Notation

I have a somewhat dynamic position on the Just/Pythagorean basis
issue. I started out, like Johnston, going for a Just basis and
getting quite confussed seing books where a modifier had to be used to
make C-E a 5:4 major third. Now, I can see more advantages in the
Pythagorean approach, but they aren't overwhelming. I'll outline the
pros and cons.

One thing I don't like about the Johnston notation is the profusion of
accidental types. I'd prefer to notate to a temperament, and leave
the fune tuning to the performer. This may run into problems with
reality, but I don't need to worry about that. It also seems that the
more accidentals, the more mental arithmetic you expect the performers
to do while they're reading the score. And the same goes for ratio or
prime lattice notations.

The main temperaments I can see value in writing around are meantone,
12-equal and schismic. I think I'll take them in turn.

meantone
--------

This is the most obvious for staff notation. You can write 5-limit
chords with out anything special happening, and reserve some new
modifiers (v and ^ look good these days) for 7- or 11-limit intervals,
with 31-equal as the basis. This is what I'd go with most of the
time.

12-equal
--------

This would mean either writing in cents deviations or using symbols
for 72-equal. You may want two extra pairs of symbols, to cover both
quartertones and sixth-tones. Say v and ^ for the former and / and \
for the latter. If three pairs of symbols is too much, a 12 note
staff would be better, but also has problems with backwards
compatibility. It would also meant that similar chords always have
similar notation.

If your scale doesn't fit meantone or schismic, cents deviations from
12-equal will probably be the best option.

The big advantage of assuming the traditional symbols refer to
12-equal is that it seems to correspond most closely to what
performers expect.

schismic
--------

For 11-limit music, 41-equal will be the basis. \ and / can then be
used for comma shifts. I think it's best to keep to a 12-note gamut,
so performers don't have to think about which way round G# and Ab are.

I'd also like the particular 12 notes to depend on an extended key
signature. I think Ellis also proposed this, although he's lumped in
with the Pythagoreanists. Anyway, for C major here are the arguments
for placing the wolf between D and A:

You get a compact structure on the lattice:

A---E---B---F#--C#--G#
/ \ / \ / \ /
Ab--Eb--Bb--F---C---G---D

This means that a piece which is rooted on those nominals will require
few comma modifiers and therefore look simpler on the page. You'll
tend to find D requires two different pitches for 5-limit harmony.
When you get beyond 5-limit, it starts to look less consistent, so
this argument is weaker. But then you might find a higher limit scale
that it makes sense to start with.

<ASIDE>

You could even make it

F#--C#--G#
\ / \ / \
A---E---B
/ \ / \ / \
F---C---G---D
\ / \ /
Eb--Bb

which would make some sense for 5-limit JI as there are lots of chords
that can be written without needing any comma shifts. I think this
matches Johnston's notation. If he didn't keep to these chords, too
bad. It doesn't make much sense for schismic anyway.

You could also try the 7-limit

A-----E-----B
/ \ F#/ \ C#/ \ G#
/ Eb\ / Bb\ / \
F-----C-----G-----D

that may be useful as a "key signature" but not really a default
scale.

</ASIDE>

The unmodified scale is more like what you would play in meantone. If
you're used to just thirds, you won't need a \ to tell you to play
them. You will have to think about what D you play. This does assume
that your performers will be familiar with the 5-limit nature of
meantone notation, which tends not to be the case.

The # and b symbols don't refer to more than half a tone. This would
be what performers would expect if they were familiar with meantone
notation. I think they should be before they get to worrying about
advanced concepts like comma shifts. Unfortunately, the symbols don't
match a 25:24 chromatic semitone, so the minor third above C is Eb/
rather than plain Eb.

You don't have to worry about the difference between G# and Ab because
they come out the same. So do D# and Eb. The wolf is placed right
out in the open where everyone can see it, instead of hidden in the
flats to bite the unwary.

My 29 note keyboard mapping fits a wolf D-A. This is an important
detail for me.

The advantages I see in a G#-Eb wolf are:

Most performers these days who don't think in 12-equal seem to think
in Pythagorean terms.

The position of the wolf is consistent with the way it's written down,
so you don't need to give extra instructions. However, if you follow
this rule you can't consider G# and Ab equivalent, so if you want to
use both you have to tell your performers the difference between them.

Intervals have a consistent way of being commatized, provided they
don't stray too far into the flats. If this is what you want, using
72-equal should make it work a lot better. With schismic temperament
you'll be led towards endless chains of fifths, with ambiguity between
12-note enharmonies. And staff notation isn't consistent this way to
start with because a minor third could be A-C or C-Eb. A 12 note
staff with 72-equal would work perfectly.

I think I'll stick to a D-A wolf for my own purposes, when I'm using
schismic temperament, but re-write for a Pythagorean assumption if a
violinist ever has to read the music.

One compromise would be to use the Pythagorean basis, but with both
comma and diesis pairs such that v==\\ and ^==//. Then, you can write
so that it makes sense in meantone if you strip out the commas. Then
again, if you want to write in meantone you can do that with less
complexity. Perhaps a lazy version of this idea, using a comma shift
only where it wouldn't be expected. So if you insist on a major tone
between C and D, write the latter as D/. And if you want a
Pythagorean major third, write it as C-E/. But leave D-F-A as D-F-A.
I think this comma shift would match Vicentino's comma symbol.

Graham

--- In tuning@y..., "Graham Breed" <graham@m...> wrote:

/tuning/topicId_21432.html#21432

>
> The # and b symbols don't refer to more than half a tone. This
would be what performers would expect if they were familiar with
meantone notation. I think they should be before they get to
worrying about advanced concepts like comma shifts.

This is a general question, and not just for Graham...

We have been studying the Monzo (HEWM) notation and it's obvious that
the "vector notation" that he (and the others) uses is based on
combining various "comma shifts."

HOWEVER, MY question is whether any of this is audible to a
performer...?? Can a performer REALLY KNOW when he is reaching a
just interval during performance??

My guess, which could be wrong, is that performers might be able to
perceive these just intervals in slow tempos, but in faster tempos it
would be impossible... (??)

________ _____ ______ _____
Joseph Pehrson

In a message dated 4/24/01 10:33:13 AM, jpehrson@rcn.com writes:

<< Can a performer REALLY KNOW when he is reaching a
just interval during performance?? >>

if they are trained to listen for beats, difference tones and product tones,
and they are familiar with the timbres they are hearing interact in
performance, and they have "adjusted" their ears to the acoustics of the
space they are in, and the barometric pressure is consistent, and they don't
have a head cold, and their instrument isn't acting up, and nobody coughs
while they are trying to listen, then... maybe. But really, it's not that
hard to hear the difference, even though all these things play a part, and
then some. Tuning a "just interval" is pretty obvious.

If you happened to hear Don Bousted's lecture at microfest, then you'll
remember the example of the recorders that slid down from an equal tempered
major third to a 5/4. You'll probably also remember it sounding not quite
right, because the player went pretty flat, making the interval smaller than
5/4. THis was clearly audible because the difference tone dipped below the
root. I didn't speak up before he showed the overhead graph of the tuning
verified this. I figured it was obvious to many others there.

--- In tuning@y..., Pitchcolor@a... wrote:

/tuning/topicId_21432.html#21514

>
> In a message dated 4/24/01 10:33:13 AM, jpehrson@r... writes:
>
> << Can a performer REALLY KNOW when he is reaching a
> just interval during performance?? >>
>
> if they are trained to listen for beats, difference tones and
product tones, and they are familiar with the timbres they are
hearing interact in performance, and they have "adjusted" their ears
to the acoustics of the space they are in, and the barometric
pressure is consistent, and they don't have a head cold, and their
instrument isn't acting up, and nobody coughs while they are trying
to listen, then... maybe. But really, it's not that hard to hear
the difference, even though all these things play a part, and
> then some. Tuning a "just interval" is pretty obvious.
>
> If you happened to hear Don Bousted's lecture at microfest, then
you'll remember the example of the recorders that slid down from an
equal tempered major third to a 5/4. You'll probably also remember
it sounding not quite right, because the player went pretty flat,
making the interval smaller than 5/4. THis was clearly audible
because the difference tone dipped below the root. I didn't speak
up before he showed the overhead graph of the tuning verified this.
I figured it was obvious to many others there.

Thank you, "Pitchcolor" and, yes, I did hear that lecture... which
does not advocate so well for the cause of hearing and playing just
intervals...

I guess the question is this:

When prescribing cents notation, as Johnny Reinhard does, there is a
certain TARGET that the performer is thinking about, even BEFORE the
pitch is articulated.

For a notation where the performer must listen for a "comma shift,"
in a fast tempo, if the performer has to listen to the QUALITY of the
interval right off the top before "adjusting" it, there may not be
that kind of target, and the adjustment may not be quick enough.

THAT IS, unless the performer has so internalized the different comma
distances that this "target" is there... which, of course, would
require a particular and probably fairly extensive type of training...

(??)
_______ _______ ______ ____
Joseph Pehrson

> > In a message dated 4/24/01 10:33:13 AM, jpehrson@r... writes:
> >
...........................................
>
> >>>>>>there is a certain TARGET that the performer is thinking
about, even BEFORE the pitch is articulated. >>>>>>>>

Hi Joseph, let me try to reduce to a few steps, the entire process of
singing "in JI" in Indian music:

(1) the performer "knows" the notes in the raga; (2) he "shapes" his
vocal cords so as to be able sound the intended note as perfectly as
possible; (3) he is NOT right on the target (except by chance), and
so "adjusts" his pitch quickly from 'off-key' to the correct pitch.
Now, it is well-known that a tone has to last a certain minimum
duration of time, before it is heard as a note. By intuition, right
judgement, and very hard and extensive training (to which you refer,
later in this post), the singer has his 'incorrect' tone adjusted
quickly enough to the correct pitch, as it starts sounding as a
note.

This becomes more challenging in the "taan-s", the fast passages.
But with sufficient talent and rigorous training, most singers do
achieve this. This is where the system of "guru-shishya-parampara"
[guru-pupil-tradition] comes in the picture. You need time, talent,
training and guidance, to get many things right. This is also where
the gharana (school) becomes all-important, because you learn to
emphasize specific aspects of aesthetics as taught in a particular
gharana.

(4) In the middle of all this, you are required to strictly follow
the format of the raga, as stipulated in each gharana.
(5) No intellectual effort is involved in all this, during
performance. It is pure and simple musical talent and hard work.
Thinking and discussion may take place every once in a while, for
clarification, during learning sessions. In the old days, even such
discussions were savagely discouraged. For example, when I was
learning, my Ustad would not tell me even the name of the raga he was
about to start teaching me. No theory, no information on the raga
(vadi-samvadi, aroha-avaroha, etc. etc.)-- just the raga in all its
depth, right from the beginning.
(6) You may come to learn some theory from your seniors -- during
those days, reading books was not even a remote possibility. In fact
hardly any books were available. No writing of any kind is involved
at any stage.

So, it takes a capable guru, very good talent, hard training,
persistent effort, and ten to twelve years, to be able to really
perform well.

I am sure hard work must be the first requirement in any music.

Regards,
Haresh.

>
> For a notation where the performer must listen for a "comma shift,"
> in a fast tempo, if the performer has to listen to the QUALITY of
the
> interval right off the top before "adjusting" it, there may not be
> that kind of target, and the adjustment may not be quick enough.
>
> THAT IS, unless the performer has so internalized the different
comma
> distances that this "target" is there... which, of course, would
> require a particular and probably fairly extensive type of
training...
>
> (??)
> _______ _______ ______ ____
> Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
>
> My guess, which could be wrong, is that performers might be able to
> perceive these just intervals in slow tempos, but in faster tempos
it
> would be impossible... (??)

Agreed . . . at faster tempos your melodic judgment would have to be
relied upon, and that's probably no better than 5 cents.

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

/tuning/topicId_21432.html#21526

>
> Hi Joseph, let me try to reduce to a few steps, the entire process
of singing "in JI" in Indian music:

Thank you so much, Haresh, for your informative commentary on singing
in Just Intonation in Indian music... and the differences between
fast and slow passages....

My guess is that it would take the SAME kind of dedication and
training to learn to perform Just Intonation in a comma-based system
in Western music.

Hopefully, 10 years goes by quickly!

Thanks for the post!

Joseph

________ _____ _____ ___
Joseph Pehrson

In a message dated 4/24/01 1:46:09 PM, jpehrson@rcn.com writes:

<< When prescribing cents notation, as Johnny Reinhard does, there is a
certain TARGET that the performer is thinking about, even BEFORE the
pitch is articulated.>>

there was at least one post that discussed the problems with this assumption;
i.e. vocalists, trombones, and strings don't have the 12ET references that
keyboard and, to a lesser extent, wind players have.

<<For a notation where the performer must listen for a "comma shift,"
in a fast tempo, if the performer has to listen to the QUALITY of the
interval right off the top before "adjusting" it, there may not be
that kind of target, and the adjustment may not be quick enough.>>

right. There's no time to listen and tune it. But it can be anticipated and
approximated if the player knows what's going on. That's all that we can
hope for most of the time even in simpler situations.

<<THAT IS, unless the performer has so internalized the different comma
distances that this "target" is there... which, of course, would
require a particular and probably fairly extensive type of training...>>

I'm of the opinion that nobody, not even pianists, "hear" in 12 tone equal
temperament- internally or externally. It plays a role in structural
perception and pitch constancy for most people, but it is by no means hard
wired or fixed. I believe that most of our tuning sense is _learned and
strngthened with time and exposure. Those 12ET reference points, which are
the crux of the whole "cents" argument, aren't really valid for perception
issues like this in my opinion. I don't think people hear in "commas" either.

In a message dated 4/25/01 3:23:05 PM Eastern Daylight Time,
Pitchcolor@aol.com writes:

>
> I'm of the opinion that nobody, not even pianists, "hear" in 12 tone equal
> temperament- internally or externally. It plays a role in structural
> perception and pitch constancy for most people, but it is by no means hard
> wired or fixed. I believe that most of our tuning sense is _learned and
> strngthened with time and exposure. Those 12ET reference points, which are
> the crux of the whole "cents" argument, aren't really valid for perception
> issues like this in my opinion. I don't think people hear in "commas"
> either.
>

The basis for your position seems to be centered on our studies and how they
fit into how you hear on the idiosyncratic level. People hear differently.
The scientific approach sometimes collides with the perceptions of particular
artists. For example, those with "perfect pitch" (attributed by the science
community to a gene) would have no trouble with cent accuracy. My situation
is relative pitch using 1200 as a basis.

Once upon a time, La Monte Young felt similarly regarding the ability to
retain "absolutely" 12-tET divisions. Modern conservatory training is
specifically in this: 12-tET ear-training, dictation, theory, piano harmony,
and in private instruction. It is very difficult to hear accurate 12-tET,
and I had a hell of a time getting decent grades.

I would agree that wind instruments have the greatest advantage, after
keyboards, for targeting specific intervals, but since I do the same things
when I intone Partch, I do not think that there is to much of a difference.

My only point with the notation is that I use it and suggest it for the
greatest choice of interval vocabulary. Any smaller pool would be suspect
for what it did not contain.

Johnny Reinhard

[Pitchcolor wrote:]
>I'm of the opinion that nobody, not even pianists, "hear" in 12 tone
>equal temperament- internally or externally. It plays a role in
>structural perception and pitch constancy for most people, but it is by
>no means hard wired or fixed.

Not hard-wired or fixed, to be sure, but as you write,

>I believe that most of our tuning sense is _learned and strngthened
>with time and exposure.

Exactly! And all of us (in the "West") are bombarded with 12-tET from
birth, through music school, and in the "real world" of performing. I
would guess that even the most microtonal composer on this list has a
good sense of 12-tET, because it is _so_ omnipresent.

>Those 12ET reference points, which are the crux of the whole "cents"
>argument, aren't really valid for perception issues like this in my
>opinion. I don't think people hear in "commas" either.

Everyone hears in different ways, but I would argue that 12-tET is a
solid point of reference for almost any musician.

JdL

--- In tuning@y..., Pitchcolor@a... wrote:

/tuning/topicId_21432.html#21591

> I'm of the opinion that nobody, not even pianists, "hear" in 12
tone equal temperament- internally or externally. It plays a role in
structural perception and pitch constancy for most people, but it is
by no means hard wired or fixed. I believe that most of our tuning
sense is _learned and strngthened with time and exposure. Those 12ET
reference points, which are the crux of the whole "cents" argument,
aren't really valid for perception issues like this in my opinion. I
don't think people hear in "commas" either.

Well, this would rather controvert the argument of using cents
notation a la Johnny Reinhard, if I am not mistaken...

I'm not sure that after many years of conservative conservatory
training players don't have 12-tET as some kind of reference. At
least they THINK they have it as some kind of reference, even if
they're wrong!

Any other comments about this to "Pitchcolor??"

_________ _____ _______
Joseph Pehrson

Haresh BAKSHI wrote:

>
>
> So, it takes a capable guru, very good talent, hard training,
> persistent effort, and ten to twelve years, to be able to really
> perform well.
>
> I am sure hard work must be the first requirement in any music.
>
> Regards,
> Haresh.
>

I wish somebody would point that out to the British pop industry which has given us The Spice
Girls, Westlife and such tosh to inspire youngsters today.

Joseph Pehrson wrote:

"I would urge him to review a few posts back, and offer his *own* comments on
practical ascii
notation of 72-tET. I'm certain he would have a valuable opinion!"

