> sagital, I never identified a particular amount of raising with the
> symbol #, and instead thought of the amount as a result of the tuning
> being used. Hence, when using 205ET, # is a tiny JND, when using
> 41ET, # is a comma, when using 12ET, # is a traditional half-step, etc
> etc. There's no reason in my mind to think of that symbol as a
> particular amount, it just means, going sharp. And so then double-#
> means I did that twice. Isn't that totally logical?

It's entirely logical, but I think it'd be destructive in practice. For a performer, a # symbol is a message that tells you to raise the note by a certain amount. It's not always the same amount, and a microtonal notation can still build in some wiggle room, but there's an automatic response between seeing a note with a certain accidental and making the action required to produce that note. Changing the size of the shift for the same symbol screws with that learned response. It's better to have shift symbols map to consistent sizes between systems.

You can also use those symbols in tablature and numerical notation where there isn't a distinctive staff to provide context. I hope the different staffs would be distinctive ;-)

This wouldn't be such a problem for MegaScore. The score's sufficiently different, visually and functionally, from the usual staff that performers would learn to distinguish the new context. The only cost is the relatively small one of unlearning the original meaning.

Graham

🔗Graham Breed <gbreed@gmail.com>

Aaron Wolf wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> >>Aaron Wolf wrote:
>>
>>
>>>Think about it this way, let's say you took regular staff and said
>>>that you simply wanted to split C to D to have two in-betweens instead
>>>of one, you make the lower one C# and the upper one Db, any complaints
>>>about that? Then say you wanted another two notes, each between C and
>>>C# and between Db and D. At that point if we treat the symbols as a
>>>generally absolute amount, you might want to say C-half-#, and C#. >>
>><snip>
>>
>>Well, that's how the regular staff works out in meantone -- >>and therefore how it worked for a significant part of music >>history. I believe there's evidence that it confuses >>musicians to switch between different interpretations, which >>is why I suggested distinct symbols for different cases in >>sagittal. (The half-sharps give 31-equal.)
> > First, are you saying that there exists a history of real use of
> half-sharp during times when meantone was popular?

No, sorry. I originally snipped a bit more but decided to add the note about 31-equal. (There is a history but not a popular one.)

> Anyway, with half and full instead of single and double... then we are
> specifying sharp as a certain amount and saying you can be double or
> half or even other proportions of that. Melodically, there is no
> reason to specify that way. Within the comma distance of MegaScore's
> staff positions there is absolutely *nothing* that will make the ear
> feel like "ah, here we are at exactly the sharp" vs "sounds like we're
> approaching the sharp position." These movements are ALL too small
> for that, so there is no perceptual reason to specify an amount in
> between a comma as the WHOLE unit to which other amounts are compared.

It means the MegaScore notation isn't consistent with standard notation either way ... for what that's worth.

Graham

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

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> I would do that, but I don't know how to get the musical
> examples typeset. I use LaTeX and I know there are ways of
> using it for music so one day I'll get round to learning them.

What about MicroABC?
http://br.geocities.com/hfmlacerda/abc/microabc-about.html

The few examples currently on the sagittal website were painstakingly
made by George, almost pixel by pixel, since the sagittal font didn't
even exist at that stage. But now it looks like one or both of us
should learn to use MicroABC since it can generate MIDI as well as scores.

>
> My suggestion, anyway, is very simple: change the default #
> and b symbols for meantones. Let's say ||\ as a compromise
> between Bb-F as a 3:2 and A-C# as a 5:4.

And do you mean keep the native fifth as the notational fifth (the one
between nominals)? Or do you mean to use a pythagorean fifth? And what
symbol for the semisharp in 31-ET? Currently /|\.

> I'm also thinking about magic, and maybe this colours my
> reasoning. The 19 note magic scale should be notated
> consistently with the 19 note meantone scale. But it can't
> be identical because there's no string of 7 notes separated
> by perfect fifths to be the nominals. So I want to base
> magic on a 5-limit notation while having it look as much as
> possible as meantone. Which by the law of the excluded
> middle means that meantone has to be consistent with 5-limit JI.

Not really following. Sounds like a bad idea to me, if you mean notate
it as if it were planar, not linear.

Magic has 5 generators to the fifth, so to notate it with
chain-of-fifth nominals you need at least 2 pairs of accidentals and
it will be nearly as bad as a chain of fifths notation for miracle,
which has 6 gens to the fifth and so needs 3 pairs of accidentals
(floor(n/2)). And you'd have to go to 41-ET to get those accidentals
/| and /|\ in the same way you go to 72-ET to get the accidentals for
miracle.

But then your notational fifth for magic is not a meantone fifth, but
a very nearly pythagorean one.

> I suppose magic and pythagorean notations should also unify
> on 41-equal.

That sounds do-able, but not meantone too.

> Now, the web page *I* would like to see is a comparison of
> sagittal with the Extended Helmholtz-Ellis JI system. The
> latter is horribly complex from what I've seen. I want to
> know if that's a problem with the notation or inherent in
> high-limit JIs.

Is there something about that on the web?

-- Dave Keenan

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

🔗Aaron Wolf <backfromthesilo@yahoo.com>

🔗Herman Miller <hmiller@IO.COM>

Graham Breed wrote:

> My suggestion, anyway, is very simple: change the default # > and b symbols for meantones. Let's say ||\ as a compromise > between Bb-F as a 3:2 and A-C# as a 5:4.
> > I'm also thinking about magic, and maybe this colours my > reasoning. The 19 note magic scale should be notated > consistently with the 19 note meantone scale. But it can't > be identical because there's no string of 7 notes separated > by perfect fifths to be the nominals. So I want to base > magic on a 5-limit notation while having it look as much as > possible as meantone. Which by the law of the excluded > middle means that meantone has to be consistent with 5-limit JI.
> > I suppose magic and pythagorean notations should also unify > on 41-equal.

The most straightforward way to notate magic[41] in Sagittal using a chain of fifths is to use the ||\ and \! accidentals for major thirds, and the )||( accidental for two major thirds up, e.g. D F||\ A)||( . There are a few gaps in this, but the ones on the end are easily filled by using the /||\ and \!!/ . You could use four-shaft arrows to fill the remaining two gaps, but having an F in the middle of a bunch of G's could be confusing.

27 B\!!/ 40 D\! 12 F)||(
25 A|) 38 D!!/ 10 F 23 A\! 36 C)||(
08 F)!!( 21 A!!/ 34 C 06 E\! 19 G)||(
32 C)!!( 04 E!!/ 17 G 30 B\! 02 D)||(
15 G)!!( 28 B!!/ 00 D 13 F||\ 26 A)||(
39 D)!!( 11 F/| 24 A 37 C||\ 09 E)||(
22 A)!!( 35 C/| 07 E 20 G||\ 33 B)||(
05 E)!!( 18 G/| 31 B 03 D||\ 16 G!)
29 B)!!( 01 D/| 14 F/||\

This goes nicely with schismatic notation for 41, in which F||\ is equivalent to G\!!/ . Obviously, G\!!/ isn't equivalent to F||\ in magic, so you have to be careful about that. The notation of 16 as G!) and 25 as A|) is also consistent with garibaldi[41] (the usual 7-limit schismatic temperament).

