cents as "training wheels"

I'm in the middle of converting a piece in the Sims 72-tET notation
to Johnny Reinhard's "cents notation."

I have an intermediate score *between* the two versions: it includes
*both* the 72-tET symbols *AND* cents notation.

I'm beginning to think maybe this could be a useful thing. I
remember cellist Dan Barrett scratching his head trying to remember
which 72-tET symbol was which [especially the quartertone ones]. If
the cents notation were there, there would be no question.

On the other hand, the Sims symbols seem to me to carry an important
visual recognition, especially since the same cents values repeat
over and over again in the 72-tET system.

Personally, I'm leaning to maybe including *both,* in my scores,
having the cents notation as a kind of "training wheels" for the Sims
notation. After all, *any and every* crutch should be used since
these dedicated microtonal systems are really quite far from the
performance practice of the average player...

Something to think about...

[Johnny Reinhard has made it clear, though, that he *only* wants
cents indications on scores for his group, no other notations
whatsoever....and I have to oblige his decision in that]

J. Pehrson

Joe,

I'm with you, and Johnny. I always include cents
alongside ratios when defining intervals.

==Mark Rankin

--- Joseph Pehrson <jpehrson@rcn.com> wrote:
> I'm in the middle of converting a piece in the Sims
> 72-tET notation
> to Johnny Reinhard's "cents notation."
>
> I have an intermediate score *between* the two
> versions: it includes
> *both* the 72-tET symbols *AND* cents notation.
>
> I'm beginning to think maybe this could be a useful
> thing. I
> remember cellist Dan Barrett scratching his head
> trying to remember
> which 72-tET symbol was which [especially the
> quartertone ones]. If
> the cents notation were there, there would be no
> question.
>
> On the other hand, the Sims symbols seem to me to
> carry an important
> visual recognition, especially since the same cents
> values repeat
> over and over again in the 72-tET system.
>
> Personally, I'm leaning to maybe including *both,*
> in my scores,
> having the cents notation as a kind of "training
> wheels" for the Sims
> notation. After all, *any and every* crutch should
> be used since
> these dedicated microtonal systems are really quite
> far from the
> performance practice of the average player...
>
> Something to think about...
>
> [Johnny Reinhard has made it clear, though, that he
> *only* wants
> cents indications on scores for his group, no other
> notations
> whatsoever....and I have to oblige his decision in
> that]
>
> J. Pehrson
>
>
>

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In a message dated 9/9/03 10:40:09 PM Eastern Daylight Time, jpehrson@rcn.com
writes:

> Personally, I'm leaning to maybe including *both,* in my scores,
> having the cents notation as a kind of "training wheels" for the Sims
> notation. After all, *any and every* crutch should be used since
> these dedicated microtonal systems are really quite far from the
> performance practice of the average player...
>
> Something to think about...
>
> [Johnny Reinhard has made it clear, though, that he *only* wants
> cents indications on scores for his group, no other notations
> whatsoever....and I have to oblige his decision in that]
>
> J. Pehrson

Joseph, have you considered that the 72-note symbols are the training wheels?
Regardless, double notation defeats the purpose of explicit meaning. It
divides the eye...and mind.

best, Johnny

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

/tuning/topicId_46826.html#46829

> In a message dated 9/9/03 10:40:09 PM Eastern Daylight Time,
jpehrson@r...
> writes:
>
>
> > Personally, I'm leaning to maybe including *both,* in my scores,
> > having the cents notation as a kind of "training wheels" for the
Sims
> > notation. After all, *any and every* crutch should be used
since
> > these dedicated microtonal systems are really quite far from the
> > performance practice of the average player...
> >
> > Something to think about...
> >
> > [Johnny Reinhard has made it clear, though, that he *only* wants
> > cents indications on scores for his group, no other notations
> > whatsoever....and I have to oblige his decision in that]
> >
> > J. Pehrson
>
>
> Joseph, have you considered that the 72-note symbols are the
training wheels?
> Regardless, double notation defeats the purpose of explicit
meaning. It
> divides the eye...and mind.
>
> best, Johnny

***Hi Johnny!

Well, I'm not really certain I agree with you on this one. Think of
the cents numbers as something like "fingering numbers" in piano
music. One doesn't always look at them, but if there is confusion,
one does. So, essentially, people would be looking only at the Sims
accidentals and only if there is *confusion* would they look at the
cents values. Anyway, this is how it appear to me at this moment.
The graphic symbols really *do* add to the facility, I believe.

Don't worry, though. For your AFMM score, there will *only* be
cents indications! :)

Joseph

--- Joseph Pehrson <jpehrson@rcn.com> wrote:

> Well, I'm not really certain I agree with you on this one. Think of
> the cents numbers as something like "fingering numbers" in piano
> music. One doesn't always look at them, but if there is confusion,
> one does. So, essentially, people would be looking only at the Sims
> accidentals and only if there is *confusion* would they look at the
> cents values. Anyway, this is how it appear to me at this moment.
> The graphic symbols really *do* add to the facility, I believe.

A fretted bass is a fretless bass with training wheels. ;)

Actually, I use Pythagorean tuning as a reference for just intonation: a
syntonic comma is slightly less than a Pythag comma, a septimal comma is
slightly more, a minor diesis less than two, an undecimal comma greater than
two, etc. If I ever get a custom bass made, it'll be a fretless lined in
53-tone Pythagorean, with twelve "main notes" solid lines and the other 41
dotted. I'll call it the "Football Field Bass".

What is the cents notation in practice? - is there an example score somewhere
online? -Justin

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> I'm in the middle of converting a piece in the Sims 72-tET notation
> to Johnny Reinhard's "cents notation."
>
> I have an intermediate score *between* the two versions: it includes
> *both* the 72-tET symbols *AND* cents notation.
>
> I'm beginning to think maybe this could be a useful thing. I
> remember cellist Dan Barrett scratching his head trying to remember
> which 72-tET symbol was which [especially the quartertone ones]. If
> the cents notation were there, there would be no question.
>
> On the other hand, the Sims symbols seem to me to carry an important
> visual recognition, especially since the same cents values repeat
> over and over again in the 72-tET system.
>
> Personally, I'm leaning to maybe including *both,* in my scores,
> having the cents notation as a kind of "training wheels" for the Sims
> notation. After all, *any and every* crutch should be used since
> these dedicated microtonal systems are really quite far from the
> performance practice of the average player...
>
> Something to think about...
>
> [Johnny Reinhard has made it clear, though, that he *only* wants
> cents indications on scores for his group, no other notations
> whatsoever....and I have to oblige his decision in that]
>
> J. Pehrson

--- In tuning@yahoogroups.com, "Justin Weaver" <improvist@u...> wrote:

/tuning/topicId_46826.html#46840

> What is the cents notation in practice? - is there an example
score somewhere
> online? -Justin
>

***Yes, there is one up. It's from my piece _Violahexy_ and it
indicates the +/- cents numbers from the nearest quartertone.

The file is called, logically, "cents notation.gif":

/tuning/files/Pehrson/

J. Pehrson

--- Joseph Pehrson <jpehrson@rcn.com> wrote:

> > What is the cents notation in practice? - is there an example
> score somewhere
> > online? -Justin
> >
>
> ***Yes, there is one up. It's from my piece _Violahexy_ and it
> indicates the +/- cents numbers from the nearest quartertone.
>
> The file is called, logically, "cents notation.gif":
>
> /tuning/files/Pehrson/

There's also Monzo's just-intonation analysis of a Robert Johnson song, which
uses both cents from 12-tet and rational exponents:

http://sonic-arts.org/monzo/rjohnson/drunken.htm

I use a +/- number type of notation myself for my music (nothing published
yet), but it indicates notes raised or lowered a comma or a fraction of a
comma, much like Eitz notation.

Danny Wier wrote:

>Actually, I use Pythagorean tuning as a reference for just intonation: a
>syntonic comma is slightly less than a Pythag comma, a septimal comma is
>slightly more, a minor diesis less than two, an undecimal comma greater than
>two, etc. If I ever get a custom bass made, it'll be a fretless lined in
>53-tone Pythagorean, with twelve "main notes" solid lines and the other 41
>dotted. I'll call it the "Football Field Bass".
>
> A fretted bass is a fretless bass with training wheels. ;)

Why do you need lines on a fretless?

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

From: "David Beardsley" <db@biink.com>

> Danny Wier wrote:
>
> >Actually, I use Pythagorean tuning as a reference for just intonation: a
> >syntonic comma is slightly less than a Pythag comma, a septimal comma is
> >slightly more, a minor diesis less than two, an undecimal comma greater
than
> >two, etc. If I ever get a custom bass made, it'll be a fretless lined in
> >53-tone Pythagorean, with twelve "main notes" solid lines and the other
41
> >dotted. I'll call it the "Football Field Bass".
> >
> > A fretted bass is a fretless bass with training wheels. ;)
>
> Why do you need lines on a fretless?

They do come in handy if one's used to a fretted bass and doesn't have
perfect pitch. I don't need them for 12-tone purposes, since my ears are
well-trained to that level, but I'm still working on microtonal eat
training. An out-of-tune bass in any situation will ruin an entire
performance and can be considered a type of torture for a listening
audience.

--- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:

> An out-of-tune bass in any situation will ruin an entire
> performance and can be considered a type of torture for a listening
> audience.

jazz?
:)

on 9/10/03 8:47 AM, Joseph Pehrson <jpehrson@rcn.com> wrote:

> --- In tuning@yahoogroups.com, Afmmjr@a... wrote:
>
> /tuning/topicId_46826.html#46829
>
>> In a message dated 9/9/03 10:40:09 PM Eastern Daylight Time,
> jpehrson@r...
>> writes:
>>
>>
>>> Personally, I'm leaning to maybe including *both,* in my scores,
>>> having the cents notation as a kind of "training wheels" for the
> Sims
>>> notation. After all, *any and every* crutch should be used
> since
>>> these dedicated microtonal systems are really quite far from the
>>> performance practice of the average player...
>>>
>>> Something to think about...
>>>
>>> [Johnny Reinhard has made it clear, though, that he *only* wants
>>> cents indications on scores for his group, no other notations
>>> whatsoever....and I have to oblige his decision in that]
>>>
>>> J. Pehrson
>>
>>
>> Joseph, have you considered that the 72-note symbols are the
> training wheels?
>> Regardless, double notation defeats the purpose of explicit
> meaning. It
>> divides the eye...and mind.
>>
>> best, Johnny
>
>
> ***Hi Johnny!
>
> Well, I'm not really certain I agree with you on this one. Think of
> the cents numbers as something like "fingering numbers" in piano
> music. One doesn't always look at them, but if there is confusion,
> one does.

Well I can't imagine having all these numbers together on the same score in
a polyphonic (? forgetting the right term) compositon, e.g. like a Bach
Prelude and Fugue, meaning fingering numbers, interval ratios, cents numbers
- where would they all go? Are there any examples of this scenario?
Especially when the prime+power notation is used it gets a little busy.

(Veering a little off-topic here, but I'd personally rather see a power in
the denominator than a negative power. I find the minus signs to be less
visually meaningful than an unsigned number.)

Anyway I'd "vote" for putting the cents numbers in 50% gray (or else a thin
font), if that is an option in the printing process.

-Kurt

> So, essentially, people would be looking only at the Sims
> accidentals and only if there is *confusion* would they look at the
> cents values. Anyway, this is how it appear to me at this moment.
> The graphic symbols really *do* add to the facility, I believe.
>
> Don't worry, though. For your AFMM score, there will *only* be
> cents indications! :)
>
> Joseph
>
>
>
>
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Danny Wier wrote:

>>>A fretted bass is a fretless bass with training wheels. ;)
>>> >>>
>>Why do you need lines on a fretless?
>> >>
>
>They do come in handy if one's used to a fretted bass and doesn't have
>perfect pitch. I don't need them for 12-tone purposes, since my ears are
>well-trained to that level, but I'm still working on microtonal eat
>training. An out-of-tune bass in any situation will ruin an entire
>performance and can be considered a type of torture for a listening
>audience.
>
Even on an instrument that has received a pro set up,
the fret lines are only going to get you in the neighborhood.
You still have to use your ear to get in tune.

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

/tuning/topicId_46826.html#46921

> > ***Hi Johnny!
> >
> > Well, I'm not really certain I agree with you on this one. Think
of
> > the cents numbers as something like "fingering numbers" in piano
> > music. One doesn't always look at them, but if there is
confusion,
> > one does.
>
> Well I can't imagine having all these numbers together on the same
score in
> a polyphonic (? forgetting the right term) compositon, e.g. like a
Bach
> Prelude and Fugue, meaning fingering numbers, interval ratios,
cents numbers
> - where would they all go? Are there any examples of this scenario?
> Especially when the prime+power notation is used it gets a little
busy.
>
> (Veering a little off-topic here, but I'd personally rather see a
power in
> the denominator than a negative power. I find the minus signs to
be less
> visually meaningful than an unsigned number.)
>
> Anyway I'd "vote" for putting the cents numbers in 50% gray (or
else a thin
> font), if that is an option in the printing process.
>
> -Kurt
>

***Well, that could be a good idea. The cents numbers, though, are
the *only* numbers on this particular score. The Sims "graphic
notation" is in front of the notes and is *not* numeric. The
question is whether using *both* notations together is a positive or
a negative.

It remains to be seen. I'm making *three* copies of this score: one
with *only* the Sims accidentals, one with *only* CENTS notation, and
*one* with both.

I'll have to think about it a bit and try it out with players before
I have a final opinion on it...

Joseph Pehrson

In a message dated 9/13/2003 2:37:12 AM Eastern Daylight Time,
kkb@breathsense.com writes:

> >***Hi Johnny!
> >
> >Well, I'm not really certain I agree with you on this one. Think of
> >the cents numbers as something like "fingering numbers" in piano
> >music. One doesn't always look at them, but if there is confusion,
> >one does.

Alas, when playing a woodwind, there are actual "fingering numbers" which
indicate the proper grippings for playing microtones. These must be distinct
from cents indications. One could of course memorize either, but both need to be
there at first.

> Well I can't imagine having all these numbers together on the same score in
> a polyphonic (? forgetting the right term) compositon, e.g. like a Bach
> Prelude and Fugue, meaning fingering numbers, interval ratios, cents numbers
> - where would they all go?

Of course not. Any instrument that is pretuned, such as a keyboard, doesn't
need cents indications at all. (It could be helpful in the instance of
coordinating with more flexibly tuned instruments, however).

Are there any examples of this scenario?
> Especially when the prime+power notation is used it gets a little busy.
>
Cents trumps ratios for performace reading. Ratios better give the
understanding of what is to be achieved and why, but cents gets you there faster. The
ready speed of cents putting the player at the right location is what makes it
rather ideal in performance circumstances, as much experience has
demonstrated.

> Anyway I'd "vote" for putting the cents numbers in 50% gray (or else a thin
> font), if that is an option in the printing process.
>
> -Kurt
>

Making the cents lighter and in a thin font defeats the purpose of easy
reading. Please take it from a reader that trains readers, it is better to have
the cents visible (and maybe not always necessary on a case to case basis to the
individual performers) than otherwise.

best, Johnny Reinhard

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> In a message dated 9/13/2003 2:37:12 AM Eastern Daylight Time,
> kkb@b... writes:
>
> > >***Hi Johnny!
> > >
> > >Well, I'm not really certain I agree with you on this one.
Think of
> > >the cents numbers as something like "fingering numbers" in piano
> > >music. One doesn't always look at them, but if there is
confusion,
> > >one does.
>
> Alas, when playing a woodwind, there are actual "fingering numbers"
which
> indicate the proper grippings for playing microtones. These must
be distinct
> from cents indications. One could of course memorize either, but
both need to be
> there at first.
>
> > Well I can't imagine having all these numbers together on the
same score in
> > a polyphonic (? forgetting the right term) compositon, e.g. like
a Bach
> > Prelude and Fugue, meaning fingering numbers, interval ratios,
cents numbers
> > - where would they all go?
>
> Of course not. Any instrument that is pretuned, such as a
keyboard, doesn't
> need cents indications at all. (It could be helpful in the
instance of
> coordinating with more flexibly tuned instruments, however).

(Sorry, but I've been very busy and am now trying to play catch-up in
reading the digests that have been in my mailbox, hence the delay in
responding to this.)

Johnny, I'm curious about something. If you don't use your cents
notation for a keyboard instrument, then what notation would you use
for a non-traditional keyboard instrument (such as your generalized
keyboard that is currently under construction), if the tuning to be
notated is one that cannot be adequately notated by either a
quartertone or meantone notation (e.g., a 22 or 29-tone octave, not
necessarily an ET)?

--George

In a message dated 9/25/2003 2:13:18 PM Eastern Daylight Time,
gdsecor@yahoo.com writes:

> Johnny, I'm curious about something. If you don't use your cents
> notation for a keyboard instrument, then what notation would you use
> for a non-traditional keyboard instrument (such as your generalized
> keyboard that is currently under construction), if the tuning to be
> notated is one that cannot be adequately notated by either a
> quartertone or meantone notation (e.g., a 22 or 29-tone octave, not
> necessarily an ET)?
>
>

Hello George:

You raise a good point. This yet needs to be thought out. Clearly, any
composer can notate any which way as there is no notation authority. At least
standard notation with cents deviations indicated will still work. However,
there may be a more tabulature-like streamlining possible.

best, Johnny Reinhard

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> In a message dated 9/25/2003 2:13:18 PM Eastern Daylight Time,
> gdsecor@y... writes:
>
> > Johnny, I'm curious about something. If you don't use your cents
> > notation for a keyboard instrument, then what notation would you
use
> > for a non-traditional keyboard instrument (such as your
generalized
> > keyboard that is currently under construction), if the tuning to
be
> > notated is one that cannot be adequately notated by either a
> > quartertone or meantone notation (e.g., a 22 or 29-tone octave,
not
> > necessarily an ET)?
>
> Hello George:
>
> You raise a good point. This yet needs to be thought out.

Yes, and very carefully. As you know, Dave Keenan and I have been
doing precisely that with our sagittal notation project for the past
year and a half. I hope you'll consider it for this purpose when we
release it (very soon).

> Clearly, any
> composer can notate any which way as there is no notation
authority. At least
> standard notation with cents deviations indicated will still work.
However,
> there may be a more tabulature-like streamlining possible.

I would not want to think of sagittal notation as a tablature, a term
that reminds me of little diagrams above the staff that I've seen in
method books to show guitar or woodwind fingerings. We have gone to
great lengths to ensure that our symbols can be employed for many
different tunings, so we have taken it for granted that the notation
would automatically be instrument-independent -- quite the opposite
of what comes to my mind when one speaks of a tablature.

Now if you want to think of the conventional staff as a tablature,
well okay. But for a whole collection of polyphonic instruments
(i.e., keyboard, guitar, fixed-pitch percussion) for which cents are
not necessary, I hope that you would prefer a single notation that
can serve them all (and in which players of flexible-pitch
instruments might also find some benefit).

--George

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> > Clearly, any
> > composer can notate any which way as there is no notation
> authority. At least
> > standard notation with cents deviations indicated will still work.
> However,
> > there may be a more tabulature-like streamlining possible.
>
> I would not want to think of sagittal notation as a tablature, a term
> that reminds me of little diagrams above the staff that I've seen in
> method books to show guitar or woodwind fingerings. We have gone to
> great lengths to ensure that our symbols can be employed for many
> different tunings, so we have taken it for granted that the notation
> would automatically be instrument-independent -- quite the opposite
> of what comes to my mind when one speaks of a tablature.

I think Johnny means to include scordatura notations when he writes
"tablature-like".

Tablature and scordatura both describe _how_to_play_ the music on a
specific instrument, but do not represent (and in the case of
scordatura, completely obscure) _how_it_sounds_. Sagittal is intended
to represent _how_it_sounds_ in an instrument-independent manner (and
even to some degree tuning-independent).

In general, there is a need for both kinds of notation. However, on
instruments which are _designed_ for the microtonal tuning used in the
piece, or for microtonal tunings in general, it is to be hoped that
tablature or scordatura are not required, since presumably a major
objective in designing such instruments is to make it easy (with
practice) to mentally and physically translate from _how_it_sounds_ to
_how_to_play_.

>I hope that you would prefer a single notation that
>can serve them all (and in which players of flexible-pitch
>instruments might also find some benefit).

Advocacy; the last thing I want to see in microtonality.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >I hope that you would prefer a single notation that
> >can serve them all (and in which players of flexible-pitch
> >instruments might also find some benefit).
>
> Advocacy; the last thing I want to see in microtonality.

Carl,

Can you please explain in more detail what you mean by the above, and
what you are referring to?

>> >I hope that you would prefer a single notation that
>> >can serve them all (and in which players of flexible-pitch
>> >instruments might also find some benefit).
>>
>> Advocacy; the last thing I want to see in microtonality.
>
>Carl,
>
>Can you please explain in more detail what you mean by the above,
>and what you are referring to?