I probably haven't been able to trace the whole thread, and I haven't any
personal interest in 72tet, so the following is a quick and dirty, if neutral
view. Ezra Sims' article on notation in Xenharmonikon XI presented both his
notation, that of Richter Herf, and that of Rudolph Rasch. I suspect that the
Richter-Herf notation, associated with the Mozarteum in Salzburg is as widely
accepted as the the Sims-Maneri version with its own institutional associations,
while Rasch's notation is associated with his Diapason Press. None differs from
the others in structure (i.e. all are viewed as alterations from 12tet) and can
be usefully applied to each of the subsets of 72. I have no attachment to a
particular set of graphics, but do find Richter Herf's double-arrow-headed 12th
tones to be counterintuitive (the single arrowheads are 6th tones), the Sims
square-root-radical quartertones to be a bit odd, so I suppose that I'd go with
the Rasch. In any case, any score composed in any of these notations will
presumably come with a brief legend beforehand, spelling out what the signs
represent.

The question of the ASCII representation is an interesting one. In order to
avoid possible misunderstandings, why not simply include an additional mod 72
number relative to C=0/72? That would be a small effort that goes a long way
towards settling any possible ambiguity, avoids the whole issue of describing
sizes of intervals in terms of fractions of tones, and may indeed have the added
benefit to be more appropriate for describing musics that are outside more
traditional tonal patterns.

This has probably not been too helpful. As the three notations of which I am
aware are structured similarly, I don't consider this to be as critical an issue
as the question of notating Just Intonation on the basis of either a Pythagorean
series or the diatonic syntonon. In _that_ discussion, especially when it comes
to the question of notating the music of Harry Partch, which only rarely relates
to the diatonic syntonon and constantly features a strong sense of
factor-identities, I come down firmly on the Pythagorean side. I like to teach
Just Intonation to players by teaching them to tune particular intervals, not
pitch classes, and the Pythagorean approach is ideal in that each interval
graphic has an invariant rational interpretation: every notated perfect fifth,
for example, should be interpreted as a ratio of 3:2. If Johnston's music is
indeed based upon the diatonic syntonon on c, then his notation may well be the
best for his music, but I believe that his notation does not fit Partch's ideas
well. But that's another discussion.

Daniel Wolf
Composer, Budapest/Morro Bay
djwolf1@matavnet.hu
http://home.snafu.de/djwolf/

--- In tuning@y..., "Daniel Wolf" <djwolf1@m...> wrote:
Ezra Sims' article on notation in Xenharmonikon XI presented
both his
> notation, that of Richter Herf, and that of Rudolph Rasch.

Can someone please explain why Sims felt the need to invent another
notation, given that he knew about these other two.

Can somoene please tell us what these two others look like. e.g. put
up a scan or post some enlarged ASCII-graphics of them, or
unambiguously describe them in words.

> I suspect
that the
> Richter-Herf notation, associated with the Mozarteum in Salzburg is
as widely
> accepted as the the Sims-Maneri version with its own institutional
associations,
> while Rasch's notation is associated with his Diapason Press.

A possible tie-breaker? Does Rasch use single-headed arrows for
anything?

> I have no attachment to a
> particular set of graphics, but do find Richter Herf's
double-arrow-headed 12th
> tones to be counterintuitive (the single arrowheads are 6th tones),

I find that counterintuitive too. Sims is no better, using single
headed arrows for twelfth-tones and HALF-headed arrows for
sixth-tones.

> the Sims
> square-root-radical quartertones to be a bit odd,

Agreed.

> so I suppose that I'd go with the Rasch.

Yes, legends. Yes, numbers mod 72. No, invisible commas a la Johnson.
But we still want a standard ASCII 72-EDO notation. The big question
is what should we use ^ and v for, if anything, given that everyone
wants to use single-headed arrows for something different?

I am looking at these alternate notations with interest. I remember a page or two of Ben Johnston's notation, the one with all the numbers for the prime harmonics etc, but it really made the page look busy. I suppose if you choose a scale without alteration (no accidentals) then modulation and other tones can be written using altered accidentals. But, how on earth would you notate a modulation to the key a comma below, like from C to c- (or however you'd notate a comma flat accdental). And thus repeating this modulation, would you end up having notes such as G---, and these being equal to some other note several commas sharp, or some other note.

For a fixed set of notes, or fixed set of ratios (which implies a 1/1 somewhere, the root of the whole scale), then that may be ok, just like, say notation in an ET. The trouble arises when you want to write string music with exactness. What I don't like is when the notation breaks down, and a perfectly nice interval get notated really horribly, just because there is a fixed notation. Certainly all of the fixed cycles of temperaments or ET scales suffer from this.

Partch's ratios seem one way out, but they don't seem to convey pitch very well, and the use of diesis like half symbols is often misread by performers, or worse they think its a flyspeck and ignore it.

I thin kthat notating a 4:5:6 on G as being G Bv D makes the third look flat, when we mean it to be just. True, we are altering it from its pythagorean position (ca.400cents), but surely the pythagorean position is the raised one?

M

--- In tuning@y..., mark.gould@a... wrote:
> I am looking at these alternate notations with interest. I remember
>a page or two of Ben Johnston's notation, the one with all the
>numbers for the prime harmonics etc, but it really made the page
>look busy.

ben's notation has worse problems than this. daniel wolf and joe
monzo have proposed a version of ben johnston's notation that makes
modulation much more straightforward.

>I suppose if you choose a scale without alteration (no accidentals)
>then modulation and other tones can be written using altered
>accidentals. But, how on earth would you notate a modulation to the
>key a comma below, like from C to c- (or however you'd notate a
>comma flat accdental).

there are some perfect examples of this in ben johnston's scores.

>And thus repeating this modulation, would you >end up having notes
>such as G---, and these being equal to some >other note several
>commas sharp, or some other note.

not quite, because in just intonation, different notes are never
really 'equal'.

> For a fixed set of notes, or fixed set of ratios (which implies a
>1/1 somewhere, the root of the whole scale), then that may be ok,
>just like, say notation in an ET. The trouble arises when you want
>to write string music with exactness. What I don't like is when the
>notation breaks down, and a perfectly nice interval get notated
>really horribly, just because there is a fixed notation.

this happens in ben johnston's notation -- the just fifth above d
must be notated a+, and the just fifth below a must be notated d-.
the wolf/monzo version eliminates these problems.

>Certainly >all of the fixed cycles of temperaments or ET scales
>suffer from >this.

what exactly do you mean?
>
> I thin kthat notating a 4:5:6 on G as being G Bv D makes the third
>look flat, when we mean it to be just. True, we are altering it from
>its pythagorean position (ca.400cents), but surely the pythagorean
>position is the raised one?

see my last couple of posts. also recall that ca. 800-1420, the
pythagorean tuning was the norm, and thirds and sixths were
considered unstable intervals.

Hi all,

You see, it is a severe problem that every composer tried to create his very individual set of signs, not only accidentals, but also other which refer to playing techniques.
As I see the problem, it should be tried to make a comprehensive book (of surely more than 500 pages ... :) containing at least all those notation techniques that have been created between 1900 and 2000, and then one could try to compare the notations pertaining to the same sounding result, and find out which one is the most practicable, and this for all notational tasks. But this will be a life's work.

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

/tuning/topicId_21432.html#48276

> Hi all,
>
> You see, it is a severe problem that every composer tried to
create his very individual set of signs, not only accidentals, but
also other which refer to playing techniques.
> As I see the problem, it should be tried to make a comprehensive
book (of surely more than 500 pages ... :) containing at least all
those notation techniques that have been created between 1900 and
2000, and then one could try to compare the notations pertaining to
the same sounding result, and find out which one is the most
practicable, and this for all notational tasks. But this will be a
life's work.

***Well, this makes sense. However, I maintain that the results
would be a compilation of personal preference based more on
*legibility* and *differentiation* than any coordinated and
integrated theoretical system...

jP

--- In tuning@yahoogroups.com, Wernerlinden@a... wrote:
> Hi all,
>
> You see, it is a severe problem that every composer tried to
create his very individual set of signs, not only accidentals, but
also other which refer to playing techniques.
> As I see the problem, it should be tried to make a
comprehensive book (of surely more than 500 pages ... :)
containing at least all those notation techniques that have been
created between 1900 and 2000, and then one could try to
compare the notations pertaining to the same sounding result,
and find out which one is the most practicable, and this for all
notational tasks. But this will be a life's work.

This project was attempted in the 90's by Gardiner Read in his
book 20th Century Microtonal Notation. However, he did not often
relate the notations to issues of tuning, and when he did he
usually got it wrong. The book has a plethora of shortcomings,
but conclusions one can draw from the work are:

1) there was no uniform approach to microtonal notation in the
20th century

2) most of the notations were only used in one or two pieces by
any particular composer.

3) the primary researcher got the tuning wrong in more cases
than not, suggesting that the notations were ambiguous with
regard to tuning

Such a volume is of relatively little practical use. There is no
unifying trend which can be culled from a catalogue of
idiosyncratic notational methods, most of which were
abandoned by their creators.

Aaron Hunt

--- In tuning@yahoogroups.com, Wernerlinden@a... wrote:
> Hi all,
>
> You see, it is a severe problem that every composer tried to create
his very individual set of signs, not only accidentals, but also other
which refer to playing techniques.
> As I see the problem, it should be tried to make a comprehensive
book (of surely more than 500 pages ... :) containing at least all
those notation techniques that have been created between 1900 and
2000, and then one could try to compare the notations pertaining to
the same sounding result, and find out which one is the most
practicable, and this for all notational tasks. But this will be a
life's work.
>

Hi Werner,

It is uncanny that you should specify 1900 to 2000, when you did not
already know of the "life work" of Boston Professor Emeritus, Gardner
Read, entitled "20th Century Microtonal Notation". George and I looked
at this remarkable work while developing Sagittal. What we mostly came
away from it with were the properties that the author considered to be
important in a microtonal notation. We believe we have satisfied them
in our 12-et-relative subset called "Trojan", but we have also gone
way beyond Read's requirements in areas where he seems to have little
appreciation for what is required, notably JI.

I don't want to appear obtuse, but it is my honest and clear opinion that fitting whatever scale you have at hand to the seven-nominal five-line stave is stupid. No matter how you choose the accidentals or other diacritic marks to your noteheads you're going to misrepresent the scale by shoehorning it into a notation which won't fit it. The notation of seven nominals with sharps flats double sharps and double flats will fit the seven nominal diatonic, in various different equal and unequal temperaments, and will after a fashion, cope with some JI.

But to suggest 15EDO and 16EDO will fit in this scheme seems perverse. That's why I prefer the generalised scale approach. True it leads to different scale staves with differing numbers of nominals, but preserves the commonalities between generalised scales with the same number of nominals. Just think, one looks at the notation and can /see/ which generalised scale the music is written in.

I think this looks messy:

> C C#j Dk Dy Eb? E Fj F#k F#y G? G#(or Ab) Aj Bbk Bby B?

and so does this

> C C/ D\ D D/ E\ E E/ G\ G G/ A\ A A/ C\

whereas, for a given scale family, the notation is always consistent, as it is for say 12/17/19/31 (without diesis symbols, and just using sharp flat and their doubles). True, there are issues here, but I'm trying for the big view.

There are those that would argue that preserving the 5-line 7 nominal notation acts as a guide to performers, permitting them to see the scale in relation to their preconceived intonational scheme. This can be useful.

But suppose we are now transported to another planet where the 11-nominal 19EDO scale is the norm: 22122212221, and they use a seven-line stave, but otherwise they use noteheads like us and sharps and flats (though they mean something slightly different). Would we write their scale in our notation or ours in theirs? Surely each would have developed *for their particular scale*. The notation symbol set is the same: sharps and flats, so there's your consistency. Worse in my opinion is the plethora of symbols used on the seven-nominal scale. One principle: generators and segments of them to determine nominals and accidentals. Fits all EDO scales. As for JI, the problem is more serious. I can't pretend to fit a notation to that. Even Partch couldn't.

All IMHO.

Mark (hoping he's rocked the boat in the nicest possible way)

--- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:
> I don't want to appear obtuse, but it is my honest and clear opinion
> that fitting whatever scale you have at hand to the seven-nominal
> five-line stave is stupid.

So I'm stupid am I, you Nazi Zionist b... Only joking. :-)

Hi Mark,

And there are performers who don't have time to learn a new staff with
a new set of nominals for every different tuning and so won't even
look at music written on them. If you're only writing for yourself it
doesn't matter much what you use, but otherwise ...

> No matter how you choose the accidentals or
> other diacritic marks to your noteheads you're going to misrepresent
> the scale by shoehorning it into a notation which won't fit it.

Yeah, but someone might be able to read it and play it. :-)

> The
> notation of seven nominals with sharps flats double sharps and double
> flats will fit the seven nominal diatonic, in various different equal
> and unequal temperaments, and will after a fashion, cope with some JI.
>

In my opinion, when accidentals are added for various comma
inflections, it not only copes with (extended) JI, but works very well
(although a 12-nominal system would work well for this too), and how
well such a system (e.g. Sagittal) handles temperaments depends only
on how closely they approximate JI.

> But to suggest 15EDO and 16EDO will fit in this scheme seems perverse.

And inventing new staves with new nominals will seem perverse to some.
No one says they fit well, but they _can_ be "shoehorned" as you say,
and this has some advantages.

> That's why I prefer the generalised scale approach. True it leads to
> different scale staves with differing numbers of nominals, but
> preserves the commonalities between generalised scales with the same
> number of nominals.

Simply calling something "generalised" doesn't help here, because
there are many different ideas about how to generalise the diatonic
scale, and there are different ideas about how to generalise staff
notation. They all keep some aspects the same and vary others. We need
to use terms that say _how_ they are generalising.

I understand the main distinction we're discussing here is whether the
nominals (and therefore staff positions) should always represent a
chain of seven approximate fifths as FCGDAEB, or should represent
whatever proper MOS scale of around 5 to 12 notes is most "natural"
for the tuning being used.

An appropriate shorthand for this might be "fifth-nominals" versus
"MOS-nominals".

I put "natural" in scare-quotes because there is an awful lot to be
decided about what makes a particular linear temperament the most
natural for any given scale, unless the scale was specifically
generated linearly. What linear temperament would you use to notate
JI, or would you use different ones for different JI scales?

> Just think, one looks at the notation and can /see/
> which generalised scale the music is written in.

And if one is not familiar with that particular linear temperament
(LT) and its MOS-nominals one must simply set it aside.

And one could just as easily indicate which LT with a few words at the
start of the score.

And in regard to fifth-nominals with comma-accidentals: Just think,
one looks at the notation and can /see/ what the harmonies are,
without knowing the details of the tuning.

> I think this looks messy: [for 15EDO]
>
> > C C#j Dk Dy Eb? E Fj F#k F#y G? G#(or Ab) Aj Bbk Bby B?

I hope you're not judging the "messiness" from this crude ASCII
approximation of the real symbols.

But in any case, I believe I said something similar myself. And yet it
can be learned and played very quickly by someone who is familiar with
12-ET. They only have to learn two new arrow-like accidentals (and
their vertical mirror images) as representing (in this case)
inflections of 1/5 and 2/5 of a semitone.

> and so does this
>
> > C C/ D\ D D/ E\ E E/ G\ G G/ A\ A A/ C\
>
> whereas, for a given scale family, the notation is always consistent,
> as it is for say 12/17/19/31

If this is a "family" to you then I'm not sure what you mean by family
now. I thought previously that you meant linear temperament, but the
line thru 12,19 and 31 does not include 17.

In fact you've given a family of the kind that makes sense with
fifth-nominals.

An ET may belong to many different and completely unrelated families
in the sense of linear temperaments, but only to one or two families
in the sense of range-of-fifth-sizes.

> (without diesis symbols, and just using
> sharp flat and their doubles). True, there are issues here, but I'm
> trying for the big view.

Well keep trying, and I'll be glad to help. There is definitely a
place for these notations and I'd like to see them done in a way that
does not conflict with Sagittal but rather leverages off it in any way
that is appropriate.

One of the things we did, to make sure we weren't closing off any
possibilities for MOS-nominal notations using sagittal accidentals,
was to not use any uppercase ASCII characters in our suggested ASCII
shorthand for the accidentals (although the ASCII longhand does use X
and Y in some uncommon symbols). So all uppercase ASCII are available
as nominals in text.

By the way, Erv Wilson has a fascinating interlocking system of
nominals for the most common (fifth-generated) LTs in an article
published in Xenharmonikon 3, 1975, 'On Linear Notations and the
Bosanquet Keyboard'.

This article is probably on Kraig Grady's site. If anyone finds it
could they please post the URL.

> There are those that would argue that preserving the 5-line 7 nominal
> notation acts as a guide to performers, permitting them to see the
> scale in relation to their preconceived intonational scheme. This can
> be useful.

Yes.

> But suppose we are now transported to another planet where the
> 11-nominal 19EDO scale is the norm: 22122212221, and they use a
> seven-line stave, but otherwise they use noteheads like us and sharps
> and flats (though they mean something slightly different). Would we
> write their scale in our notation or ours in theirs? Surely each would
> have developed *for their particular scale*. The notation symbol set is
> the same: sharps and flats, so there's your consistency.

Ah .. the idealism of youth. ;-) The thing is, we're on _this_ planet
with its history of human and cultural evolution as given. In any
case, I'm not sure what you were trying to establish with the above
thought-experiment. You might try again.

> Worse in my
> opinion is the plethora of symbols used on the seven-nominal scale.

Well, with Sagittal, we've got that plethora down to a very few
symbols (8 up/down pairs) needed to notate zillions of the most common
tunings: 9-limit JI plus odd-harmonics to 15, and about 50 of the most
popular ETs under 100 (and many LTs although we have not spent much
time on these so far).

And if 8 vertically-mirrored pairs still seems too many. I note that
the symbol set has its own internal logic. All but one of them is
constructed from only 4 simpler parts taken 1 or 2 at a time. And
within this set of 8 symbol-pairs there's an even smaller set of 3
pairs that does most of the work; those representing the 5 and 7
commas and the 11 diesis, which should be familiar from the HEWM
system for notating 72-ET.