What about magic[19] vs. meantone[19], though? Magic[19] has the /| \! accidentals which can be ignored in meantone. Also, both the ||\ and )||( sharps are used, which in meantone are equivalent.

03 E\! 09 G)||(
15 C)!!( 02 E!!/ 08 G 14 B\! 01 D)||(
07 G)!!( 13 B!!/ 00 D 06 F||\ 12 A)||(
18 D)!!( 05 F/| 11 A 17 C||\ 04 E)||(
10 A)!!( 16 C/|

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

🔗Graham Breed <gbreed@gmail.com>

Aaron Wolf wrote:

> Basically, I have to agree with you that MegaScore is not consistent
> with standard notation, but as far as I'm concerned, it does use the
> best aspects of standard notation. I don't personally care as much
> that it is similar to standard notation as that it uses the best
> notation ideas, and some of those come from standard notation which
> itself has some wonderful aspects along with its inadequacies.

My point is that it should be either identical to standard staff notation or distinctively different. Generally it makes a very good call on these issues. I'm only unhappy about the accidentals but that's really not a big deal.

Both you and the other Aaron are talking about ideas or logic. These are important for the initial learning, and also for the notation as an illustration of theoretical ideas. I think MegaScore is extremely good on this latter point. It shows you the pitch contours and relative sizes of intervals (because it's basically an x-y plot) and also anchors them to the familiar staff. So in this case the logic arguments will help readers understand it. But still, I think casual readers would be able to get what they want from sagittal accidentals (because they're arrows).

> But the "unlearning original meaning" of the # symbol isn't an issue
> if the WAY the person originally learned it was to mean "the next
> higher note in the system." I'm arguing not just that such an idea is
> logical, but that I myself may have always thought of it mostly that
> way throughout my formal education, rather than as an amount of
> change. In my case, # meant go to the next guitar fret from the
> natural. A 205ET guitar (ridiculous of course) would then be
> consistent with MegaScore using the same interpretation of the symbol.
> Hence, to me MegaScore does not require unlearning in this case.

Sure, so does anybody have a time machine so that we can make sure musicians get the right initial training? So maybe that would work for a guitar. It would certainly work for a re-mapped keyboard, but so would staff-tablature. I really don't think wind players learn that way. With the dizi, I learned each key separately. Because the music's all diatonic there's no need to even think about the relative pitches.

All I know supports the idea that wind players learn pitches by rote learning. Johnny Reinhard talked about playing into a tuning device until the fingering and everything else for each distinct pitch becomes intuitive. I've also seen presentations and performances involving Stephen Altoft and his 19-edo trumpet. He learned the fingering and tuning slide positions for each of the 19 notes. The tuning slide goes all over the place. A different position for each note. But for every note he plays he goes directly to the correct position. So that's muscle memory, not logic. Both are on the list to give comments if I have anything wrong.

Sorry for not remembering if you've said this before, but have you played a re-fretted guitar? I have, and to a great extent you have to learn finger positions, not count frets. For tablature I numbered the original 12 frets and used microtonal accidentals to specify which of the two possibilities to play. It uses meantone temperament, so there are obvious pairs of frets going down the neck. Whatever the logic you have to think intuitively about C-C# being a consistent span. But your mileage may vary.

I also have a book on learning the erhu. (I don't (yet) have an erhu to play.) There's a graph, which I've seen in other books as well, showing which pitches are played in which keys. But it doesn't say anything about a 12 note superscale. So "next higher note in the system" doesn't mean anything. All the music is diatonic (although the erhu is flexible pitch) and in numerical notation. There are indications for (I think) which finger to play a some notes with, so it's a kind of hybrid tablature. There's one accidental used in the theoretical text at the back of the book!

Graham

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
<snip>
> Sure, so does anybody have a time machine so that we can
> make sure musicians get the right initial training? So
> maybe that would work for a guitar. It would certainly work
> for a re-mapped keyboard, but so would staff-tablature. I
> really don't think wind players learn that way. With the
> dizi, I learned each key separately. Because the music's
> all diatonic there's no need to even think about the
> relative pitches.
>

To a degree, most non-polyphonic instrumentalists, and particularly
those with specified keys, like flute, (as opposed to fretless like
violin or trombone), don't actually learn any real sense of theory or
scales or relationships at all from notation. They simply associate
mechanical actions with the symbols, almost in the style of a tablature.
Hence, none of those instrumentalists would be able to make any useful
sense of any new system like MegaScore whatsoever. They would
basically have to learn a totally new way of thinking no matter what.
So concern for the "amount" of a sharp isn't even relevant to such a
person. They will have to learn a bit of theory just to understand
the existence of the concepts shown in MegaScore, and along with that
theory, they will probably be revising all sorts of previous
conceptions they originally learned.
I guess I'm agreeing with you but saying that regardless of the
notation issue, those people with the mindset like the hypothetical
flute player will need to kind of start over no matter what. It isn't
bias in the notation requiring that, but bigger issues beyond that.

> All I know supports the idea that wind players learn pitches
> by rote learning. Johnny Reinhard talked about playing into
> a tuning device until the fingering and everything else for
> each distinct pitch becomes intuitive. I've also seen
> presentations and performances involving Stephen Altoft and
> his 19-edo trumpet. He learned the fingering and tuning
> slide positions for each of the 19 notes. The tuning slide
> goes all over the place. A different position for each
> note. But for every note he plays he goes directly to the
> correct position. So that's muscle memory, not logic. Both
> are on the list to give comments if I have anything wrong.
>

Right, so how would the issues of logic here be a problem? If they
aren't thinking logically, but by rote, in the first place... well,
they can either learn the new system by rote, or they can see it
logically the way I do. It would be silly to try to make the logic of
a system adapt to someone who is taking a rote rather than logical
approach. The logic aspect should try to fit those who might already
be thinking logically.

> Sorry for not remembering if you've said this before, but
> have you played a re-fretted guitar? I have, and to a great
> extent you have to learn finger positions, not count frets.
> For tablature I numbered the original 12 frets and used
> microtonal accidentals to specify which of the two
> possibilities to play. It uses meantone temperament, so
> there are obvious pairs of frets going down the neck.
> Whatever the logic you have to think intuitively about C-C#
> being a consistent span. But your mileage may vary.
>

I don't own a refretted guitar, but I've played a couple. Because the
music theory concepts and images were already in my head, I played
immediately and related it to that, and it was no problem. I
definitely wasn't counting frets, I think more likely I was thinking a
little bit in terms of absolute proportions of the strings.

> I also have a book on learning the erhu. (I don't (yet)
> have an erhu to play.) There's a graph, which I've seen in
> other books as well, showing which pitches are played in
> which keys. But it doesn't say anything about a 12 note
> superscale. So "next higher note in the system" doesn't
> mean anything. All the music is diatonic (although the erhu
> is flexible pitch) and in numerical notation. There are
> indications for (I think) which finger to play a some notes
> with, so it's a kind of hybrid tablature. There's one
> accidental used in the theoretical text at the back of the book!
>

Well, the "next note higher" idea obviously requires some concept of a
closed system, whether equal or diatonic or whatever.