George is selling a notation system here, and he's done it before
even more directly.

Advocacy is a common problem in CS -- programming languages,
operating systems, text editors, etc. It's considered harmful.

Paul used to push the decatonic scales pretty hard. Those
scales may deserve it, but thankfully, he's stopped doing it.

The idea is to avoid politics -- where more energy is invested
in arguing about what to do than actually doing anything.

I can't see the point in rushing to replace the 12-tET standard
that's caused so many problems with any other standard. George
has argued that a standard is necessary for progress. I don't
believe it.

What I mean by the "last thing" is, instead of 'we need a
standard to have music', I'd rather, 'we have so much music we
need a standard to keep it from falling apart'.

Like the C language -- it was so popular, they created a
standard... in 1988! (or something). As opposed to Java, which
Sun controls, and pushes with a huge hype machine. It's utterly
failed to deliver on its promise to deliver end-user apps.

-Carl

>What I mean by the "last thing" is, instead of 'we need a
>standard to have music', I'd rather, 'we have so much music we
>need a standard to keep it from falling apart'.

Or maybe, 'I've transcribed every microtonal composition I
could get my hands on into universal notation X, and made deals
with many composers that in exchange for the transcription,
the scores shall be freely available on the universal notation
X website.'

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >I hope that you would prefer a single notation that
> >> >can serve them all (and in which players of flexible-pitch
> >> >instruments might also find some benefit).
> >>
> >> Advocacy; the last thing I want to see in microtonality.
> >
> >Carl,
> >
> >Can you please explain in more detail what you mean by the above,
> >and what you are referring to?
>
> George is selling a notation system here, and he's done it before
> even more directly.

How about: "Dave and George have worked very hard on a notation
system here, and they're not selling it, but giving it away. They're
also taking an occasional time-out from their work to address
situations when it can fill a particular need (with the hope that
their work has not been in vain)."

> Advocacy is a common problem in CS -- programming languages,
> operating systems, text editors, etc. It's considered harmful.
>
> Paul used to push the decatonic scales pretty hard. Those
> scales may deserve it, but thankfully, he's stopped doing it.
>
> The idea is to avoid politics -- where more energy is invested
> in arguing about what to do than actually doing anything.

And I think that we've spent considerably more time doing something
about the problem (elaborated on below) than we've spent promoting
our solution. All of our current work has been off-list, but as
intensive as ever, and a look at last year's tuning-math archives
will give you some idea of how much effort we've been putting into it.

> I can't see the point in rushing to replace the 12-tET standard
> that's caused so many problems with any other standard.

Our notation expands (rather than replaces) the 12-ET standard.

> George
> has argued that a standard is necessary for progress. I don't
> believe it.

I once transcribed Partch's _Two Greek Studies_ for Harmonic Canon to
play on my Scalatron. The manuscript, which was in the form of a
tablature, was almost impossible to understand without rewriting it
in a notation that I could read (which is exactly what I had to do).
There are other times when I've copied parts from someone else's
notation into one that I was more comfortable with. This would not
have been necessary if there were some sort of standard notation.

But which standard? It's one thing for a newcomer to microtonality
to discover that it's necessary to learn a new notation, but it's
much more daunting to discover that the new notation that one has
learned is not the end of the matter. By working and reworking the
notation through at least a half-dozen generations of versions (and
without releasing anything until we're completely satisfied that what
we have will not require any more major changes), we have done our
best to ensure that this scenario would not occur due to any inherent
fault or shortcoming of the sagittal notation, since it uses the same
symbols to mean (generally) the same things in *all* tunings for
*all* instruments.

> What I mean by the "last thing" is, instead of 'we need a
> standard to have music', I'd rather, 'we have so much music we
> need a standard to keep it from falling apart'.
>
> Like the C language -- it was so popular, they created a
> standard... in 1988! (or something). As opposed to Java, which
> Sun controls, and pushes with a huge hype machine. It's utterly
> failed to deliver on its promise to deliver end-user apps.

Well, we'll just have to wait and see if sagittal delivers as
promised!

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >What I mean by the "last thing" is, instead of 'we need a
> >standard to have music', I'd rather, 'we have so much music we
> >need a standard to keep it from falling apart'.
>
> Or maybe, 'I've transcribed every microtonal composition I
> could get my hands on into universal notation X, and made deals
> with many composers that in exchange for the transcription,
> the scores shall be freely available on the universal notation
> X website.'

Hopefully, someday we will have software than could do this. The
commercial musical notation products that are out there right now
aren't very promising in this regard.

--George

>How about: "Dave and George have worked very hard on a notation
>system here, and they're not selling it, but giving it away. They're
>also taking an occasional time-out from their work to address
>situations when it can fill a particular need (with the hope that
>their work has not been in vain)."

Sorry I came down so hard. I was using selling as synonymous with
promoting, as is common usage. I still don't see the point of
repeatedly mentioning it before it's available.

>And I think that we've spent considerably more time doing something
>about the problem (elaborated on below) than we've spent promoting
>our solution. All of our current work has been off-list, but as
>intensive as ever, and a look at last year's tuning-math archives
>will give you some idea of how much effort we've been putting into it.

I know you've worked hard.

>> I can't see the point in rushing to replace the 12-tET standard
>> that's caused so many problems with any other standard.
>
>Our notation expands (rather than replaces) the 12-ET standard.

Yeah; that's a fair summary of my criticism of it.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >I hope that you would prefer a single notation that
> >> >can serve them all (and in which players of flexible-pitch
> >> >instruments might also find some benefit).
> >>
> >> Advocacy; the last thing I want to see in microtonality.
> >
> >Carl,
> >
> >Can you please explain in more detail what you mean by the above,
> >and what you are referring to?
>
> George is selling a notation system here, and he's done it before
> even more directly.

Hmm. I assume you mean "selling" figuratively, since the notation is
being offered freely.

This is a fine line isn't it? What's the difference between "advocacy"
in your usage, and explaining the benefits of something new, so people
can make an informed choice as to whether to adopt it or not?

> The idea is to avoid politics -- where more energy is invested
> in arguing about what to do than actually doing anything.

Hoo boy. I really don't think we can be accused of that in regard to
the development of sagittal. I feel that all the energy so far has
gone into _getting_it_right_ from the point of view of utility,
simplicity, readability, completeness etc.

> I can't see the point in rushing to replace the 12-tET standard
> that's caused so many problems with any other standard.

The Sagittal notation system allows for _augmenting_ rather than
replacing 12-tET-based notation, if that's what you want to do.

But if you think 12-tET-based notation has caused so many problems
then why wouldn't you want to replace it? And who is rushing? People
have been inventing limited microtonal notations for over a hundred
years. Many have been surveyed by Prof Gardner Read in his book "20th
Century Microtonal Notations". George and I and many others who helped
in the project, (including your good self) have been thinking about
notation issues for years, and have built on the lessons learned in
many of the earlier attempts. Sagittal attempts to allow the same
semantics as most special-purpose notations that have ever been used
before, but with a consistent set of accidental symbols used across
all of them.

> George
> has argued that a standard is necessary for progress. I don't
> believe it.

I don't think he would have said "necessary", or if he did, I don't
think he meant it in the mathematical sense. Don't you think a
standard might be beneficial? If you're concerned that it may be too
limiting, wait until you understand its full scope.

The only thing I can think of that it won't do, is something
semantically equivalent to Johnston notation, where the nominals are
assumed to be in the 5-limit JI major.
A E B
F C G D
Sagittal does assume that the nominals (and there could be more than
7) form a linear (or very nearly linear) sequence.

Since no-one can be forced to use it, it must stand or fall on its own
merits. But that isn't much use if no one knows what those merits are,
because we're accused of "advocacy" when we try to explain.

> What I mean by the "last thing" is, instead of 'we need a
> standard to have music', I'd rather, 'we have so much music we
> need a standard to keep it from falling apart'.

Yes. The latter may already be true.

> Like the C language -- it was so popular, they created a
> standard... in 1988! (or something). As opposed to Java, which
> Sun controls, and pushes with a huge hype machine. It's utterly
> failed to deliver on its promise to deliver end-user apps.

You can rest assured there will be no huge hype machine behind
sagittal. It's a free product designed by volunteers in their spare
time, and still open to improvement.

> Or maybe, 'I've transcribed every microtonal composition I
> could get my hands on into universal notation X, and made deals
> with many composers that in exchange for the transcription,
> the scores shall be freely available on the universal notation
> X website.'

I'm not sure I follow. Are you saying that in order to get people
interested in using the sagittal notation system, we're not only going
to have to design it for free, but provide a free transcription
service? I'm so exhausted from helping design it that it's quite an
effort now to push on and actually write it up and _explain_ it. But
rest assured that we _are_ working on that.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Sorry I came down so hard. I was using selling as synonymous with
> promoting, as is common usage. I still don't see the point of
> repeatedly mentioning it before it's available.

Yes. I can understand how that must be annoying. You can't imagine how
frustrating it is for us too. But there are only so many hours in a
day and we have jobs and families (fortunately). But it has come a
long way since we realised we'd gotten into fine details that no-one
else was following and took it off the tuning-math list.

we're working on the explanations, and the font, and the methods for
getting to use the font in Sibelius and Finale, and believe me, they
haven't made it easy for us.

But it's hard for us to resist telling you bits and pieces about it,
when the opportunity arises. :-)

> >Our notation expands (rather than replaces) the 12-ET standard.
>
> Yeah; that's a fair summary of my criticism of it.

Oh dear. We are cynical aren't we. :-)

George should have said it _optionally_ expands the 12-ET standard.

What the sagittal system is, is a logical and readable set of
accidental symbols that we believe cover almost every conceivable
musical purpose, combined with a way of deciding which is the right
one to use for a given purpose.

History has shown that in things of this ilk, evolution, not
revolution, is the rule. Witness the virtual demise of most of the
beautifully designed object oriented languages that were _not_ derived
from C.

So if you hope for something radically different from what's in use
now, to eventually become the norm, then there had better be a
migration path that can be taken a little step at a time. But people
like you are free to take a leap and start using the symbols in
revolutionary ways, while still being faithful to the general meaning
of the symbols.

I seem to remember that your desire was for notations whose nominals
were designed for a specific linear temperament. There could be more
or less than 7 and they would be in a chain of generators, not
necessarily a chain of fifths. When you do that, you are still going
to need special accidental symbols when you go outside of your nominals...

And boy do we have the accidentals for you! We'll even throw in a free
set of steak-knives. ;-)

>> >Our notation expands (rather than replaces) the 12-ET standard.
>>
>> Yeah; that's a fair summary of my criticism of it.
>
>Oh dear. We are cynical aren't we. :-)

Too much coffee, I guess. :)

No, sorry for the belligerent post. I guess I'm sore that issues I
raised in the thread starting here...

/tuning-math/message/5246

...were never addressed, and aren't addressed when the topic of
sagittal notation comes up.

>What the sagittal system is, is a logical and readable set of
>accidental symbols that we believe cover almost every conceivable
>musical purpose, combined with a way of deciding which is the right
>one to use for a given purpose.

See? It's like a car brochure. It doesn't really tell me anything
about what sagittal notation is!

>So if you hope for something radically different from what's in use
>now, to eventually become the norm, then there had better be a
>migration path that can be taken a little step at a time. But people
>like you are free to take a leap and start using the symbols in
>revolutionary ways, while still being faithful to the general meaning
>of the symbols.

It all depends on how you generalize conventional notation. My post,
'quick summary on my thought on notation' presents an argument that
sagittal notation is actually the more radically different proposal.

>I seem to remember that your desire was for notations whose nominals
>were designed for a specific linear temperament. There could be more
>or less than 7 and they would be in a chain of generators, not
>necessarily a chain of fifths. When you do that, you are still going
>to need special accidental symbols when you go outside of your
>nominals...
>
>And boy do we have the accidentals for you! We'll even throw in a
>free set of steak-knives. ;-)

:) You remember correctly, and I'll graciously accept the accidentals.

I'm after accidentals for the simplest commas, with (if possible) the
harder-to-read accidentals being mapped to the more complex commas,
and finally the most complex commi being notated with multiple
accidentals.

But also in that thread, I assert that by forcing 7 nominals, you
ruin the mapping from commas to accidentals. Care to rebut that?

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >What the sagittal system is, is a logical and readable set of
> >accidental symbols that we believe cover almost every conceivable
> >musical purpose, combined with a way of deciding which is the right
> >one to use for a given purpose.
>
> See? It's like a car brochure. It doesn't really tell me anything
> about what sagittal notation is!

OK. But it tells you a lot about what it isn't. :-)

> >So if you hope for something radically different from what's in use
> >now, to eventually become the norm, then there had better be a
> >migration path that can be taken a little step at a time. But people
> >like you are free to take a leap and start using the symbols in
> >revolutionary ways, while still being faithful to the general meaning
> >of the symbols.
>
> It all depends on how you generalize conventional notation. My post,
> 'quick summary on my thought on notation' presents an argument that
> sagittal notation is actually the more radically different proposal.

I just reread it, but I'm afraid I don't understand how it argues the
above. Perhaps it's a bit too condensed. Or perhaps I am. :-) Please
explain.

> >I seem to remember that your desire was for notations whose nominals
> >were designed for a specific linear temperament. There could be more
> >or less than 7 and they would be in a chain of generators, not
> >necessarily a chain of fifths. When you do that, you are still going
> >to need special accidental symbols when you go outside of your
> >nominals...
> >
> >And boy do we have the accidentals for you! We'll even throw in a
> >free set of steak-knives. ;-)
>
> :) You remember correctly, and I'll graciously accept the accidentals.
>
> I'm after accidentals for the simplest commas, with (if possible) the
> harder-to-read accidentals being mapped to the more complex commas,
> and finally the most complex commi being notated with multiple
> accidentals.

That's basically what we've done. We don't recommend multiple
accidentals (except for the combinations with conventional sharps and
flats, and the schisma accent marks) but there's nothing to stop you
doing it, while still remaining faithful to the comma meanings of the
symbols.

> But also in that thread, I assert that by forcing 7 nominals, you
> ruin the mapping from commas to accidentals. Care to rebut that?

Sure. Every Sagittal accidental has, as its primary meaning, a
particular comma which can be considered as simply a prime-exponent
vector (a monzo). This does not depend in any way on the meaning of
the nominals. It doesn't even assume octave equivalence.

Can you confirm this, George?

The "olympian" (extreme precision) Sagittal system will have unique
accidentals for hundreds of commas in the 23-limit if you need them,
and within about 0.4 cents of any comma at all. The simplest commas
have the simplest symbols.

>> >So if you hope for something radically different from what's in use
>> >now, to eventually become the norm, then there had better be a
>> >migration path that can be taken a little step at a time. But people
>> >like you are free to take a leap and start using the symbols in
>> >revolutionary ways, while still being faithful to the general
>> >meaning of the symbols.
>>
>> It all depends on how you generalize conventional notation. My post,
>> 'quick summary on my thought on notation' presents an argument that
>> sagittal notation is actually the more radically different proposal.
>
>I just reread it, but I'm afraid I don't understand how it argues the
>above. Perhaps it's a bit too condensed. Or perhaps I am. :-) Please
>explain.

It argues that conventional notation is more a notation of the type
'nominals for elements of a core scale, with accidentals for basic
commas' than of the type 'nominals for a 7-tone chain of fifths, with
accidentals that let us cover the master system'.

Probably it's too condensed.

>> But also in that thread, I assert that by forcing 7 nominals, you
>> ruin the mapping from commas to accidentals. Care to rebut that?
>
>Sure. Every Sagittal accidental has, as its primary meaning, a
>particular comma which can be considered as simply a prime-exponent
>vector (a monzo). This does not depend in any way on the meaning of
>the nominals. It doesn't even assume octave equivalence.

Would you consider a notation system with 10 nominals using your
accidental set 'sagittal'?

-Carl

Carl,

One thing I noticed on rereading that thread was that George's
arguments as to why he didn't see much benefit to himself, in your
proposals, tended to obscure the fact that you _can_ do them using the
sagittal accidentals.

As evidence that we actually did take your comments on board at that
time, I offer the fact that in all three of our ASCIIfications of the
Sagittal accidentals, we made sure not to use any of the digits 0 to
9, or the uppercase letters A to L (12 letters), and in two of them we
also avoided the uppercase letters M to W and Z (24 letters total).
This is in contrast to the ASCIIfications of several other notations
available in Scala that use "7" and "L". It wasn't that we couldn't
have used them, since in the most compact version we use every other
printable ASCII character except "e", "l" and ":" (because we couldn't
convincingly assign an up or down direction or an opposite-direction
partner to these three). We avoided the digits and uppercase letters
specifically to allow for textual descriptions of notations with more
than 7 nominals, or nominals other than A to G (and German H).

Take the notations described on Graham Breed's excellent deciomal
notation page.
http://x31eq.com/decimal_notation.htm

Here are the long and short ASCII versions of what I think are the
appropriate Sagittal accidentals corresponding to Graham's various
combinations.

Graham's ASCII-Sagittal Comma interpretation
short long (prime exponents)
------------------------------------------------
^^^ or m^ # /||\ [-11,7]
^^ or m t# ||) [-17,9,0,1]
/^ ^ /|\ [-5,1,0,0,1]
^ f |) [6,-2,0,-1]
/ / /| [-4,4,-1]
\ \ \! [4,-4,1]
v t !) [-6,2,0,1]
\v v \!/ [5,-1,0,0,-1]
vv or w fb !!) [17,-9,0,-1]
vvv or wv b \||/ [11,-7]

You can see their graphical versions in Scala using SET NOTATION SA72.

You can check whether they are valid accidentals for decimal notation
by running their prime exponents thru the MIRACLE mapping to find out
how many generators each corresponds to.

Regards,
-- Dave Keenan

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

/tuning/topicId_46826.html#47301

> Hopefully, someday we will have software than could do this. The
> commercial musical notation products that are out there right now
> aren't very promising in this regard.
>
> --George

***It could be noted that the new version of the Sibelius software,
Sibelius 3, which is out next month, adds *no* new microtonal
features, at least that's what it seems. The only microtonal
addition is the ability to use glissandi over barlines, which is,
indeed, a helpful feature for my *own* music...

J. Pehrson

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

/tuning/topicId_46826.html#47310
>
> I'm not sure I follow. Are you saying that in order to get people
> interested in using the sagittal notation system, we're not only
going
> to have to design it for free, but provide a free transcription
> service? I'm so exhausted from helping design it that it's quite an
> effort now to push on and actually write it up and _explain_ it. But
> rest assured that we _are_ working on that.

***Personally, I believe the *most* important thing is to get many
people involved in thinking about this and testing this. Who would
care if it took another 5 years?! It's never been done, at least so
it appears. The worst thing would be to come out with something
inferior that then, obviously, people would shoot down and it would
be "dead in the water..."

And, the documentation and explanation shouldn't be rushed, either,
but should be available in a "dummies" kind of way, for the maximal
popular appreciation.

Maybe it will succeed if done properly and be a system that
microtonalists and the, ultimately, a larger public will adopt.

[Personally I feel the quartertones in the Sims 72-tET system are
awful, and wouldn't feel too bad about replacing *those*... :) ]

J. Pehrson

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

/tuning/topicId_46826.html#47324

> Would you consider a notation system with 10 nominals using your
> accidental set 'sagittal'?
>
> -Carl

***How awful.... Sorry, Carl... :)

J. Pehrson

hi Joe and George,

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> /tuning/topicId_46826.html#47301
>
> > Hopefully, someday we will have software than could do this.
> > The commercial musical notation products that are out there
> > right now aren't very promising in this regard.
> >
> > --George
>
>
> ***It could be noted that the new version of the Sibelius software,
> Sibelius 3, which is out next month, adds *no* new microtonal
> features, at least that's what it seems. The only microtonal
> addition is the ability to use glissandi over barlines, which is,
> indeed, a helpful feature for my *own* music...
>
> J. Pehrson

hang on just a little while longer ... i'm planning to have
all of this and more in my software, release 1.0 scheduled
for February 2004.

-monz

>/tuning/topicId_46826.html#47324
>
>> Would you consider a notation system with 10 nominals using your
>> accidental set 'sagittal'?
>>
>> -Carl
>
>
>***How awful.... Sorry, Carl... :)
>
>J. Pehrson

Try reading Beethoven with 4 nominals and get back to me.

-Carl

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

/tuning/topicId_46826.html#47341

> >/tuning/topicId_46826.html#47324
> >
> >> Would you consider a notation system with 10 nominals using your
> >> accidental set 'sagittal'?
> >>
> >> -Carl
> >
> >
> >***How awful.... Sorry, Carl... :)
> >
> >J. Pehrson
>
> Try reading Beethoven with 4 nominals and get back to me.
>
> -Carl

***I get your drift, Carl! Still, it's going to take some "getting
used to..." :)

JP

I wrote: "You can check whether they are valid accidentals for decimal
notation by running their prime exponents thru the MIRACLE mapping to
find out how many generators each corresponds to."