> One
> principle: generators and segments of them to determine nominals and
> accidentals. Fits all EDO scales. As for JI, the problem is more
> serious. I can't pretend to fit a notation to that. Even Partch
> couldn't.

Well I believe Sagittal does it. I believe George provided the key
that made it manageable, with his proposal to construct arrow-like
accidentals from a small number of simple components in a logical manner.

In my opinion, notating JI is the key to notating everything else.

> Mark (hoping he's rocked the boat in the nicest possible way)

There's not much of a boat to rock. We're mostly floundering in an
open sea. But I do hope the Sagittal system is some kind of raft we
can cling to, and maybe build on.

The camera-ready copy of our introductory Sagittal article has been
mailed off to John Chalmers for publication in Xenharmonikon 18,
hopefully early in the new year.

Regards,
-- Dave Keenan

I wrote:
> By the way, Erv Wilson has a fascinating interlocking system of
> nominals for the most common (fifth-generated) LTs in an article
> published in Xenharmonikon 3, 1975, 'On Linear Notations and the
> Bosanquet Keyboard'.

Here it is:

http://www.anaphoria.com/xen3a.PDF

When you've digested that, then we can talk.

--- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:

/tuning/topicId_21432.html#50345

> I don't want to appear obtuse, but it is my honest and clear
opinion
> that fitting whatever scale you have at hand to the seven-nominal
> five-line stave is stupid.

***Well, Mark, I would try, first to get some performers who have not
played microtonality before to tell you which they prefer. After you
have done that, and elicited their responses, you'll be in a better
position to evaluate the "stupidity" of it all...

J. Pehrson

>

All you have to do is ask Dave!
http://www.anaphoria.com/xen3a.PDF
http://www.anaphoria.com/xen3b.PDF
the following also has a few interesting uses of notation based on Keyboard patterns
http://www.anaphoria.com/keygrid.PDF

The generalized keyboard pattern can use the type of varied line patterns whch one could put on a keyboard.
On the other hand i thing Dave and Georges notation could also be used on the beginning of the staff in some fashion

>
> From: "Dave Keenan" <d.keenan@bigpond.net.au>
> Subject: Re: Notation
>
>
>
> By the way, Erv Wilson has a fascinating interlocking system of
> nominals for the most common (fifth-generated) LTs in an article
> published in Xenharmonikon 3, 1975, 'On Linear Notations and the
> Bosanquet Keyboard'.
>
> This article is probably on Kraig Grady's site. If anyone finds it
> could they please post the URL.
>
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

>And there are performers who don't have time to learn a new staff
>with a new set of nominals for every different tuning and so won't
>even look at music written on them. If you're only writing for
>yourself it doesn't matter much what you use, but otherwise ...

Pardon me, but this argument sounds like a bit of a... false dilema,
is it? Performers have to know and practice scales, there's simply
no way around it. Would you want your diatonic piece played by a
musician who 'didn't have the time' to learn the diatonic scale and
couldn't play one standing to save his life?

While some people are on-sight "machines", in my experience the
majority of pianists can read on sight only a subset of available
structures. They're amazing with Brahms or ragtime but if you
throw them some octatonic music they're stuck, and are no better
than average at reading it. They might complain, but chances are
they or someone else will stop and learn the patterns. If the
music is compelling, people will learn the skills to play it.

>The camera-ready copy of our introductory Sagittal article has been
>mailed off to John Chalmers for publication in Xenharmonikon 18,
>hopefully early in the new year.

It has?

-Carl

hi,

I think that my line of thinking was performed in an abstract sense, if you will. I understand the need for performers to be engaged in microtonality. I am not suggesting that fitting other scales/intonations to the 7nominal 5-line stave isn't useful, and I said so. What I am trying to get at is a notation that 'reveals' the structure of the scale in question, and chose to base my ideas on generators of EDO 'circles'. The stupidity is in the seeming feeling that the 'shoehorning' method is /the/ way to notate these scales.

It is perfectly possible to write 19EDO eleven nominal music on a seven nominal stave. I have done so myself, for performers. My beef is that if we're going to be rigorous and exact and formalised with everything else (see tuning maths for this sort of thing), then what's wrong in using these notations as accurate representations (in a graphical sense) of the scales they embody? Nobody might play this music perhaps in this form, except those sitting at generalised keyboards where, suddenly, it all makes sense. Of course, there are those who would consider this a kind of extended-halberstadt view, and I am not averse to this.

Mark

PS, the notation for 15EDO, as proposed by another chap beginning with C, that I had also put up myself here, notates Porcupine easily - it's the 'black notes' of the stave/keyboard. 2222223 in 15EDO. Assuming 3333335 as another form , I get 23EDO as another Porcupine representation, or is this too 'way-out' to be useable?
M

On Tuesday, December 23, 2003, at 06:58 am, tuning@yahoogroups.com wrote:

>> I don't want to appear obtuse, but it is my honest and clear
> opinion
>> that fitting whatever scale you have at hand to the seven-nominal
>> five-line stave is stupid.
>
>
> ***Well, Mark, I would try, first to get some performers who have not
> played microtonality before to tell you which they prefer. After you
> have done that, and elicited their responses, you'll be in a better
> position to evaluate the "stupidity" of it all...
>
> J. Pehrson

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> [Dave Keenan:]
> >The camera-ready copy of our introductory Sagittal article has been
> >mailed off to John Chalmers for publication in Xenharmonikon 18,
> >hopefully early in the new year.
>
> It has?
>
> -Carl

Yes, it has!

--George

--- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:
> hi,
>
> I think that my line of thinking was performed in an abstract
sense, if
> you will. I understand the need for performers to be engaged in
> microtonality. I am not suggesting that fitting other
> scales/intonations to the 7nominal 5-line stave isn't useful, and I
> said so. What I am trying to get at is a notation that 'reveals'
the
> structure of the scale in question, and chose to base my ideas on
> generators of EDO 'circles'. The stupidity is in the seeming
feeling
> that the 'shoehorning' method is /the/ way to notate these scales.
>
> It is perfectly possible to write 19EDO eleven nominal music on a
seven
> nominal stave. I have done so myself, for performers. My beef is
that
> if we're going to be rigorous and exact and formalised with
everything
> else (see tuning maths for this sort of thing), then what's wrong
in
> using these notations as accurate representations (in a graphical
> sense) of the scales they embody?

Mark,

Consider for a moment the difference between notating *scales* and
*tunings*. As a *tuning*, 19-ET can be notated using only
conventional sharps and flats (with 7 nominals); likewise, for a
*meantone scale* which is a subset of 19-ET, the same notation would
be the logical choice.

Now if you're notating a subset of 19-ET that uses a different
generating interval (say a major or minor 3rd), then (following your
logic above) you would most likely want a staff with a different
number of nominals. For the sake of *accuracy*, might you also want
symbols other than conventional (single and double) sharps and flats,
since these required accidentals may be nowhere near a "semitone" in
size (not likely in 19, but there are other tunings, such as a
Miracle MOS scale, where this would be the case; more about this
below)?

Thus, for a single *tuning* you might have 2 or 3 different
notations! Suppose you switch *scales* within a composition
(alternating between them from one measure to the next), then do you
propose to switch notations (including staff configurations) that
often? Pity the poor performer!

The Sagittal notation that Dave Keenan and I have developed was
intended to notate *tunings* rather than *scales*. Granted there are
some ET's (tunings) that do not work well with 7 nominals; for these
we recommend that they be notated as subsets of larger ET's (e.g., 15
as a subset of 60, or 16 as a subset of 48).

But suppose that you were to notate one of these using a different
staff. Earlier in the year Dave Keenan pointed out that, because we
have such a generous assortment of new accidentals that keep the same
harmonic meanings across all tunings, it would be possible to use
some of these as accidentals (in lieu of sharps and flats) in
situations where a non-conventional staff (having other than 7
nominals) is employed, in which case the accidental could reflect the
true nature (i.e., both approximate size and harmonic meaning) of the
alterations in pitch required for the new staff. While many
performers might not wish to read something like this, certainly it
would be valuable for purposes of studying new scales, and the new
symbols would have the same meanings in other scale systems or
tunings in which they might be used.

Does this make any sense?

--George

>Now if you're notating a subset of 19-ET that uses a different
>generating interval (say a major or minor 3rd), then (following your
>logic above) you would most likely want a staff with a different
>number of nominals. For the sake of *accuracy*, might you also want
>symbols other than conventional (single and double) sharps and flats,
>since these required accidentals may be nowhere near a "semitone" in
>size

George,

It can be argued that conventional accidentals represent not
semitones but movements on the chain of generators. By this view
it is not inaccurate to use conventional accidentals for microtonal
music.

>Thus, for a single *tuning* you might have 2 or 3 different
>notations!

19-tET is not a tuning, it is a scale. A single scale-based
notation will suffice for any tuning of that scale which
respects its map (ie standard notation for the diatonic scale
*as tuned in* 12- 19- or 31-tET).

>Suppose you switch *scales* within a composition
>(alternating between them from one measure to the next), then do
>you propose to switch notations (including staff configurations)
>that often? Pity the poor performer!

I'd like to hear Mark's answer... you already know that my answer
is yes, though I don't know what you mean by "staff configurations".
But note also my recent claim that if you do not wish to change
notations, the result will still be on par with Sagittal.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Now if you're notating a subset of 19-ET that uses a different
> >generating interval (say a major or minor 3rd), then (following
your
> >logic above) you would most likely want a staff with a different
> >number of nominals. For the sake of *accuracy*, might you also
want
> >symbols other than conventional (single and double) sharps and
flats,
> >since these required accidentals may be nowhere near a "semitone"
in
> >size
>
> George,
>
> It can be argued that conventional accidentals represent not
> semitones but movements on the chain of generators. By this view
> it is not inaccurate to use conventional accidentals for microtonal
> music.

True, but I don't think that it's a good idea to give conventional
symbols new meanings that are open to misinterpretation, even if
there is an underlying logic. New symbols would make it obvious to
anyone that this is not an ordinary notation.

> >Thus, for a single *tuning* you might have 2 or 3 different
> >notations!
>
> 19-tET is not a tuning,

If 19-ET isn't a tuning, then what is?

> it is a scale.

Well, yes, it could be. But more usually a scale that uses pitches
of 19-ET would be some subset of that tuning, e.g., a major or minor
scale. And major and minor *scales* are not restricted to 19-ET, but
may also be in other *tunings*, such as Pythagorean, meantone, 12-ET,
31-ET, 55-ET, or a well temperament, to give a few examples. I would
therefore consider a *scale* to consist of a specific number of tones
(or notes) in certain relationships (perhaps defined by a generating
interval within a given size range) but a *tuning* to consist of
pitches separated by intervals that are *exactly* defined.

> A single scale-based
> notation will suffice for any tuning of that scale which
> respects its map (ie standard notation for the diatonic scale
> *as tuned in* 12- 19- or 31-tET).
>
> >Suppose you switch *scales* within a composition
> >(alternating between them from one measure to the next), then do
> >you propose to switch notations (including staff configurations)
> >that often? Pity the poor performer!
>
> I'd like to hear Mark's answer...

I infer from his last reply that a conventional staff would probably
be useful as a practical expedient for the performer, but that it
would be better for the theorist or composer to work with an
alternate staff configuration that conformed to the number of
nominals in the scale.

I am wondering whether Monz's Tonalsoft software-in-development will
allow user-defined staff configurations and automated translation of
these into a conventional staff configuration that could be read by
the performer.

> you already know that my answer
> is yes, though I don't know what you mean by "staff configurations".

If you used a 5-line staff for one set of nominals and a 4-line staff
for another set, then your configuration of staff lines would
constantly be changing. Or if you kept a 5-line staff for both sets
of nominals but had the "octave" (or 1:2) as different numbers of
steps on the staff, then you would need some way of indicating where
the changes in configuration were occurring. I have a feeling that
it wouldn't be very practical for either performance or theoretical
purposes. However, what about having two staff configurations in
parallel, i.e., one above the other? This would be useful for all
concerned, whether performer, composer, or theorist.

--George

>

Hello Mark!
Both of these seem feasible on a keyboard ( i think it is actually better than novaro's sugestion) and would use them. although if i added wind or strings i think i would use something based on the horrible staff we are stuck with although
the Klavarscribo might be appealing. What performers will and will not do varies on the personal basis of their own inclination. Any blanket statement is questionable. I think what could be adopted would be the use of the symbols which might
be reapplied into those cases that don't easily fall with dave and georges notation

>
> From: Mark Gould <mark.gould@argonet.co.uk>
>
>
>
> PS, the notation for 15EDO, as proposed by another chap beginning with
> C, that I had also put up myself here, notates Porcupine easily - it's
> the 'black notes' of the stave/keyboard. 2222223 in 15EDO. Assuming
> 3333335 as another form , I get 23EDO as another Porcupine
> representation, or is this too 'way-out' to be useable?
> M
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

Happy Christmas, Hanukka, Hogmanay and all festivals of the Winter and the turning year to all on the list.

As for my responses about notation:

1. I can understand the need for a workaround notation for performers, if that is what is required.

2. I would prefer my performers just to use one stave type throughout, so I don't expect stave changes, but then, if they were professionals committed to microtones they wouldn't complain - especially if the visual acoustic logic is apparent to them. My feeling is that professional performers who are advocates /will/ learn new notations, so long as they convey the acoustic/expressive intent in a suitably clear graphic manner.

3. I think the notation I propose is merely a visualisation tool, and useful for generalised keyboard conceptions. hopefully it can be also a performance tool, and perhaps one day that may be so

4. My work is aimed at EDO scales in the main, but it is perfectly possible to use a mean /tone/ of whatever generator type that results in the same number of nominals operating in the same manner as EDO nominals.

5. I like the idea of sharps and flats that mean the same thing in a 'meta' manner, in relation to the scale they are operating in, Plus once the player has got the scale in their eye and ear I imagine that the sharps and flats would apply contextually. Different languages use the same alphabet but have different sounds. Less symbols for the player to learn.

I'll talk more later, after the festivities.

Mark

>> George,
>>
>> It can be argued that conventional accidentals represent not
>> semitones but movements on the chain of generators. By this view
>> it is not inaccurate to use conventional accidentals for microtonal
>> music.
>
>True, but I don't think that it's a good idea to give conventional
>symbols new meanings that are open to misinterpretation, even if
>there is an underlying logic. New symbols would make it obvious to
>anyone that this is not an ordinary notation.

I'm all for new symbols. It's just, if your notation package
didn't support them, or for some reason wasn't generating MIDI from
them, it's nice to know it's an option (that is, that a single pair
of symbols is enough).

>> >Thus, for a single *tuning* you might have 2 or 3 different
>> >notations!
>>
>> 19-tET is not a tuning,
>
>If 19-ET isn't a tuning, then what is?

I know, it's weird. But in the sense Gene's been enforcing lately,
in the context of your message, I don't believe you meant to say
19-tET is a tuning, because you can't really notate tunings.

>> it is a scale.
>
>Well, yes, it could be. But more usually a scale that uses pitches
>of 19-ET would be some subset of that tuning, e.g., a major or minor
>scale.

My point exactly!

>And major and minor *scales* are not restricted to 19-ET, but
>may also be in other *tunings*, such as Pythagorean, meantone, 12-ET,
>31-ET, 55-ET, or a well temperament, to give a few examples.

That's right, but now look at the original context...

>Thus, for a single *tuning* you might have 2 or 3 different
>notations!

...I guess what I really should have said is that you can't notate
tunings. In the universe I'm trying to describe, tunings are
defined as what you can change without changing the notation.
Something like...

temperament (wedgie)
scale (T[n]) <---- Notations are defined here.
tuning (map and generators)

Maybe Gene has some input here.

>I would
>therefore consider a *scale* to consist of a specific number of tones
>(or notes) in certain relationships (perhaps defined by a generating
>interval within a given size range) but a *tuning* to consist of
>pitches separated by intervals that are *exactly* defined.

It doesn't sound like there's any difference between tuning and
scale here.

>> you already know that my answer
>> is yes, though I don't know what you mean by "staff configurations".
>
>If you used a 5-line staff for one set of nominals and a 4-line staff
>for another set, then your configuration of staff lines would
>constantly be changing.

Ah. As I say, I don't think staff configuration is important to
anything. My preference is simply to show one octave of the scale
with consecutive lines and spaces from the bottom line to the top
space, however many lines that takes. But it doesn't really have
any bearing on the bigger notation issue.

>Or if you kept a 5-line staff for both sets
>of nominals but had the "octave" (or 1:2) as different numbers of
>steps on the staff, then you would need some way of indicating where
>the changes in configuration were occurring.

It's why God gave us clefs!

>I have a feeling that
>it wouldn't be very practical for either performance or theoretical
>purposes.

I'm going to have to strongly disagree on both points.

>However, what about having two staff configurations in
>parallel, i.e., one above the other? This would be useful for all
>concerned, whether performer, composer, or theorist.

That would be useful for wasting paper.

-Carl

Hi Mark,

>1. I can understand the need for a workaround notation for
>performers, if that is what is required.

I don't think it is. If you're new to a scale and trying to get it
down, which is easier: learning a host of new accidentals and trying
to apply precise offsets to pitches you know to get the scale, or
getting it under your fingers and learning to recognize it on the
page? Is it easier to have the scale appearing as different shapes
in different places? Are performers just machines that apply offsets,
with no need to know what scale they're using?

And with all the fuss about standardizing correctly (ie, figuring
out an ideal standard before it gets entrenched), I'm surprised
that expediency is being used as such a key part of the arguement.

>2. I would prefer my performers just to use one stave type
>throughout, so I don't expect stave changes,

Howabout clef changes?

>but then, if they were professionals
>committed to microtones they wouldn't complain

Forget microtones. Are you commited to microtones? It's a
sickness of the mind. I'm committed to music, and performers
who are likewise will learn to play the music they love!