Honestly, I'm thinking of the MegaStaff for myself to be used for pure
composition, synth stuff, along with the associated keyboard, and for
vocals and other fretless instruments. I'm not thinking of relating
it in any way to any fixed pitch instruments, even those with the
ability to bend sharp or flat. It doesn't seem practical for that in
my mind. I'm not thinking about how to notate for performers who
would actually play off the score, but just how to visually clearly
express the musical idea and composition. I'll leave it to tablature
and finger-charts and other rote instrument notations to indicate how
to play. This all gets at a lot of discussions recently had. It
really comes down to what is the purpose. If any guitar would ever
play off MegaScore, it would only be a fretless one, and I don't think
even then that I'd use it to read from and play like a traditional
score. Besides everything else, it is too big to show enough on a
page. But it is good for conceptualizing and composing and teaching...

Best,
Aaron

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

--- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@...> wrote:
> Well, the "next note higher" idea obviously requires some concept of
> a closed system, whether equal or diatonic or whatever.

Mr Wolf,

On thinking further about your "next higher note in the system" point
of view, I realise that it doesn't really get us anywhere. We still
have to know how _far_ it is to the next note (since there _are_ no
205 frets to the octave), so it just takes us back to having to
remember that although it is about 100 cents on a conventional staff,
it is only about 6 cents on the megastaff.

I have just been enjoying playing with StaffBuilder and reading Mr
Hunt's design criteria.

I see that if you want to keep perfect fifths spanning 4 "positions"
of the macro level of the staff (same as on conventional) and have
fifths close to just, and subdivide the macro level at most twice, and
subdivide ony by a factor of 2 or 3 each time, (all very desirable
properties) then 41-ET is a totally forced move. Nothing else comes
close. That is really a major discovery. Well done, Mr Hunt.

And of the further subdivisions of 41, having the same size of best
fifth, 205 has the highest odd consistency limit for approximating JI,
although it is only 9 limit.

But I couldn't help noting Mr Hunt's "Conventional Expectations"
principle:
"A novel notation system should fulfil as many conventional
expectations as possible."

That is indeed the basis of my objection to the way he has used the
conventional accidentals for the inflections. It fulfils _no_
conventional expectation for those symbols, apart from the barest
minimum expectation that sharps raise pitch and flats lower it.

It is certainly possible to fulfil more conventional expectations than
that.

-- Dave Keenan

🔗Graham Breed <gbreed@gmail.com>

Aaron Wolf wrote:

> To a degree, most non-polyphonic instrumentalists, and particularly
> those with specified keys, like flute, (as opposed to fretless like
> violin or trombone), don't actually learn any real sense of theory or
> scales or relationships at all from notation. They simply associate
> mechanical actions with the symbols, almost in the style of a tablature.
> Hence, none of those instrumentalists would be able to make any useful
> sense of any new system like MegaScore whatsoever. They would
> basically have to learn a totally new way of thinking no matter what.
> So concern for the "amount" of a sharp isn't even relevant to such a
> person. They will have to learn a bit of theory just to understand
> the existence of the concepts shown in MegaScore, and along with that
> theory, they will probably be revising all sorts of previous
> conceptions they originally learned.
> I guess I'm agreeing with you but saying that regardless of the
> notation issue, those people with the mindset like the hypothetical
> flute player will need to kind of start over no matter what. It isn't
> bias in the notation requiring that, but bigger issues beyond that.

Anybody using numerical notation (and there are a lot, if not in your neighborhood) will need to know scales. And even with staff notation they need to respond to key signatures. But yes, it's mostly a question of starting over, and so not a big deal that there's a little inconsistency.

> Right, so how would the issues of logic here be a problem? If they
> aren't thinking logically, but by rote, in the first place... well,
> they can either learn the new system by rote, or they can see it
> logically the way I do. It would be silly to try to make the logic of
> a system adapt to someone who is taking a rote rather than logical
> approach. The logic aspect should try to fit those who might already
> be thinking logically. The problem I foresee is that the MegaScore has a note that you identify with, for example, C. The structure of the staff points to it being C. And the theory behind it is that this note really is C -- not an arbitrary note that happens to have the same pitch. So the flute player learns to use the same fingering and so on for this new C as for the old C. Then, there's an accidental which looks like a sharp, and is designed to look like a sharp. So the intuitive action associated with a C with a sharp in front of it is to play it as C sharp. But in fact it should be played almost identically to C. That's where the problem would arise. Logic has to overrule intuition until the rote learning takes effect.

> Honestly, I'm thinking of the MegaStaff for myself to be used for pure
> composition, synth stuff, along with the associated keyboard, and for
> vocals and other fretless instruments. I'm not thinking of relating
> it in any way to any fixed pitch instruments, even those with the
> ability to bend sharp or flat. It doesn't seem practical for that in
> my mind. I'm not thinking about how to notate for performers who
> would actually play off the score, but just how to visually clearly
> express the musical idea and composition. I'll leave it to tablature
> and finger-charts and other rote instrument notations to indicate how
> to play. This all gets at a lot of discussions recently had. It
> really comes down to what is the purpose. If any guitar would ever
> play off MegaScore, it would only be a fretless one, and I don't think
> even then that I'd use it to read from and play like a traditional
> score. Besides everything else, it is too big to show enough on a
> page. But it is good for conceptualizing and composing and teaching...

I think MegaScore would work very well for a lot of instrumentalists. It's distinctively different to a conventional staff while retaining enough landmarks to get a learner oriented. Each note is distinct, so it's suitable for rote learning. A lot of mistakes will result in a note only slightly off. If you want to treat each note within a JND equally it may well be the best notation.

It might even work for a guitar. Think of an instrument with 41 frets per octave. You can use the staff position to tell you the fret and the accidentals (which would all have to indication sharpening) for string bending. I think 41 is on the borderline of what will work for a guitar.

The real problems I expect with MegaScore are not to do with the accidentals. The most obvious and probably critical one is the size of the score. So it comes down to whether people want to devote that much more space for the sake of better pitch discrimination. Another problem may be that performers can't distinguish neighboring staff positions clearly enough. I don't expect that'll matter but only empirical evidence will show it.

The first advantage of sagittal notation is that it's simple for simple scales. So if you only want 12 notes you only have to learn 12 notes. That's an advantage for progressive rote learning -- MegaScore only makes sense once you've got 41 under your belt. It also means you don't need to devote any more space on the page for simple but different scales.

Paradoxically, sagittal may also be the optimum notation for expert performers. Athenian sagittal is obviously horribly complex for newbies, and takes longer to get the hang of than MegaScore or the AFMM notation. But if you're rote learning pitches it's not a big deal to rote learn the symbols as well. The result is that different notes are clearly distinct, and the visual clues are all in the immediate vicinity of the note -- no need to navigate a large staff or look to the top for the cents. It may make no measurable difference or it may be the decisive feature.

Speculation quickly becomes pointless. Sagittal and MegaScore are both doing different things and optimal within their design goals. I'd like to see good studies comparing them or at least feedback from a large number of musicians with extensive training in both systems. The pessimist in me says this will never happen. Probably an inferior system will take over because some influential musicans start using it without thinking the issues through. That's the way it usually goes.