When I did so, I found that I'd got it wrong for the multi-shaft
sagittals (by wrongly assuming 72-ET).

I've posted a followup on tuning-math under the subject:
"Sagittal accidentals for Decimal/MIRACLE notation" at
/tuning-math/message/6900

-- Dave Keenan

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> It all depends on how you generalize conventional notation. My post,
> >> 'quick summary on my thought on notation' presents an argument that
> >> sagittal notation is actually the more radically different proposal.
> >
> >I just reread it, but I'm afraid I don't understand how it argues the
> >above. Perhaps it's a bit too condensed. Or perhaps I am. :-) Please
> >explain.
>
> It argues that conventional notation is more a notation of the type
> 'nominals for elements of a core scale, with accidentals for basic
> commas' than of the type 'nominals for a 7-tone chain of fifths, with
> accidentals that let us cover the master system'.

I'm not sure what you mean by "master system", but I think Sagittal is
neither of these, but rather 'nominals for a 7-tone chain of fifths,
with accidentals for many commas'

The same conventional notation has been used historically for both
Pythagorean and meantone as well as 12-ET, and in all cases the
following is a chain of fifths: Ab Eb Bb F C G D A E B F# C# G#, with
Ab being lower or higher or the same as G# at the case may be.

Doesn't that make it clear that conventional notation can equally be
considered to be 'nominals for a 7-tone chain of fifths, with
accidentals for basic commas (namely multiples of the apotome 3^7/2^11)'.

But as I have indicated elsewhere, we can indeed use sagittal
accidentals to make a notation having 'nominals for a 10-tone chain of
secors, with accidentals for basic commas'.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
[GS:]
> >> >Our notation expands (rather than replaces) the 12-ET standard.
> >> [CL:]
> >> Yeah; that's a fair summary of my criticism of it.
> >[DK:]
> >Oh dear. We are cynical aren't we. :-)
> [CL:]
> Too much coffee, I guess. :)
>
> No, sorry for the belligerent post. I guess I'm sore that issues I
> raised in the thread starting here...
>
> /tuning-math/message/5246
>
> ...were never addressed, and aren't addressed when the topic of
> sagittal notation comes up.

I tried to address them in the ensuing correspondence). See my
response to your comment below.

> ...
[DK:]
> >I seem to remember that your desire was for notations whose
nominals
> >were designed for a specific linear temperament. There could be
more
> >or less than 7 and they would be in a chain of generators, not
> >necessarily a chain of fifths. When you do that, you are still
going
> >to need special accidental symbols when you go outside of your
> >nominals...
> >
> >And boy do we have the accidentals for you! We'll even throw in a
> >free set of steak-knives. ;-)
> [CL:]
> :) You remember correctly, and I'll graciously accept the
accidentals.
>
> I'm after accidentals for the simplest commas, with (if possible)
the
> harder-to-read accidentals being mapped to the more complex commas,
> and finally the most complex commi being notated with multiple
> accidentals.
>
> But also in that thread, I assert that by forcing 7 nominals, you
> ruin the mapping from commas to accidentals. Care to rebut that?

In my message:
/tuning-math/message/5267
I drew the following conclusion:

<< The broader point that I was trying to make seems to have gotten
lost in all of the details of the discussion. I was trying to show
that there is no particular advantage in using decimal notation to
notate music that is *not* based on the Miracle geometry (e.g.,
Partch's music, which is better understood in reference to an 11-
limit tonality diamond), but for which the tones may still be very
suitably mapped onto a decimal keyboard. The advantage of decimal
notation comes into effect only when and if you are using the Miracle
temperament itself, i.e., exploiting the tonal relationships that are
unique to Miracle. Likewise, if I play something in 31, 41, or 72-ET
on a decimal keyboard that was composed by someone utterly ignorant
of Miracle as an organizing principle for tonality (as I believe
*all* of us were up until a couple of years ago -- myself included),
is the decimal notation going to benefit me in any way if the
composition which I am playing was not conceived as being decatonic?
I think not. These three divisions can be treated as *either*
heptatonic *or* decatonic, and I could even show you a unidecatonic
MOS subset of 31-ET (with a very useful tetrad that occurs in 5
places). But it would be unrealistic to expect anyone to learn three
different notations for one tonal system, according to which tonal
relationships are exploited in a given piece. (Or suppose that a
piece is heptatonic in one place and decatonic in another. Do we
switch notations in the middle of the page?)

My point is that alternate tunings often do not tie us down to
specific tonal organizations, so the choice of a tuning is often not
enough to determine how many nominals would be "best" for its
notation. Since we are already acquainted with a notation that uses
7 nominals, and if that works reasonably well for many alternative
tunings, then why not have a generalized notation that builds on that?

So I would therefore require a microtonal musician to learn no more
than one new notation. A composer may wish to do otherwise when
composing, but a translation would be provided for the player. >>

Here is a portion of your reply from:
/tuning-math/message/5272
with my present comments.

> >[GS:]
> >The issue that I raise is: how many different notations can you
> >expect a person to learn?
> [CL:]
> As many as he needs to play the music he wants to.

Not the answer I expected! In the real world I believe that a
performer would want to have to learn as *few* different notations as
possible. So if it is possible to design a single notation that can
notate many different tunings reasonably well, then I believe it
should be done.

> [GS:]
> >But it would be unrealistic to expect anyone to learn three
> >different notations for one tonal system, according to which
> >tonal relationships are exploited in a given piece.
> [CL:]
> Perhaps we'll have to agree to disagree.

Which is evidently where we're still at.

> [GS:]
> >(Or suppose that a piece is heptatonic in one place and decatonic
> >in another. Do we switch notations in the middle of the page?)
> [CL:]
> Absolutely! Just like switching clefs or key signatures.

I tried to take this idea of having multiple notations for a single
tuning to a rather ridiculous extreme, but (much to my surprise) you
didn't agree, so the best we can do is agree to disagree. But I
wonder how many performers would agree with you, especially if the
notation were liable to switch back and forth every few measures?

BTW (Dave, are you listening?), back when these messages were
exchanged, I actually tried figuring out what sagittal accidentals
might be used for 10 nominals for Miracle. What I ended up with was
so unconventional, both with respect to our present way of thinking
harmonically (by prime factors in ratios) and to the harmonic
meanings of the sagittal symbols themselves, that I could only
conclude that it was not worth the trouble even for a composer to use
decimal notation. The Miracle relationships (involving commas and
decimal nominals) can easily be discerned by using a diagram of the
decimal keyboard labeled with a 72-ET notation (using 7 nominals,
sagittal or otherwise) -- and this is something that Joseph Pehrson
ought to be using.

So, to repeat your assertion:

> But also in that thread, I assert that by forcing 7 nominals, you
> ruin the mapping from commas to accidentals. Care to rebut that?

I answer with the following: In a Pythagorean sequence of tones
(with 7 nominals), the position in the sequence determines the power
of 3, and the prime factors above 3 may all be expressed in the
accidentals. In a sequence of tones separated by some other
generator (such as a secor), the prime factors contained or implied
in the relationships of those tones vary from one tone to another, so
any comma-to-accidental relationship is much less useful (and much
more complicated.)

But if it would make you happy, you could use sagittal symbols with
10 nominals for Miracle. I just don't think any performer will want
to read it that way.

--George

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> [DK:]
> > >I seem to remember that your desire was for notations whose
nominals
> > >were designed for a specific linear temperament. There could be
more
> > >or less than 7 and they would be in a chain of generators, not
> > >necessarily a chain of fifths. When you do that, you are still
going
> > >to need special accidental symbols when you go outside of your
> > >nominals...
> > >
> > >And boy do we have the accidentals for you! We'll even throw in a
> > >free set of steak-knives. ;-)
> > [CL:]
> > :) You remember correctly, and I'll graciously accept the
accidentals.
> >
> > I'm after accidentals for the simplest commas, with (if possible)
the
> > harder-to-read accidentals being mapped to the more complex
commas,
> > and finally the most complex commi being notated with multiple
> > accidentals.
> [DK:]
> That's basically what we've done. We don't recommend multiple
> accidentals (except for the combinations with conventional sharps
and
> flats, and the schisma accent marks) but there's nothing to stop you
> doing it, while still remaining faithful to the comma meanings of
the
> symbols.
>
> > But also in that thread, I assert that by forcing 7 nominals, you
> > ruin the mapping from commas to accidentals. Care to rebut that?
>
> Sure. Every Sagittal accidental has, as its primary meaning, a
> particular comma which can be considered as simply a prime-exponent
> vector (a monzo). This does not depend in any way on the meaning of
> the nominals. It doesn't even assume octave equivalence.
>
> Can you confirm this, George?

If "this" refers to the above statement, then I agree -- but please
see my answer to this in my message just prior to this one.

If "this" refers to the following statement,

> The "olympian" (extreme precision) Sagittal system will have unique
> accidentals for hundreds of commas in the 23-limit if you need them,
> and within about 0.4 cents of any comma at all. The simplest commas
> have the simplest symbols.

then I agree.

--George

>In my message:
>/tuning-math/message/5267
>I drew the following conclusion:
>
><< The broader point that I was trying to make seems to have gotten
>lost in all of the details of the discussion. I was trying to show
>that there is no particular advantage in using decimal notation to
>notate music that is *not* based on the Miracle geometry (e.g.,
>Partch's music, which is better understood in reference to an 11-
>limit tonality diamond), but for which the tones may still be very
>suitably mapped onto a decimal keyboard. The advantage of decimal
>notation comes into effect only when and if you are using the Miracle
>temperament itself, i.e., exploiting the tonal relationships that
>are unique to Miracle.

But this isn't true. There are many decatonic scales in the world
outside of the miracle temperament.

>Likewise, if I play something in 31, 41, or 72-ET
>on a decimal keyboard that was composed by someone utterly ignorant
>of Miracle as an organizing principle for tonality (as I believe
>*all* of us were up until a couple of years ago -- myself included),
>is the decimal notation going to benefit me in any way if the
>composition which I am playing was not conceived as being decatonic?
>I think not.

Which is why the number of nominals should match the number of tones
in the basic scale, for 'diatonic' music. That's music where chords
are build on scale degrees.

Note that triads, both major and minor, are easily recognized in
conventional notation. And it's easy to see when they're not in
the current key, because they'll require an accidental.

Here's an example...

http://lumma.org/tuning/diatonic-triads.png

Now, how would I notate the same thing, but with tetrads made
on degrees 1,4,7,9, in Paul Erlich's pentachordal major decatonic?

!
Pentachordal major decatonic in 22-tet.
10
!
109.091 !....2
218.182 !....4
381.818 !....7
490.909 !....9
600.000 !...11
709.091 !...13
872.727 !...16
981.818 !...18
1090.909 !..20
2/1 !.......22
!

>But it would be unrealistic to expect anyone to learn three
>different notations for one tonal system, according to which tonal
>relationships are exploited in a given piece.

Here's our fundamental disagreement. What's a tonal system?
In the example above, you give 31-tET, 41-tET, and 72-tET as
tonal systems. These are tunings that *contain* tonal systems.

>(Or suppose that a
>piece is heptatonic in one place and decatonic in another. Do we
>switch notations in the middle of the page?)

I answered this affirmatively in the original thread, comparing it
to key signature or clef changes in conventional notation.

>> [GS:]
>> >(Or suppose that a piece is heptatonic in one place and decatonic
>> >in another. Do we switch notations in the middle of the page?)
>> [CL:]
>> Absolutely! Just like switching clefs or key signatures.
>
>I tried to take this idea of having multiple notations for a single
>tuning to a rather ridiculous extreme, but (much to my surprise) you
>didn't agree, so the best we can do is agree to disagree. But I
>wonder how many performers would agree with you, especially if the
>notation were liable to switch back and forth every few measures?

Performers are able to learn multiple clefs, transpose on sight, etc.
etc. If the music really switches back and forth between tonal
systems, I think they'd even appreciate different notations.

Notation which does not reflect the music in an abstract sense, but
which is supposed to make it easier to play on instruments, is tab.
But you repeatedly state that sagittal is not tab.

>So, to repeat your assertion:

Which I'm trying to remember my reasoning behind....

>> But also in that thread, I assert that by forcing 7 nominals, you
>> ruin the mapping from commas to accidentals. Care to rebut that?
>
>I answer with the following: In a Pythagorean sequence of tones
>(with 7 nominals), the position in the sequence determines the power
>of 3, and the prime factors above 3 may all be expressed in the
>accidentals. In a sequence of tones separated by some other
>generator (such as a secor), the prime factors contained or implied
>in the relationships of those tones vary from one tone to another, so
>any comma-to-accidental relationship is much less useful (and much
>more complicated.)

I disagree. In the meantone diatonic scale, the position in the
sequence of nominals tells you the powers of 3 and 5. There's
one accidental, representing 25:24.

-Carl

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

> Which is why the number of nominals should match the number of tones
> in the basic scale, for 'diatonic' music. That's music where chords
> are build on scale degrees.

My feeling is that the number of nominals should be in a scale-like
range anyway--my proposal is nine nominals for effective 7-limit,
without any connection to scales, and I think 7-10 is a good range to
shoot for.

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> BTW (Dave, are you listening?), back when these messages were
> exchanged, I actually tried figuring out what sagittal accidentals
> might be used for 10 nominals for Miracle. What I ended up with was
> so unconventional, both with respect to our present way of thinking
> harmonically (by prime factors in ratios) and to the harmonic
> meanings of the sagittal symbols themselves, that I could only
> conclude that it was not worth the trouble even for a composer to use
> decimal notation.

See my reply on tuning-math - the second one in the thread
"Sagittal accidentals for Decimal/MIRACLE notation".

>The same conventional notation has been used historically for both
>Pythagorean and meantone as well as 12-ET,

I have no data on 12-tone notation being used in the pythagorean
days. Anybody?

12-tET of course supports meantone. There is the issue of using
the 25:24 accidental for 16:15 (since the diesis vanishes), and
indeed this is all but forbidden in conventional notation unless
it greatly reduces the number of accidentals otherwise.

But in all these cases, the basic scale is a chain of 7 fifths!!

The most egregious historical example of breaking what I'm talking
about that I can think of is using 7 nominals for octatonic
composition. There's precious little of that, though...

>Doesn't that make it clear that conventional notation can equally
>be considered to be 'nominals for a 7-tone chain of fifths, with
>accidentals for basic commas (namely multiples of the apotome //

The apotome doesn't properly occur in meantone.

Let's consider the 7-tone diatonic in meantone with 6 nominals --
let's cut B. B is a 9/8 (or any of its 81:80 variants) from A,
or a 16/15 (or any of its 81:80 variants) from C. By using the
25:24 accidental to get these motions, you're messing with the
mapping from commas to accidentals.

>But as I have indicated elsewhere, we can indeed use sagittal
>accidentals to make a notation having 'nominals for a 10-tone
>chain of secors, with accidentals for basic commas'.

[sigh of relief] Great!

-Carl

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> > Which is why the number of nominals should match the number of tones
> > in the basic scale, for 'diatonic' music. That's music where chords
> > are build on scale degrees.

Carl,

I think your usage of 'diatonic' here is confusing even if you do put
it in quotes. Maybe you should use "generalised-diatonic", although
that has other meanings too. Maybe you need to use
"Lumma-generalised-diatonic", and include a brief reminder of what you
mean by it, often, as you did above.

> My feeling is that the number of nominals should be in a scale-like
> range anyway--my proposal is nine nominals for effective 7-limit,
> without any connection to scales, and I think 7-10 is a good range to
> shoot for.

Gene,

You should have a look at my posts on accidentals for decimal on the
tuning-math list, and apply the same method to your 9-nominals system,
coming up with a list of commas for accidentals, from which we can
choose sagittal symbols.

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

/tuning/topicId_46826.html#47351

> My point is that alternate tunings often do not tie us down to
> specific tonal organizations, so the choice of a tuning is often
not
> enough to determine how many nominals would be "best" for its
> notation. Since we are already acquainted with a notation that
uses
> 7 nominals, and if that works reasonably well for many alternative
> tunings, then why not have a generalized notation that builds on
that?

***That's a truly sensible idea... of course...

> Not the answer I expected! In the real world I believe that a
> performer would want to have to learn as *few* different notations
as
> possible. So if it is possible to design a single notation that
can
> notate many different tunings reasonably well, then I believe it
> should be done.
>

***I have trouble getting performers, and I mean *seasoned New York
professionals* going much past quartertones, under *any* condition.
And some of these people are people who have played microtonality
before... This is the *reality* if we are talking about real, live
acoustic players here...

>
> I tried to take this idea of having multiple notations for a single
> tuning to a rather ridiculous extreme, but (much to my surprise)
you
> didn't agree, so the best we can do is agree to disagree. But I
> wonder how many performers would agree with you, especially if the
> notation were liable to switch back and forth every few measures?
>

***They would never play this music, only under the greatest duress.
This would be
either "augenmusik," "studienmusik," "theoriemusikschaft..."
or "wercklichenstudientheoriemusikgekraftwerke..."

> BTW (Dave, are you listening?), back when these messages were
> exchanged, I actually tried figuring out what sagittal accidentals
> might be used for 10 nominals for Miracle. What I ended up with
was
> so unconventional, both with respect to our present way of thinking
> harmonically (by prime factors in ratios) and to the harmonic
> meanings of the sagittal symbols themselves, that I could only
> conclude that it was not worth the trouble even for a composer to
use
> decimal notation.

***Personally, I've always seen decimal notation, when I can
understand it, as being nothing but trouble... :)

The Miracle relationships (involving commas and
> decimal nominals) can easily be discerned by using a diagram of the
> decimal keyboard labeled with a 72-ET notation (using 7 nominals,
> sagittal or otherwise) -- and this is something that Joseph Pehrson
> ought to be using.
>

***Well, on my keyboard, which is presently a standard Halberstadt, I
already have 72-tET accidentals for Blackjack. I do see the decimal
patterns, though, since Dave Keenan "color coded" my 72-tET stickers
and the are placed in decimal patterns on the keyboard, so I can see
how the "generator circles" of Blackjack really work...

So, I believe I'm already doing this to a degree, yes??

Thanks!

Joseph

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >The same conventional notation has been used historically for both
> >Pythagorean and meantone as well as 12-ET,
>
> I have no data on 12-tone notation being used in the pythagorean
> days. Anybody?

It doesn't have to have been the full 12, just more than 7. You
probably know that our present day accidentals started their evolution
when someone decided they needed two kinds of B. One a fifth above E
and the other a fifth below F. They decided to write them with
different shaped (lowercase) "b"s. The one a fifth above E was written
with a square loop and the one a fifth below F was written with a
round loop - "square-b" and "round-b". The Germans used "h" instead of
square-b, but when more such alternatives were required, round-b
evolved into our present-day flat symbol and was combined with other
letters so for example we had E and Eb. Square-b evolved into our
present day symmetric natural symbol, and grew even more "pointy bits"
to become our sharp symbol.

This all started back when proper tuning was still considered to be
Pythagorean, well before the rise of meantone. See
http://sonic-arts.org/dict/notation.htm

> 12-tET of course supports meantone. There is the issue of using
> the 25:24 accidental for 16:15 (since the diesis vanishes), and
> indeed this is all but forbidden in conventional notation unless
> it greatly reduces the number of accidentals otherwise.
>
> But in all these cases, the basic scale is a chain of 7 fifths!!

I don't see anyone disagreeing about that. I think I've lost the point
of all this.

Dave:
> >Doesn't that make it clear that conventional notation can equally
> >be considered to be 'nominals for a 7-tone chain of fifths, with
> >accidentals for basic commas (namely multiples of the apotome //

Carl:
> The apotome doesn't properly occur in meantone.

The important work here is "properly", since it certainly _can_ be
considered to occur. It should be obvious that in any temperament, an
accidental will have more than one possible comma interpretation. We
assign the apotome (3^7/2^11) as the _primary_ interp of the standard
sharp and flat, since this works in Pythagorean _and_ meantone, in the
historical manner.

> Let's consider the 7-tone diatonic in meantone with 6 nominals --
> let's cut B. B is a 9/8 (or any of its 81:80 variants) from A,
> or a 16/15 (or any of its 81:80 variants) from C. By using the
> 25:24 accidental to get these motions, you're messing with the
> mapping from commas to accidentals.

Using what 24:25 accidental to get what motions, in what way?

> >But as I have indicated elsewhere, we can indeed use sagittal
> >accidentals to make a notation having 'nominals for a 10-tone
> >chain of secors, with accidentals for basic commas'.
>
> [sigh of relief] Great!