>Plus once the player has got the scale in their eye and ear I
>imagine that the sharps and flats would apply contextually.

Indeed.

-Carl

In a message dated 12/24/03 6:09:47 PM Eastern Standard Time, ekin@lumma.org
writes:

> Forget microtones. Are you commited to microtones? It's a
> sickness of the mind. I'm committed to music, and performers
> who are likewise will learn to play the music they love!
>

Care to clarify?

Johnny

>>Forget microtones. Are you commited to microtones? It's a
>>sickness of the mind. I'm committed to music, and performers
>>who are likewise will learn to play the music they love!
>
>Care to clarify?

It just seems that obsessing over tuning theory can lead one
out of touch with reality. I speak from experience. :)

-Carl

--- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:

/tuning/topicId_21432.html#50405

> 2. I would prefer my performers just to use one stave type
throughout,
> so I don't expect stave changes, but then, if they were
professionals
> committed to microtones they wouldn't complain - especially if the
> visual acoustic logic is apparent to them. My feeling is that
> professional performers who are advocates /will/ learn new
notations,
> so long as they convey the acoustic/expressive intent in a suitably
> clear graphic manner.
>

***Ahem... I believe this is a "theoretical" opinion, Mark! Have you
actually worked with performers?? I wish Johnny Reinhard would
actually "weigh in" here (rather than worrying about the idiotic 1
cent situation... :) since he has had more experience here than I
have or that practically anybody else on this planet.

You will note that Reinhard's preferred notation uses our "regular
ol'" Pythagorean-based 5-line staff and regular 12-tET pitches, with
deviations in numbers (cents) from those "regular notes..." This is
not by just coincidence: this is the easiest thing for performers to
play.

I think, similarly, systems such as Sagittal shouldn't be hard for
the, either, since these systems also build upon "the known" in
music. I'm so happy they do and I'm advocating the use of Sagittal
for everybody (happily George and Dave "adjusted" it a bit for my
*own* purposes).

But, frankly, I think that believing that performers will take an
interest in the *theory* and like new notations for microtonality is
really "pie in the sky..." (Unless, that is, the perfomer is the
theorist/composer himself... and that is happening more and more
frequently nowadays! :)

Oh... Seasons Greetings to everybody from Grosse Pointe Michigan
public library. Have a great Holiday!

Joseph Pehrson

>***Ahem... I believe this is a "theoretical" opinion, Mark! Have you
>actually worked with performers??

What are you saying Joseph, that your experience with performers is
universal for all directors/performers? Get a grip!

-Carl

>>***Ahem... I believe this is a "theoretical" opinion, Mark!
>>Have you actually worked with performers??
>
>What are you saying Joseph, that your experience with performers
>is universal for all directors/performers? Get a grip!

Admittedly it's hard. In the case of the begrudged Microthon '99,
my performers wouldn't have touched Sagittal, cents offset, or
anything else. Notation isn't really the key issue, rehearsal is.
As long as your notation and your music make sense, you can get
it done if you have time to rehearse. Indeed, with practice,
even amateurs can execute extended JI with no special notation at
all!

Without rehearsals you're doomed, no matter what notation you use,
unless you're into sound effects, some quartertone ornaments or
something.

Whether Sagittal is easier than generalized remains to be seen.
Joseph, have you ever tried to rehearse a piece from generalized
notation? Do you feel you've ever achieved extended JI with an
ensemble in *any* notation? I'm listening to Blacklight here,
which is fantastic by the way, but if I'm not mistaken it's a cello
solo with a keyboard accompaniment. Fantastic cello performance,
but the cello part is certainly no 'acid test' of microtonal
notation. How was the keyboard scored?

Wow, your soundclick page has a lot more stuff than your mp3.com
page did the last time I was there (IIRC). I'll have to get
busy downloading... Is _Stringing_ microtonal? Most of the
microtonal works here appear to be solo with electronic
accompaniment....

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Admittedly it's hard. In the case of the begrudged Microthon '99,
> my performers wouldn't have touched Sagittal, cents offset, or
> anything else. Notation isn't really the key issue, rehearsal is.
> As long as your notation and your music make sense, you can get
> it done if you have time to rehearse. Indeed, with practice,
> even amateurs can execute extended JI with no special notation at
> all!
>
> Without rehearsals you're doomed, no matter what notation you use,
> unless you're into sound effects, some quartertone ornaments or
> something.

You may be doomed anyway. See these candid comments by a performer.
/sibelius-list/message/6889

> Whether Sagittal is easier than generalized remains to be seen.

Sagittal _is_ generalized. Only in a different way.

You must have missed
/tuning/topicId_21432.html#50360
where I wrote (in reply to Mark Gould):

----------------------------------------------------------------------
"Simply calling something "generalised" doesn't help here, because
there are many different ideas about how to generalise the diatonic
scale, and there are different ideas about how to generalise staff
notation. They all keep some aspects the same and vary others. We need
to use terms that say _how_ they are generalising.

I understand the main distinction we're discussing here is whether the
nominals (and therefore staff positions) should always represent a
chain of seven approximate fifths as FCGDAEB, or should represent
whatever proper MOS scale of around 5 to 12 notes is most "natural"
for the tuning being used.

An appropriate shorthand for this might be "fifth-nominals" versus
"MOS-nominals".

I put "natural" in scare-quotes because there is an awful lot to be
decided about what makes a particular linear temperament the most
natural for any given scale, unless the scale was specifically
generated linearly. What linear temperament would you use to notate
JI, or would you use different ones for different JI scales?"
----------------------------------------------------------------------

>> Whether Sagittal is easier than generalized remains to be seen.
>
>Sagittal _is_ generalized. Only in a different way.

Sagittal is a specific proposal, an instance, which is how it affords
the fancy name. Since I'm not advocating any particular brand of
sauce I can't afford such a name. "Generalized", in whatever way is
appropriate (including Sagittal, where appropriate) seems to convey
my meaning.

>"Simply calling something "generalised" doesn't help here,
//
>An appropriate shorthand for this might be "fifth-nominals" versus
>"MOS-nominals".

Maybe you missed my post when I wrote...

>() Finally, the notation need not be made of a single chain of
>generators, nor even be based on chains at all.

...Care to suggest another name?

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Whether Sagittal is easier than generalized remains to be seen.
> >
> >Sagittal _is_ generalized. Only in a different way.
>
> Sagittal is a specific proposal, an instance, which is how it affords
> the fancy name. Since I'm not advocating any particular brand of
> sauce I can't afford such a name. "Generalized", in whatever way is
> appropriate (including Sagittal, where appropriate) seems to convey
> my meaning.
>
> >"Simply calling something "generalised" doesn't help here,
> //
> >An appropriate shorthand for this might be "fifth-nominals" versus
> >"MOS-nominals".
>
> Maybe you missed my post when I wrote...
>
> >() Finally, the notation need not be made of a single chain of
> >generators, nor even be based on chains at all.
>
> ...Care to suggest another name?

If you can tell me in what sense such an apparently free-for-all way
of assigning nominals is "generalised", then I might be able to
suggest an appropriate short descriptive name for it.

When we say "generalised" here, I understand it to mean that we take
the standard notation as applied to the diatonic scale and choose some
aspect(s) of it which we then apply consistently in the notation of
other (possibly non-diatonic) scales. Sagittal, as you correctly point
out, is an instance of the class of notations that attempt to
consistently apply the aspect whereby the nominals form a chain of 7
approximate fifths (whether or not these are all actually _in_ the
scale being notated). Until now, I assumed the class of notations you
were promoting were consistently applying that aspect whereby the
nominals are merely some proper MOS of a cardinality capable of being
perceived as a "melodic gestalt", i.e. having around 5 to 12 notes.

If there is no limitation at all on what sets of pitches you might
consider for nominals, then I'm not sure there is any sense in which
it can be considered as generalised from standard diatonic notation,
and I would find "arbitrary-nominals" to be a suitable shorthand.

If however you do have in mind some limitations on what can be
assigned as nominals in your "generalised" notation, then it would be
good to be clear about what those are.

Perhaps the only requirement you have is that it should be a "melodic
gestalt", in which case "melodic-gestalt-nominals" would be a suitable
shorthand. But I forsee enormous problems with establishing what is
and isn't a "melodic gestalt". And if the nominals are not required to
be in any way regular then it will be extremely difficult to learn the
notation of the _harmonies_ of such a scale; things like which pairs
of notes form intervals of a perfect fifth, etc.

>> >() Finally, the notation need not be made of a single chain of
>> >generators, nor even be based on chains at all.
>>
>> ...Care to suggest another name?
>
>If you can tell me in what sense such an apparently free-for-all way
>of assigning nominals is "generalised", then I might be able to
>suggest an appropriate short descriptive name for it.

The apparently free-for-all way generalizes one very important
thing; nominals represent a musical structure that is a focal point
of composition. Usually (for me) this means a single-chain linear
temperament (and since the diatonic scale is one, other things will
be generalized also) but I'd rather keep the recommendation flexible.

>Sagittal, as you correctly point
>out, is an instance of the class of notations that attempt to
>consistently apply the aspect whereby the nominals form a chain of 7
>approximate fifths (whether or not these are all actually _in_ the
>scale being notated). Until now, I assumed the class of notations you
>were promoting were consistently applying that aspect whereby the
>nominals are merely some proper MOS of a cardinality capable of being
>perceived as a "melodic gestalt", i.e. having around 5 to 12 notes.

Kleismic[8] is a quintessential example of a non-MOS that I'd base
a notation on.

>If there is no limitation at all on what sets of pitches you might
>consider for nominals,

I imagine that not everyone wishes to restrict themselves to linear
temperaments.

>Perhaps the only requirement you have is that it should be a "melodic
>gestalt", in which case "melodic-gestalt-nominals" would be a suitable
>shorthand. But I forsee enormous problems with establishing what is
>and isn't a "melodic gestalt".

I forsee enormous problems with establishing anything about the
nature/success of a new music, but it doesn't bother me.

>And if the nominals are not required to
>be in any way regular then it will be extremely difficult to learn the
>notation of the _harmonies_ of such a scale; things like which pairs
>of notes form intervals of a perfect fifth, etc.

I have gone at length on to how to pick nominals such that harmonic
structures are represented correctly. Sagittal's comparative failure
at this has been one of the points I've been trying to drive home.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Kleismic[8] is a quintessential example of a non-MOS that I'd base
> a notation on.

But in the kleismic case there _are_ no proper MOS with 5 to 14 notes,
so you're forced to use either something improper, or something that's
not a MOS. You choose a proper non-MOS, which is probably a good idea.
However the 8 are still in a contigious chain of generators and
therefore still regular (specifically linear).

> I imagine that not everyone wishes to restrict themselves to linear
> temperaments.

I agree. But that is a different question from whether the nominals of
their notation might best be restricted in this way, except when there
is no choice (as in the kleismic example). But I understand you are
saying this would not be best.

> >And if the nominals are not required to be
> >in any way regular then it will be extremely difficult to learn the
> >notation of the _harmonies_ of such a scale; things like which pairs
> >of notes form intervals of a perfect fifth, etc.
>
> I have gone at length on to how to pick nominals such that harmonic
> structures are represented correctly.

Can you point me to these. Please point me to (or remind me of) some
examples where the nominals are not arranged linearly by some
generator (and optionally some non-octave period).

> Sagittal's comparative failure
> at this has been one of the points I've been trying to drive home.

I understand you to be saying that, compared to the system you have in
mind, Sagittal fails to pick nominals so that harmonic structures are
represented correctly. Is that correct?

If so, it seems an extraordinary claim, given that the consistent
representation of harmonic structures across many different tunings
has been a powerful overriding principle for the whole of the
development of Sagittal, and we believe we have acheived this to a
very high degree.

So, please explain what you mean by "represented correctly" in
relation to harmonic structures, and please provide examples of these
alleged failures and how you would do it differently.

Are you referring to the stuff where you considered it best to apply
the nominals to various periodicity blocks in JI, apparently based on
a misunderstanding that Paul Erlich's "The Forms of Tonality" was
advocating this?

I remember you supported Ben Johnston's choice of nominals (apparently
without realizing it at first) in the case where the underlying scale
is diatonic. This has D:A as a wolf while F:C, C:G, G:D, A:E, E:B are
perfect fifths and similar inconsistencies with the thirds, thereby
making any sort of modulation something of a nightmare. If you still
feel that this is an example of "harmonic structures [being]
represented correctly", then I'm afraid your successes will always
look like failure to me, and vice versa. And you might refer to your
class of notations as "generalized-Johnston".

>> I imagine that not everyone wishes to restrict themselves to linear
>> temperaments.
>
>I agree. But that is a different question from whether the nominals
>of their notation might best be restricted in this way,

I'm believe the nominals are best restricted by what 'they' use in
composition.

>> I have gone at length on to how to pick nominals such that harmonic
>> structures are represented correctly.
>
>Can you point me to these. Please point me to (or remind me of) some
>examples where the nominals are not arranged linearly by some
>generator (and optionally some non-octave period).

You've got my recipe right. I don't know any general rules for
arbitrary structures, but if you throw me one I'll try to come up
with a notation for it.

>> Sagittal's comparative failure
>> at this has been one of the points I've been trying to drive home.
>
>I understand you to be saying that, compared to the system you have
>in mind, Sagittal fails to pick nominals so that harmonic structures
>are represented correctly. Is that correct?

That's correct.

>If so, it seems an extraordinary claim, given that the consistent
>representation of harmonic structures across many different tunings
>has been a powerful overriding principle for the whole of the
>development of Sagittal, and we believe we have acheived this to a
>very high degree.

For the scale for which the custom nominals were designed it seems
obvious. Across different scales I recently stated that the custom
nominals would fare no worse than Sagittal (since Sagittal is in
fact a custom system for the diatonic scale). That statement is
open to refutation.

>Are you referring to the stuff where you considered it best to apply
>the nominals to various periodicity blocks in JI, apparently based on
>a misunderstanding that Paul Erlich's "The Forms of Tonality" was
>advocating this?

It was based on no such misunderstanding, and no I'm not referring
to it.

>I remember you supported Ben Johnston's choice of nominals (apparently
>without realizing it at first)

You can see a distillation of that thread here...

http://lumma.org/tuning/tuning-math_notation_thread.txt

...sorry I don't have time to find Yahoo references. The message
numbers aren't in the e-mail headers that I can find.

>So, please explain what you mean by "represented correctly" in
>relation to harmonic structures, and please provide examples of
>these alleged failures and how you would do it differently.

Why don't we work out an example together?

! 08_kleismic.scl
!
Proper subset of Kleismic (in 19-tET).
8
!
63.158 !.....D
315.789 !....E
378.947 !....F
631.579 !....G
694.737 !....H
947.368 !....A
1010.526 !...B
2/1 !........C
!

A pattern of 1-4-6 gives the following triads...

C F H ~ 4:5:6 [1M]
D G A ~ 15:21:25 [2s]
E H B ~ 4:5:6 [3M]
F A C ~ 5:7:8 [4S]
G B D ~ 28:35:40 [5%]
H C E ~ 15:20:24 [6m]
A D F ~ 35:42:60 [7%]
B E G ~ 15:20:24 [8m]

Hear them...

http://lumma.org/tuning/kleismic/kleismic_triads.mid

...Is this the most stable major mode? The 2->3 in 2s->3M
sounds like too big of a step or something.

Here's a progression...

H-----H-----H.....G.....A-----A...H---H
F.....E-----E-----E.....F.....E----...F
C-----C.....B-----B.....C-----C-------C
1M____6m____3M____8m____4S__sus6__6m__1M

See it...
http://lumma.org/tuning/kleismic/kleismic_example.png

Hear it...
http://lumma.org/tuning/kleismic/kleismic_example.mid

Two others...

http://lumma.org/tuning/kleismic/kleismic_example2.mid
H-----H-----H.....G-----G-----G...F---F
F.....E-----E-----E.....D.....C-------C
C-----C.....B-----B.....A-----A----...H
1M____6m____3M____8m____2s__sus4__4S__1M

http://lumma.org/tuning/kleismic/kleismic_example3.mid
H-----H-----H.....G..B..C^....A..G..H
F.....E-----E-----E-----E.....F-----F
C-----C.....B-----B.....H..B..C-----Cv
1M____6m____3M____8m____6m____4S____1M

How would this look in Sagittal?

-Carl

[I wrote...]
>Across different scales I recently stated that the custom
>nominals

By this I mean, any single system.

>would fare no worse than Sagittal (since Sagittal is in
>fact a custom system for the diatonic scale).

-C.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Sagittal's comparative failure
> >> at this has been one of the points I've been trying to drive home.
> >
> >I understand you to be saying that, compared to the system you have
> >in mind, Sagittal fails to pick nominals so that harmonic structures
> >are represented correctly. Is that correct?
>
> That's correct.
>
> >If so, it seems an extraordinary claim, given that the consistent
> >representation of harmonic structures across many different tunings
> >has been a powerful overriding principle for the whole of the
> >development of Sagittal, and we believe we have acheived this to a
> >very high degree.
>
> For the scale for which the custom nominals were designed it seems
> obvious. Across different scales I recently stated that the custom
> nominals would fare no worse than Sagittal (since Sagittal is in
> fact a custom system for the diatonic scale). That statement is
> open to refutation.

If you only mean that the nominals of Sagittal are preferably 7 notes
in a chain of fifths FCGDAEB, then that's correct. But nothing
prevents the Sagittal comma accidentals from being used with other
systems of nominals.

> >So, please explain what you mean by "represented correctly" in
> >relation to harmonic structures, and please provide examples of
> >these alleged failures and how you would do it differently.
>
> Why don't we work out an example together?

So you charge Sagittal with the crime of "comparative failure to
correctly represent harmonic structures" and then you want me to do
all the work to prove it innocent! That hardly seems fair. But I guess
I have no choice. Sigh.