Graham

🔗Graham Breed <gbreed@gmail.com>

🔗Robert walker <robertwalker@robertinventor.com>

Hi There,

I'm just dipping in on this discussion - still very pre-occupied with the Tune Smithy 3.0 release.

Anyway in FTS I use # b in various ways depending on the context - sometimes as an indication of the amount of pitch adjustment, sometimes as a "next / previous" step indicator, also in the scordatura type keyboard scores.

The next / previous step approach is needed when you are interested to know how far a note has been moved measured in terms of the number of scale degrees, rather than the amount of the pitch displacement.

There I use b or # for one scale degree, ## or bb for two and so on - or if user prefers and the number of scale degrees is high, # and b are used for two scale degrees, so then it goes: + - , # b, #+ b-, ##+ bb- etc.

It is just easier to read than +1 +2 +3 etc when there are lots of numbers around e.g. scale degree 6 raised by 3 scale degrees is easier to read as 6#+ than as 6+3, means the same thing. The context is clearly different from its normal use as a pitch indicator so there is no confusion. The symbols # and b are easier for musicians to read as increments than e.g. ^ v etc.

I've not had any complaints from users of the software.

In other places such as the chord progression player, then the #s and bs are used in their normal sense to show the amount of the pitch adjustment. I'll also be adding in Sagittal some time after the next release and for that, naturally, the accidentals will be used to indicate the amount of the pitch adjustment.

Another use of them is the scordatura score. There the notation is used as a way to tell the musician where to place their fingers to play the notes not as a pitch indication. They work because of the trained response of eye to fingers. Then the ear can be used to fine tune once one has got to the approximate pitch in that way.

So in the same way - if reading a keyboard score for instance, then you can use the accidentals just as an indication of which key to press on the keyboard - in that case there is no distinction of #s and bs, and the score is shown just like any 12 t score, but with instructions to the user about how to tune each note - which need not even tune the notes as shown on the score to anywhere near the usual pitches. One can read such a score very easily even if the pitches played are far away from the usual pitches - even if the usual "Octave" on the score is retuned to a 3/2 or 3/1 or whatever, it doesn't matter as all that is needed is the usual eye / hand coordination to read the score and a willingness to accept that the notes that result will sound differently pitched from the ones you usually get.

If one had access to a keyboard with split keys that could be retuned arbitrarily in the same way one could use a scordatura score with distinctions of flats / sharps, or fine shades of accidentals etc - again the accidentals would just show you which keys to press, not used as an indication of the pitches expected at all.

For keyboard players then a scordatura score showing which fingers to use for the notes is far easier to read than a score that shows the pitches to play - in the case where the keyboard is to be retuned in some unusual fashion (such as non octave or whatever) - basically there is nothing to learn and you can pick up any such score for any tuning system whatsoever, and so long as the keyboard is correctly tuned to match the score then you can play it straight off without any learning whatsoever.

So anyway - that's just to say - that I find also there are lots of different contexts where one can use the # / b symbols, and it doesn't seem to cause any problems unless there is some confusion about which context is intended. So - this is just to give examples of a couple of other possible ways that they could be used in addition to the conventional sense and the MegaScore sense.

The scordatura sense in particular I think seems obviously eminently sensible, is about as far as you can get from pitch indication - and doesn't cause any problems to the player. Scordatura scores in one form or another have been with us for centuries for string music, where if there was to be any cognitive dissonance, you would think it would be felt particularly acutely.

To answer your point Dave, it may be that if you aren't going to fulfull conventional expectations, it may be that it works better if you fulfill none of them or few of them, rather than to fulfill many but not all.

It would be confusing if e.g. to make up a deliberately confusing system - the accidentals had the same meaning as Sagittal pure j.i. notation (as an adjustment applied to pythagorean 12-t) for all notes except for E alone, where it was used for an adjustment of a comma instead of a semitone. Or if one were to write the first page of a piece in Sagittal and the second page in MegaScore, then that might be pretty confusing and not a very good idea unless one had good reasons for it - though the systems are distinct enough, particlarly with the change in the number of lines in the staff, that one could imagine a performer fluent in both could make the transition without too much trouble even so.

So, perhaps the reason Megascore works for users of the system is that it is sufficiently distinct from conventional score, also indeed from Sagittal - to not cause any cognitive dissonance?

As a programmer ones main aim is to make something that is user friendly and works for the users of ones programs. Suggestions from theorists (including ideas one may consider and maybe reject oneself before the software was even written) are likely to be looked on more favourably if they help one with those aims. So that's a reason for favouring familiar symbols if one possibly can do it without confusion, and if one can explain it to ones users in a way that make them acceptable and won't hinder them in other ways. I don't think MegaScore would hinder understanding of Sagittal or other type conventional staff + accidental type pitch height indicating systems, nor do Scordatura scores, or the accidentals for scale degree increments notaitons, in my opinion, so they are all (along with perhaps many more options) acceptable notations to use in a program interface

Thanks,

Robert

🔗Aaron Wolf <backfromthesilo@yahoo.com>

Dave,

Wonderful insights!

As for the "next higher" issue, all I can say with certain is this is
how I've been thinking about it:

My rudimentary theory education basically taught me that no possible
note EXISTS within 100 cents, and then all through my music degree,
the people I found to be questioning or differing from that only
brought it up on my instigation for the most part. Hence, next
possible note was always taught basically as a standard half-step.

What I love about the average JND concept is that I can actually
pretend that the *NEW* 205ET system, the "next higher" note really
*is* the very next *possible*. In other words, instead of my
thinking, "oh, # means next note, but there's tons of possible
systems, so which is this?" - I think: "Ah, I now understand that
notes a lot closer than 100 cents exist, the next closer note in music
as a whole is a JND!" Because a JND by definition is the closest we
can be to be perceptibly different.

As for the REAL fact that harmony requires more precision, my desire
is STRONGLY against having different inflection symbols for that
precision, because once we are within a single JND, it truly does not
matter exactly how far the pitch is from the natural or the next JND
or from some absolute, it only matters that it is relatively matched
to concurrent pitches.

For example, if I want the pitches Re to Do to be tuned to 4:7,
certainly it *does* matter whether Do stays at 1/1 and Re is sharped
to 8/7 vs whether Re is 9/8 and Do flats to 63/32. But those are all
more than a JND away, so I can clearly notate in MegaScore which one
is to stay diatonic and which is to adjust, or even a compromise.
Now, once I have notated Re to be within a JND of 9/8 and Do to be
within a JND of 63/32, I believe it is *totally* musicially irrelevant
which of those pitches WITHING its own JND range adjusts flat or sharp
to make the pure JI harmony. What matters melodically is that I've
identified the JND general location of each pitch. What matters
harmonically is that they are a true JI 4:7. It will be absolutely
imperceptible to any listener exactly the specifics within the JND of
what adjusting is done to make the JI pure. Again, all that matters
is *that* the JI is pure, and melodically, where the pitches are in a
system of average JNDs.

In many cases, the ear is even less perceptible to changes larger than
a JND, but by defintion, the JND is our unit to work with.