But as I pointed out later on tuning-math, there are many difficult
questions to be answered before we can decide which accidentals to use
when notating tunings other than an actual MIRACLE temperament in a
decimal notation (or tunings other than ennealimmal in Gene's
9-nominal notation). Sagittal, with chain-of-fifth nominals, does not
notate everything as if it was an extended meantone, but based on best
approximations of ratios.

I've spent way too much time on this as it is. I need to get back to
documenting what we already have.

The fifth (or equivalently the twelfth) is the best general-purpose
notational generator, not because it comes from a good temperament
(e.g meantone), but because it is the simplest rational interval after
the octave. i.e. simply because it is the next prime.

George Secor:
> The Miracle relationships (involving commas and
> > decimal nominals) can easily be discerned by using a diagram of the
> > decimal keyboard labeled with a 72-ET notation (using 7 nominals,
> > sagittal or otherwise) -- and this is something that Joseph Pehrson
> > ought to be using.

Joseph Pehrson:
> ***Well, on my keyboard, which is presently a standard Halberstadt, I
> already have 72-tET accidentals for Blackjack. I do see the decimal
> patterns, though, since Dave Keenan "color coded" my 72-tET stickers
> and the are placed in decimal patterns on the keyboard, so I can see
> how the "generator circles" of Blackjack really work...
>
> So, I believe I'm already doing this to a degree, yes??

Yes! (although they are open chains, not circles, remember)

By the way, thanks for the reality check re performers.

hi George,

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

> ... <snip> ... (Or suppose that a
> piece is heptatonic in one place and decatonic
> in another. Do we switch notations in the middle
> of the page?)

i *like* that idea!!

> <snip>
>
> But if it would make you happy, you could use
> sagittal symbols with 10 nominals for Miracle.
> I just don't think any performer will want
> to read it that way.

you're probably right
... but *i* like decimal notation for miracle. :)

------

... for those who are having trouble following:

example of decimal notation, about 1/4 down the page
http://sonic-arts.org/monzo/blackjack/blackjack.htm

explanation of decimal notation
http://sonic-arts.org/dict/decimal.htm

-monz

>> > Which is why the number of nominals should match the number of tones
>> > in the basic scale, for 'diatonic' music. That's music where chords
>> > are build on scale degrees.
>
>Carl,
>
>I think your usage of 'diatonic' here is confusing even if you do put
>it in quotes. Maybe you should use "generalised-diatonic", although
>that has other meanings too.

I define this term in the post that's being referenced here (quick
summary of thoughts on notation).

-Carl

>> 12-tET of course supports meantone. There is the issue of using
>> the 25:24 accidental for 16:15 (since the diesis vanishes), and
>> indeed this is all but forbidden in conventional notation unless
>> it greatly reduces the number of accidentals otherwise.
>>
>> But in all these cases, the basic scale is a chain of 7 fifths!!
>
>I don't see anyone disagreeing about that. I think I've lost the point
>of all this.

So none of these cases constitutes a historical example of one set
of nominals being used to notate another basic scale. The octatonic
music of the 20th century does provide such an example.

>> Let's consider the 7-tone diatonic in meantone with 6 nominals --
>> let's cut B. B is a 9/8 (or any of its 81:80 variants) from A,
>> or a 16/15 (or any of its 81:80 variants) from C. By using the
>> 25:24 accidental to get these motions, you're messing with the
>> mapping from commas to accidentals.
>
>Using what 24:25 accidental to get what motions, in what way?

To get the pitch formerly known as B! Show us how it's done. How
do you notate diatonic music with six nominals in an acceptable
manner?

>The fifth (or equivalently the twelfth) is the best general-purpose
>notational generator, not because it comes from a good temperament
>(e.g meantone), but because it is the simplest rational interval after
>the octave. i.e. simply because it is the next prime.

You keep saying this, but not why you think it's true. A little
reflection should show that your reasoning here leads you down the
same path as searching for good linear temperaments. You didn't
restrict yourself to the octave and fifth then (but you did restrict
yourself to an octave, which we now know is a mistake).

-Carl

In a message dated 9/29/2003 11:47:31 PM Eastern Daylight Time,
jpehrson@rcn.com writes:

> ***I have trouble getting performers, and I mean *seasoned New York
> professionals* going much past quartertones, under *any* condition.
> And some of these people are people who have played microtonality
> before... This is the *reality* if we are talking about real, live
> acoustic players here...
>
>

S'funny, I don't have trouble getting seasoned professions to play microtones
at all.

Johnny : )

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

/tuning/topicId_46826.html#47376

> George Secor:
> > The Miracle relationships (involving commas and
> > > decimal nominals) can easily be discerned by using a diagram
of the
> > > decimal keyboard labeled with a 72-ET notation (using 7
nominals,
> > > sagittal or otherwise) -- and this is something that Joseph
Pehrson
> > > ought to be using.
>
> Joseph Pehrson:
> > ***Well, on my keyboard, which is presently a standard
Halberstadt, I
> > already have 72-tET accidentals for Blackjack. I do see the
decimal
> > patterns, though, since Dave Keenan "color coded" my 72-tET
stickers
> > and the are placed in decimal patterns on the keyboard, so I can
see
> > how the "generator circles" of Blackjack really work...
> >
> > So, I believe I'm already doing this to a degree, yes??
>
> Yes! (although they are open chains, not circles, remember)

***Hi Dave!

Oh, sure... I just mis-termed that... I guess the secor Miracle
generator never really comes back around exactly, unless it's at
some astronomical cycle... yes??

>
> By the way, thanks for the reality check re performers.

***Well, this is what *I've been experiencing, personally. I
understand there are other opinions on this subject...

best,

Joseph

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

> The fifth (or equivalently the twelfth) is the best
> general-purpose notational generator, not because it comes
> from a good temperament (e.g meantone), but because it is
> the simplest rational interval after the octave.
> i.e. simply because it is the next prime.

kudos to you, Dave! this has been my feeling all along,
but i never expressed it well in this thread.

-monz

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> 12-tET of course supports meantone. There is the issue of using
> >> the 25:24 accidental for 16:15 (since the diesis vanishes), and
> >> indeed this is all but forbidden in conventional notation unless
> >> it greatly reduces the number of accidentals otherwise.
> >>
> >> But in all these cases, the basic scale is a chain of 7 fifths!!
> >
> >I don't see anyone disagreeing about that. I think I've lost the
point
> >of all this.
>
> So none of these cases constitutes a historical example of one set
> of nominals being used to notate another basic scale. The octatonic
> music of the 20th century does provide such an example.

how about pentatonic music?

> >> Let's consider the 7-tone diatonic in meantone with 6 nominals --
> >> let's cut B. B is a 9/8 (or any of its 81:80 variants) from A,
> >> or a 16/15 (or any of its 81:80 variants) from C. By using the
> >> 25:24 accidental to get these motions, you're messing with the
> >> mapping from commas to accidentals.
> >
> >Using what 24:25 accidental to get what motions, in what way?
>
> To get the pitch formerly known as B! Show us how it's done. How
> do you notate diatonic music with six nominals in an acceptable
> manner?

this is a ridiculous, pointless request. who would use 6 nominals
from a chain of fifths as a basis for notation?

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> ***Hi Dave!
>
> Oh, sure... I just mis-termed that... I guess the secor Miracle
> generator never really comes back around exactly, unless it's at
> some astronomical cycle... yes??

since you're using 72-equal (in theory and notation), it would take a
chain of 72 secors (7/72-oct. intervals) to come back to where you
started, and form a circle. dave keenan depicted this circle of
secors here:

http://www.uq.net.au/~zzdkeena/Music/Miracle/Miracle72Sliderule.gif

of course, you're only using a chain of 20 secors . . .

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
[Dave Keenan:]
> >But as I have indicated elsewhere, we can indeed use sagittal
> >accidentals to make a notation having 'nominals for a 10-tone
> >chain of secors, with accidentals for basic commas'.
>
> [sigh of relief] Great!
>
> -Carl

Carl, let's call a truce. There's no point in continuing a debate
over how many nominals are "best" to notate something when:

1) We clearly have different priorities in mind;
2) It can be done the way you want with the symbols that we have.

Now here's the next problem: Since we have so many sagittal symbols
to choose from, Dave and I will have to arrive at some
recommendations as to which are the *best* symbols to be used with a
different number of nominals for tunings such as Miracle. Dave
presents some good ideas here:

/tuning-math/message/6900

I find that for

Graham's ASCII-Sagittal Comma interp. secors
short long (prime exp, no 2)
-----------------------------------------------------
^^^ or m^ $# ~||| [5,0,0,0,1,0,0,-1] -30
^^ or m _# )||( [-1,2] apotome-25S -20

much simpler ratios (121:128 and 27:28) might be used instead:

^^^ or m^ h# (||( [0,0,0,-2] 11M+11M -30
^^ or m m (|\ [-3,0,1] 7L -20

Perhaps Dave and I should discuss this off list or on tuning-math (if
others wish to participate in the discussion), but preferably later,
when we have more time.

--George

>> So none of these cases constitutes a historical example of one set
>> of nominals being used to notate another basic scale. The octatonic
>> music of the 20th century does provide such an example.
>
>how about pentatonic music?

I had considered that, but since the scale is a strict subset of
the core scale, I don't think this qualifies.

>> >> Let's consider the 7-tone diatonic in meantone with 6 nominals --
>> >> let's cut B. B is a 9/8 (or any of its 81:80 variants) from A,
>> >> or a 16/15 (or any of its 81:80 variants) from C. By using the
>> >> 25:24 accidental to get these motions, you're messing with the
>> >> mapping from commas to accidentals.
>> >
>> >Using what 24:25 accidental to get what motions, in what way?
>>
>> To get the pitch formerly known as B! Show us how it's done. How
>> do you notate diatonic music with six nominals in an acceptable
>> manner?
>
>this is a ridiculous, pointless request. who would use 6 nominals
>from a chain of fifths as a basis for notation?

Exactly.

-Carl

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

> >> >> Let's consider the 7-tone diatonic in meantone with 6
nominals --
> >> >> let's cut B. B is a 9/8 (or any of its 81:80 variants) from
A,
> >> >> or a 16/15 (or any of its 81:80 variants) from C. By using
the
> >> >> 25:24 accidental to get these motions, you're messing with the
> >> >> mapping from commas to accidentals.
> >> >
> >> >Using what 24:25 accidental to get what motions, in what way?
> >>
> >> To get the pitch formerly known as B! Show us how it's done.
How
> >> do you notate diatonic music with six nominals in an acceptable
> >> manner?
> >
> >this is a ridiculous, pointless request. who would use 6 nominals
> >from a chain of fifths as a basis for notation?
>
> Exactly.

so why are you making it?

>> Exactly.
>
>so why are you making it?

To better understand what happens when we notate a decatonic
scale with 7 nominals, as Dave and George were proposing.

-Carl

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

> >> Exactly.
> >
> >so why are you making it?
>
> To better understand what happens when we notate a decatonic
> scale with 7 nominals, as Dave and George were proposing.
>
> -Carl

the situation is completely different. a 6-tone chain of fifths is
not a distributionally even scale or even an altered version of one,
so it's unfit as a basis for notating anything.

notating the my decatonic scales of 22-equal using 7 nominals is a
mess, as alison monteith discovered on her own. but it's a profoundly
different kind of mess, infinitely more manageable than the kind you
were requesting others to delve into here.

>the situation is completely different. a 6-tone chain of fifths is
>not a distributionally even scale or even an altered version of one,
>so it's unfit as a basis for notating anything.

What gets wrecked if one's basis isn't distrib. even?

>notating the my decatonic scales of 22-equal using 7 nominals is a
>mess, as alison monteith discovered on her own. but it's a profoundly
>different kind of mess, infinitely more manageable than the kind you
>were requesting others to delve into here.

At issue was a specific assertion about commas being mapped to
accidentals. I'm still trying to figure it out. Presumably, any
linear temperament allows one to notate the lattice with only one
accidental, but meantone with 6 nominals doesn't seem to work.
So presumably my assertion is correct, but what's required, any
MOS?

-Carl

>Now here's the next problem: Since we have so many sagittal symbols
>to choose from, Dave and I will have to arrive at some
>recommendations as to which are the *best* symbols to be used with a
>different number of nominals for tunings such as Miracle.

Not sure I understand the problem, but if it's what I think it is
it's a non-problem. You ask Gene for the TM reduced basis for
miracle at the limit you're interested in, find the comma that's
not tempered out, go to your comma-accidental map, pick out
the corresponding accidental, and you're done. Aside from the
open issue of the restrictions placed on the nominals to get it
all to work.

Hrm... maybe you need a nominal for each pitch of the ET that
you get if you temper out all the commas in the basis. . . .

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >the situation is completely different. a 6-tone chain of fifths is
> >not a distributionally even scale or even an altered version of
one,
> >so it's unfit as a basis for notating anything.
>
> What gets wrecked if one's basis isn't distrib. even?

you yourself said that one begins a set of nominals forming a
periodicity block (on the tuning-math list; maybe you should reply to
this over there).

> >notating the my decatonic scales of 22-equal using 7 nominals is a
> >mess, as alison monteith discovered on her own. but it's a
profoundly
> >different kind of mess, infinitely more manageable than the kind
you
> >were requesting others to delve into here.
>
> At issue was a specific assertion about commas being mapped to
> accidentals. I'm still trying to figure it out. Presumably, any
> linear temperament allows one to notate the lattice with only one
> accidental,

that won't work once you get beyond the set of primes that you're
allowing the linear temperament to approximate. of course, george and
dave's proposal is not based on any temperament at all.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Now here's the next problem: Since we have so many sagittal
symbols
> >to choose from, Dave and I will have to arrive at some
> >recommendations as to which are the *best* symbols to be used with
a
> >different number of nominals for tunings such as Miracle.
>
> Not sure I understand the problem, but if it's what I think it is
> it's a non-problem.

your explanation doesn't support that assertion.

> You ask Gene for the TM reduced basis for
> miracle at the limit you're interested in,

that seems irrelevant.

> find the comma that's
> not tempered out,

there's no such thing, unless you mean a specific MOS of miracle. in
which case, there will be an infinite number of ratio-
representations, and *that's* where TM reduction would come in.

> Hrm... maybe you need a nominal for each pitch of the ET that
> you get if you temper out all the commas in the basis. . . .

how did ET come in?

i think we should move this to tuning-math . . .

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

/tuning/topicId_46826.html#47397

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > ***Hi Dave!
> >
> > Oh, sure... I just mis-termed that... I guess the secor Miracle
> > generator never really comes back around exactly, unless it's at
> > some astronomical cycle... yes??
>
> since you're using 72-equal (in theory and notation), it would take
a
> chain of 72 secors (7/72-oct. intervals) to come back to where you
> started, and form a circle. dave keenan depicted this circle of
> secors here:
>
> http://www.uq.net.au/~zzdkeena/Music/Miracle/Miracle72Sliderule.gif
>
> of course, you're only using a chain of 20 secors . . .

***Right... so then Blackjack would spiral on infinately??

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_46826.html#47397
>
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> >
> > > ***Hi Dave!
> > >
> > > Oh, sure... I just mis-termed that... I guess the secor
Miracle
> > > generator never really comes back around exactly, unless it's
at
> > > some astronomical cycle... yes??
> >
> > since you're using 72-equal (in theory and notation), it would
take
> a
> > chain of 72 secors (7/72-oct. intervals) to come back to where
you
> > started, and form a circle. dave keenan depicted this circle of
> > secors here:
> >
> >
http://www.uq.net.au/~zzdkeena/Music/Miracle/Miracle72Sliderule.gif
> >
> > of course, you're only using a chain of 20 secors . . .
>
>
> ***Right... so then Blackjack would spiral on infinately??

blackjack *is* your chain of only 20 secors! dave's point was that
it's just that, a chain, since it doesn't meet itself to form a
circle.

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

/tuning/topicId_46826.html#47417

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> >
> > /tuning/topicId_46826.html#47397
> >
> > > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> > wrote:
> > >
> > > > ***Hi Dave!
> > > >
> > > > Oh, sure... I just mis-termed that... I guess the secor
> Miracle
> > > > generator never really comes back around exactly, unless it's
> at
> > > > some astronomical cycle... yes??
> > >
> > > since you're using 72-equal (in theory and notation), it would
> take
> > a
> > > chain of 72 secors (7/72-oct. intervals) to come back to where
> you
> > > started, and form a circle. dave keenan depicted this circle of
> > > secors here:
> > >
> > >
> http://www.uq.net.au/~zzdkeena/Music/Miracle/Miracle72Sliderule.gif
> > >
> > > of course, you're only using a chain of 20 secors . . .
> >
> >
> > ***Right... so then Blackjack would spiral on infinately??
>
> blackjack *is* your chain of only 20 secors! dave's point was that
> it's just that, a chain, since it doesn't meet itself to form a
> circle.

***Hi Paul!

I'm glad you're making me think about this, since I'm obviously
stumbling all over myself... :)

OK, so I mean the secor, the Miracle generator:

What you're saying is when you let it continue on 72 times then it
*does* close since it's practically equal to 72 steps, yes?

And how close is it *exactly* to 72-tET in it's 72 step incarnation??

Thanks!

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> ***Hi Paul!
>
> I'm glad you're making me think about this, since I'm obviously
> stumbling all over myself... :)
>
> OK, so I mean the secor, the Miracle generator:
>
> What you're saying is when you let it continue on 72 times then it
> *does* close since it's practically equal to 72 steps, yes?

yes, usually it's either exactly equal to, or quite close to, 7 steps
of 72-equal.

> And how close is it *exactly* to 72-tET in it's 72 step
>incarnation??

just as there is an infinite variety of meantone generators
(including the *exact* fifth of 31-equal -- why not?), there is also
an infinite variety of miracle generators (including *exactly* 7/72-
octave). but since we call the latter the secor after george secor,
we might as well use as one example george's choice,
http://www.sonic-arts.org/dict/secor.htm
116.715594098207 cents

and as an additional example the 9-limit rms optimum
/tuning/topicId_22626.html#22626
116.729676636048 cents

the first differs from 7/72 octave by 0.05 cents; stacked 72 times
and octave-reduced, it misses the starting point by 3.53 cents.

the second differs from 7/72 octave by 0.06 cents; stacked 72 times
and octave reduced, it missed the starting point by 4.54 cents.

>> find the comma that's
>> not tempered out,
>
>there's no such thing, unless you mean a specific MOS of miracle. in
>which case, there will be an infinite number of ratio-
>representations, and *that's* where TM reduction would come in.

Right.

>> Hrm... maybe you need a nominal for each pitch of the ET that
>> you get if you temper out all the commas in the basis. . . .
>
>how did ET come in?

Sorry, you're right, 1 accidental if it's an MOS, via the
Hypothesis.

-Carl

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

> Sorry, you're right, 1 accidental if it's an MOS, via the
> Hypothesis.
>
> -Carl

1 accidental?

>> Sorry, you're right, 1 accidental if it's an MOS, via the
>> Hypothesis.
>>
>> -Carl
>
>1 accidental?

...is all you need to notate the system (where an accidental
includes an up and down pair).

-Carl

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

> >> Sorry, you're right, 1 accidental if it's an MOS, via the
> >> Hypothesis.
> >>
> >> -Carl
> >
> >1 accidental?
>
> ...is all you need to notate the system (where an accidental
> includes an up and down pair).
>
> -Carl

i must have missed what you mean by "the system". certainly 5-limit
JI requires *two* pairs of accidentals to notate, normally the
sharp/flat pair and the comma up/comma down pair.

>> >> Sorry, you're right, 1 accidental if it's an MOS, via the
>> >> Hypothesis.
>> >>
>> >> -Carl
>> >
>> >1 accidental?
>>
>> ...is all you need to notate the system (where an accidental
>> includes an up and down pair).
>>
>> -Carl
>
>i must have missed what you mean by "the system". certainly 5-limit
>JI requires *two* pairs of accidentals to notate, normally the
>sharp/flat pair and the comma up/comma down pair.

? In the case of an MOS, the comma is tempered out. In conventional
notation there is only one accidental pair.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >> Sorry, you're right, 1 accidental if it's an MOS, via the
> >> >> Hypothesis.
> >> >>
> >> >> -Carl
> >> >
> >> >1 accidental?
> >>
> >> ...is all you need to notate the system (where an accidental
> >> includes an up and down pair).
> >>
> >> -Carl
> >
> >i must have missed what you mean by "the system". certainly 5-
limit
> >JI requires *two* pairs of accidentals to notate, normally the
> >sharp/flat pair and the comma up/comma down pair.
>
> ? In the case of an MOS, the comma is tempered out.

what do you mean? this is certainly not true, especially in JI! dave
and george's system, at least, is based on the 7-tone MOS of perfect
fifths, and does not assume that any comma is tempered out. if the
notation is used for a system where the comma is tempered out, the
comma accidental becomes useless in that system, but this is not the
general case.

> In conventional
> notation there is only one accidental pair.

conventional notation refers to 1-dimensional pitch systems, and more
recently, to a '0-dimensional' one (12-equal).