I'd first like to point out that if you want to choose an example to
make life difficult for a chain of fifths based notation, you would
choose a linear temperament where many generators are required to
generate a single perfect fifth. They don't come much worse than
kleismic in this regard.

> ! 08_kleismic.scl
> !
> Proper subset of Kleismic (in 19-tET).
> 8
> !
> 63.158 !.....D
> 315.789 !....E
> 378.947 !....F
> 631.579 !....G
> 694.737 !....H
> 947.368 !....A
> 1010.526 !...B
> 2/1 !........C
> !

You might have saved me some time here by also tellling me what this
looked like as a chain of kleismic generators (minor thirds). I get

CEGADFHB

By the way, why do you prefer this to ACEGBDFH, which at least notates
all the minor thirds except FH so that we recognise them _as_ thirds
from our prior experience with diatonic notation. I think ACEGBDFH
minimises the clashes between the two notations (kleismic and diatonic).

>
> A pattern of 1-4-6 gives the following triads...
>
> C F H ~ 4:5:6 [1M]
> D G A ~ 15:21:25 [2s]
> E H B ~ 4:5:6 [3M]
> F A C ~ 5:7:8 [4S]
> G B D ~ 28:35:40 [5%]
> H C E ~ 15:20:24 [6m]
> A D F ~ 35:42:60 [7%]

Shouldn't that be
A D F ~ 35:42:50 [7dim]

> B E G ~ 15:20:24 [8m]

> ...Is this the most stable major mode?

I have no idea.

Since this is in 19-ET we can notate it without using any Sagittal
accidentals at all. To minimise accidentals I choose the chain of
generators as

E# G# B D F Ab Cb D#
(Fb) (B#)

I note that in 19-ET a wholetone is 3 steps, a diatonic semitone is 2
steps and a chromatic semitone is 1 step. Hence the two enharmonic
spellings in parenthesis.

> Here's a progression...
>
> H-----H-----H.....G.....A-----A...H---H
> F.....E-----E-----E.....F.....E----...F
> C-----C.....B-----B.....C-----C-------C
> 1M____6m____3M____8m____4S__sus6__6m__1M

> How would this look in Sagittal?

In "Sagittal":

Cb----B#----B#....B.....D-----D...B#--Cb
Ab....G#----G#----G#....Ab....G#---...Ab
Fb----E#....D#----D#....Fb----E#------Fb

Fb____E#m___G#___G#m_Fbaug6_E#msm7_E#m_Fb
no 5 no 5

To greatly reduce the number of accidentals on the staff you can put
E#, G#, Ab and Cb into a key signature in this and the following examples.

> Two others...
>
> http://lumma.org/tuning/kleismic/kleismic_example2.mid
> H-----H-----H.....G-----G-----G...F---F
> F.....E-----E-----E.....D.....C-------C
> C-----C.....B-----B.....A-----A----...H
> 1M____6m____3M____8m____2s__sus4__4S__1M

In "Sagittal":

Cb----B#----B#....B-----B-----B...Ab--Ab
Ab....G#----G#----G#....F.....Fb------Fb
Fb----E#....D#----D#....D-----D----...Cb

> http://lumma.org/tuning/kleismic/kleismic_example3.mid
> H-----H-----H.....G..B..C^....A..G..H
> F.....E-----E-----E-----E.....F-----F
> C-----C.....B-----B.....H..B..C-----Cv
> 1M____6m____3M____8m____6m____4S____1M

Ididn't see where you defined the symbols ^ and v, but judging by the
chord names, they shouldn't be there.

E# G# B D F Ab Cb D#
(Fb) (B#)

> Cb----B#----B#....B..D#.E#....D..B..Cb
> Ab....G#----G#----G#----G#....Ab----Ab
> Fb----E#....D#----D#....B#.D#.Fb----Fb

So how has this failed to correctly notate harmonic structures?

I think most people would agree that learning 2 new enharmonic
spellings is far easier than learning 28 new dyadic relationships
between 8 new nominals!

--Dave Keenan

>> For the scale for which the custom nominals were designed it seems
>> obvious. Across different scales I recently stated that the custom
>> nominals would fare no worse than Sagittal (since Sagittal is in
>> fact a custom system for the diatonic scale). That statement is
>> open to refutation.
>
>If you only mean that the nominals of Sagittal are preferably 7 notes
>in a chain of fifths FCGDAEB, then that's correct. But nothing
>prevents the Sagittal comma accidentals from being used with other
>systems of nominals.

Yes, that would be fine. My only 'gripes' are forcing 7 nominals and
approximating compound commas with other commas and calling it strict
JI (no matter how close the size of the commas, I expect notation to
accurately encode the rationals unless tempering is allowed).

>> >So, please explain what you mean by "represented correctly" in
>> >relation to harmonic structures, and please provide examples of
>> >these alleged failures and how you would do it differently.
>>
>> Why don't we work out an example together?
>
>So you charge Sagittal with the crime of "comparative failure to
>correctly represent harmonic structures" and then you want me to do
>all the work to prove it innocent! That hardly seems fair.

Since the details of Sagittal are unknown to me, I couldn't do it.

>But I guess I have no choice. Sigh.

Yeah, notating music is such a drag.

>I'd first like to point out that if you want to choose an example to
>make life difficult for a chain of fifths based notation, you would
>choose a linear temperament where many generators are required to
>generate a single perfect fifth. They don't come much worse than
>kleismic in this regard.

But kleismic[8] is very triadic, which the diatonic scale is good
at. Perhaps our next example should be harmonics 8-16. We can use
the same music! In fact, my part doesn't change at all!

Here are the sound examples...

http://lumma.org/tuning/kleismic/mode8_example.mid
http://lumma.org/tuning/kleismic/mode8_example2.mid
http://lumma.org/tuning/kleismic/mode8_example3.mid

>> ! 08_kleismic.scl
>> !
>> Proper subset of Kleismic (in 19-tET).
>> 8
>> !
>> 63.158 !.....D
>> 315.789 !....E
>> 378.947 !....F
>> 631.579 !....G
>> 694.737 !....H
>> 947.368 !....A
>> 1010.526 !...B
>> 2/1 !........C
>> !
>
>You might have saved me some time here by also tellling me what this
>looked like as a chain of kleismic generators (minor thirds). I get
>
>CEGADFHB

That's right; the 6/5s are 3rds.

>By the way, why do you prefer this to ACEGBDFH, which at least notates
>all the minor thirds except FH so that we recognise them _as_ thirds
>from our prior experience with diatonic notation. I think ACEGBDFH
>minimises the clashes between the two notations (kleismic and diatonic).

Only for this mode; it doesn't change anything on the whole. But if
this is indeed the most stable major mode, maybe it should be given
special treatment.

>> A pattern of 1-4-6 gives the following triads...
>>
>> C F H ~ 4:5:6 [1M]
>> D G A ~ 15:21:25 [2s]
>> E H B ~ 4:5:6 [3M]
>> F A C ~ 5:7:8 [4S]
>> G B D ~ 28:35:40 [5%]
>> H C E ~ 15:20:24 [6m]
>> A D F ~ 35:42:60 [7%]
>
>Shouldn't that be
>A D F ~ 35:42:50 [7dim]

Yes, sorry.

>> B E G ~ 15:20:24 [8m]
>
>> ...Is this the most stable major mode?
>
>I have no idea.
>
>Since this is in 19-ET we can notate it without using any Sagittal
>accidentals at all. To minimise accidentals I choose the chain of
>generators as
>
> E# G# B D F Ab Cb D#
>(Fb) (B#)

Shouldn't the last note be Ebb?

>I note that in 19-ET a wholetone is 3 steps, a diatonic semitone is
>2 steps and a chromatic semitone is 1 step. Hence the two enharmonic
>spellings in parenthesis.
>
>> Here's a progression...
>>
>> H-----H-----H.....G.....A-----A...H---H
>> F.....E-----E-----E.....F.....E----...F
>> C-----C.....B-----B.....C-----C-------C
>> 1M____6m____3M____8m____4S__sus6__6m__1M
>
>> How would this look in Sagittal?
>
>In "Sagittal":
>
>Cb----B#----B#....B.....D-----D...B#--Cb
>Ab....G#----G#----G#....Ab....G#---...Ab
>Fb----E#....D#----D#....Fb----E#------Fb
>
>Fb____E#m___G#___G#m_Fbaug6_E#msm7_E#m_Fb
> no 5 no 5
>
>To greatly reduce the number of accidentals on the staff you can put
>E#, G#, Ab and Cb into a key signature in this and the following
>examples.
>
>> Two others...
>>
>> http://lumma.org/tuning/kleismic/kleismic_example2.mid
>> H-----H-----H.....G-----G-----G...F---F
>> F.....E-----E-----E.....D.....C-------C
>> C-----C.....B-----B.....A-----A----...H
>> 1M____6m____3M____8m____2s__sus4__4S__1M
>
>In "Sagittal":
>
>Cb----B#----B#....B-----B-----B...Ab--Ab
>Ab....G#----G#----G#....F.....Fb------Fb
>Fb----E#....D#----D#....D-----D----...Cb
>
>> http://lumma.org/tuning/kleismic/kleismic_example3.mid
>> H-----H-----H.....G..B..C^....A..G..H
>> F.....E-----E-----E-----E.....F-----F
>> C-----C.....B-----B.....H..B..C-----Cv
>> 1M____6m____3M____8m____6m____4S____1M
>
>I didn't see where you defined the symbols ^ and v, but judging
>by the chord names, they shouldn't be there.

I thought the sound examples would have revealed they were 8ves.

> E# G# B D F Ab Cb D#
>(Fb) (B#)
>
>> Cb----B#----B#....B..D#.E#....D..B..Cb
>> Ab....G#----G#----G#----G#....Ab----Ab
>> Fb----E#....D#----D#....B#.D#.Fb----Fb
>
>So how has this failed to correctly notate harmonic structures?

You're using enharmonics to keep the spellings straight, and this
could get arbitrarily difficult.

It's also wrong because it requires accidentals in every key of
the scale, and both sharps and flats the key signatures.

>I think most people would agree that learning 2 new enharmonic
>spellings is far easier than learning 28 new dyadic relationships
>between 8 new nominals!

I respectfully disagree. How long do you think it would take to
get fast with the Hs? Speaking for myself, 2-3 weeks, which is a
very good lead time for a typical premiere.

Something new must be learned either way. "Play an 8th above C"
is a command any musician claiming to play kleismic[8] has to be
able to perform.

Here, marked with stars, are the number of enharmonic adjustments
that must be made to maintain diatonic relationships...

E# F G# Ab B Cb D *D#
F G# Ab B Cb D *D# *E#
G# Ab B Cb D *D# *E# *F
Ab B Cb D *D# *E# *F *G#
B Cb D *D# *E# *F *G# *Ab
Cb D *D# *E# *F *G# *Ab *B
D *D# *E# *F *G# *Ab *B *Cb
D# E# F G# Ab B Cb D

My way...

C D E F G H A B
D E F G H A B C
E F G H A B C D
F G H A B C D E
G H A B C D E F
H A B C D E F G
A B C D E F G H
B C D E F G H A

-Carl

>Perhaps our next example should be harmonics 8-16. We can use
>the same music! In fact, my part doesn't change at all!
>
>Here are the sound examples...
>
>http://lumma.org/tuning/kleismic/mode8_example.mid
>http://lumma.org/tuning/kleismic/mode8_example2.mid
>http://lumma.org/tuning/kleismic/mode8_example3.mid

//

>>I think most people would agree that learning 2 new enharmonic
>>spellings is far easier than learning 28 new dyadic relationships
>>between 8 new nominals!
>
>I respectfully disagree. How long do you think it would take to
>get fast with the Hs? Speaking for myself, 2-3 weeks, which is a
>very good lead time for a typical premiere.
>
>Something new must be learned either way. "Play an 8th above C"
>is a command any musician claiming to play kleismic[8] has to be
>able to perform.

So assuming we believe Miller, we only need to learn nominal
systems for 5, 6, 8 and 9 tones (I'd add 10). How's that for
universal? As for accidentals, linear temperaments aren't a
problem, and 'for everything else, there's Sagittal'.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Yes, that would be fine. My only 'gripes' are forcing 7 nominals and
> approximating compound commas with other commas and calling it strict
> JI (no matter how close the size of the commas, I expect notation to
> accurately encode the rationals unless tempering is allowed).

And yet, you also wish to avoid "accidental pileup". I think it should
be obvious that these two desires are totally incompatible with each
other.

Even Johnny Reinhard only requires ratios to be notated to within half
a cent. The olympian (high precision) sagittal JI notation will have
similar resolution (while notating about a thousand of the most common
ratios exactly).

I'm concerned that you may be seriously out of touch with reality here
and possibly in need of intervention. ;-)

However, I should point out that although George and I would strongly
discourage it, it is possible to pile up multiple sagittal accidentals
against a single note to exactly represent any ratio you wish. But why
anyone would want to, given the accuracy possible with single symbols
(optionally in conjunction with conventional sharps and flats), I
don't know.

> >> >So, please explain what you mean by "represented correctly" in
> >> >relation to harmonic structures, and please provide examples of
> >> >these alleged failures and how you would do it differently.
> >>
> >> Why don't we work out an example together?

I note that you did not define what you meant by "represented
correctly" and so you were free to move the target if I looked like
hitting it.

It seems (below) as if you are simply defining "represented correctly"
as "represented Carl's way". Please explain otherwise.

> >So you charge Sagittal with the crime of "comparative failure to
> >correctly represent harmonic structures" and then you want me to do
> >all the work to prove it innocent! That hardly seems fair.
>
> Since the details of Sagittal are unknown to me, I couldn't do it.

But you didn't let that stop you slandering it.

> >CEGADFHB
>
> That's right; the 6/5s are 3rds.

I'm not sure what you mean by this. GA, AD, FH and HB are not usually
read as thirds (from diatonic notation). And the 5:6 AD is not even a
third in the sense of spanning 2 steps of your 8-note scale either. So
I can't see how this can be true on any reading. But it's probably not
important.

> >Since this is in 19-ET we can notate it without using any Sagittal
> >accidentals at all. To minimise accidentals I choose the chain of
> >generators as
> >
> > E# G# B D F Ab Cb D#
> >(Fb) (B#)
>
> Shouldn't the last note be Ebb?

That is a valid alternative spelling of it, but I don't believe it is
needed to correctly spell any of the harmonies in your examples.

> >I didn't see where you defined the symbols ^ and v, but judging
> >by the chord names, they shouldn't be there.
>
> I thought the sound examples would have revealed they were 8ves.

I didn't listen to them. Sorry. I had enough work to do.

As if these symbols ^ v haven't already been used as accidentals with
too many different meanings, now you want to use them for octaves! :-)

I thought at first that they were intended as kleismic chromatic
accidentals to allow you to extend the chain of generators.
Incidentally do you propose to have your chromatic accidentals
represent 8 generators or 7?

> >So how has this failed to correctly notate harmonic structures?
>
> You're using enharmonics to keep the spellings straight, and this
> could get arbitrarily difficult.

So I've cleared Sagittal of your allegations by correctly notating all
the harmonic structures, but now you want to say I've cheated because
I used 2 enharmonics in 8 notes, whereas you have _only_ redefined 6
of the nominals and added a new one. Is that correct?

You think it may get worse on modulation, but it does not. The full
cycle of 19 may be seen in
http://dkeenan.com/Music/ChainOfMinor3rds.htm
(the second chain listed).

In fact I've just noticed that your examples can be notated even more
simply in "Sagittal",by using this segment of the chain for your 8.

B D F Ab Cb D# F# A
(B#)

> It's also wrong because it requires accidentals in every key of
> the scale, and both sharps and flats the key signatures.

Come on Carl, give us a break. That isn't "wrong". It's just a choice
that one can make. Your preference differs from mine (and a lot of
others). That doesn't make mine "wrong".

I happen to think it's easier to allow both sharps and flats in key
signatures than to redefine all the nominals. But I don't say your
choice is "wrong".

> >I think most people would agree that learning 2 new enharmonic
> >spellings is far easier than learning 28 new dyadic relationships
> >between 8 new nominals!
>
> I respectfully disagree. How long do you think it would take to
> get fast with the Hs?

It isn't just the Hs. You have to learn new meanings for most of the
others too, which will be forever clashing with their diatonic
meanings that you then have to try to _un_learn.

> Speaking for myself, 2-3 weeks, which is a
> very good lead time for a typical premiere.

And how long do you think it would take to learn that E# and B# are
the same as Fb and Cb respectively. A day? Maybe less depending what
the instrument is.

> Something new must be learned either way.

Yes. However, I estimate the task of learning your notation to be at
least 10 times that of learning the two enharmonics for the
diatonic-based notation. Of course a lot depends on the instrument
being played.

But these are mere expressions of opinion.

I think your actual failure to notice your mistake in ratio-ing and
naming your A D F chord says more than any of these.

No one having seen it notated as D F Ab could have missed the fact
that it is a diminished chord.

-- Dave Keenan

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> So assuming we believe Miller, we only need to learn nominal
> systems for 5, 6, 8 and 9 tones (I'd add 10). How's that for
> universal?

You seem to be forgetting that custom nominals for linear temperaments
require different systems having the same cardinality, including 7.
For example the porcupine-7 is quite different from the diatonic-7. So
it isn't anywhere near that simple.

>> So assuming we believe Miller, we only need to learn nominal
>> systems for 5, 6, 8 and 9 tones (I'd add 10). How's that for
>> universal?
>
>You seem to be forgetting that custom nominals for linear temperaments
>require different systems having the same cardinality, including 7.
>For example the porcupine-7 is quite different from the diatonic-7. So
>it isn't anywhere near that simple.