In barbershop notation, the standard thing today is to notate a D and
a C and theorists can identify that it is part of a D7 chord, then
instruction is given basically to "lock that 7th" with no clarity on
who should adjust how to that, just do it. This is obviously
inadequately vague, although some learn ways to work with this by
rote, which means some people get it and some don't and that's that.

With MegaScore, if I notated an approximate 4:7 within the JND
specificity, and then said "lock that 7th" I think any singer would
probably already be locked once they got in range of the JND since no
other interval would make much sense without moving more than a JND away.

I know this is a bold claim, but I'm arguing that harmonic absolutes
are clearly more important than melodic absolutes. I'm arguing that
the JND is our absolute limit for needing any melodic specificity, and
that harmonic specificity should not be notated with symbols next to
notes. Symbols next to notes indicate an absolute adjustment relative
to prior notes or following notes or to a key center. Harmonic
precision is independent of that, it only matters how it matches to
concurrent notes. The only inflection marking that would do that
would be something saying "this is the 5 identity of the chord" and
not something that had anything to do with specifically raising or
lowering the pitch. I'm not sure that's the best way to do it, but
I'm not opposed to that idea, or maybe the idea of different note-head
shapes indicating such things...

So again, I'm actually arguing that the JND concept should be some
sort of standard and that # is defined as "the next possible pitch"
which is equivalent to saying "the next JND." And that should be its
new standard definition (a bold assertion for sure). But I'm saying
this is consistent with a major aspect of its historical standard use.
And any other system between standard and JND can go ahead and make
up their own NEW symbols and not bother with #. Ok this last stuff is
maybe over-the-top, but the MAIN important point I'm making is about
these perceptual differences between melody and harmony, and how that
makes very precise single-note tuning markings a bad idea.

It's kind of like how Hermode tuning works, or the average JI concept
of the Haaken Continuum feature... Their argument is that melodic
shifting of even comma size and larger can be ignored to a degree
while creating some compromise resulting in pure harmony. If that
wasn't at least partly true, then Hermode tuning truly wouldn't be
even successful enough to get past concept and actually exist. What
I'm arguing for is something like a Hermode tuning for the 205ET, JND
specific system. In fact, I think I'll recommend this to Mr. Hunt
specifically. The point is that within a JND, any compromise can be
done to create the simplest JI ratio for that very small adjustment room.

So, with this way of looking at it, when would you ever need "next
note in the system" to be specified differently? We would just
understand by definition that a JND is obviously the next perceptible
note... no other specific need exist.

Best,
Aaron Wolf

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@> wrote:
> > Well, the "next note higher" idea obviously requires some concept of
> > a closed system, whether equal or diatonic or whatever.
>
> Mr Wolf,
>
> On thinking further about your "next higher note in the system" point
> of view, I realise that it doesn't really get us anywhere. We still
> have to know how _far_ it is to the next note (since there _are_ no
> 205 frets to the octave), so it just takes us back to having to
> remember that although it is about 100 cents on a conventional staff,
> it is only about 6 cents on the megastaff.
>
> I have just been enjoying playing with StaffBuilder and reading Mr
> Hunt's design criteria.
>
> I see that if you want to keep perfect fifths spanning 4 "positions"
> of the macro level of the staff (same as on conventional) and have
> fifths close to just, and subdivide the macro level at most twice, and
> subdivide ony by a factor of 2 or 3 each time, (all very desirable
> properties) then 41-ET is a totally forced move. Nothing else comes
> close. That is really a major discovery. Well done, Mr Hunt.
>
> And of the further subdivisions of 41, having the same size of best
> fifth, 205 has the highest odd consistency limit for approximating JI,
> although it is only 9 limit.
>
> But I couldn't help noting Mr Hunt's "Conventional Expectations"
> principle:
> "A novel notation system should fulfil as many conventional
> expectations as possible."
>
> That is indeed the basis of my objection to the way he has used the
> conventional accidentals for the inflections. It fulfils _no_
> conventional expectation for those symbols, apart from the barest
> minimum expectation that sharps raise pitch and flats lower it.
>
> It is certainly possible to fulfil more conventional expectations than
> that.
>
> -- Dave Keenan
>

🔗Aaron Wolf <backfromthesilo@yahoo.com>

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

--- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@...> wrote:
> What I love about the average JND concept is that I can actually
> pretend that the *NEW* 205ET system, the "next higher" note really
> *is* the very next *possible*. In other words, instead of my
> thinking, "oh, # means next note, but there's tons of possible
> systems, so which is this?" - I think: "Ah, I now understand that
> notes a lot closer than 100 cents exist, the next closer note in music
> as a whole is a JND!" Because a JND by definition is the closest we
> can be to be perceptibly different.

So in other words, it only makes sense if you fool yourself? ;-)

> As for the REAL fact that harmony requires more precision, my desire
> is STRONGLY against having different inflection symbols for that
> precision, because once we are within a single JND, it truly does not
> matter exactly how far the pitch is from the natural or the next JND
> or from some absolute, it only matters that it is relatively matched
> to concurrent pitches.

In case you're assuming that sagittal forces you to specify pitches
more precisely than a megascore-JND, I must point out that it does
not. Both Athenian (pythagorean-fifth-based) and Trojan
(12ET-fifth-based) subsystems of Sagittal have essentially the same
resolution as megascore (Athenian is similar to 224 ET and Trojan to
216-ET). Each symbol can notate a specified non-overlapping no-gaps
_range_ of pitches. They require only 10 symbols in addition to sharp
and flat, and these 10 symbols are constructed from a smaller set of
"flags" or half arrow heads whose pitch values add. e.g.
/| + /| = //|
/| + |) = /|)

And as Graham mentioned, if your personal JND happens to be bigger,
you can use a simpler subsystem of sagittal, or if smaller, a more
complex subsystem. But you don't have to unlearn one subsystem to move
to another, they are all consistent with each other. Symbols do change
size between subsystems, but only slightly, not by factors of 16 or 20.

> I know this is a bold claim, but I'm arguing that harmonic absolutes
> are clearly more important than melodic absolutes.

I see nothing bold in that. I think it is well accepted.

> I'm arguing that
> the JND is our absolute limit for needing any melodic specificity,

I suspect many people find 72-ET to be close enough to a continuum for
melodic purposes.

> and
> that harmonic specificity should not be notated with symbols next to
> notes. Symbols next to notes indicate an absolute adjustment relative
> to prior notes or following notes or to a key center. Harmonic
> precision is independent of that, it only matters how it matches to
> concurrent notes. The only inflection marking that would do that
> would be something saying "this is the 5 identity of the chord" and
> not something that had anything to do with specifically raising or
> lowering the pitch. I'm not sure that's the best way to do it, but
> I'm not opposed to that idea, or maybe the idea of different note-head
> shapes indicating such things...

It is possible to do both, to some degree. i.e. To have a symbol
represent both an approximate adjustment relative to some other pitch,
_and_ a particular identity of the chord. This is what Sagittal
attempts to do.

For example, we have symbols for the 5-comma up /| and down \! and
7-comma up |) and down !)