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >> Sorry, you're right, 1 accidental if it's an MOS, via the
> >> >> Hypothesis.
> >> >>
> >> >> -Carl
> >> >
> >> >1 accidental?
> >>
> >> ...is all you need to notate the system (where an accidental
> >> includes an up and down pair).
> >>
> >> -Carl
> >
> >i must have missed what you mean by "the system". certainly 5-
limit
> >JI requires *two* pairs of accidentals to notate, normally the
> >sharp/flat pair and the comma up/comma down pair.
>
> ? In the case of an MOS, the comma is tempered out. In
conventional
> notation there is only one accidental pair.
>
> -Carl

even if the comma is tempered out, you'll still need more accidental
pairs if you want to notate a higher-dimensional tuning system -- one
which represents N more primes and tempers out less than N more
independent commas.

>> >certainly 5-limit
>> >JI requires *two* pairs of accidentals to notate, normally the
>> >sharp/flat pair and the comma up/comma down pair.
>>
>> ? In the case of an MOS, the comma is tempered out.
>
>what do you mean?

You said JI and meant it. Just a misunderstanding.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> So none of these cases constitutes a historical example of one set
> of nominals being used to notate another basic scale. The octatonic
> music of the 20th century does provide such an example.

OK. I think I get it now. I think you're saying that we can't claim
that conventional notation has been used historically in a manner
independent of any particular temperament, because it has always been
used for chains of fifths, even though one is Pythagorean and another
is meantone. And the only thing you can think of that supports such an
argument from history is octatonic.

Well, you can have it that way if you like, because I have already
said that even without a history that includes Pythagorean and
meantone, the fifth is still the best overall choice for notational
generator. I'll explain why below.

> >> Let's consider the 7-tone diatonic in meantone with 6 nominals --
> >> let's cut B. B is a 9/8 (or any of its 81:80 variants) from A,
> >> or a 16/15 (or any of its 81:80 variants) from C. By using the
> >> 25:24 accidental to get these motions, you're messing with the
> >> mapping from commas to accidentals.
> >
> >Using what 24:25 accidental to get what motions, in what way?
>
> To get the pitch formerly known as B! Show us how it's done. How
> do you notate diatonic music with six nominals in an acceptable
> manner?

Why would I want to? With the fifth as the generator of nominals, the
natural number of nominals is 7. 6 is improper. You say "By doing X
you're doing a bad thing". And I say "But I'm not doing X". And you
say "Do X". This isn't making much sense to me. Sorry.

To notate the note a fifth above E in an open meantone (or in
Pythagorean), without using the letter B, I would use an accidental
that primarily represented a Pythagorean limma (2^8/3^5), and then B
would be C-limma-down. Then I would only need 5 nominals. But I don't
see what point you are trying to make here.

> >The fifth (or equivalently the twelfth) is the best general-purpose
> >notational generator, not because it comes from a good temperament
> >(e.g meantone), but because it is the simplest rational interval after
> >the octave. i.e. simply because it is the next prime.
>
> You keep saying this, but not why you think it's true. A little
> reflection should show that your reasoning here leads you down the
> same path as searching for good linear temperaments. You didn't
> restrict yourself to the octave and fifth then
...

No. A little reflection allows me to explain that, as it stands now,
the semantic foundations of Sagittal notation have absolutely nothing
to do with any temperament. It isn't surprising that you might think
otherwise, since George and I were confused about that ourselves for a
very long time.

You may remember that around the same time that George first presented
a proto-sagittal as a notation primarily for certain popular ETs up to
and including 72-ET, Gene was looking for good sets of commas for a
one-accidental-per-comma-per-prime notation for ratios. And the two
ideas cross-fertilised.

We quickly got beyond 72-ET, but for a very long time there was a
constant tension between basing the notation on some equal temperament
versus basing it on ratios and thereby keeping it open. The problem
with a notation based on ratios is that, to keep everyone happy, you
need a huge number of different accidentals, or you need to allow long
strings of accidentals, possibly pointing in contradictory directions,
against a single note. So it is natural to want to close the system by
making the accidentals refer to notes of some temperament. This has
been done before, but someone always finds the temperament to be too
limiting. Kraig eloquently made this point quite recently.

In the development of Sagittal, you probably remember 217-ET being
mentioned a lot at one stage, and later 494-ET and 612-ET, and even
1600-ET. So we kept stretching and stretching the
temperament-connection until finally, in May this year, it snapped.

One of the last things to go was George's 5*7*13-schismina (4095:4096,
0.4 c) which was a source of much economy in the notation. I came up
with symbols that fitted the overall system but that allowed ratios of
13 to be notated differently from the nearby ratios of 35. George
wrote at the time that this was "both upsetting and intriguing".

We soon realised we could have our cake and eat it too - that every
symbol could represent a single unique comma ratio but that users who
want to notate rational tunings are free to choose larger or smaller
sets of symbols to trade off economy-of-symbols against
accuracy-of-representation (for those ratios which are not represented
exactly by the chosen symbols). We then set about standardising a few
such sets. One of them, the Athenian set, which you can see in Scala
right now, looks suspiciously like the old 217-ET set. But that's
because it makes sense to choose subsets where the commas are
relatively evenly spaced, and that meet certain other criteria. But
there is a big difference between looking to temperaments to help
choose good subsets, and basing the whole notation system on a
particular temperament.

We have also used a temperament to help decide on the actual symbols
to be used for the comma ratios in the superset. This is an
8-dimensional temperament with a maximum error of 0.39 cents. The 8
dimensions relate to the 9 flags (including the accent mark) that make
up the symbols, less one degree of freedom because a certain
combination is set equal to the apotome. But again, this is in the
symbology, not the semantics, so there is nothing to prevent someone
in the future from deciding that they need unique symbols for more
ratios, and extending the system with another flag type representing
something around half a cent. But we find this fairly unlikely and for
practical reasons (of making fonts etc.) we have closed the superset
for now with _only_ about 600 symbols!

So the first part of my belief is that it is far better to have a
notation system whose semantics are based on precise ratios and then
use that to also notate temperaments, rather than trying to find the
ultimate temperament and then using a notation based on that to notate
both ratios and other temperaments.

Then if that's accepted, the second part is that it is best if the
simplest or most popular ratios have the simplest notations. The
properties of simplicity and popularity are so much in alignment in
regard to ratios of the lowest primes that we don't really need to
decide which one we mean. I understand that you agree with this, and
so it should be obvious that the simplest accidental is no accidental
at all and so the simplest ratios should be represented by nominals
alone. When we agree that powers of 2 will not be represented at all,
or will be represented by an octave number, or by a distance of N
staff positions or a clef, then surely you agree that the next
simplest thing is to represent powers of three by the nominals.

So I imagine it's the first part of my belief that you want more
argument for.

Well I think the fact that we have Graham proposing MIRACLE
temperament with 10 nominals and Gene proposing ennealimmal
temperament with 9 nominals should make it clear that there is
unlikely to ever be agreement on which is the ultimate temperament for
notating everything else including ratios.

You seem to have been assuming that George and I were merely
championing some other (fifth-generated) temperament as the ultimate
for notating everything else. I hope I have explained why this is not so.

But there may well be some merit in notating a linear temperament
using a natural number of nominals for that temperament and
accidentals representing chromatic commas that arise from that choice
of nominals in that temperament. And this can certainly be done using
sagittal accidentals.

It's only when we start trying to apply such a temperament-based
notation to things for which the temperament mapping does not predict
the best approximations to the simplest ratios, that it comes unstuck.
For example when Graham applies a 10-nominal MIRACLE-based notation to
22-ET, in two different ways, I find it very unclear what the
accidentals really mean (across tunings) and what the rules are. But
go ahead and work on it if you want.

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

/tuning/topicId_46826.html#47419

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > ***Hi Paul!
> >
> > I'm glad you're making me think about this, since I'm obviously
> > stumbling all over myself... :)
> >
> > OK, so I mean the secor, the Miracle generator:
> >
> > What you're saying is when you let it continue on 72 times then
it
> > *does* close since it's practically equal to 72 steps, yes?
>
> yes, usually it's either exactly equal to, or quite close to, 7
steps
> of 72-equal.
>
> > And how close is it *exactly* to 72-tET in it's 72 step
> >incarnation??
>
> just as there is an infinite variety of meantone generators
> (including the *exact* fifth of 31-equal -- why not?), there is
also
> an infinite variety of miracle generators (including *exactly* 7/72-
> octave). but since we call the latter the secor after george secor,
> we might as well use as one example george's choice,
> http://www.sonic-arts.org/dict/secor.htm
> 116.715594098207 cents
>
> and as an additional example the 9-limit rms optimum
> /tuning/topicId_22626.html#22626
> 116.729676636048 cents
>
> the first differs from 7/72 octave by 0.05 cents; stacked 72 times
> and octave-reduced, it misses the starting point by 3.53 cents.
>
> the second differs from 7/72 octave by 0.06 cents; stacked 72 times
> and octave reduced, it missed the starting point by 4.54 cents.

***Thanks, Paul, for this info. and sorry about my momentary
confusion (temporary insanity...)

It's pretty clear in my mind now...

Joseph

>even if the comma is tempered out, you'll still need more accidental
>pairs if you want to notate a higher-dimensional tuning system -- one
>which represents N more primes and tempers out less than N more
>independent commas.

Yup.

-Carl

>OK. I think I get it now.
//
>
>Well, you can have it that way if you like, because I have already
>said that even without a history that includes Pythagorean and
>meantone, the fifth is still the best overall choice for notational
>generator. I'll explain why below.

Ok, cool.

>> >> Let's consider the 7-tone diatonic in meantone with 6 nominals --
>> >> let's cut B. B is a 9/8 (or any of its 81:80 variants) from A,
>> >> or a 16/15 (or any of its 81:80 variants) from C. By using the
>> >> 25:24 accidental to get these motions, you're messing with the
>> >> mapping from commas to accidentals.
>> >
>> >Using what 24:25 accidental to get what motions, in what way?
>>
>> To get the pitch formerly known as B! Show us how it's done. How
>> do you notate diatonic music with six nominals in an acceptable
>> manner?
>
>Why would I want to? With the fifth as the generator of nominals, the
>natural number of nominals is 7. 6 is improper. You say "By doing X
>you're doing a bad thing". And I say "But I'm not doing X". And you
>say "Do X". This isn't making much sense to me. Sorry.

But you are (or were) advocating doing X, but trying to force 7
nominals on other scales. It is, as you say, improper to do so. Which
is what I was trying to point out. It looks as though I've succeeded!

>> >The fifth (or equivalently the twelfth) is the best general-purpose
>> >notational generator, not because it comes from a good temperament
>> >(e.g meantone), but because it is the simplest rational interval
>> >after the octave. i.e. simply because it is the next prime.
>>
>> You keep saying this, but not why you think it's true. A little
>> reflection should show that your reasoning here leads you down the
>> same path as searching for good linear temperaments. You didn't
>> restrict yourself to the octave and fifth then
>...
>
>No. A little reflection allows me to explain that, as it stands now,
>the semantic foundations of Sagittal notation have absolutely nothing
>to do with any temperament.

I should have said, "good PBs" there. [I think of PBs as temperaments,
which always gets me into trouble.]

>We quickly got beyond 72-ET, but for a very long time there was a
>constant tension between basing the notation on some equal temperament
>versus basing it on ratios and thereby keeping it open. The problem
>with a notation based on ratios is that, to keep everyone happy, you
>need a huge number of different accidentals,

With, say, 19-limit JI, I don't see a way around this.

With linear temperaments, you only need 1 accidental pair at a time,
as I've pointed out. The particular comma involved will depend on
the limit and the number of notes in the base scale. This could be
handled two ways. The first way I suggested is to get a list of simple
19-limit commas and assign accidental pairs to them. The same
accidentals could be used for planar temperaments, JI, whatever, with
more than one pair in use at a time.

If average use ("gimme 9 notes of such-and-such temperament in the
13-limit") turns out to require more commas than can fit on a list,
you could try assigning (an) accidental(s) for each *temperament*,
with the understanding that it/they would take on TM-reduced value(s)
for the limit and scale cardinality being used.

>We soon realised we could have our cake and eat it too - that every
>symbol could represent a single unique comma ratio but that users who
>want to notate rational tunings are free to choose larger or smaller
>sets of symbols to trade off economy-of-symbols against
>accuracy-of-representation (for those ratios which are not represented
>exactly by the chosen symbols).

Great. That's the master list idea.

>We have also used a temperament to help decide on the actual symbols
>to be used for the comma ratios in the superset. This is an
>8-dimensional temperament

Representing how many harmonic dimensions?

>So the first part of my belief is that it is far better to have a
>notation system whose semantics are based on precise ratios and then
>use that to also notate temperaments, rather than trying to find the
>ultimate temperament and then using a notation based on that to notate
>both ratios and other temperaments.

Wow; this is exactly what I've been saying all along!!

>Then if that's accepted, the second part is that it is best if the
>simplest or most popular ratios have the simplest notations.

Right. And it's this aspect that makes the search more-or-less
equivalent to the search for good PBs.

>I understand that you agree with this, and so it should be obvious
>that the simplest accidental is no accidental at all and so the
>simplest ratios should be represented by nominals alone. When we
>agree that powers of 2 will not be represented at all, or will be
>represented by an octave number, or by a distance of N staff positions
>or a clef, then surely you agree that the next simplest thing is to
>represent powers of three by the nominals.

Well, that's a weighted-complexity approach. But even with most
weighted-complexity lists I've seen, non-rational-generator
temperaments appear.

>Well I think the fact that we have Graham proposing MIRACLE
>temperament with 10 nominals and Gene proposing ennealimmal
>temperament with 9 nominals should make it clear that there is
>unlikely to ever be agreement on which is the ultimate temperament
>for notating everything else including ratios.

It was the ultimate-temperament aspect of the project I objected
to since the beginning!

>You seem to have been assuming that George and I were merely
>championing some other (fifth-generated) temperament as the
>ultimate for notating everything else. I hope I have explained
>why this is not so.

Ok, ok, I think we're more on the same page now. But certainly
the project didn't start out this way, and even in the last few
days I saw a blurb for George and/or you looking very confused
about non-heptatonic systems.

-Carl

on 9/25/03 12:00 PM, Afmmjr@aol.com <Afmmjr@aol.com> wrote:

> In a message dated 9/25/2003 2:13:18 PM Eastern Daylight Time,
> gdsecor@yahoo.com writes:
>
>> Johnny, I'm curious about something. If you don't use your cents
>> notation for a keyboard instrument, then what notation would you use
>> for a non-traditional keyboard instrument (such as your generalized
>> keyboard that is currently under construction), if the tuning to be
>> notated is one that cannot be adequately notated by either a
>> quartertone or meantone notation (e.g., a 22 or 29-tone octave, not
>> necessarily an ET)?
>>
>>
>
> Hello George:
>
> You raise a good point. This yet needs to be thought out. Clearly, any
> composer can notate any which way as there is no notation authority. At least
> standard notation with cents deviations indicated will still work. However,
> there may be a more tabulature-like streamlining possible.
>
> best, Johnny Reinhard

Yes, I'm just getting caught up on my email too...

I also wanted to comment on this. Carl and I are working on getting the
"xmw" spec fleshed out and implemented on my softsynth organ. So a
"12-tone" keyboard ceases to be a "fixed pitch" scenario. I'm looking
forward to being able to have automatically generated notation driven from
the xmw-style MIDI input - thought this is still a bit of a dream at this
moment.

(I assume you all talked about the xmw thing a long time ago - I wasn't here
then.)

Being able to modulate based on the organ pedal is a great thrill. I find
it not too hard to assimilate (though it isn't anything like second nature)
for improvistion purposes, and even within the realm of the possible for
adapting existing organ pieces, with slight modifications to the pedal line.
But this is off the topic and I'll eventually start another thread for this.

The point here being that scores with ratio notation and/or cents notation
plus fingering notation seems like a real possibility looming in my future,
and something I would want to make the best of. Using a separate staff per
voice would help relieve the clutter, but of course eats pages for
breakfast. You orchestra types are used to that but us organists ain't.

Your point about using 50% gray being a problem is well-taken. Probably
putting fingering numbers in gray is a better idea. The other issue is
leaving a place for people to write in their own fingering numbers, which is
probably more to the point in most cases. Canned fingering is of limited
use for many. I don't know whether this applies for woodwind fingering.

-Kurt

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Ok, ok, I think we're more on the same page now. But certainly
> the project didn't start out this way

Right. We used various temperaments as cranes to climb up by, with
each one helping to build the next higher one, but now that we've
reached geostationary orbit we can throw away the cranes. :-)

For a more detailed response, see
/tuning-math/message/6923

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> Right. We used various temperaments as cranes to climb up by, with
> each one helping to build the next higher one, but now that we've
> reached geostationary orbit we can throw away the cranes. :-)

That's a great description, Dave!

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > Right. We used various temperaments as cranes to climb up by, with
> > each one helping to build the next higher one, but now that we've
> > reached geostationary orbit we can throw away the cranes. :-)
>
> That's a great description, Dave!

Thanks. But I have to admit that I combined famous analogies from two
great philosophers, Ludwig Wittgenstein and Daniel Dennett.

You can see the Wittgenstein quote here, in C K Ogden's translation of
the "Tractatus Logico-philosophicus". It is the second-last
proposition in this awesome work of a mere 68 pages.
http://www.kfs.org/~jonathan/witt/t654en.html
It's a while since I read the whole thing, but I still get goosebumps
when I think about it.

The other is in Dennetts "Darwins Dangerous Idea" where he explains
that that's how evolution works, cranes building ever more powerful
cranes, all from the ground up. And that so far, every time someone
has though they had found something that could only be explained by a
skyhook, close investigation has shown yet another crane. Evolution is
smarter than we are.

Wittgenstein is a thorough-going mystic and Dennett a card-carrying
materialist, and yet they are not so far apart philosophically. Maybe
its because, if there's only one kind of stuff making up the universe,
it doesn't much matter whether you call it matter or spirit.

I know this is way off topic, but I couldn't resist. Sorry.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> I know this is way off topic, but I couldn't resist. Sorry.

Even if I'm the only one that feels this way, you don't have to apologize for items like that.

Then again, now that I know you are a mere (if high-minded) demi-plagarist, I may never speak to you again... :)

Cheers,
Jon

hi Dave,

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

> Thanks. But I have to admit that I combined famous analogies
> from two great philosophers, Ludwig Wittgenstein and
> Daniel Dennett.
>
> <substantial snip>
>
> I know this is way off topic, but I couldn't resist. Sorry.

i'm happy to see the old Dave Keenan back !! :)

(after his long grueling journey in Sagittalia!)

-monz

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

> You should have a look at my posts on accidentals for decimal on the
> tuning-math list, and apply the same method to your 9-nominals system,
> coming up with a list of commas for accidentals, from which we can
> choose sagittal symbols.

For the 5-limit, you could take the nominals as representing 27/25,
and the sharps as representing 6561/6250; the added comma could be the
ennealimma, 2/(27/25)^9. To extend this to the 7-limit, add another
small comma, namely 4375/4374. Ignoring both of these commas would be
the usual proceedure, since they don't amount to much.

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

> At issue was a specific assertion about commas being mapped to
> accidentals. I'm still trying to figure it out. Presumably, any
> linear temperament allows one to notate the lattice with only one
> accidental, but meantone with 6 nominals doesn't seem to work.
> So presumably my assertion is correct, but what's required, any
> MOS?

Why do you say it doesn't seem to work?

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

> We have also used a temperament to help decide on the actual symbols
> to be used for the comma ratios in the superset. This is an
> 8-dimensional temperament with a maximum error of 0.39 cents. The 8
> dimensions relate to the 9 flags (including the accent mark) that
make
> up the symbols, less one degree of freedom because a certain
> combination is set equal to the apotome.

What commas are being tempered out?

> Well I think the fact that we have Graham proposing MIRACLE
> temperament with 10 nominals and Gene proposing ennealimmal
> temperament with 9 nominals should make it clear that there is
> unlikely to ever be agreement on which is the ultimate temperament
for
> notating everything else including ratios.

My proposal is simply intended to notate effective 7-limit JI
(extendible to 11-limit) not everything.

>> At issue was a specific assertion about commas being mapped to
>> accidentals. I'm still trying to figure it out. Presumably, any
>> linear temperament allows one to notate the lattice with only one
>> accidental, but meantone with 6 nominals doesn't seem to work.
>> So presumably my assertion is correct, but what's required, any
>> MOS?
>
>Why do you say it doesn't seem to work?

There's no way to tile the lattice with six nominals and a single
accidental, while ignoring 81:80.