The sounds will be mapped to the notation quite differently... is that
what you mean? So even though a third in meantone[7] is not the same
as in porcupine[7], fifths still go ?A-?E, ?B-?F, etc.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> So assuming we believe Miller, we only need to learn nominal
> >> systems for 5, 6, 8 and 9 tones (I'd add 10). How's that for
> >> universal?
> >
> >You seem to be forgetting that custom nominals for linear temperaments
> >require different systems having the same cardinality, including 7.
> >For example the porcupine-7 is quite different from the diatonic-7. So
> >it isn't anywhere near that simple.
>
> The sounds will be mapped to the notation quite differently... is that
> what you mean? So even though a third in meantone[7] is not the same
> as in porcupine[7], fifths still go ?A-?E, ?B-?F, etc.

Yes. The two different 7-tone MOS sound quite different. If each MOS
is written using nominals A to G we have

Seconds

Quality in Quality in
meantone porcupine
-------------------------
AB major wide neutral
BC minor wide neutral
CD major wide neutral
DE major wide neutral
EF minor wide neutral
FG major wide neutral
GA major narrow supermajor

Thirds

Quality in Quality in
meantone porcupine
-------------------------
AC minor minor
BD minor minor
CE major minor
DF minor minor
EG minor minor
FA major major
GB major major

Fourths

Quality in Quality in
meantone porcupine
-------------------------
AD perfect perfect
BE perfect perfect
CF perfect perfect
DG perfect perfect
EA perfect super
FB augmented super
GC perfect super

etc.

>>Yes, that would be fine. My only 'gripes' are forcing 7 nominals and
>>approximating compound commas with other commas and calling it strict
>>JI (no matter how close the size of the commas, I expect notation to
>> accurately encode the rationals unless tempering is allowed).
>
>And yet, you also wish to avoid "accidental pileup". I think it should
>be obvious that these two desires are totally incompatible with each
>other.

How could not forcing 7 nominals could contribute to accidental
pileup? Allowing approximations helps of course, and please see the
tuning-math distillation for my thoughts on that. Basically I believe
in a link between how music is represented in the real world (notation,
the capabilities of instruments, etc.) and what is possible in the
imagination. The imagination can push reality and in rare cases
transcend it slightly, and reality can inspire imagination (improv for
example), but they are linked. Thus a notation which tempers to me
indicates music which tempers. Accidental pileup to me is a strong
argument for temperament, not for tempered notation under the moniker
"strict JI" (my quote, which you responded to).

One of the most successful microtonal works ever realized (IMO) is
the Chrysalid Requiem, an extended-limit piece done in Johnston
notation -- one of the worse combinations imaginable for pileup.
Admittedly the performers took cues from a synthesizer, but they
did achieve accurate extended JI in performance, which is quite
remarkable.

>However, I should point out that although George and I would strongly
>discourage it, it is possible to pile up multiple sagittal accidentals
>against a single note to exactly represent any ratio you wish. But why
>anyone would want to, given the accuracy possible with single symbols
>(optionally in conjunction with conventional sharps and flats), I
>don't know.

Why wouldn't they just adopt the temperament represented by the
accidentals?

>I note that you did not define what you meant by "represented
>correctly" and so you were free to move the target if I looked like
>hitting it.
>
>It seems (below) as if you are simply defining "represented correctly"
>as "represented Carl's way". Please explain otherwise.

Sorry for the oversight. I've explained several times in the past,
though perhaps not with the exact and admittedly unfortunate phrase,
that "represented correctly" means the generic intervals of the scale
look the same on the staff no matter what their quality (major or
minor, etc.). Your suggested notation doesn't do this.

>>>So you charge Sagittal with the crime of "comparative failure to
>>>correctly represent harmonic structures" and then you want me to
>>>do all the work to prove it innocent! That hardly seems fair.
>>
>> Since the details of Sagittal are unknown to me, I couldn't do it.
>
>But you didn't let that stop you slandering it.

I would hardly call my remarks "slander". They are based on a model of
what is possible, no matter what the specifics of Sagittal are. That
model could be flawed, and that's why we're having this discussion (at
least that's why I'm into it).

>>>CEGADFHB
>>
>>That's right; the 6/5s are 3rds.
>
>I'm not sure what you mean by this. GA, AD, FH and HB are not
>usually read as thirds (from diatonic notation).

Indeed.

>And the 5:6 AD is not even a third in the sense of spanning 2 steps
>of your 8-note scale either. So I can't see how this can be true on
>any reading. But it's probably not important.

There are two "disjoint" thirds in this scale, being that it is not
MOS.

>>>I didn't see where you defined the symbols ^ and v, but judging
>>>by the chord names, they shouldn't be there.
>>
>>I thought the sound examples would have revealed they were 8ves.
>
>I didn't listen to them. Sorry. I had enough work to do.

Wow, you really aren't curious as to how this sounds? You don't
play an instrument (or do you?). Do you even like microtonal music?

Frankly, Dave, this is disgusting. We're talking about 4 files,
12 seconds each, less than 2 kilobytes together. I took the time
to make these examples, and you have the nerve to suggest that I
should have done the Sagittal examples too? Another glimpse into
the most exquisite arrogance I have ever seen on these lists.

One nice thing about e-mail is that it waits. There's no need
to reply until you have time. Another nice thing is that it's
voluntary.

>I thought at first that they were intended as kleismic chromatic
>accidentals to allow you to extend the chain of generators.
>Incidentally do you propose to have your chromatic accidentals
>represent 8 generators or 7?

Because this is non-MOS there are three possible accidental pairs.
Let...

# and b show 648:625 (4 generators, about 63 cents)
^ and v show 419904:390625 (8 generators, about 126 cents)
+ and - show 78125:69984 (7 generators, about 190 cents)

C D E F G H A B

C Cv C# Cv C# Cv C# Cv
D D D# D# D# D# D# D#
E E- E Ev E# Ev E# Ev
F F F F# F# F# F# F#
G G- G G- G Gv G# Gv
H H H H H H H# H#
A A- A A- A A- A Ab
B B B B B B B B

...since 8+7+4=19, we can drop one of these, I think. But that
would require some pileup, so I won't suffer us it right now.

>You think it may get worse on modulation, but it does not. The full
>cycle of 19 may be seen in
>http://dkeenan.com/Music/ChainOfMinor3rds.htm
>(the second chain listed).

By the way, using WIDTH and HEIGHT attributes simply cause the
client browser to resize an image -- it's already downloaded.
Thus, the small version of the diagram merely costs the user a
click.

>> >So how has this failed to correctly notate harmonic structures?
>>
>> You're using enharmonics to keep the spellings straight, and this
>> could get arbitrarily difficult.
>
>So I've cleared Sagittal of your allegations by correctly notating all
>the harmonic structures, but now you want to say I've cheated because
>I used 2 enharmonics

Because of the enharmonics, you haven't....

>....() Systems in which a given scale interval (2nd, 3rd, etc.) always
>covers the same distance on the staff. ("diatonic" notations)
>
//
>
>() For diatonic music, the latter type of notation is preferable.
>
>() Regarding the latter type, the number of nominals is crucial.
>
>() A single notation of the latter type has occupied generations of
>musicians in our culture.

...provided a "diatonic notation". This isn't any better than
"correctly" or "wrong", a very poor choice of words I admit.

>> >I think most people would agree that learning 2 new enharmonic
>> >spellings is far easier than learning 28 new dyadic relationships
>> >between 8 new nominals!
>>
>> I respectfully disagree. How long do you think it would take to
>> get fast with the Hs?
>
>It isn't just the Hs. You have to learn new meanings for most of the
>others too, which will be forever clashing with their diatonic
>meanings that you then have to try to _un_learn.

One can easily know both if he/she practices them together.

>> Speaking for myself, 2-3 weeks, which is a
>> very good lead time for a typical premiere.
>
>And how long do you think it would take to learn that E# and B# are
>the same as Fb and Cb respectively. A day? Maybe less depending what
>the instrument is.

Actually, to "get fast" with a new system of enharmonics, it would
take me about as long.

>> Something new must be learned either way.
>
>Yes. However, I estimate the task of learning your notation to be
>at least 10 times that of learning the two enharmonics for the
>diatonic-based notation. Of course a lot depends on the instrument
>being played.
>
>But these are mere expressions of opinion.

Maybe you've come up with a way of learning this stuff I haven't
thought of. How long'd it take you to get fast with diatonic
notation?

>I think your actual failure to notice your mistake in ratio-ing and
>naming your A D F chord says more than any of these.

Huh? I hit 60 instead of 50? What does this have to do with
anything?

>No one having seen it notated as D F Ab could have missed the fact
>that it is a diminished chord.

It's a particular kind of "diminished" chord, and the % sign was
meant to convey that I intend to interpret it as a dissonance
(whether it really is depends on how progressions really turn out to
work in this tuning). Ironically, I specifically used % instead of
"d" to avoid confusion with "diminished".

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Frankly, Dave, this is disgusting. We're talking about 4 files,
> 12 seconds each, less than 2 kilobytes together. I took the time
> to make these examples, and you have the nerve to suggest that I
> should have done the Sagittal examples too? Another glimpse into
> the most exquisite arrogance I have ever seen on these lists.
>
> One nice thing about e-mail is that it waits. There's no need
> to reply until you have time. Another nice thing is that it's
> voluntary.

Sure. You say on a public forum that a notation system I have spent a
lot of time working on and happen to think works pretty well, is a
failure, without even knowing the details, and without anyone else
knowing the details, and I should just take my time replying, or maybe
not even reply at all.

Good point. Consider this discussion voluntarily ended. From my side
at least.

-- Dave Keenan

>> Frankly, Dave, this is disgusting. We're talking about 4 files,
>> 12 seconds each, less than 2 kilobytes together. I took the time
>> to make these examples, and you have the nerve to suggest that I
>> should have done the Sagittal examples too? Another glimpse into
>> the most exquisite arrogance I have ever seen on these lists.
>>
>> One nice thing about e-mail is that it waits. There's no need
>> to reply until you have time. Another nice thing is that it's
>> voluntary.
>
>Sure. You say on a public forum that a notation system I have spent a
>lot of time working on and happen to think works pretty well, is a
>failure, without even knowing the details, and without anyone else
>knowing the details, and I should just take my time replying, or maybe
>not even reply at all.
>
>Good point. Consider this discussion voluntarily ended. From my side
>at least.

It seems pointless to reply to a discussion that's been ended, but
what the heck.

I have never called Sagittal a failure. It is you who come on a
public forum and discuss Sagittal, but you never provide any examples.
I ask for some and you get snotty. You apparently only reply to
save face or something, and don't even bother to look at the examples
I've provided. I hope you get over your distaste for notating music,
even in your own system, by the time it debuts.

-Carl

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

/tuning/topicId_21432.html#50445

> >***Ahem... I believe this is a "theoretical" opinion, Mark! Have
you
> >actually worked with performers??
>
> What are you saying Joseph, that your experience with performers is
> universal for all directors/performers? Get a grip!
>
> -Carl

***Hi Carl,

Was this implied? I don't think so. I simply said that based upon
my own experiences with performers, they are *results-driven* and are
interested in *performing* not in studying notational systems. Maybe
Johnny Reinhard, who has the most experience, can "weigh in" on this.

Happy Holidays to *you* too! :)

JP

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

/tuning/topicId_21432.html#50449

> >>***Ahem... I believe this is a "theoretical" opinion, Mark!
> >>Have you actually worked with performers??
> >
> >What are you saying Joseph, that your experience with performers
> >is universal for all directors/performers? Get a grip!
>
> Admittedly it's hard. In the case of the begrudged Microthon '99,
> my performers wouldn't have touched Sagittal, cents offset, or
> anything else.

***Glad you're calming down a bit on this Carl! :)

In all of my posts, I merely try to speak from my *own* experience,
and I wouldn't presume trying to generalize "everybody's" possible
situations... So, I'm very interested in hearing if your *own*
experiences are different from my own...

Notation isn't really the key issue, rehearsal is.
> As long as your notation and your music make sense, you can get
> it done if you have time to rehearse. Indeed, with practice,
> even amateurs can execute extended JI with no special notation at
> all!
>
> Without rehearsals you're doomed, no matter what notation you use,
> unless you're into sound effects, some quartertone ornaments or
> something.
>
> Whether Sagittal is easier than generalized remains to be seen.
> Joseph, have you ever tried to rehearse a piece from generalized
> notation?

***Quite frankly, Carl, I don't believe I would want to try to
rehearse a piece with a notation that is not fundamentally based on
our "normal" 12-tET system, with alterations.

OK, so I'm a pessimist about such. You're welcome, though, to try
yourself and report back on your findings. I would be *very*
interested. (My presumption is that the performers would look at you
crosseyed... but that's presumptuous... :)

Do you feel you've ever achieved extended JI with an
> ensemble in *any* notation?

***Well, I like to think that Blackjack does that in the sense that
it's an "adaptive" JI, or a JI being achieved *vertically.* This is
the instruction I give my performers.

However, I understand that this result is somewhat subject to
debate... (even Johnny Reinhard disagrees with it...)

I'm listening to Blacklight here,
> which is fantastic by the way,

***Thanks!

but if I'm not mistaken it's a cello
> solo with a keyboard accompaniment. Fantastic cello performance,
> but the cello part is certainly no 'acid test' of microtonal
> notation. How was the keyboard scored?
>

***Well, there's more than one sound in the "keyboard" part, although
I agree that the "organ" predominates. The use of such timbre was
somewhat encouraged by Paul Erlich who had said before that I wasn't
using timbres where JI could really be noticed.

Actually, the keyboard part is in "Blackjack 72-tET" notation (I was
using the Sims at this point) just as the cello part is.

HOWEVER, not every pitch is in the score. It's more designed as
a "cue sheet" for the performer than as an analytical document,
although a fair amount of analysis could be done from it. I didn't
want to include *more* information than was necessary for the
performer...

> Wow, your soundclick page has a lot more stuff than your mp3.com
> page did the last time I was there (IIRC).

***Well, I think that was partially because I included some stuff
that used to be on the *Tuning Punks.* I offered, by the way, to
host Tuning Punks, but I have not heard from John Starrett. Maybe he
doesn't have the original mp3s anymore... which would be a shame. He
seems to be hard to reach nowadays...

I'll have to get
> busy downloading...

***Thanks, Carl. I try to keep pieces free for downloading, since
not everybody has the broadest connection... I'm really more
interested in *sheet music* sales through my publisher than in
selling "mp3 moments..." :)

Is _Stringing_ microtonal?

***Yes, there are microtonal elements in the glissandi, and some
quartertones. It isn't an *endemic* microtonal work, however...

Most of the
> microtonal works here appear to be solo with electronic
> accompaniment....
>

***That's a fair assessment. I think I tend to think of electronics
as a "microtonal crutch..." since they are accurate. So I tend to
use electronics with microtonal works.

Glad you're acting more like Santa and less like the Grinch as in
your previous post. :)

JP

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

/tuning/topicId_21432.html#50486

> I think most people would agree that learning 2 new enharmonic
> spellings is far easier than learning 28 new dyadic relationships
> between 8 new nominals!
>
> --Dave Keenan

***I find, personally (see, I said now "personally", Carl.. I'm being
more careful.. :) that having new dyadic relationships is a big
problem. This is one reason that I am skeptical about even
the "conventional" notation for 19-tET.

Sure, it uses our "regular" accidentals and harmonics, similar to 12-
tET, but the fact that the step sizes are only about 60 cents (OK...
63 cents, nice to have a Palm Pilot here... :) makes the translation
of this system an "entirely different animal..."

Of course, for 19-tET with an instrument with *fixed* pitch, such as
Neil Haverstick does with his guitars, this is a different matter...
but for instruments with variable pitch, the fact that the nominals
*read* like our 12-tET ones and are yet *different* is a big
problem... (This "problem" also extends to the JI assumptions of Ben
Johnston's notation as well, I believe.)

The above comments are strictly IMHO, IMHO...

JP

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

/tuning/topicId_21432.html#50548

> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > Frankly, Dave, this is disgusting. We're talking about 4 files,
> > 12 seconds each, less than 2 kilobytes together. I took the time
> > to make these examples, and you have the nerve to suggest that I
> > should have done the Sagittal examples too? Another glimpse into
> > the most exquisite arrogance I have ever seen on these lists.
> >
> > One nice thing about e-mail is that it waits. There's no need
> > to reply until you have time. Another nice thing is that it's
> > voluntary.
>
> Sure. You say on a public forum that a notation system I have spent
a
> lot of time working on and happen to think works pretty well, is a
> failure, without even knowing the details, and without anyone else
> knowing the details, and I should just take my time replying, or
maybe
> not even reply at all.
>
> Good point. Consider this discussion voluntarily ended. From my side
> at least.
>
> -- Dave Keenan

***Actually, although Carl's _manner_ is sometimes a bit abrupt
(Scrooge, not Santa, etc...) I find that this discussion and the so-
called "defense" of Sagittal *very* illuminating.

So Lumma has provided some "illumination" after all... even if the
discussion has not been the pinnacle of civility...

J. Pehrson

1] adapt some logographical form(s) of Asian musi-notationality to
micro-/macro-/xeno-tonal. ie Chink-o _qin_/_ch'in_ nota.system "futuriz'd" &"blown.up"
fer bet'r visualztion - esp'ly in'em darker-than-bleedin'-necess stages,
orchie-pits, & chi-chi trendi studios!

2] I 'eard of a blind albino Japan biwa/gittarista/composer - she scores in
her own BigDot/BigBump Braille-graph system she reads toe-&-heel.
toe-&-heel.toe-&-heel. (websearch: _orthography_, _graphemic systems_, _visual acuity_,
_visual design_, _graphic design_, _ergonomic design_... more writing systems:
"omniglot" website, for a nice sci-fi touch: either official StarTrekkie or
unofficial Teresh BORG)

3] Colour'd light cues jus pop'd in.a mind jus freakin now... would look
good ... get somebod an arts grant or 2 (websearch: _colour organs_,
_synaethesia_, _visual semantics_)

HanumanZhang
|-|--|
FightWebEntrpy¡ChingaMuerte!¡VIVA.BANDWIDTH.KONZERVATION! ;) *gigglabyte!*

"Even a refrigerator can conform to the XML
Infoset, as long as it has a door sticker
saying "No information items inside". "
--Eve Maler

In a message dated 2003:12:29 08:15:14 PM, jpehrson@rcn.com writes:

>So Lumma has provided some "illumination" after all... even if the
>discussion has not been the pinnacle of civility...