So for example a 7-limit otonality on G is notated G B\! D F!). The 1
and 3 identities have no arrows, the 5 identity has a straight flag or
barb on the arrow and the 7 identity has a curved flag or arc. Moving
that by any number of fifths or fourths maintains the same
relationship between symbols and identities. e.g. C E\! G Bb!). But
also shifting it up by a major third (or down by a minor third) leaves
the identities recognisable because of the way half-arrowheads add in
sagittal.
e.g. E\! G#\\! B\! D\!)

\! + \! = \\!
!) + \! = \!)

Unfortunately, going down by a major third (or up by a minor third) is
not so obvious since it involves flag subtraction.
e.g. C/| E G/| Bb!(
Here one has to learn that !) + /| = !( or equivalently !) - \! = !(
or |) - /| = |(

> So again, I'm actually arguing that the JND concept should be some
> sort of standard and that # is defined as "the next possible pitch"
> which is equivalent to saying "the next JND." And that should be its
> new standard definition (a bold assertion for sure).

I don't think it will ever happen. The size of a JND varies enormously
between people, timbres, chords, tempos, etc, etc.

...
> It's kind of like how Hermode tuning works, or the average JI concept
> of the Haaken Continuum feature... Their argument is that melodic
> shifting of even comma size and larger can be ignored to a degree
> while creating some compromise resulting in pure harmony. If that
> wasn't at least partly true, then Hermode tuning truly wouldn't be
> even successful enough to get past concept and actually exist. What
> I'm arguing for is something like a Hermode tuning for the 205ET, JND
> specific system. In fact, I think I'll recommend this to Mr. Hunt
> specifically. The point is that within a JND, any compromise can be
> done to create the simplest JI ratio for that very small adjustment
room.
>
> So, with this way of looking at it, when would you ever need "next
> note in the system" to be specified differently? We would just
> understand by definition that a JND is obviously the next perceptible
> note... no other specific need exist.

I think you're fooling yourself. In fact I think you may even be
contradicting yourself. Didn't you just point out that some folks
treat a comma (or half a comma) as a JND (Hermode tuning).

However, even if I were to adopt your view I would still argue that
the Tartini semi-sharp should be used for a single JND so that a sharp
gets you nearly halfway between staff positions and thereby maintains
"conventional expectations" to a greater degree. Even to someone who
has never seen a Tartini semisharp before, its meaning is obvious. It
is clearly a sharp symbol cut in half. The Couper backwards flat is
less obvious but can be improved by making it deliberately narrower
than the forward flat, as I have done for the version included with
the sagittal font.

I am beginning to suspect that Mr Hunt's abhorrence of "non standard"
accidentals, even ones as standard and obvious as these, may be based
more on a marketing principle than any principle of cognitive or
perceptual psychology.

-- Dave

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> It is possible to do both, to some degree. i.e. To have a symbol
> represent both an approximate adjustment relative to some other pitch,
> _and_ a particular identity of the chord. This is what Sagittal
> attempts to do.
>
> For example, we have symbols for the 5-comma up /| and down \! and
> 7-comma up |) and down !)
>
> So for example a 7-limit otonality on G is notated G B\! D F!). The 1
> and 3 identities have no arrows, the 5 identity has a straight flag or
> barb on the arrow and the 7 identity has a curved flag or arc. Moving
> that by any number of fifths or fourths maintains the same
> relationship between symbols and identities. e.g. C E\! G Bb!). But
> also shifting it up by a major third (or down by a minor third) leaves
> the identities recognisable because of the way half-arrowheads add in
> sagittal.
> e.g. E\! G#\\! B\! D\!)
>
> \! + \! = \\!
> !) + \! = \!)
>
> Unfortunately, going down by a major third (or up by a minor third) is
> not so obvious since it involves flag subtraction.
> e.g. C/| E G/| Bb!(
> Here one has to learn that !) + /| = !( or equivalently !) - \! = !(
> or |) - /| = |(
>

Dave, I think that is all definitely leading toward markings for
HARMONIC purpose. My whole point was that they shouldn't be that way
exactly. I'm saying that the 5-comma vs 7-comma isn't important,
because it isn't the size of the comma but the harmonic identity that
matters. By using comma size, you are specifying location relative to
an absolute. In other words, the F in GBDF could be the same note from
one chord to the next, but change identity in the chord. I don't want
to have to think about a 7-comma F being a 5 identity of another root,
that gets very confusing, much more than a non-harmonic simply melodic
location. Obviously, I do have to admit that sagittal is functional,
but I just think it requires more theoretical background than MegaScore
which seems more obvious a way to express these things to someone.

> > So again, I'm actually arguing that the JND concept should be some
> > sort of standard and that # is defined as "the next possible pitch"
> > which is equivalent to saying "the next JND." And that should be
its
> > new standard definition (a bold assertion for sure).
>
> I don't think it will ever happen. The size of a JND varies enormously
> between people, timbres, chords, tempos, etc, etc.
>

Hmm, that's a good point. Overall, my impression of MegaScore is that
the 41ET staff is near the largest JND for the most casual untrained
listener, and so the focus can be on that, and the inflections are as
they are called - inflections, so subtle that they aren't all that
important. I think most singers could get used to the idea of a real
shift for a position change and accept that the inflection amount is
just so subtle that you could hear it but shouldn't really anything
really noticeable. The reality of all this is that it will take a lot
of trials and testing to see how people really react in all sorts of
different contexts.

> I think you're fooling yourself. In fact I think you may even be
> contradicting yourself. Didn't you just point out that some folks
> treat a comma (or half a comma) as a JND (Hermode tuning).
>

I think contradicting more than fooling. Yes, I recognize now
especially since you point it out that JNDs vary substantially.

> However, even if I were to adopt your view I would still argue that
> the Tartini semi-sharp should be used for a single JND so that a sharp
> gets you nearly halfway between staff positions and thereby maintains
> "conventional expectations" to a greater degree. Even to someone who
> has never seen a Tartini semisharp before, its meaning is obvious. It
> is clearly a sharp symbol cut in half. The Couper backwards flat is
> less obvious but can be improved by making it deliberately narrower
> than the forward flat, as I have done for the version included with
> the sagittal font.
>

I like the Tartini semisharp and I can deal with the Couper backwards
flat. In fact, I think I even agree with you that it could be better
than the single / double. I do think it is a minor difference though,
and I prefer either semisharp and sharp or sharp and double sharp to the
suggestion of sagittal for MegaScore. I mostly have been arguing that
Aaron Hunt's use of the symbols is not awful or confusing or illogical.
However, I really do agree with you that these semi symbols would be a
better option.

> I am beginning to suspect that Mr Hunt's abhorrence of "non standard"
> accidentals, even ones as standard and obvious as these, may be based
> more on a marketing principle than any principle of cognitive or
> perceptual psychology.

Maybe, but we can't totally fault him on that. I think such marketing
principles will doom sagittal regardless of its merits. Getting people
to actually use it is a big step in any invention's success. Look at
Esperanto (something I actually know very little about, but I think it
is a good analogy...)

Best,
Aaron Wolf

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

--- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@...> wrote:
> Dave, I think that is all definitely leading toward markings for
> HARMONIC purpose. My whole point was that they shouldn't be that way
> exactly.

I'm not following you. Of course they are markings for a harmonic
purpose. Indicating harmonic identities is a harmonic purpose.