-Carl

hi Joe, George, and Dave,

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

> hi George,
>
>
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > ... <snip> ... (Or suppose that a
> > piece is heptatonic in one place and decatonic
> > in another. Do we switch notations in the middle
> > of the page?)
>
>
> i *like* that idea!!
>
>
>
> > <snip>
> >
> > But if it would make you happy, you could use
> > sagittal symbols with 10 nominals for Miracle.
> > I just don't think any performer will want
> > to read it that way.
>
>
> you're probably right
> ... but *i* like decimal notation for miracle. :)
>
>
> ------
>
> ... for those who are having trouble following:
>
> example of decimal notation, about 1/4 down the page
> http://sonic-arts.org/monzo/blackjack/blackjack.htm
>
> explanation of decimal notation
> http://sonic-arts.org/dict/decimal.htm
>
>
>
>
> -monz

i've added a new graphic to my "blackjack" page which is
a score of Graham Breed's blackjack "comma-pump" chord
progression, in my 4-line-staff adaptation of Graham's
decimal notation:

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

(just below the pitch-height graph of my MIDI-file
of Graham's progression, and just above the 3,5-limit
lattice mouseover applet.)

Joe, i think *you* in particular will be interested in
seeing this.

George and Dave, could you make some sagittal versions of
this, perhaps in both heptatonic and decimal, for comparison?

i was going to include a 72edo-HEWM version, but (as can
be seen with the lattice applet) the "puns" let certain
pitches have two meanings whose spellings are so different
that i couldn't be bothered sorting it all out.

this is actually very interesting to me, as it shows that
the structure of blackjack is such that the decimal notation
is far better suited to it than the HEWM which is based on
pythagorean/meantone/12edo.

i'm not saying that the decimal notation is *perfect* either
... this particular chord progression implies all
7-limit tetrads (both otonal and utonal), and the decimal
notation is too simple to give a good representation of
the different varieties of interval-sizes: there are
3-, 5-, and 7-limit intervals in every chord, and IMO
each of those varieties should be clearly distinguished
by its own set of symbols.

BTW, i've also updated the Dictionary 72edo page so that
the table showing the HEWM notations of the complete system
is easier to read.

http://sonic-arts.org/dict/72edo.htm

-monz

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

> i've added a new graphic to my "blackjack" page which is
> a score of Graham Breed's blackjack "comma-pump" chord
> progression, in my 4-line-staff adaptation of Graham's
> decimal notation:
>
> http://sonic-arts.org/monzo/blackjack/blackjack.htm
>
>
> (just below the pitch-height graph of my MIDI-file
> of Graham's progression, and just above the 3,5-limit
> lattice mouseover applet.)
>
>
>
> Joe, i think *you* in particular will be interested in
> seeing this.
>
> George and Dave, could you make some sagittal versions of
> this, perhaps in both heptatonic and decimal, for comparison?
>
>
>
> i was going to include a 72edo-HEWM version, but (as can
> be seen with the lattice applet) the "puns" let certain
> pitches have two meanings whose spellings are so different
> that i couldn't be bothered sorting it all out.
>
> this is actually very interesting to me, as it shows that
> the structure of blackjack is such that the decimal notation
> is far better suited to it than the HEWM which is based on
> pythagorean/meantone/12edo.

oh, the heck with it ... i went ahead and created a 72edo-HEWM
score of Graham's comma-pump progression, right under the
decimal score.

i avoided the problems described above by simply using
the simplest 72edo notation for any blackjack notes which
have multiple representations.

... it would be interesting to see what some of the other
72edo versions look like.

-monz

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

> i've added a new graphic to my "blackjack" page which is
> a score of Graham Breed's blackjack "comma-pump" chord
> progression, in my 4-line-staff adaptation of Graham's
> decimal notation:
>
> http://sonic-arts.org/monzo/blackjack/blackjack.htm
>
>
> (just below the pitch-height graph of my MIDI-file
> of Graham's progression, and just above the 3,5-limit
> lattice mouseover applet.)

nice. it's too bad, though, that this page doesn't present blackjack
in the "standard" key (centered around the dyad G-D), because then so
many other blackjack resources could be linked in with it.

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

/tuning/topicId_46826.html#47531

> i've added a new graphic to my "blackjack" page which is
> a score of Graham Breed's blackjack "comma-pump" chord
> progression, in my 4-line-staff adaptation of Graham's
> decimal notation:
>
> http://sonic-arts.org/monzo/blackjack/blackjack.htm
>
>
> (just below the pitch-height graph of my MIDI-file
> of Graham's progression, and just above the 3,5-limit
> lattice mouseover applet.)
>
>
>
> Joe, i think *you* in particular will be interested in
> seeing this.

***Yes, of course, I am very interested in this. I still get "goose
bumps" whenever I hear this progression. Without a doubt I "fuhle
luft von anderem planeten" every time I listen to this!

I can see where you're going with the decimal notation with this. It
doesn't take an Einstein, though, to realize that, since Miracle is
based on a cycle of 10, a notation based on a cycle of 10 is going to
be the easiest!

But, the larger question still remains. Does one create a *notation*
for every tuning? Of course, a *custom* notation is going to be the
most applicable. HOWEVER, performers (and even composers!) don't
want to learn a different entire notation for every tuning! The only
people who want to do that are microtonal theorists! :)

>
> George and Dave, could you make some sagittal versions of
> this, perhaps in both heptatonic and decimal, for comparison?
>
>
>
> i was going to include a 72edo-HEWM version, but (as can
> be seen with the lattice applet) the "puns" let certain
> pitches have two meanings whose spellings are so different
> that i couldn't be bothered sorting it all out.
>
> this is actually very interesting to me, as it shows that
> the structure of blackjack is such that the decimal notation
> is far better suited to it than the HEWM which is based on
> pythagorean/meantone/12edo.
>

***Well, that wouldn't be rocket science, no/yes? (see above)...

>
>
> i'm not saying that the decimal notation is *perfect* either
> ... this particular chord progression implies all
> 7-limit tetrads (both otonal and utonal), and the decimal
> notation is too simple to give a good representation of
> the different varieties of interval-sizes: there are
> 3-, 5-, and 7-limit intervals in every chord, and IMO
> each of those varieties should be clearly distinguished
> by its own set of symbols.
>
>
>
> BTW, i've also updated the Dictionary 72edo page so that
> the table showing the HEWM notations of the complete system
> is easier to read.
>
> http://sonic-arts.org/dict/72edo.htm
>
>

***I note, Monz, that the first part of the Blackjack page has
the "correct standard" Blackjack key now, which is great.

However, as we go along, toward the bottom of the Blackjack page, we
go back to the older F-C-G key...

You probably don't have to change that, but shouldn't you at least
indicate that it's a different key someplace (with a very brief
explanation). Otherwise, when people find different pitches they're
not going to follow the page, if they're viewing it for the first
time...

NOTATION NEWS!:

I do have some notation news for you, Monz. Sagittal has jarred my
brain, and stirred it up like scrambled eggs.

For this reason, upon looking at your HEWM notation, I have (for
myself) uncategorically concluded that your HEWM notation is the
*BEST* for 72-tET!

Of course, since I've been working with the Sims, and so many people
use it, I'm not so inclined to switch...

But, the HEWM makes the most sense, with quartertones as arrows, and
the plusses and minuses for the small syntonic comma...

Bet you didn't think I would conclude that! :)

Joe P.

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

/tuning/topicId_46826.html#47533

> oh, the heck with it ... i went ahead and created a 72edo-HEWM
> score of Graham's comma-pump progression, right under the
> decimal score.
>
> i avoided the problems described above by simply using
> the simplest 72edo notation for any blackjack notes which
> have multiple representations.

***Monz, I'm not understanding the problem. Could you please explain
it to me? Blackjack is a finite set of 21 pitches, yes, so why was
there a problem notating the comma pump in Blackjack?? I'm not
getting it.

thanks!

Joe P.

hi Joe,

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> /tuning/topicId_46826.html#47531
>
>
> > i've added a new graphic to my "blackjack" page which is
> > a score of Graham Breed's blackjack "comma-pump" chord
> > progression, in my 4-line-staff adaptation of Graham's
> > decimal notation:
> >
> > http://sonic-arts.org/monzo/blackjack/blackjack.htm
> >
> >
> > (just below the pitch-height graph of my MIDI-file
> > of Graham's progression, and just above the 3,5-limit
> > lattice mouseover applet.)
> >
> >
> >
> > Joe, i think *you* in particular will be interested in
> > seeing this.
>
>
> ***Yes, of course, I am very interested in this. I still
> get "goose bumps" whenever I hear this progression. Without
> a doubt I "fuhle luft von anderem planeten" every time I
> listen to this!

i have to agree with you there. in one quick stroke,
Graham did for blackjack what pages of theorizing could
never do. (well, OK ... it was only in writing until i
made the MIDI-file, so i'll take some credit too.)

> I can see where you're going with the decimal notation with
> this. It doesn't take an Einstein, though, to realize that,
> since Miracle is based on a cycle of 10, a notation based on
> a cycle of 10 is going to be the easiest!
>
> But, the larger question still remains. Does one create a
> *notation* for every tuning? Of course, a *custom* notation
> is going to be the most applicable. HOWEVER, performers
> (and even composers!) don't want to learn a different entire
> notation for every tuning! The only people who want to do
> that are microtonal theorists! :)

Joe, believe me, i understand your quibbles about this.

my own feeling about it is that any given piece of music
should be offered in *many* different notations. if enough
different kinds of pieces are notated simultaneously in
different notations like this, then we can all *see* what
works and what doesn't.

> ***I note, Monz, that the first part of the Blackjack page
> has the "correct standard" Blackjack key now, which is great.
>
> However, as we go along, toward the bottom of the Blackjack
> page, we go back to the older F-C-G key...
>
> You probably don't have to change that, but shouldn't you at
> least indicate that it's a different key someplace (with a
> very brief explanation). Otherwise, when people find
> different pitches they're not going to follow the page,
> if they're viewing it for the first time...

yes, i have to admit that the original blackjack page was
done during the heady days of its (re)discovery back in 2001,
then i changed some things while i was still very involved
in it as the standard notation for it evolved. but as the
years have passed now, i haven't been composing in blackjack
and have quite forgotten about the standard usage, so when i
go to add new updates to the page i do them with my old notational
standard. i'd like to update all of that to make it consistent,
or as you say, at least make note of it for the unsuspecting
reader. thanks.

>
> NOTATION NEWS!:
>
> I do have some notation news for you, Monz. Sagittal has
> jarred my brain, and stirred it up like scrambled eggs.
>
> For this reason, upon looking at your HEWM notation, I have
> (for myself) uncategorically concluded that your HEWM notation
> is the *BEST* for 72-tET!

holy moly, i never expected that from *you*!!!!!!!!!

>
> Of course, since I've been working with the Sims, and so
> many people use it, I'm not so inclined to switch...
>
> But, the HEWM makes the most sense, with quartertones as
> arrows, and the plusses and minuses for the small syntonic
> comma...
>
> Bet you didn't think I would conclude that! :)

Joe, i thought that even if i could get paul, Dave, Graham,
and whomever else to agree with me on HEWM, i figured that
*you* would be the *one* person who never would agree.
i'm stunned.

anyway, i'm glad that you finally see the logic behind my
presentation. as i said in so many of my posts arguing for
HEWM's adoption, i have spent a lot of time, effort, and
thought on the problem of notation.

-monz

hi Joe,

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> /tuning/topicId_46826.html#47533
>
> > oh, the heck with it ... i went ahead and created a 72edo-HEWM
> > score of Graham's comma-pump progression, right under the
> > decimal score.
> >
> > i avoided the problems described above by simply using
> > the simplest 72edo notation for any blackjack notes which
> > have multiple representations.
>
> ***Monz, I'm not understanding the problem. Could you
> please explain it to me? Blackjack is a finite set of
> 21 pitches, yes, so why was there a problem notating the
> comma pump in Blackjack?? I'm not getting it.

look on the mouseover lattice applet i made on my blackjack page,
and at the new 72edo-HEWM score i've just provided.

let's start with the very first chord, which i notated as
D> : F< : Av : C< , which in 72edo degrees is 14-28-51-70.

you can see from the lattice that this can be analyzed as an
otonal tetrad whose "root" is F< , 72edo-degree 28. the lattice
is only 5-limit, so 72edo-degree 14 (D>) in this chord looks
like a 225:128 above the "root" but really should be representing
a 7:4 above the "root". the only way i can think of to
represent it in 72edo-HEWM in a "meaningful" way is Ebv- ,
which i think is rather cumbersome.

i.e., spelled in "root position" as a 4:5:6:7 tetrad, the
chord should be F< : Av : C< : Ebv- .

to some extent, these problems are merely the result of
trying to force blackjack to fit into the rational implications
on the lattice -- it *is* a temperament, which means that
there is no direct unambiguous 1-to-1 mapping to the lattice.

... but this is *exactly* why i think the decimal notation is
so good! it avoids the preconceived notions that one has when
one uses a notation derived from Pythagorean/meantone/12edo,
which is what my 72edo-HEWM, and your Sims/Maneri 72edo, are.

... and that was only the very first chord that i used as
an example! if you tried to figure out how to notate the
entire progression in either HEWM or Sims/Maneri, you'd see
right away what i'm talking about.

-monz

hi paul,

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

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > i've added a new graphic to my "blackjack" page which is
> > a score of Graham Breed's blackjack "comma-pump" chord
> > progression, in my 4-line-staff adaptation of Graham's
> > decimal notation:
> >
> > http://sonic-arts.org/monzo/blackjack/blackjack.htm
> >
> >
> > (just below the pitch-height graph of my MIDI-file
> > of Graham's progression, and just above the 3,5-limit
> > lattice mouseover applet.)
>
> nice. it's too bad, though, that this page doesn't
> present blackjack in the "standard" key (centered around
> the dyad G-D), because then so many other blackjack
> resources could be linked in with it.

thanks for the critique. yes, i do eventually hope to include
a version of Graham's comma-pump in Sims/Maneri notation,
and based on the G-D standard. can only do so much in a day ...

-monz

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

/tuning/topicId_46826.html#47575

> Joe, i thought that even if i could get paul, Dave, Graham,
> and whomever else to agree with me on HEWM, i figured that
> *you* would be the *one* person who never would agree.
> i'm stunned.
>

***Well, like I said, Sagittal has stirred my brain like a bunch of
fried eggs. I'm examining everything again from the "ground up!"

> anyway, i'm glad that you finally see the logic behind my
> presentation. as i said in so many of my posts arguing for
> HEWM's adoption, i have spent a lot of time, effort, and
> thought on the problem of notation.
>
>
***Yep. It's substantially better than the Sims. Of course, several
people are already using the Sims.

On the other hand, my music is *much* different from several of
the "Boston group" and I don't know any of them besides Julia Werntz,
so it might not matter much if I change it anyway...

But, at the moment, I'm really excited about the Sagittal notation,
because I respect all the thinking behind it, and I want to be a part
of a system that has this kind of flexibility and which has such an
*informed* idea of microtonality behind it... (I hope Dave and George
are reading this... it's coming out rather nicely...)

However, I would like to use a subset of Sagittal that is applicable
for my own music, where the symbols are adequately differentiated.

It appears that these guys are throwing away their trojan
impediments, and we may give birth to something truly usable!!!

Joe P.

hi Joe,

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

/tuning/topicId_46826.html#47580

> look on the mouseover lattice applet i made on my blackjack page,
> and at the new 72edo-HEWM score i've just provided.

... that's of Graham Breed's blackjack comma-pump, at
http://sonic-arts.org/monzo/blackjack/blackjack.htm

> let's start with the very first chord, which i notated as
> D> : F< : Av : C< , which in 72edo degrees is 14-28-51-70.
>
> you can see from the lattice that this can be analyzed as an
> otonal tetrad whose "root" is F< , 72edo-degree 28. the lattice
> is only 5-limit, so 72edo-degree 14 (D>) in this chord looks
> like a 225:128 above the "root" but really should be representing
> a 7:4 above the "root". the only way i can think of to
> represent it in 72edo-HEWM in a "meaningful" way is Ebv- ,
> which i think is rather cumbersome.
>
> i.e., spelled in "root position" as a 4:5:6:7 tetrad, the
> chord should be F< : Av : C< : Ebv- .
>
>
> to some extent, these problems are merely the result of
> trying to force blackjack to fit into the rational implications
> on the lattice -- it *is* a temperament, which means that
> there is no direct unambiguous 1-to-1 mapping to the lattice.
>
> ... but this is *exactly* why i think the decimal notation is
> so good! it avoids the preconceived notions that one has when
> one uses a notation derived from Pythagorean/meantone/12edo,
> which is what my 72edo-HEWM, and your Sims/Maneri 72edo, are.
>
>
> ... and that was only the very first chord that i used as
> an example! if you tried to figure out how to notate the
> entire progression in either HEWM or Sims/Maneri, you'd see
> right away what i'm talking about.

i wrote that quickly, and didn't even begin to go into some
of the thornier problems that a Pythagorean/meantone-based
notation like Sims/Maneri or 72edo-HEWM would encounter in
trying to notate blackjack.

for example, i did use F< as the "root" of that first chord.
but according to the lattice (3^3 * 5^2), the correct
72edo-HEWM notation for that note should really be E#< .
in JI-HEWM it would be E#-- .

of course, because blackjack is a temperament, that "root"
could also be considered to be Gbbb++++ in JI-HEWM
(this is the note at 3^-4 * 5^-4) ... i'm not even going
to try to figure out the 72edo-HEWM equivalent of that one.

do you begin to see how convoluted this becomes?

it's far easier to just call that note F< , but doing
so causes some of the harmonic "meaning" of the notation
to be lost -- and preserving that harmonic "meaning"
is really one of two main reasons to preserve the
pythagorean/meantone basis of the notation, the other
main reason being practical considerations of performance.

looking at the lattice of Graham's comma-pump, you should
be able to see that blackjack can be latticed as a cylinder
which wraps around at the ampersand's comma (3^7 * 5^6).

to me, all of this argues much in favor of decimal notation.

Joe, on a different but related situation, i'd like it if
you would take a look at the first page of my transcription
of Haba's _2nd Quartet_ into my "quarter-tone-staff" notation:

http://sonic-arts.org/dict/qt-staff.htm

to me, the structure and tonal relationships of Haba's
harmonies and melodies are *far* more transparent in the
quarter-tone-staff notation than in Haba's own score,
which simply uses some new quarter-tone accidentals with
the usual 5-line-staff pythagorean/meantone notation.

yes, of course a string player confronted with the
quarter-tone-staff notation would have a hard time with it,
whereas Haba's own score would be much easier to grapple with.

but listen to the excerpt and look at the quarter-tone-staff
while you listen, and i think that with just a little time
spent becoming familiar with it, you'll find that it becomes
very easy to get used to it.

finally, also note how easily 72edo may be notated on the
quarter-tone-staff (near the bottom of the page):

http://sonic-arts.org/dict/72edo.htm

-monz

hi paul,

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

> hi paul,
>
> --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
>
> > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> >
> > > i've added a new graphic to my "blackjack" page which is
> > > a score of Graham Breed's blackjack "comma-pump" chord
> > > progression, in my 4-line-staff adaptation of Graham's
> > > decimal notation:
> > >
> > > http://sonic-arts.org/monzo/blackjack/blackjack.htm
> > >
> > >
> > > (just below the pitch-height graph of my MIDI-file
> > > of Graham's progression, and just above the 3,5-limit
> > > lattice mouseover applet.)
> >
> > nice. it's too bad, though, that this page doesn't
> > present blackjack in the "standard" key (centered around
> > the dyad G-D), because then so many other blackjack
> > resources could be linked in with it.
>
>
>
> thanks for the critique. yes, i do eventually hope to include
> a version of Graham's comma-pump in Sims/Maneri notation,
> and based on the G-D standard. can only do so much in a day ...

if someone would be kind enough to write out Graham's
comma-pump in the blackjack standard notation, i'll make
the musical illustration graphic for the webpage.

-monz

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

/tuning/topicId_46826.html#47580

> > ***Monz, I'm not understanding the problem. Could you
> > please explain it to me? Blackjack is a finite set of
> > 21 pitches, yes, so why was there a problem notating the
> > comma pump in Blackjack?? I'm not getting it.
>
>
>
> look on the mouseover lattice applet i made on my blackjack page,
> and at the new 72edo-HEWM score i've just provided.
>
> let's start with the very first chord, which i notated as
> D> : F< : Av : C< , which in 72edo degrees is 14-28-51-70.
>
> you can see from the lattice that this can be analyzed as an
> otonal tetrad whose "root" is F< , 72edo-degree 28. the lattice
> is only 5-limit, so 72edo-degree 14 (D>) in this chord looks
> like a 225:128 above the "root" but really should be representing
> a 7:4 above the "root". the only way i can think of to
> represent it in 72edo-HEWM in a "meaningful" way is Ebv- ,
> which i think is rather cumbersome.
>

***Hi Monz. I see what you're getting at, but since there is no
actual pitch Ebv- in Blackjack, it isn't really a consideration is
it? You've notated it using the vocabulary you have by including the
D>. Again, notation doesn't always have to perfectly reflect
*theory*. It's nice when it does, but I really don't think it's so
much to get "hung up" about. For me, the important thing is to
notate something so that it can be *performed* but I admit, that's my
*own* bias...