::tongue-hard-as-Hell-in-cheek, teeth-ruff, MeanJellyBeanGrin:: fuckcivility
summa us 'ere are _Artistes_...
IMHO nowadays, rudeness shouldn't phaze anyways (if ya have any nano-sec
sense of tolerance, decorum & spine) - it's someone else's blinkin' Issue till
ya yaself dig in and ask fer bloody ammo...then it beckons ya to make it ya
own bleedin Personal Issue...

/start.plug/ Ya peeps want _Pax Civilitas_ come on down offa ya high-alt
"High Art" pedanticles to the ConLang List cabaret ... hoist a heavy few where the
peeps are all quite gracious cheerful humourous down-ta-Earthie Hobbity
xeno-lingua-types! & quite-a-few are nifty-keenan micro-musical and intensely
erudite - even reJoycean "pagan" poetic polymaths {a la Sri Guru John "DorianBleu"
Chalmers}- waaay out beyond the conventional scholarly statist-GUI norm {a la
msr.Brian "the Vitriolic Brainie" MC. & sensei Warren "Scarlet Aardvark" Burt
& Mr. Kraig "KrasiGelapMeru" Grady & Randy "10zenmagnumopus" Winchester-san...
& ohblast'd be I if I forget Herr Herman "PorcupineSiddhartha" Miller}...
[caveat: just don't bring in AuxLang irrealpoliTicks or
religio-sophiecallgirl insect.antic.ism and it will be "All cool" & Apollonairyean like apple
PIE, otherwiseass, all velvet gloves & ridin' bets are off and the
all-called-out HammUrung Apocalistpesticide begins... dun dun...tan dun] /pulls.plug/

Hanuman "StitchSpaceBaby" Zhangster, bbc, bs-ba, esq.
& *berp!* (insomnia
brain-fart)

"When you're trying to do something you should feel absolutely alone, like a
spark in the blackness of the universe."-Xenakis

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> >
>
> All you have to do is ask Dave!
> http://www.anaphoria.com/xen3a.PDF

I'd like to comment on page 5 of this document. In this paper, Wilson
has been considering systems generated by "fifths" (or equivalently,
the complementary "fourths") -- ranging from *under* 4/7 oct. to
*over* 3/5 oct. -- a considerably wider range than Dave likes to
admit, and with a period that is always one octave. At this point he
mentions the following possibilities for systems of nominals: 5, 7,
8, 9, 11, 12, and 13. Absent from this list are 6 and 10. 10 is of
course the number of nominals in the decatonic system described in my
papers, as well as in the quite different decimal system developed by
others here in connection with Miracle temperament.

The next thing Wilson says is that he has yet to consider systems
based instead on "semi-fifths" and "semi-fourths". This would bring
him a step closer to the general view of "linear temperament"
espoused especially on the tuning-math list, and in this list's
database, where one begins with the just lattice and then tempers out
any reasonable smallish JI interval, or comma -- or in higher prime
limits, some group thereof -- so as to yield a system where only one
dimension (that which Carl and Graham and Mark and I propose notating
with iterative application of an accidental drawn from a single pair,
perhaps the convetional #/b) extends infinitely (not counting the
octave dimension). In some cases (as in meantone, where 81/80 is
tempered out; schsimic, where 32805/32768 is tempered out; and
even 'pelogic', where 135/128 is tempered out) this leads to a
generator that is roughly a "fifth"/"fourth"; in some cases we do
get "semi-fifths", in some cases we do get "semi-fourths"; but in
other cases we get different generators entirely (such as the ~116.7
cent "secor" for Miracle temperament); and some cases turn out, even
when assuming octave-equivalence, to naturally have a period that is
not 1 octave but rather . . ., 1/5 octave, 1/4 octave, 1/3 octave, or
1/2 octave (the latter being the case for my decatonic temperaments),
as exemplified in my recent post "Grady, Monzo, Comma, Temperament" --
where all the examples mentioned happen to actually be
understandable simply as multiple interlocking chains
of "fifths"/"fourths". All these types of "linear temperament" occur
with equal "naturalness" qualitatively speaking. Please have a look at

http://lumma.org/tuning/erlich/erlich-tFoT.pdf

to begin to visually see this process in action.

--- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:

> Mark
>
> PS, the notation for 15EDO, as proposed by another chap beginning
with
> C, that I had also put up myself here, notates Porcupine easily -
it's
> the 'black notes' of the stave/keyboard. 2222223 in 15EDO.

I'm glad you're paying such close attention, Mark!

> Assuming
> 3333335 as another form , I get 23EDO as another Porcupine
> representation, or is this too 'way-out' to be useable?
> M

Actually, the standard "next-higher form" of Porcupine would be
3333334 in 22-equal. I've the fourth mode of this scale in _Improv_
performed at Microthon #1 and the seventh mode of this scale in
_Glassic_ performed at Microthon #2. The scale offers two good major
triads and two good minor triads, one of the distinguishing features
of porcupine. 23-equal does have usable major and minor triads but
they do not occur when the scale 3333335 is used -- thus this has a
hard time qualifying as a 'porcupine' scale.

When in doubt, look at the first graph here:

http://tonalsoft.com/enc/eqtemp.htm

I show the porcupine line passing through 15-, 37-, 59-, 22-, 29-,
and 7-equal. The 7-note porcupine scale in these tunings would be
2222223, 5555557, 888888e, 3333334, 4444445, and 1111111,
respectively. 23-equal is off the porcupine line as it should be.

More directly (but perhaps more abstractly) one can look at the table
just below the first graph (the one you were just looking at) on

http://tonalsoft.com/enc/eqtemp.htm

and see that porcupine is associated with the vanishing of
the "maximal diesis"; then look at the honeycomb chart just below
that titled "small 5-limit intervals", note the arrow (vector)
corresponding to the "maximal diesis" -- it takes you two hexes west
and three hexes northwest -- and then examine the honeycomb lattices
for various ETs to see if the maximal diesis vanishes in them. Here's
the honeycomb lattice for 15-equal:

/tuning/files/perlich/15.gif
or
/tuning-math/files/Paul/15p.gif

One can see that starting at one red "0", then proceeding two hexes
west and three hexes northwest, one lands on another red "0", so
the 'maximal diesis' does indeed vanish in 15-equal, and 15-equal
belongs to the porcupine family. Observe that the same is true for 22-
equal:

/tuning/files/perlich/22.gif
or
/tuning-math/files/Paul/22p.gif

and for 29-equal:

/tuning-math/files/Paul/29p.gif

and for 37-equal:

/tuning-math/files/Paul/37p.gif

and for 59-equal:

/tuning-math/files/Paul/59p.gif

and even for 7-equal:

/tuning-math/files/Paul/7p.gif

However, here's 23-equal:

/tuning-math/files/Paul/23p.gif

One can see that the 'maximal diesis' doesn't vanish here, nor does
it even correspond to 1 degree of 23-equal -- it actually corresponds
to 2 degrees of 23-equal.

If this is unclear, perhaps I should run through a parallel
illustration for meantone/diatonic scales (those where the syntonic
comma vanishes) vs. those that don't fit into this category. Or if
you have time, try to run through this parallel yourself, and see if
that doesn't illuminate things by way of a more familiar analogy.

-Paul

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

> Kleismic[8] is a quintessential example of a non-MOS that I'd base
> a notation on.

I'm a bit startled to see you say this, as it appeared in the recent
past that you agreed with me that you need some form of a DE/CS/old-
MOS scale as a basis for notation.

Your ensuing discussion with Dave is a bit frustrating because there
are plenty of such scales you could be using in your argument against
Dave, but you choose this one instead, and Dave doesn't fully explore
the problems inherent in such a scheme.

Let's begin. Will you take a decent chunk of the 5-limit lattice and
show how you'd notate it using Kleismic[8], please?

You seem to be overrating proper scales here. The prototypical
Western notation, and that used by HEWM, Sagittal, etc., is based on
the Pythagorean diatonic scale, which is actually slightly improper.

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

> ***Well, I like to think that Blackjack does that in the sense that
> it's an "adaptive" JI, or a JI being achieved *vertically.* This
is
> the instruction I give my performers.
>
> However, I understand that this result is somewhat subject to
> debate... (even Johnny Reinhard disagrees with it...)

Well, I don't think Johnny would disagree if you were to actually
*notate* it this way, using cents notation. For example, the "raw"
Blackjack (that is, 72-equal) tuning of a 'harmonic seventh chord' on
C would be notated in cents as

C E-17 G Bb-33

Johnny would not consider this as acheiving JI vertically. But if you
were to adjust each pitch by only 1 cent (2 cents for the E), and
write

C-1 E-15 G+1 Bb-32

then you would indeed be notating a vertical JI sonority as
accurately and precisely as possible in cents notation. If you make
such adaptive 1 cent and occasional 2 cent adjustments to the notated
pitches in your Blackjack chords, then even Johnny could not deny
that you were composing in adaptive JI.

>> Kleismic[8] is a quintessential example of a non-MOS that I'd base
>> a notation on.
>
>I'm a bit startled to see you say this, as it appeared in the recent
>past that you agreed with me that you need some form of a DE/CS/old-
>MOS scale as a basis for notation.

It is certainly preferable, but my assertion is that notation should
follow composition intent and vice versa. So if one must have a
non-DE scale, then the notation should follow.

>Your ensuing discussion with Dave is a bit frustrating because there
>are plenty of such scales you could be using in your argument against
>Dave, but you choose this one instead,

I purposely chose an example I thought my scheme would have the
hardest time with (and again with harmonics 8-16), to see how bad
it might get.

I still think I prefer the 8-nominal notation, since Sagittal requires
enharmonics even for a single mode of the scale. Had my example
included a melody, I think it would have revealed the undesirable
effects of such a reliance on enharmonics. I was hoping to add such an
example later in the thread.

>Dave doesn't fully explore the problems inherent in such a scheme.
>
>Let's begin. Will you take a decent chunk of the 5-limit lattice and
>show how you'd notate it using Kleismic[8], please?

Not right now (I'm severely hung over, for I think the 3rd time in
my life). But I don't think such a demonstration would show anything
(aside from the obvious problems). All I'm trying to notate are the
cross set and interval matrix of the scale -- no desire to notate
5-limit JI should be implied -- and I've already shown those.

>You seem to be overrating proper scales here. The prototypical
>Western notation, and that used by HEWM, Sagittal, etc., is based on
>the Pythagorean diatonic scale, which is actually slightly improper.

I think DE is more important than propriety for a notation, but for
composition only actually trying both kleismic[7] and kleismic[8]
will tell.

-Carl

> Hi Paul!

Viggo Bruns methods seems to be far better in picking these type (6 and 10) of structures and
definately fills in some gaps that such methods as this chart seem to miss.
Where on this chart would you put the 6 or 10 tone MOS scales?

I will say that I don't like mixing greek and english alphabets, although right this minute, i
could be talked into it.

>
> From: "Paul Erlich" <paul@stretch-music.com>
>
>
> --- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> > >
> >
> > All you have to do is ask Dave!
> > http://www.anaphoria.com/xen3a.PDF
>
> I'd like to comment on page 5 of this document. In this paper, Wilson
> has been considering systems generated by "fifths" (or equivalently,
> the complementary "fourths") -- ranging from *under* 4/7 oct. to
> *over* 3/5 oct. -- a considerably wider range than Dave likes to
> admit, and with a period that is always one octave. At this point he
> mentions the following possibilities for systems of nominals: 5, 7,
> 8, 9, 11, 12, and 13. Absent from this list are 6 and 10. 10 is of
> course the number of nominals in the decatonic system described in my
> papers, as well as in the quite different decimal system developed by
> others here in connection with Miracle temperament

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> > http://www.anaphoria.com/xen3a.PDF
>
> I'd like to comment on page 5 of this document. In this paper, Wilson
> has been considering systems generated by "fifths" (or equivalently,
> the complementary "fourths") -- ranging from *under* 4/7 oct. to
> *over* 3/5 oct. -- a considerably wider range than Dave likes to
> admit, and with a period that is always one octave.

That "admit" is somewhat ambiguous. I certainly admit that Wilson
considers such extreme "fifths" for notational purposes in his
article. That was my point in recommending it as a launching point for
investigation of systems of nominals for more general linear temperaments.

I expect you only meant that I recommend not allowing fifths outside
4/7 oct to 3/5 oct in a 7-chain-of-fifth-nominals notation. That's
quite correct, and for obvious enough reasons. When you go outside of
that range you can no longer maintain FCGDAEB as a chain of fifths at
the same time as having pitch order be ABCDEFG. Certain pairs of
pitches run into each other at the 5-ET and 7-ET extremes and cross
over if you go beyond these. So one of these things has to give
(FCGDAEB or ABCDEFG). Or does it?

Wilson seems to have an approach where they both give a little.

Another reason I point to this article is that some people seem quite
happy to simply redefine the nominals A to G for whatever generator
they are using, whereas I suspect this will cause confusion. I would
prefer to see different letters (or other characters) used in cases
where the diatonic relationships are not preserved.

There are aspects of Wilson's scheme that few people seem to like,
such as the mixing of Greek and Roman letters. But maybe something
along these lines can be done to come up with an interlocking system
of nominals that go to even greater extremes in the size of the linear
generator, and that cope with non-octave periods. After all, we've got
another 19 letters in our ordinary uppercase alphabet to start with.

Of course letter-names are one thing, and staves are another. But
Wilson has some interesting ideas here too. It think it would be neat
to be able to look at a blank staff and know whether this was a
diatonic staff or a pajara staff or a kleismic staff etc.

-- Dave Keenan

>I would
>prefer to see different letters (or other characters) used in cases
>where the diatonic relationships are not preserved.

I've been thinking about that. Despite Paul's negative experience
with performers and extra numbers, Graham's numbering has the
advantage that subtraction can guide in learning the new generic
intervals. Another approach would be to go fishing deeper in the
alphabet.

>Of course letter-names are one thing, and staves are another. But
>Wilson has some interesting ideas here too. It think it would be neat
>to be able to look at a blank staff and know whether this was a
>diatonic staff or a pajara staff or a kleismic staff etc.

I balked at the unevenly-spaced staff lines when I first saw them,
and thought it would be too visually confusing to have to figure out
if a note head was tangent to the top or bottom of a wide pair of
lines. But maybe it isn't as bad as I thought.

-Carl

I wrote:
"When you go outside of [the 4/7 oct to 3/5 oct] range you can no
longer maintain FCGDAEB as a chain of fifths at the same time as
having pitch order be ABCDEFG."

That's not quite right. The sharps and flats come into it too, at the
4/7 oct extreme. If you go beyond that you can't have e.g. FCGDAEBF#
as a chain of fifths at the same time as having pitch order be ABCDEFF#G.

-- Dave Keenan

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:

> Viggo Bruns methods seems to be far better in picking these type
(6 and 10) of structures and
> definately fills in some gaps that such methods as this chart seem
to miss.

How does Brun's algorithm manage to be more complete than brute force?

>
> From: "Gene Ward Smith" <gwsmith@svpal.org>
>

Actually Viggo Brun methods picks out constant structures which the brute force of "linear
temperments" (an act like building a fence where regardless of the territory the distance between
post is the same)
misses. I don't understand why this algorithm works so well and i have in the past played with it
switching the sequence in midstream so to speak . One can really shape it to one wishes as opposed
to turning it on and waiting for a final answer. I know that Erv stated to me thattheir were
certain scales he knew of that he could not fine an easy way to generate or exxplain and Viggo's
method hit quite a few of these.
But you are more adroit at math than me so possibly you might be able shed so light on this

>
> How does Brun's algorithm manage to be more complete than brute force?
>
> ________________________________________________________________________
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

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

/tuning/topicId_21432.html#50666

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > ***Well, I like to think that Blackjack does that in the sense
that
> > it's an "adaptive" JI, or a JI being achieved *vertically.* This
> is
> > the instruction I give my performers.
> >
> > However, I understand that this result is somewhat subject to
> > debate... (even Johnny Reinhard disagrees with it...)
>
> Well, I don't think Johnny would disagree if you were to actually
> *notate* it this way, using cents notation. For example, the "raw"
> Blackjack (that is, 72-equal) tuning of a 'harmonic seventh chord'
on
> C would be notated in cents as
>
> C E-17 G Bb-33
>
> Johnny would not consider this as acheiving JI vertically. But if
you
> were to adjust each pitch by only 1 cent (2 cents for the E), and
> write
>
> C-1 E-15 G+1 Bb-32
>
> then you would indeed be notating a vertical JI sonority as
> accurately and precisely as possible in cents notation. If you make
> such adaptive 1 cent and occasional 2 cent adjustments to the
notated
> pitches in your Blackjack chords, then even Johnny could not deny
> that you were composing in adaptive JI.

***Hi Paul,

Yes, this makes sense and, in fact, I had discussed this possibility
with Johnny at one point (the idea of "adjusting" Blackjack with
cents deviations to achieve JI).

I imagine, though, that one could question why one would use
Blackjack at all in such a case, rather than devising some "true" JI
system that would maintain even the linearities using the cents
system...

JP

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> > Hi Paul!
>
> Viggo Bruns methods seems to be far better in picking these type >
(6 and 10) of structures and
> definately fills in some gaps that such methods as this chart seem
>to miss.