> I'm saying that the 5-comma vs 7-comma isn't important,
> because it isn't the size of the comma but the harmonic identity
> that matters. By using comma size, you are specifying location
> relative to an absolute.

So ignore the fact that they represent commas and just consider them
as indicating harmonic identities.

> In other words, the F in GBDF could be the same note from
> one chord to the next, but change identity in the chord. I don't want
> to have to think about a 7-comma F being a 5 identity of another root,
> that gets very confusing, much more than a non-harmonic simply melodic
> location.

But strict just intonation just _is_ that confusing, no matter how you
notate it. It seems that you may actually just be arguing for
temperament, or at least some kind of adaptive JI with the roots in a
temperament. That's really quite independent of notation. Sagittal
notation of such a temperament will of course be much simpler than
sagittal notation of strict JI.

But a temperament in which a 7-limit otonality could be notated simply
GBDF would have 5-limit errors greater than those of 12-ET.

If you're saying that 41-ET (or schismic/garibaldi temperament) is an
accurate enough temperament for 7-limit JI then that's fine (although
many will disagree with you) and I note that it requires only two
sagittal symbols (and their inversions) on a conventional staff, one
of which can be an obvious double of the other /| and //|

> Obviously, I do have to admit that sagittal is functional,
> but I just think it requires more theoretical background than MegaScore
> which seems more obvious a way to express these things to someone.

If you're saying that 41-ET is representated more cleanly by megascore
than by sagittal on a conventional staff, then I certainly agree with
you. But this is not the case for other temperaments such as meantones
e.g. 19 and 31-ET.

> Hmm, that's a good point. Overall, my impression of MegaScore is that
> the 41ET staff is near the largest JND for the most casual untrained
> listener, and so the focus can be on that, and the inflections are as
> they are called - inflections, so subtle that they aren't all that
> important. I think most singers could get used to the idea of a real
> shift for a position change and accept that the inflection amount is
> just so subtle that you could hear it but shouldn't really anything
> really noticeable. The reality of all this is that it will take a lot
> of trials and testing to see how people really react in all sorts of
> different contexts.

I think the 41-ET staff is absolutely brilliant. And I feel it is
_complementary_ to sagittal, not a competitor. Sagittal is primarily a
universal set of accidentals from which subsets can be chosen for any
desired accuracy and used with any staff.

> Maybe, but we can't totally fault him on that.

Agreed.

> I think such marketing
> principles will doom sagittal regardless of its merits.

I think you are wrong. We have so far concentrated on documenting the
full system in all its gruesome detail so that "guru level" users have
the information they need to implement it in software for the benefit
of ordinary users.

We have tried some "marketing", namely the mythology, which we now
understand appeals to some, but others just find it annoying.

Our best marketing so far comes unasked and unselfconsciously from
satisfied users. There is quite a bit of it on the web. Much of it in
the Yahoo groups "tuning" and MakeMicroMusic", but also on the wider
web. Just google Sagittal Notation or Sagittal Font, and don't forget
the common misspelling "Saggital".

> Getting people
> to actually use it is a big step in any invention's success.

Yes indeed.

> Look at
> Esperanto (something I actually know very little about, but I think
> it is a good analogy...)

I don't, because Esperanto had many competitors, namely natural
languages, any one of which could do the job. There is no other single
microtonal notation system that can do all that sagittal can do. That
could only be approached by a motley collection of many mutually
incompatible systems.

-- Dave Keenan

🔗Aaron Wolf <backfromthesilo@yahoo.com>

🔗Graham Breed <gbreed@gmail.com>

🔗Aaron Wolf <backfromthesilo@yahoo.com>

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

🔗Aaron Wolf <backfromthesilo@yahoo.com>

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

🔗Aaron Wolf <backfromthesilo@yahoo.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@...> wrote:
>
> --- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@> wrote:
> > I understand, and no I'm not satisfied with 41ET as a functional
> > 7-limit temperament, though it is clearly better than 12ET.
> >
> > My point was that by using different commas as the basis for the
> > accidental, that links the harmonic tuning to the melodic absolute
> > tuning more than I think is necessary and adds extra confusion. My
> > desire is to truly have them independent so that whenever I do not
> > want to specify the manner in which the harmony is achieved (exactly
> > which notes flat or sharp how much), I can still specify the main
> > melodic function clearly and simply and also identify the desired
> > harmony and identities of everything.
>
> Sounds like you just want an extended form of chord notation e.g. Bdim
> Gm7 etc. But for JI and with the roots shown on a staff instead of
> given as letters.
>

Naw... I want to be able to notate the polytonal aspects of multiple
parts. I don't want to just focus on harmony, I want to really deal
with the use of melody and even of harmonic tension through slides and
leading motions that do not harmonize well but lead to harmonic
resolutions. Chord notation is crappy at dealing with voice leading.
But a MegaStaff for showing 41 could do the voice leading and then a
JI notation or identity marks for harmony could be added below the
staff or something. That's about what I already do by marking ratios
by notes on a traditional staff.

> > I think what I'm talking about would truly be called an adaptive
> > tuning. I might be happy with a 41ET-based adaptive tuning that
> > achieves pure JI. I'll have to explore that further, but it very well
> > might meet my desires fully.
>
> I expect it would.
>
> -- Dave Keenan
>

I wish I could easily try 41 adaptive, such as if I had a 41-ET
keyboard with built in Hermode-like adaption... I'm not sure
otherwise how to realize this idea or how to test whether 41ET
adaptive tuning would satisfy me or not...

Thanks for being part of this discussion that is helping clarify these
ideas anyway.

Regards,
The Wolf

🔗Graham Breed <gbreed@gmail.com>

Dave Keenan wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> >>I would do that, but I don't know how to get the musical >>examples typeset. I use LaTeX and I know there are ways of >>using it for music so one day I'll get round to learning them.
> > What about MicroABC?
> http://br.geocities.com/hfmlacerda/abc/microabc-about.html

That's the one! I should learn that.

> The few examples currently on the sagittal website were painstakingly
> made by George, almost pixel by pixel, since the sagittal font didn't
> even exist at that stage. But now it looks like one or both of us
> should learn to use MicroABC since it can generate MIDI as well as scores.

I'll need it as soon as I start writing papers that need music notation. For now I'm happy with the mathematics.

>>My suggestion, anyway, is very simple: change the default # >>and b symbols for meantones. Let's say ||\ as a compromise >>between Bb-F as a 3:2 and A-C# as a 5:4.
> > And do you mean keep the native fifth as the notational fifth (the one
> between nominals)? Or do you mean to use a pythagorean fifth? And what
> symbol for the semisharp in 31-ET? Currently /|\.

I mean leave the nominals as they are but translate # to ||\ and b to the equivalent. That means thirds and fifths involving one nominal a little bit off relative to JI notation.

>>I'm also thinking about magic, and maybe this colours my >>reasoning. The 19 note magic scale should be notated >>consistently with the 19 note meantone scale. But it can't >>be identical because there's no string of 7 notes separated >>by perfect fifths to be the nominals. So I want to base >>magic on a 5-limit notation while having it look as much as >>possible as meantone. Which by the law of the excluded >>middle means that meantone has to be consistent with 5-limit JI.
> > Not really following. Sounds like a bad idea to me, if you mean notate
> it as if it were planar, not linear.