> i.e., spelled in "root position" as a 4:5:6:7 tetrad, the
> chord should be F< : Av : C< : Ebv- .
>
>
> to some extent, these problems are merely the result of
> trying to force blackjack to fit into the rational implications
> on the lattice -- it *is* a temperament, which means that
> there is no direct unambiguous 1-to-1 mapping to the lattice.
>

***That makes sense.

Would you mind, Monz, if I were to make a couple more comments on the
Blackjack page?? You include the colorful lattice that Paul made
with the equivalent degrees of Blackjack mapped to 12-equal.

May I suggest that there is a *better* graphic that Paul made that
should be substituted for that?

He has one where he shows all the different intervals in color, but
shows what the actual JUST INTERVALS are, and by how many cents
Blackjack is off. I think that's a MUCH more interesting graphic
than the one comparing Blackjack to 12-equal...

Also, don't you think it might be nice to include the *most important
graphic of all!* for Blackjack? That is the lattice that Paul made
which is now on Dave Keenan's website:

http://www.uq.net.au/~zzdkeena/Music/Miracle/Blackjack7LatticeGD.gif

(I believe Dave has a new website, but it's not up on the search
engine yet...)

This is the lattice I use all the time in my composing. I don't
think Dave would mind if you were to use that.

It might also be nice to include a link to the Blackjack Radio
Station, which has some of my *own* Blackjack pieces:

http://stations.mp3s.com/stations/354/blackjack1.html

[It's down at this very moment, but all of mp3.com is down at this
moment... they are probably working on it...]

Thanks again!

Joe P.

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

/tuning/topicId_46826.html#47589
>
> Joe, on a different but related situation, i'd like it if
> you would take a look at the first page of my transcription
> of Haba's _2nd Quartet_ into my "quarter-tone-staff" notation:
>
> http://sonic-arts.org/dict/qt-staff.htm
>
>
> to me, the structure and tonal relationships of Haba's
> harmonies and melodies are *far* more transparent in the
> quarter-tone-staff notation than in Haba's own score,
> which simply uses some new quarter-tone accidentals with
> the usual 5-line-staff pythagorean/meantone notation.
>
> yes, of course a string player confronted with the
> quarter-tone-staff notation would have a hard time with it,
> whereas Haba's own score would be much easier to grapple with.
>
> but listen to the excerpt and look at the quarter-tone-staff
> while you listen, and i think that with just a little time
> spent becoming familiar with it, you'll find that it becomes
> very easy to get used to it.
>
>
***Hi Monz,

It's hard to argue agains the fact that, visually, the quartertone
relationships show up much better in the quartertone notation (again,
not a "rocket science"-type discovery...). It reminds me, to an
extent of the old notations for electronic music that Karlheinz
Stockhausen and such like were using back in the '50s and '60s... I
always enjoyed looking at those...

But, of course, a traditional quartet would rather play from the
traditional notation... Training them otherwise would cost serious $,
if they are paid professionals...

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> /tuning/topicId_46826.html#47589
> >
> > Joe, on a different but related situation, i'd like it if
> > you would take a look at the first page of my transcription
> > of Haba's _2nd Quartet_ into my "quarter-tone-staff" notation:
> >
> > http://sonic-arts.org/dict/qt-staff.htm
> >
> > <etc.> ... with just a little time spent becoming familiar
> > with it, you'll find that it becomes very easy to get used
> > to it.
> >
> >
> ***Hi Monz,
>
> It's hard to argue agains[t] the fact that, visually,
> the quartertone relationships show up much better in the
> quartertone notation (again, not a "rocket science"-type
> discovery...). It reminds me, to an extent of the old
> notations for electronic music that Karlheinz Stockhausen
> and such like were using back in the '50s and '60s...
> I always enjoyed looking at those...

i was always fascinated with those Stockhausen "scores"
in younger years too, and they've probably always been
in the back of my mind as some type of inspiration as i've
been developing ideas for my software over the past 2 decades
and for my webpages over the past 5 years.

> But, of course, a traditional quartet would rather play
> from the traditional notation... Training them otherwise
> would cost serious $, if they are paid professionals...

ah, *NOW* you're hitting the nail on the head! when a
musical notation causes you to spend more money than you
would have had to otherwise, then i guess it's a bad notation.

-monz

on 9/28/03 5:08 PM, Carl Lumma <ekin@lumma.org> wrote:

>> /tuning/topicId_46826.html#47324
>>
>>> Would you consider a notation system with 10 nominals using your
>>> accidental set 'sagittal'?
>>>
>>> -Carl
>>
>>
>> ***How awful.... Sorry, Carl... :)
>>
>> J. Pehrson
>
> Try reading Beethoven with 4 nominals and get back to me.

Well, heck, I'll chime in here. Try reading Messiaen with 7 nominals!

Of course, I haven't had the *alternative* experience of more nominals, but
I think there is a strong case that it might be worth learning a new nominal
system to avoid the accidental mess that octatonic creates. But I'd want to
design the staff to be familiar anyway, and I've missed any discussions of
how additional nominals might be translated into an expanded staff, so I'm a
little undereducated to be commenting any further.

-Kurt

>
> -Carl

>Well, heck, I'll chime in here. Try reading Messiaen with 7 nominals!
>
>Of course, I haven't had the *alternative* experience of more nominals,
>but I think there is a strong case that it might be worth learning a
>new nominal system to avoid the accidental mess that octatonic creates.

I've suggested as much in this thread, and in the parent thread on
tuning-math.

>But I'd want to design the staff to be familiar anyway, and I've missed
>any discussions of how additional nominals might be translated into an
>expanded staff, so I'm a little undereducated to be commenting any
>further.

The most obvious way is just to do what we currently do... keep going.
But to avoid having to train the eye to remember where the octaves are
in all the different systems, one might use staves with a number of
positions (spaces and lines) equal to the number of nominals; one octave
to a staff. A clef could specify the octave. When a part goes briefly
out of the home octave (not long enough to justify two or more staves
for that part), a new octave clef could be thrown, or ledger lines or
8va markings could be used.

-Carl

hi Kurt (and Johnny),

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

> on 9/28/03 5:08 PM, Carl Lumma <ekin@l...> wrote:
>
> > Try reading Beethoven with 4 nominals and get back to me.
>
> Well, heck, I'll chime in here. Try reading Messiaen
> with 7 nominals!

:)

good one.

> Of course, I haven't had the *alternative* experience
> of more nominals, but I think there is a strong case
> that it might be worth learning a new nominal system
> to avoid the accidental mess that octatonic creates.
> But I'd want to design the staff to be familiar anyway,
> and I've missed any discussions of how additional
> nominals might be translated into an expanded staff,
> so I'm a little undereducated to be commenting any further.

i just posted about this the other day, but if you missed it,
it's an example of how an expanded set of nominals might
be translated into a *reduced* staff:

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

(the last two graphics. see the blackjack page to compare
the decimal notation of Graham's comma-pump with the 72edo-HEWM
version.)

why a reduced staff instead of an expanded one?

because i'm a firm believer in the idea that the range of
the lines and spaces on a staff should cover one instance
of the identity-interval (interval of equivalence),
which is usually the "8ve".

the usual diatonic nominals give an excellent representation
of the pitch periodicity, only covering one "8ve" and then
repeating identically for all other "8ve"-registers. it's
simply a stupid accident of history that the staff doesn't
do the same, and it should.

some of my notational inventions are to be adapted to the
usual 5-line diatonic staff, but others also modify the staff.
so every one of those which does modify the staff utilizes
this concept of visual "8ve" periodicity. for another example
besides decimal, see my quarter-tone-staff notation, which
i've just updated to include a graphic showing the degrees
and nominals-with-accidentals:

http://sonic-arts.org/dict/qt-staff.htm

Johnny, it strikes me that this notation combined with
+/- cents would be a great way to notate your preferred system.

i also have another system which is like this but for 12edo,
which would be excellent for notating Messiaen's octatonic.
hopefully i'll someday get around to making a webpage about
that for the Dictionary.

-monz

hi Carl,

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

> But to avoid having to train the eye to remember where
> the octaves are in all the different systems, one might
> use staves with a number of positions (spaces and lines)
> equal to the number of nominals; one octave to a staff.
> A clef could specify the octave. When a part goes briefly
> out of the home octave (not long enough to justify two or
> more staves for that part), a new octave clef could be thrown,
> or ledger lines or 8va markings could be used.

we must be reading each others minds. while you were typing
this, i was typing my latest posts pointing to my webpages
illustrating decimal and quarter-tone-staff notation, both
of which use this principle you describe.

... great minds thinking alike again ...

:)

-monz

>i just posted about this the other day, but if you missed it,
>it's an example of how an expanded set of nominals might
>be translated into a *reduced* staff:
>
>http://sonic-arts.org/dict/decimal.htm

Dunno why you use 4 lines for decimal, requiring ledgers for
the basic octave. A 5- or 6-line staff seems better.

For 7 nominals a 4-line staff seems ideal.

-Carl

Wasn't the renaissance all about changing the number of staves to be used in
music? Aren't leger lines a vestigial remnant of that idea?

Unfortunately, choice is a bad thing when reading music, same as when driving
a car. It leads to accidents.

best, Johnny

hi Johnny,

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

> Wasn't the renaissance all about changing the number of
> staves to be used in music? Aren't leger lines a vestigial
> remnant of that idea?

yes, that was one of the developments in musical notation
that didn't last.

> Unfortunately, choice is a bad thing when reading music,
> same as when driving a car. It leads to accidents.

wow, how interesting! that's exactly the analogy i use
in teaching my students the importance of always looking
ahead in the music! for those too young to drive, i use
riding a bicycle the same way.

the dialog goes like this:

(inevitably, the students always respond the same way,
which is why this works so well -- they already understand
the concept and i'm just showing them a new application):

ME:
when you're driving (or riding a bike), do you just keep
your eyes fixed on where you *are*, or do you look ahead?

STUDENT:
look ahead.

ME:
why?

STUDENT:
to avoid crashing.

ME:
same thing when you're playing your music.

-monz

hi Carl,

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

> > i just posted about this the other day, but if you missed it,
> > it's an example of how an expanded set of nominals might
> > be translated into a *reduced* staff:
> >
> > http://sonic-arts.org/dict/decimal.htm
>
> Dunno why you use 4 lines for decimal, requiring ledgers for
> the basic octave. A 5- or 6-line staff seems better.
>
> For 7 nominals a 4-line staff seems ideal.

using one ledger-line for the basic octave allows one to
stack staves on top of each other for other octave-registers,
eliminating the need for other ledger-lines.

for a scale of n nominals, i always use (n/2)-1 staff-lines.
this maps the nominals right onto the lines and spaces and
leaves the reference pitch "blank" (i.e., a ledger-line).

-monz

Along the same lines, when teaching composition,

Teacher: Do you enter a car and start it before you know the actual
destination?

This is to emphasize the need for form before starting the writing.

best, J

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

> for a scale of n nominals, i always use (n/2)-1 staff-lines.

(n/2) staff lines lets you start at the bottom blank, and an octave
will be the top blank, which seems pretty neat. (n/2)-2 staff lines
is similar, only now you can draw a middle-C type line for notes
between two staves, and start and end on one of these. You also need
to allow for odd numbers of nominals; (n+1)/2 staff lines let you
start on the bottom line, and end on the top line, with the new
octave starting on the bottom line of the staff on top.

>using one ledger-line for the basic octave allows one to
>stack staves on top of each other for other octave-registers,
>eliminating the need for other ledger-lines.

Can you give an example?

-Carl

hi Carl,

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

> >using one ledger-line for the basic octave allows one to
> >stack staves on top of each other for other octave-registers,
> >eliminating the need for other ledger-lines.
>
> Can you give an example?

two illustrations of the beginning of Haba's _2nd Quartet_, here:

http://sonic-arts.org/dict/qt-staff.htm

-monz

>> >using one ledger-line for the basic octave allows one to
>> >stack staves on top of each other for other octave-registers,
>> >eliminating the need for other ledger-lines.
>>
>> Can you give an example?
>
>two illustrations of the beginning of Haba's _2nd Quartet_, here:
>
>http://sonic-arts.org/dict/qt-staff.htm

I'm afraid I'm not following you. Can you explain in more detail?

-Carl

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

> > ***I note, Monz, that the first part of the Blackjack page

this page, right?
http://sonic-arts.org/monzo/blackjack/blackjack.htm

> > has the "correct standard" Blackjack key now, which is great.

maybe i missed something, but it isn't now . . .

> > However, as we go along, toward the bottom of the Blackjack
> > page, we go back to the older F-C-G key...

am i completely dense, or what? i don't see any part of the page that
has the "correct standard" key, it all seems to be in the older F-C-G
key. it's too bad, because all the colorful graphics we've
accumulated for blackjack would make great additions to the page, if
it switched to the standard key.

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Joe,
>
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> >
> > /tuning/topicId_46826.html#47533
> >
> > > oh, the heck with it ... i went ahead and created a 72edo-HEWM
> > > score of Graham's comma-pump progression, right under the
> > > decimal score.
> > >
> > > i avoided the problems described above by simply using
> > > the simplest 72edo notation for any blackjack notes which
> > > have multiple representations.
> >
> > ***Monz, I'm not understanding the problem. Could you
> > please explain it to me? Blackjack is a finite set of
> > 21 pitches, yes, so why was there a problem notating the
> > comma pump in Blackjack?? I'm not getting it.
>
>
>
> look on the mouseover lattice applet i made on my blackjack page,
> and at the new 72edo-HEWM score i've just provided.
>
> let's start with the very first chord, which i notated as
> D> : F< : Av : C< , which in 72edo degrees is 14-28-51-70.
>
> you can see from the lattice that this can be analyzed as an
> otonal tetrad whose "root" is F< , 72edo-degree 28. the lattice
> is only 5-limit, so 72edo-degree 14 (D>) in this chord looks
> like a 225:128 above the "root" but really should be representing
> a 7:4 above the "root". the only way i can think of to
> represent it in 72edo-HEWM in a "meaningful" way is Ebv- ,
> which i think is rather cumbersome.
>
> i.e., spelled in "root position" as a 4:5:6:7 tetrad, the
> chord should be F< : Av : C< : Ebv- .
>
>
> to some extent, these problems are merely the result of
> trying to force blackjack to fit into the rational implications
> on the lattice -- it *is* a temperament, which means that
> there is no direct unambiguous 1-to-1 mapping to the lattice.
>
> ... but this is *exactly* why i think the decimal notation is
> so good! it avoids the preconceived notions that one has when
> one uses a notation derived from Pythagorean/meantone/12edo,
> which is what my 72edo-HEWM, and your Sims/Maneri 72edo, are.
>
>
> ... and that was only the very first chord that i used as
> an example! if you tried to figure out how to notate the
> entire progression in either HEWM or Sims/Maneri, you'd see
> right away what i'm talking about.
>
>
>
> -monz

the real problem, of course, is that the progression is a "comma
pump" illustrating one of the commas (in this case, 2401:2400) that
vanishes in the tuning -- and by definition, such a progression can't
be adequately notated using ji, where would would have to either
notate it "drifting" by 2401:2400 each time it goes around, or
arbitrarily introduce a 2401:2400 shift at some point in the
progression. hopefully, the problems in notating the 'classic' I-IV-
ii-V-I or I-vi-ii-V-I comma pump using ji are clear to you; this is
simply another example of the type (except that here, the comma that
vanishes doesn't vanish in 12-equal either!)

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

> if someone would be kind enough to write out Graham's
> comma-pump in the blackjack standard notation, i'll make
> the musical illustration graphic for the webpage.
>
>
>
> -monz

if you mean "standard key" rather than "standard notation", all you
have to do is transpose it down exactly 150 cents. if that isn't a
mechanically simple task for you, i'd be happy to do it myself. let
me know.

on 10/6/03 1:18 AM, monz <monz@attglobal.net> wrote:

> hi Kurt (and Johnny),
>
> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
>> on 9/28/03 5:08 PM, Carl Lumma <ekin@l...> wrote:
>>
>>> Try reading Beethoven with 4 nominals and get back to me.
>>
>> Well, heck, I'll chime in here. Try reading Messiaen
>> with 7 nominals!
>>
>> Of course, I haven't had the *alternative* experience
>> of more nominals, but I think there is a strong case
>> that it might be worth learning a new nominal system
>> to avoid the accidental mess that octatonic creates.
>> But I'd want to design the staff to be familiar anyway,
>> and I've missed any discussions of how additional
>> nominals might be translated into an expanded staff,
>> so I'm a little undereducated to be commenting any further.
>
> i just posted about this the other day, but if you missed it,
> it's an example of how an expanded set of nominals might
> be translated into a *reduced* staff:
>
> http://sonic-arts.org/dict/decimal.htm
>
> (the last two graphics. see the blackjack page to compare
> the decimal notation of Graham's comma-pump with the 72edo-HEWM
> version.)

Yes, I didn't look because I assumed "decimal" referred to something
numeric!

> some of my notational inventions are to be adapted to the
> usual 5-line diatonic staff, but others also modify the staff.
> so every one of those which does modify the staff utilizes
> this concept of visual "8ve" periodicity. for another example
> besides decimal, see my quarter-tone-staff notation, which
> i've just updated to include a graphic showing the degrees
> and nominals-with-accidentals:
>
> http://sonic-arts.org/dict/qt-staff.htm

Yes, and I see I should have looked at this before I replied to the "letters
vs. numbers" thread since I see you are doing some of the things I was
talking about: different shades of gray lines, and staff positions that
don't map to nominals.

However, I'd like to see some music on that staff, to make it clearer. Are
the multiple names on the same line/space intended to be enharmonic
equivalents or just accidentals that might share the same staff position?

> i also have another system which is like this but for 12edo,
> which would be excellent for notating Messiaen's octatonic.

I'd like to see this, but after giving more thought I realize that going to
8 nominals (but maybe you were suggesting 12), while cleaning up the
notation, would reduce the directness of the mapping onto the keyboard. Its
a catch-22 for octatonic on the traditional keyboard. I'm not sure which
problem is worse, but I'd like to try playing some Messiaen written in an
8-nominal notation to find out.

This is a good reason to have more colors than black and white on the
standard keyboard, since the black and white are after all redundant with
the keyboard structure. A different coloring (even a different pattern of
black and white) would be more helpful for use with an octatonic nominal
system.

Meanwhile I suppose a 12-nominal system would serve better to clean up
notation while creating less conflicts with the white-key-nominal bias of
the standard keyboard.

-Kurt

>
>
>
> -monz

on 10/6/03 9:50 AM, Gene Ward Smith <gwsmith@svpal.org> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
>> for a scale of n nominals, i always use (n/2)-1 staff-lines.
>
> (n/2) staff lines lets you start at the bottom blank, and an octave
> will be the top blank, which seems pretty neat. (n/2)-2 staff lines
> is similar, only now you can draw a middle-C type line for notes
> between two staves, and start and end on one of these. You also need
> to allow for odd numbers of nominals; (n+1)/2 staff lines let you
> start on the bottom line, and end on the top line, with the new
> octave starting on the bottom line of the staff on top.

I'm weak on terminology, but assuming ledger line = "middle-C type line".

The practice of avoiding ledger lines and even staying strictly inside the
staff (not using the position below the bottom line or above the top one)
would seem to create less problems in a stacked-staff situation, allowing
either odd or even nominals with less confusion.

Any use of ledger or spaces just outside the staff would imply a continuity
of the line/space pattern which the odd-nominal situation breaks. However,
I suppose it might be tolerated if stacked staves are stacked with a tight
spacing so that an (imaginary) additional line below the upper staff of a
pair would fall on a space in the lower, e.g.

________________ B

________________ G

________________ E

________________ C
________________ B

________________ G

________________ E

________________ C

And I suppose with this convention understood, you could throw in ledger
lines using the same positioning as would be used for the first lines on an
additional staff.

And, now that I've actually seen this (having drawn it), I suppose the
approach of using the spaces just outside the staff might be an improvement
rather than a problem because it gives space between the staves:

B
________________ A

________________ F

________________ D
C
B
________________ A

________________ F

________________ D
C

though I'm still undecided.

-Kurt

on 10/5/03 11:58 PM, Carl Lumma <ekin@lumma.org> wrote:

>> Well, heck, I'll chime in here. Try reading Messiaen with 7 nominals!
>>
>> Of course, I haven't had the *alternative* experience of more nominals,
>> but I think there is a strong case that it might be worth learning a
>> new nominal system to avoid the accidental mess that octatonic creates.
>
> I've suggested as much in this thread, and in the parent thread on
> tuning-math.