Of course there are many other such methods, including more general
ones. All periodicity blocks (not torsional blocks) are CS scales in
their JI/untempered form; then all one has to do is temper out all
but one of the unison vectors to get a 'linear' scale. These things
tend to get discussed on tuning-math since they were not received
well here in the early stages.

> Where on this chart would you put the 6 or 10 tone MOS scales?

Wilson's chart shows scales where the generator is about a
fifth/fourth and the period is an octave. Thus they don't belong on
it. A higher-dimensional chart would be needed. Not unrelated is the
big ET/Linear Temperament chart that's first on Monz's ET page:

http://tonalsoft.com/enc/eqtemp.htm

Every green line here implies a generator/period combination and thus
a family of MOSs* (these data are given in the table below the
chart). The generator varies gently as one moves along the line (I
did not attempt to show this explicitly on the chart as it was
already cluttered enough). For example, the meantone line, since it
crosses the numbers 7, 12, and 19, implies MOSs of those
cardinalities (and if you mouse-over "zoom 1", you'll see it crosses
2 and 5 as well). At the point where the generator is just the right
size to close on itself, I put the number corresponding to the
relevant ET. Now if you look at the diaschismic line, since it
crosses the number 10, 12, and 22, you get MOSs* of those
cardinalities. And so on. The chart also shows the quality of
approximation of all the 5-limit consonances, but could be extended
into higher dimensions to show higher-limit consonances, and then one
would probably add more lines, such as for Miracle, etc.

*the latest from you is that some of these may not really be called
MOSs, so the academic term "distributionally even" or DE scale would
be better -- it means that each generic interval comes in no more
than two specific sizes.

> I will say that I don't like mixing greek and english alphabets,
although right this minute, i
> could be talked into it.
>
>
> >
> > From: "Paul Erlich" <paul@s...>
> >
> >
> > --- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...>
wrote:
> > > >
> > >
> > > All you have to do is ask Dave!
> > > http://www.anaphoria.com/xen3a.PDF
> >
> > I'd like to comment on page 5 of this document. In this paper,
Wilson
> > has been considering systems generated by "fifths" (or
equivalently,
> > the complementary "fourths") -- ranging from *under* 4/7 oct. to
> > *over* 3/5 oct. -- a considerably wider range than Dave likes to
> > admit, and with a period that is always one octave. At this point
he
> > mentions the following possibilities for systems of nominals: 5,
7,
> > 8, 9, 11, 12, and 13. Absent from this list are 6 and 10. 10 is of
> > course the number of nominals in the decatonic system described
in my
> > papers, as well as in the quite different decimal system
developed by
> > others here in connection with Miracle temperament
>
> -- -Kraig Grady
> North American Embassy of Anaphoria Island
> http://www.anaphoria.com
> The Wandering Medicine Show
> KXLU 88.9 FM WED 8-9PM PST

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

> I expect you only meant that I recommend not allowing fifths outside
> 4/7 oct to 3/5 oct in a 7-chain-of-fifth-nominals notation.

Sorry, I should have said "in some other contexts" and probably
should have said "used to" too. You once had a more stringent
requirement on what you'd consider a "fifth", having to do with no
better fifths appearing in a chain of a certain length . . .

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> I wrote:
> "When you go outside of [the 4/7 oct to 3/5 oct] range you can no
> longer maintain FCGDAEB as a chain of fifths at the same time as
> having pitch order be ABCDEFG."
>
> That's not quite right. The sharps and flats come into it too, at
the
> 4/7 oct extreme. If you go beyond that you can't have e.g. FCGDAEBF#
> as a chain of fifths at the same time as having pitch order be
ABCDEFF#G.

Yup -- on my standard-keyboard 11-note 'pelogic' mapping (used
typically with a marimba-type sound), the fifths are 677 cents, and
the white keys appear in order of pitch, but start playing the black
keys, and funny things can happen! The easiest way to get around it
is just to remember that major and minor triads are switched -- so of
course F# has to be lower than F since the third in a D minor triad
is lower than the third in a D major triad . . .

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

> ***Hi Paul,
>
> Yes, this makes sense and, in fact, I had discussed this
possibility
> with Johnny at one point (the idea of "adjusting" Blackjack with
> cents deviations to achieve JI).
>
> I imagine, though, that one could question why one would use
> Blackjack at all in such a case, rather than devising some "true"
JI
> system that would maintain even the linearities

?

>using the cents
> system...
>
> JP

The reason might have to do, in part, with keeping *pitch shifts* at
a minimum -- in addition to all the other advantages you and I know
temperament offers over strict JI. You could compose at your
Blackjack keyboard and get a pretty good idea of what the music would
sound like, knowing that all the horizontal and vertical shifts would
be quite small (and perhaps inaudible to you, though not to Johnny).

In a message dated 2003:12:31 12:14:48 AM, kraiggrady@anaphoria.com writes:

>I will say that I don't like mixing greek and english alphabets, although
>right this minute, i
>could be talked into it.

Meaneth thee Greco- und Roman alphabets, praytell right und truefull?

Thee only "poor'ly Englishe" _alpha_beta_ I knoweth ov ist thee
"Anglo-Saxon runic."

--- *DiDJiBuNgA!!* ">Teenage Aboriginal Walkabout Turtles"....---

Hanuman "Stitch" Zhang, ManglaLanger (mangle + manga + lang)
http://www.boheme-magazine.net

Language[s] change[s]: vowels shift, phonologies crash-&-burn, grammars
leak, morpho-syntactics implode, lexico-semantics mutate, lexicons explode,
orthographies reform, typographies blip-&-beep, slang flashes, stylistics
warp... linguistic (R)evolutions mark each-&-every quantum leap...
languages are "naturally evolved wild systems...
So language does not impose order on a chaotic universe,
but reflects its own wildness back." - Gary Snyder

"Some Languages Are Crushed to Powder but Rise Again as New Ones" -
title of a chapter on pidgins and creoles, John McWhorter,
_The Power of Babel: A Natural History of Language_

= ¡gw'araa legooset caacaa!
¡reez'arvaa. saalvaa. reecue. scoopaa-goomee en reezijcloo! =

[Fight Linguistic Waste!
Save, Salvage, Recover, Scavenge and Recycle!]

>

I stand corrected . I reserve the one you mention though for 'talking to trees'

>
> Message: 25
> Date: Wed, 31 Dec 2003 17:36:00 EST
> From: czhang23@aol.com
> Subject: Re: Re: Notation
>
> Thee only "poor'ly Englishe" _alpha_beta_ I knoweth ov ist thee
> "Anglo-Saxon runic."
>
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

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

/tuning/topicId_21432.html#50737

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > ***Hi Paul,
> >
> > Yes, this makes sense and, in fact, I had discussed this
> possibility
> > with Johnny at one point (the idea of "adjusting" Blackjack with
> > cents deviations to achieve JI).
> >
> > I imagine, though, that one could question why one would use
> > Blackjack at all in such a case, rather than devising some "true"
> JI
> > system that would maintain even the linearities
>
> ?
>
> >using the cents
> > system...
> >
> > JP
>
> The reason might have to do, in part, with keeping *pitch shifts*
at
> a minimum -- in addition to all the other advantages you and I know
> temperament offers over strict JI. You could compose at your
> Blackjack keyboard and get a pretty good idea of what the music
would
> sound like, knowing that all the horizontal and vertical shifts
would
> be quite small (and perhaps inaudible to you, though not to Johnny).

***Well, of course, it would be quite easy to add the small cents
indicators. But would the JI "enthusiasts" really call this JI?? I,
myself, believe in this kind of temperament, but I'm sure it violates
JI "orthodoxy..." :)

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_21432.html#50737
>
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> >
> > > ***Hi Paul,
> > >
> > > Yes, this makes sense and, in fact, I had discussed this
> > possibility
> > > with Johnny at one point (the idea of "adjusting" Blackjack
with
> > > cents deviations to achieve JI).
> > >
> > > I imagine, though, that one could question why one would use
> > > Blackjack at all in such a case, rather than devising
some "true"
> > JI
> > > system that would maintain even the linearities
> >
> > ?
> >
> > >using the cents
> > > system...
> > >
> > > JP
> >
> > The reason might have to do, in part, with keeping *pitch shifts*
> at
> > a minimum -- in addition to all the other advantages you and I
know
> > temperament offers over strict JI. You could compose at your
> > Blackjack keyboard and get a pretty good idea of what the music
> would
> > sound like, knowing that all the horizontal and vertical shifts
> would
> > be quite small (and perhaps inaudible to you, though not to
Johnny).
>
>
> ***Well, of course, it would be quite easy to add the small cents
> indicators. But would the JI "enthusiasts" really call this JI??
I,
> myself, believe in this kind of temperament, but I'm sure it
violates
> JI "orthodoxy..." :)
>
> JP

So what? And anyway, I never said it would be strict JI -- I said it
would be adaptive JI. That is, most of the chords you're using (such
as ~4:5:6:7, etc.) could be notated so that each would sound, even to
Johnny, like a vertically JI chord within itself. And this would
require tiny adjustments, averaging about 1 cent, of each pitch
depending on the chordal context. For a 4:5:6:7 chord, for example,
you'd lower the bottom note by 2 cents, raise the next note by 1
cents, and leave the top two notes unchanged. Voila -- a just
sonority!

In a message dated 1/2/04 3:50:31 PM Eastern Standard Time, jpehrson@rcn.com
writes:

> ***Well, of course, it would be quite easy to add the small cents
> indicators. But would the JI "enthusiasts" really call this JI?? I,
> myself, believe in this kind of temperament, but I'm sure it violates
> JI "orthodoxy..." :)
>
> JP
>

JI enthusiasts will call it JI. You are needlessly intimidated. Besides,
changing a tempered note to un-tempered is not tempering in any classic sense.

best, Johnny

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> In a message dated 1/2/04 3:50:31 PM Eastern Standard Time,
jpehrson@r...
> writes:
>
>
> > ***Well, of course, it would be quite easy to add the small cents
> > indicators. But would the JI "enthusiasts" really call this
JI?? I,
> > myself, believe in this kind of temperament, but I'm sure it
violates
> > JI "orthodoxy..." :)
> >
> > JP
> >
>
> JI enthusiasts will call it JI. You are needlessly intimidated.
Besides,
> changing a tempered note to un-tempered is not tempering in any
classic sense.
>
> best, Johnny

There are some JI enthusiasts who insist that the horizontal/melodic
intervals, as well as the vertical/harmonic intervals, be simple
ratios. Adaptive JI does not fulfill the former criterion but only
the latter one. Hence Monz's dictionary entry for "adaptive JI" calls
it a form of temperament -- you may want to induce him to word that
differently.

Let's look at a concrete Blackjack example (thanks Monz), Graham
Breed's "comma pump" chord progression. In the current standard,
degree 0 will be a quartertone below the conventional B.

chord..72-eq..72-eq...adaptive.JI
number.degree..cents..cents

..1.....70....1166.7..1167
........51.....850.....851
........28.....466.7...465
........14.....233.3...234

..2......0.......0......-1 (or 1199 in the next lower octave)
........56.....933.3...934
........37.....616.7...618
........14.....233.3...232

..3.....58.....966.7...967
........42.....700.....700
........23.....383.3...384
.........0.......0......-2 (or 1198 in the next lower octave)

..4.....58.....966.7...965
........44.....733.3...734
........28.....466.7...467
.........9.....150.....151

..5.....63....1050....1049
........44.....733.3...733
........28.....466.7...466
........14.....233.3...235

..6.....63....1050....1050
........44.....733.3...734
........21.....350.....348
.........7.....116.7...117

..7.....70....1166.7..1166
........51.....850.....850
........35.....583.3...583
........21.....350.....352

..1.....70....1166.7..1167
........51.....850.....851
........28.....466.7...465
........14.....233.3...234

I know one could find a better solution, but I'm assuming Joseph will
be working from a simple "center-to-72-equal" rule that will work not
only for 2401:2400-pumps like this one, but for 225:224-pumps as
well -- or any other chord progression that might occur in
Blackjack . . .

Comments?

on 1/2/04 3:43 PM, Afmmjr@aol.com <Afmmjr@aol.com> wrote:

> In a message dated 1/2/04 3:50:31 PM Eastern Standard Time, jpehrson@rcn.com
> writes:
>
>
>> ***Well, of course, it would be quite easy to add the small cents
>> indicators. But would the JI "enthusiasts" really call this JI?? I,
>> myself, believe in this kind of temperament, but I'm sure it violates
>> JI "orthodoxy..." :)
>>
>> JP
>>
>
> JI enthusiasts will call it JI. You are needlessly intimidated. Besides,
> changing a tempered note to un-tempered is not tempering in any classic sense.

But it still might be tampering. ;)

-Kurt

>
> best, Johnny
>

In a message dated 2004:01:02 11:00:08 PM, paul@stretch-music.com writes:

re: the idea of "adjusting" Blackjack with cents deviations to achieve JI

>> > > I imagine, though, that one could question why one would use
>> > > Blackjack at all in such a case, rather than devising
>> > > some "true" JI system that would maintain even the linearities ?
>> > >using the cents system...
>> > >
>> > > JP

eh? a meantone/quasi-just, 0_o? er...or... just exactly _what_ are you
just "hinting" at 0_o????

>> > The reason might have to do, in part, with keeping *pitch shifts*
>>> at a minimum -- in addition to all the other advantages you and I
>>>know temperament offers over strict JI. You could compose at your
>> > Blackjack keyboard and get a pretty good idea of what the music
>> would sound like, knowing that all the horizontal and vertical shifts
>>> would be quite small (and perhaps inaudible to you, though not to
>>>Johnny).

*snarfle!* lets not get into that pitch-recogno issue again...pretty pleas
e...

>> ***Well, of course, it would be quite easy to add the small cents
>> indicators. But would the JI "enthusiasts" -

AiYaH! fanatical purists IMMHO

>>really call this JI?? I,
>> myself, believe in this kind of temperament, but I'm sure it
>>violates JI "orthodoxy..." :)
>>
>> JP

LMAO

Vive Heresy Intonationale!
"Real" microtonalists & sur-real xenotonalists,
unite & throw off your slavish ratios... hoary chains of pure 4ths &
5ths...
... the weight of oppressive beatless, lifeless generators!

*googolplexgigglabyte!*

I play with JI ... wish I had AI ;)

thanx to the List, I have a thievin' magpie's toybox full of neat-o scales &
modes to Mix & Match (&Scratch) at will...

---|-----|--------|-------------|---------------------|
Hanuman Zhang
"Space is a practiced place." -- Michel de Certeau
"Space is the Place for the Human Race." -- William S. Burroughs

"... simple, chaotic, anarchic and menacing.... This is what people of today
have lost and need most - the ability to experience permanent bodily and
mental ecstasy, to be a receiving station for messages howling by on the ether from
other worlds and nonhuman entities, those peculiar short-wave messages which
come in static-free in the secret pleasure center in the brain." - Slava Ranko
(Donald L. Philippi)

The German word for "noise" _Geräusch_ is derived from _rauschen_ "the
sound of the wind," related to _Rausch_ "ecstasy, intoxication" hinting at some
of the possible aesthetic, bodily effects of noise in music. In Japanese
Romaji: _uchu_ = "universe"... _uchoten_ = "ecstasty," "rapture"..._uchujin_ =
[space] alien!

"When you're trying to do something you should feel absolutely alone, like a
spark in the blackness of the universe."-Xenakis

"For twenty-five centuries, Western knowledge has tried to look upon the
world. It has failed to understand that the world is not for the beholding. It
is for the hearing. It is not legible, but audible. ... Music is a herald,
for change is inscribed in noise faster than it transforms society. ...
Listening to music is listening to all noise, realizing that its appropriation and
control is a reflection of power, that is essentially political." - Jacques
Attali, _Noise: The Political Economy of Music_

"The sky and its stars make music in you." - Dendera, Egypt wall
inscription

"Sound as an isolated object of reproduction, call it our collective memory
bank... Any sound can be you." - DJ Spooky that Subliminal Kid (a.k.a. Paul D.
Miller)

"Overhead, without any fuss, the stars were going out."
--Arthur C. Clarke, _The Nine Billion Names of God_

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

/tuning/topicId_21432.html#50849

> Let's look at a concrete Blackjack example (thanks Monz), Graham
> Breed's "comma pump" chord progression. In the current standard,
> degree 0 will be a quartertone below the conventional B.
>
> chord..72-eq..72-eq...adaptive.JI
> number.degree..cents..cents
>
> ..1.....70....1166.7..1167
> ........51.....850.....851
> ........28.....466.7...465
> ........14.....233.3...234
>
> ..2......0.......0......-1 (or 1199 in the next lower octave)
> ........56.....933.3...934
> ........37.....616.7...618
> ........14.....233.3...232
>
> ..3.....58.....966.7...967
> ........42.....700.....700
> ........23.....383.3...384
> .........0.......0......-2 (or 1198 in the next lower octave)
>
> ..4.....58.....966.7...965
> ........44.....733.3...734
> ........28.....466.7...467
> .........9.....150.....151
>
> ..5.....63....1050....1049
> ........44.....733.3...733
> ........28.....466.7...466
> ........14.....233.3...235
>
> ..6.....63....1050....1050
> ........44.....733.3...734
> ........21.....350.....348
> .........7.....116.7...117
>
> ..7.....70....1166.7..1166
> ........51.....850.....850
> ........35.....583.3...583
> ........21.....350.....352
>
> ..1.....70....1166.7..1167
> ........51.....850.....851
> ........28.....466.7...465
> ........14.....233.3...234
>
> I know one could find a better solution, but I'm assuming Joseph
will
> be working from a simple "center-to-72-equal" rule that will work
not
> only for 2401:2400-pumps like this one, but for 225:224-pumps as
> well -- or any other chord progression that might occur in
> Blackjack . . .
>
> Comments?

***Well, this is very interesting, but it all seems like "spare
change..." to me... :)

(Some will disagree, however... :) :)

JP