There's no obvious linear notation that fits with the 7 nominals. And no obvious alternative octave size for that matter. If you write it as a chain of major thirds it goes off the scale. So there has to be a compromise.

The 19 note magic scale can be written as a periodicity block. That means there are no notes that differ by the tempered syntonic comma. So each note has a unique meantone representation, and you can even use 19-note enharmonies. But you can still use comma accidentals to remind the reader that it isn't meantone. When you use more than 19 notes the comma shifts become important.

> Magic has 5 generators to the fifth, so to notate it with
> chain-of-fifth nominals you need at least 2 pairs of accidentals and
> it will be nearly as bad as a chain of fifths notation for miracle,
> which has 6 gens to the fifth and so needs 3 pairs of accidentals
> (floor(n/2)). And you'd have to go to 41-ET to get those accidentals
> /| and /|\ in the same way you go to 72-ET to get the accidentals for
> miracle.
> I'm thinking in mixed sagittal, as I usually do, so here I mean 2
pairs of single-shaft accidentals in addition to conventional sharp
and flat (or the equivalent larger set of multishaft sagittals).

That's right. So for smaller sets you need to break the chain of fifths.

> But then your notational fifth for magic is not a meantone fifth, but
> a very nearly pythagorean one.

Yes. But the accidentals don't take you to pythagorean notes. So the (or some) accidentals would likely be shared with meantone notation.

>>I suppose magic and pythagorean notations should also unify >>on 41-equal.
> > That sounds do-able, but not meantone too.

Certainly not if meantone and pythagorean share notations for the spirals of fifths.

>>Now, the web page *I* would like to see is a comparison of >>sagittal with the Extended Helmholtz-Ellis JI system. The >>latter is horribly complex from what I've seen. I want to >>know if that's a problem with the notation or inherent in >>high-limit JIs.
> > Is there something about that on the web?

http://www.plainsound.org/ on Marc Sabat's page under research. The "Tunable Interval Melodic Steps" article is interesting because it gives a reasonably systematic list of JI intervals.

Graham

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

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Dave Keenan wrote:
> > Magic has 5 generators to the fifth, so to notate it with
> > chain-of-fifth nominals you need at least 2 pairs of accidentals and
> > it will be nearly as bad as a chain of fifths notation for miracle,
> > which has 6 gens to the fifth and so needs 3 pairs of accidentals
> > (floor(n/2)). And you'd have to go to 41-ET to get those accidentals
> > /| and /|\ in the same way you go to 72-ET to get the accidentals for
> > miracle.
> > I'm thinking in mixed sagittal, as I usually do, so here I mean 2
> pairs of single-shaft accidentals in addition to
> conventional sharp
> and flat (or the equivalent larger set of multishaft sagittals).
>
> That's right. So for smaller sets you need to break the
> chain of fifths.
>
> > But then your notational fifth for magic is not a meantone fifth, but
> > a very nearly pythagorean one.
>
> Yes. But the accidentals don't take you to pythagorean
> notes. So the (or some) accidentals would likely be shared
> with meantone notation.

I'm not sure we're talking about the same thing. Here's the kind of
chain-of-fifths based notation for Magic[19] I had in mind. You may
need Show Options/Use Fixed Width Font to see the columns correctly.
Major thirds (generators) are horizontal and line-wrap, minor thirds
are diagonal, fifths are vertical.

E\ G#\\
Cb// Eb/ G B\ D#\\
Gb// Bb/ D F#\ A#\\
Db// F/ A C#\ E#\\
Ab// C/

One would just have to learn that G#\\ to Cb// etc were major thirds
even though they are spelled as sort of doubly diminished fourths.

OK. I guess I see what you're talking about now. If you use #\ instead
of # for meantones then more notes of 19-EDO will have the same
notation whether notated as Meantone[19] or Magic[19].

-- Dave

🔗Carl Lumma <carl@lumma.org>

🔗Graham Breed <gbreed@gmail.com>

Dave Keenan wrote:

> I'm not sure we're talking about the same thing. Here's the kind of
> chain-of-fifths based notation for Magic[19] I had in mind. You may
> need Show Options/Use Fixed Width Font to see the columns correctly.
> Major thirds (generators) are horizontal and line-wrap, minor thirds
> are diagonal, fifths are vertical.
> > E\ G#\\
> Cb// Eb/ G B\ D#\\
> Gb// Bb/ D F#\ A#\\
> Db// F/ A C#\ E#\\
> Ab// C/

That's it. In pure sagittal there'd be two pairs of two shaft symbols and a single pair of one shaft symbols.

> One would just have to learn that G#\\ to Cb// etc were major thirds
> even though they are spelled as sort of doubly diminished fourths.

Yes. And as doubly diminished fourths won't be that common outside of magic temperaments you won't go far wrong by assuming this is generally the case. Maybe the accidentals can be chosen so that the magic unison vector becomes a suitably small interval in JI.

Another feature is that all fifths that approximate 3:2 are spelt correctly. That's also true of schismatic temperament. In both cases the fifths will typically be tuned almost pure. So they can share the comma shift symbol with just intonation. Performers can learn that when they see a score with these comma shifts, they should play correctly spelt fifths pure.

(In 22-equal, for example, you still need comma shifts but the fifths are significantly wider. For such tunings, even within a magic framework, I'd suggest a distinct single shaft accidental.)

There are various cues that will suggest a magic context. The music will tend to drift along a spiral of thirds rather than fifths. The score will have a relatively small set of accidentals with comma shifts. Pythagorean intevals will be rare. All this will enforce the habit of tuning major thirds a little flat and making those doubly diminished fourths into major thirds.

I'm leaving the 7-limit intervals to one side. The temperaments I mention all have 225:224 as a unison vector so there'll be a natural consistency.

> OK. I guess I see what you're talking about now. If you use #\ instead
> of # for meantones then more notes of 19-EDO will have the same
> notation whether notated as Meantone[19] or Magic[19].

The idea is that certain intervals will be consistent between temperaments. A meantone score will mix apparently Pythagorean with (nearly) 5-limit thirds. It'll also have no comma shifts and imply bad fifths between nominals and other notes. This should suggest a meantone context to the performer so that they can flatten the fifths and interpret triads on the nominals as approximating the 5-limit.

If a score contains comma shifts, then a third on the nominals will naturally be played as pythagorean. Similarly, if sharps and flats are used to give pythagorean intervals but nothing else the performer can assume the nominals should be pythagorean.

If a performer misreads the context, the errors should be minimal because the accidentals will guide them towards the correct notes.

This all seems to me to be the way sagittal should work -- at least for reasonably accurate temperaments on a conventional staff. It ties in with other design choices like having a consistent set of symbols with the number of shafts and direction of the arrow indicating the size. Maybe it won't work in practice, but until we know that it's the simple, consistent system I suggest.

I proposed a system for magic with 9 nominals on tuning-math. I think that's the natural "native" notation for magic. Only experience can show how it compares with adapting to a conventional staff. The two approaches are naturally inconsistent (like with MegaScore) but can still share the set of accidentals.

Graham