Yes, sorry, I was replying prematurely to a big message backlog. Given the
Beethoven reference I thought it unlikely that Messiaen would come up, so I
went ahead and replied. But it turned out interesting anyway.

>> But I'd want to design the staff to be familiar anyway, and I've missed
>> any discussions of how additional nominals might be translated into an
>> expanded staff, so I'm a little undereducated to be commenting any
>> further.
>
> The most obvious way is just to do what we currently do... keep going.
> But to avoid having to train the eye to remember where the octaves are
> in all the different systems, one might use staves with a number of
> positions (spaces and lines) equal to the number of nominals; one octave
> to a staff. A clef could specify the octave. When a part goes briefly
> out of the home octave (not long enough to justify two or more staves
> for that part), a new octave clef could be thrown, or ledger lines or
> 8va markings could be used.

Yes, I like this too, and see my reply to Gene's post.

-Kurt

>
> -Carl

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

/tuning/topicId_46826.html#47671

> Wasn't the renaissance all about changing the number of staves to
be used in
> music? Aren't leger lines a vestigial remnant of that idea?
>
> Unfortunately, choice is a bad thing when reading music, same as
when driving
> a car. It leads to accidents.
>
> best, Johnny

***Yes, particularly when one is changing something as very basic as
the basic Western staff...

Joseph P.

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

/tuning/topicId_46826.html#47697

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > > ***I note, Monz, that the first part of the Blackjack page
>
> this page, right?
> http://sonic-arts.org/monzo/blackjack/blackjack.htm
>
> > > has the "correct standard" Blackjack key now, which is great.
>
> maybe i missed something, but it isn't now . . .
>
> > > However, as we go along, toward the bottom of the Blackjack
> > > page, we go back to the older F-C-G key...
>
> am i completely dense, or what? i don't see any part of the page
that
> has the "correct standard" key, it all seems to be in the older F-C-
G
> key. it's too bad, because all the colorful graphics we've
> accumulated for blackjack would make great additions to the page,
if
> it switched to the standard key.

***Hi Paul,

No, the "density" is over here... Sorry. When I first looked at the
page, I thought that Monz had changed the key of the very first
graphic, but he hasn't... :(

Joseph

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

/tuning/topicId_46826.html#47698

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > hi Joe,
> >
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> >
> > > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > >
> > > /tuning/topicId_46826.html#47533
> > >
> > > > oh, the heck with it ... i went ahead and created a 72edo-HEWM
> > > > score of Graham's comma-pump progression, right under the
> > > > decimal score.
> > > >
> > > > i avoided the problems described above by simply using
> > > > the simplest 72edo notation for any blackjack notes which
> > > > have multiple representations.
> > >
> > > ***Monz, I'm not understanding the problem. Could you
> > > please explain it to me? Blackjack is a finite set of
> > > 21 pitches, yes, so why was there a problem notating the
> > > comma pump in Blackjack?? I'm not getting it.
> >
> >
> >
> > look on the mouseover lattice applet i made on my blackjack page,
> > and at the new 72edo-HEWM score i've just provided.
> >
> > let's start with the very first chord, which i notated as
> > D> : F< : Av : C< , which in 72edo degrees is 14-28-51-70.
> >
> > you can see from the lattice that this can be analyzed as an
> > otonal tetrad whose "root" is F< , 72edo-degree 28. the lattice
> > is only 5-limit, so 72edo-degree 14 (D>) in this chord looks
> > like a 225:128 above the "root" but really should be representing
> > a 7:4 above the "root". the only way i can think of to
> > represent it in 72edo-HEWM in a "meaningful" way is Ebv- ,
> > which i think is rather cumbersome.
> >
> > i.e., spelled in "root position" as a 4:5:6:7 tetrad, the
> > chord should be F< : Av : C< : Ebv- .
> >
> >
> > to some extent, these problems are merely the result of
> > trying to force blackjack to fit into the rational implications
> > on the lattice -- it *is* a temperament, which means that
> > there is no direct unambiguous 1-to-1 mapping to the lattice.
> >
> > ... but this is *exactly* why i think the decimal notation is
> > so good! it avoids the preconceived notions that one has when
> > one uses a notation derived from Pythagorean/meantone/12edo,
> > which is what my 72edo-HEWM, and your Sims/Maneri 72edo, are.
> >
> >
> > ... and that was only the very first chord that i used as
> > an example! if you tried to figure out how to notate the
> > entire progression in either HEWM or Sims/Maneri, you'd see
> > right away what i'm talking about.
> >
> >
> >
> > -monz
>
> the real problem, of course, is that the progression is a "comma
> pump" illustrating one of the commas (in this case, 2401:2400) that
> vanishes in the tuning -- and by definition, such a progression
can't
> be adequately notated using ji, where would would have to either
> notate it "drifting" by 2401:2400 each time it goes around, or
> arbitrarily introduce a 2401:2400 shift at some point in the
> progression. hopefully, the problems in notating the 'classic' I-IV-
> ii-V-I or I-vi-ii-V-I comma pump using ji are clear to you; this is
> simply another example of the type (except that here, the comma
that
> vanishes doesn't vanish in 12-equal either!)

***Monz... this kinda skipped our notice, and it was what the passage
was all about!

Dumb and dumber... only I'll take claim to the latter... :)

JP

hi Carl,

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

> >> >using one ledger-line for the basic octave allows one to
> >> >stack staves on top of each other for other octave-registers,
> >> >eliminating the need for other ledger-lines.
> >>
> >> Can you give an example?
> >
> >two illustrations of the beginning of Haba's _2nd Quartet_, here:
> >
> >http://sonic-arts.org/dict/qt-staff.htm
>
> I'm afraid I'm not following you. Can you explain in more detail?

right now that quarter-tone-staff webpage has 3 graphics:

1) an illustration of how 24edo is mapped to the staff,

2) the beginning of Haba's _2nd Quartet_ notated on a
page which consists of one "system", containing several
quarter-tone-staves stacked on top of each other to indicate
a several-8ve range,

3) the actual published score of that same Haba excerpt,
using Haba's quarter-tone accidentals with regular 5-line
staff notation.

by comparing the published score with my renotation, you
should be able to figure it out, and to see why i think
the quarter-tone-staff notation is superior.

putting each quarter-tone on its own line/space makes
the polyphony much more transparent.

... and how about that? without even trying, i brought this
much-digressed thread back around to its original subject-line!
ha!

-monz

>> >> >using one ledger-line for the basic octave allows one to
>> >> >stack staves on top of each other for other octave-registers,
>> >> >eliminating the need for other ledger-lines.
>> >>
>> >> Can you give an example?
>> >
>> >two illustrations of the beginning of Haba's _2nd Quartet_, here:
>> >
>> >http://sonic-arts.org/dict/qt-staff.htm
>>
>> I'm afraid I'm not following you. Can you explain in more detail?
>
//
>putting each quarter-tone on its own line/space makes
>the polyphony much more transparent.

But I don't see how requiring a ledger line for the basic octaves
makes the staves more stackable. If you go from say, the bottom
line to the top space, this would seem to be perfectly stackable.

There are also times when stacking might not make sense... for
parts (as opposed to a score), and in particular if the extra
range is only needed for a moment. So ledger lines, 8va notation
and clef changes still have there place IMO.

-Carl

hi Kurt,

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

> on 10/6/03 1:18 AM, monz <monz@a...> wrote:
>
> > hi Kurt (and Johnny),
> >
> > --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> >
> >> on 9/28/03 5:08 PM, Carl Lumma <ekin@l...> wrote:
> >>
> >>> Try reading Beethoven with 4 nominals and get back to me.
> >>
> >> Well, heck, I'll chime in here. Try reading Messiaen
> >> with 7 nominals!
> >>
> >> Of course, I haven't had the *alternative* experience
> >> of more nominals, but I think there is a strong case
> >> that it might be worth learning a new nominal system
> >> to avoid the accidental mess that octatonic creates.
> >> But I'd want to design the staff to be familiar anyway,
> >> and I've missed any discussions of how additional
> >> nominals might be translated into an expanded staff,
> >> so I'm a little undereducated to be commenting any further.
> >
> > i just posted about this the other day, but if you missed it,
> > it's an example of how an expanded set of nominals might
> > be translated into a *reduced* staff:
> >
> > http://sonic-arts.org/dict/decimal.htm
> >
> > (the last two graphics. see the blackjack page to compare
> > the decimal notation of Graham's comma-pump with the 72edo-HEWM
> > version.)
>
> Yes, I didn't look because I assumed "decimal" referred to
> something numeric!

understandable!

> > some of my notational inventions are to be adapted to the
> > usual 5-line diatonic staff, but others also modify the staff.
> > so every one of those which does modify the staff utilizes
> > this concept of visual "8ve" periodicity. for another example
> > besides decimal, see my quarter-tone-staff notation, which
> > i've just updated to include a graphic showing the degrees
> > and nominals-with-accidentals:
> >
> > http://sonic-arts.org/dict/qt-staff.htm
>
> Yes, and I see I should have looked at this before I replied
> to the "letters vs. numbers" thread since I see you are doing
> some of the things I was talking about: different shades of
> gray lines, and staff positions that don't map to nominals.

i was smiling to myself in amusement as i just read your post,
since i wrote the one you're responding to here earlier today.
:)

> However, I'd like to see some music on that staff, to make
> it clearer.

are you and Carl having trouble seeing my graphic of
the Haba quartet? what's going on? that's a perfectly
clear example of a published piece of music renotated
in my quarter-tone-staff notation.

> Are the multiple names on the same line/space intended to
> be enharmonic equivalents or just accidentals that might
> share the same staff position?

enharmonic equivalents. all the note-names which appear
on one line or space have the same pitch.

> > i also have another system which is like this but for 12edo,
> > which would be excellent for notating Messiaen's octatonic.
>
> I'd like to see this, but after giving more thought I realize
> that going to 8 nominals (but maybe you were suggesting 12),
> while cleaning up the notation, would reduce the directness
> of the mapping onto the keyboard.

i never addressed the problem of changing nominals for either
12edo or octatonic. i merely came up with what i think is
a better staff notation for it.

here's a "quick-and-dirty" ASCII diagram of my 12edo-staff,
showing the mapping and two typical scales:

mapping of 12edo to 12edo-staff:

-- C
B
----A@/Bb------------------------------------------
A
----G#/Ab------------------------------------------
G
----F#/Gb------------------------------------------
F
----E----------------------------------------------
D#/Eb
----D----------------------------------------------
C#/Db
-- C

12edo diatonic C-major scale:

-- --C--
B
-------------------------------------------------
A
-------------------------------------------------
G
-------------------------------------------------
F
--------------E----------------------------------

----------D--------------------------------------

-- --C--

12edo octatonic scale, starting on C:

-- --C--
B
--------------------------------------------------
A
---------------------G#/Ab------------------------

------------------F#/Gb---------------------------
F
--------------------------------------------------
D#/Eb
-----------D--------------------------------------

-- --C--

> Its a catch-22 for octatonic on the traditional keyboard.
> I'm not sure which problem is worse, but I'd like to try
> playing some Messiaen written in an 8-nominal notation to
> find out.

if you refer me to a relevant Messiaen piece, i'll try to
notate some of it on my staff. it would be good if you
could provide a page or excerpt of the score in a graphic file.

-monz

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

/tuning/topicId_46826.html#47732

> hi Kurt,
>
> here's a "quick-and-dirty" ASCII diagram of my 12edo-staff,
> showing the mapping and two typical scales:
>
>
>
> mapping of 12edo to 12edo-staff:

etc.

if you're viewing this on the stupid Yahoo web interface,
which eliminates "unnecessary" spaces, my ASCII diagrams
will be all messed up. use this link to see it properly:

/tuning/topicId_46826.html#47732?expand=1

-monz

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

> 12edo octatonic scale, starting on C:
>
>
> -- --C--
> B
> --------------------------------------------------
> A
> ---------------------G#/Ab------------------------
>
> ------------------F#/Gb---------------------------
> F
> --------------------------------------------------
> D#/Eb
> -----------D--------------------------------------
>
> -- --C--

i put the letter-name notation on the staff to
better illustrate the scale. but of course, in
an actual musical score, the complicated-looking
letters and accidentals don't appear -- that's the
whole point: the 12edo-staff notation simplifies that.

here's the 12edo octatonic scale beginning on C,
as it would appear using "whole notes" (semibreves) :

(again, on the Yahoo web interface use "Expand Messages"
mode to view it correctly)

-- --O--
O
---------------[-----------------------------------
O
----------------------------O----------------------

-----------------------O---------------------------
O
---------------------------------------------------
O
------------O--------------------------------------

-- --O--

my opinion is that the octatonic scale in this notation
is just as "transparent" as the diatonic. and so is
any other 12edo scale, such as the "whole-tone scale":

-- --O--

--------------------------------O-------------------

----------------------------O-----------------------

-----------------------O----------------------------

------------------O---------------------------------

------------O---------------------------------------

-- --O--

-monz

hi Carl,

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

> > > > > > using one ledger-line for the basic octave allows one
> > > > > > to stack staves on top of each other for other
> > > > > > octave-registers, eliminating the need for other
> > > > > > ledger-lines.
> > > > >
> > > > > Can you give an example?
> > > >
> > > > two illustrations of the beginning of Haba's
> > > > _2nd Quartet_, here:
> > > >
> > > > http://sonic-arts.org/dict/qt-staff.htm
> > >
> > > I'm afraid I'm not following you. Can you explain in
> > > more detail?
> >
> >
> > putting each quarter-tone on its own line/space makes
> > the polyphony much more transparent.
>
> But I don't see how requiring a ledger line for the basic octaves
> makes the staves more stackable. If you go from say, the bottom
> line to the top space, this would seem to be perfectly stackable.

to stack staves, there has to be one or more lines left out
so as to provide a space which separates the 8ves.

the way i do it, the same vertical distance on the page is
always preserved between every note in the tuning.

this is in contrast to the regular "grand staff" combining
two 5-line staves, one treble and one bass, in which "middle-C"
has the same relation to the treble staff as all of its
other notes, and the same relation to the bass staff as
all of *its* other notes, but it is *not* equidistant
between the staves. that's mandatory in my staff notations.

> There are also times when stacking might not make sense... for
> parts (as opposed to a score), and in particular if the extra
> range is only needed for a moment. So ledger lines, 8va notation
> and clef changes still have there place IMO.

that's a good point, but one staff in my noation only covers
one 8ve, and every instrument has a bigger range than that,
so even in parts, at least 2 or 3 staves would be stacked.

-monz

>to stack staves, there has to be one or more lines left out
>so as to provide a space which separates the 8ves.

Ah. This does seem better than a darkened line or more than
3 positions worth of whitespace.

>> There are also times when stacking might not make sense... for
>> parts (as opposed to a score), and in particular if the extra
>> range is only needed for a moment. So ledger lines, 8va notation
>> and clef changes still have there place IMO.
>
>that's a good point, but one staff in my noation only covers
>one 8ve,

Right, that's what we're talking about.

>and every instrument has a bigger range than that, so even in
>parts, at least 2 or 3 staves would be stacked.

Depends. We're only talking about a position or two less than
conventional notation. With 10 nominals, that's not going to
be much more than a 1/5th-octave reduction, at most.

-Carl

I don't know if anyone has mentioned it, but it all good meaning I feel I
need to:

Paul and Monz, I have trouble reading your posts because you use only lower
case. I don't know how other feel, and I'm sure you enjoy it for some reason.
But I do not get the same level of comprehension when I read longer passages.
My eyes kind of gloss.

On the other hand, it is a softer, gentler, Paul. best, Johnny

hi Johnny,

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

> I don't know if anyone has mentioned it, but it all good
> meaning I feel I need to:
>
> Paul and Monz, I have trouble reading your posts because
> you use only lower case. I don't know how other feel, and
> I'm sure you enjoy it for some reason. But I do not get
> the same level of comprehension when I read longer passages.
> My eyes kind of gloss.
>
> On the other hand, it is a softer, gentler, Paul. best, Johnny

yes, i remember you mentioned this before to paul.

in fact, paul and i both decided to do this while we were
chatting one night on Yahoo Messenger. i just like it
better, as it really *does* have a softer, gentler look.

i try to avoid the eye-glazing-over thing by keeping paragraphs
very short (generally one sentence) and using lots of white
space in my emails and posts.

... maybe you've been reading too much German lately? ;-)

-monz

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

/tuning/topicId_46826.html#47758

> hi Johnny,
>
> --- In tuning@yahoogroups.com, Afmmjr@a... wrote:
>
> > I don't know if anyone has mentioned it, but it all good
> > meaning I feel I need to:
> >
> > Paul and Monz, I have trouble reading your posts because
> > you use only lower case. I don't know how other feel, and
> > I'm sure you enjoy it for some reason. But I do not get
> > the same level of comprehension when I read longer passages.
> > My eyes kind of gloss.
> >
> > On the other hand, it is a softer, gentler, Paul. best, Johnny
>
>
>
> yes, i remember you mentioned this before to paul.
>
> in fact, paul and i both decided to do this while we were
> chatting one night on Yahoo Messenger. i just like it
> better, as it really *does* have a softer, gentler look.
>
> i try to avoid the eye-glazing-over thing by keeping paragraphs
> very short (generally one sentence) and using lots of white
> space in my emails and posts.
>
> ... maybe you've been reading too much German lately? ;-)
>
>
>
> -monz

***This is a little off topic, but I find when using Yahoo messenger
or MSN messenger I *also* type with only lowercase. I don't know why
that is... maybe the small screen makes writing more informal.

For email I still use capitalization, although I have several friends
who only use lower case in email, particularly some *younger*
friends...

Joseph Pehrson

on 10/4/03 12:52 PM, monz <monz@attglobal.net> wrote:

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
>> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>>
>> /tuning/topicId_46826.html#47589
>>>
>>> Joe, on a different but related situation, i'd like it if
>>> you would take a look at the first page of my transcription
>>> of Haba's _2nd Quartet_ into my "quarter-tone-staff" notation:
>>>
>>> http://sonic-arts.org/dict/qt-staff.htm
>>>
>>> <etc.> ... with just a little time spent becoming familiar
>>> with it, you'll find that it becomes very easy to get used
>>> to it.
>>>
>>>
>> ***Hi Monz,
>>
>> It's hard to argue agains[t] the fact that, visually,
>> the quartertone relationships show up much better in the
>> quartertone notation (again, not a "rocket science"-type
>> discovery...). It reminds me, to an extent of the old
>> notations for electronic music that Karlheinz Stockhausen
>> and such like were using back in the '50s and '60s...
>> I always enjoyed looking at those...
>
>
> i was always fascinated with those Stockhausen "scores"
> in younger years too, and they've probably always been
> in the back of my mind as some type of inspiration as i've
> been developing ideas for my software over the past 2 decades
> and for my webpages over the past 5 years.
>
>
>
>> But, of course, a traditional quartet would rather play
>> from the traditional notation... Training them otherwise
>> would cost serious $, if they are paid professionals...
>
>
> ah, *NOW* you're hitting the nail on the head! when a
> musical notation causes you to spend more money than you
> would have had to otherwise, then i guess it's a bad notation.

Are you sure there won't be some pieces that an orchestra/quartet would like
to perform for which a new notation will mean more bang for you musical
buck? ;)

If so, it is just a matter of educating. Good things will save money! If
someone was paying me to play new Messiaen pieces they'd save money by
training me on a better notation! Many environmental issues are won this
way!

-Kurt

>
>
>
> -monz

hi Kurt,

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

> Are you sure there won't be some pieces that an
> orchestra/quartet would like to perform for which a
> new notation will mean more bang for you musical buck? ;)
>
> If so, it is just a matter of educating. Good things
> will save money! If someone was paying me to play new
> Messiaen pieces they'd save money by training me on
> a better notation! Many environmental issues are won
> this way!

you know, that's a good point. as Partch said over and
over in his book, *significant music* is what determines
what stays and what goes in the world of music, whether
it's tuning, notation, whatever.

-monz

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

/tuning/topicId_46826.html#47776

> hi Kurt,
>
> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
> > Are you sure there won't be some pieces that an
> > orchestra/quartet would like to perform for which a
> > new notation will mean more bang for you musical buck? ;)
> >
> > If so, it is just a matter of educating. Good things
> > will save money! If someone was paying me to play new
> > Messiaen pieces they'd save money by training me on
> > a better notation! Many environmental issues are won
> > this way!
>
>
>
> you know, that's a good point. as Partch said over and
> over in his book, *significant music* is what determines
> what stays and what goes in the world of music, whether
> it's tuning, notation, whatever.
>
>
>
> -monz

***This kind of training, though, is pretty much what
seasoned "professionals" don't want to do in any case... They like to
think that their schooling is *over* and they're just up there to
play pieces in as convenient way as possible. Now there *are* some
exceptions, but they tend to be performers who are also *composers...*

J. Pehrson