Yahoo Tuning Groups Ultimate Backup tuning Sault vs Ellis

>Here is a comparison of Sault's Dodekaphone vs Ellis' Duodene:
>
>Sault: 6 6/5's 7 5/4's 9 3/2's, for a total of 22
>Ellis: 6 6/5's 8 5/4's 9 3/2's for a total of 23
>
>Sault: 5 major triads 6 minor triads for a total of 11
>Ellis: 6 major triads 6 minor triads for a total of 12
>
>The advantage appears to be with Ellis,

But Peter's criterion isn't consonances, it's "correlations",
the number of intervals that are also in the scale.

Peter, in your application NATURAL, you seem to be insisting
on inversion symmetry. That is, if I change the 10th degree
from 9:16 to 9:5, the 2nd degree changes from 8:9 to 9:10.
So you can't test scales like Ellis' Duodene.

By the way Alexander Ellis was a great music theorist, who
translated Helmholtz's On The Sensations of Tone into English
and provided extensive footnotes. I'm sure you'd love this
text. It is basically where our (in this community) literature
starts.

-Carl

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> Here is a comparison of Sault's Dodekaphone vs Ellis' Duodene:
>
> Sault: 6 6/5's 7 5/4's 9 3/2's, for a total of 22
> Ellis: 6 6/5's 8 5/4's 9 3/2's for a total of 23
>
> Sault: 5 major triads 6 minor triads for a total of 11
> Ellis: 6 major triads 6 minor triads for a total of 12
>
> The advantage appears to be with Ellis, and the Duodene to be a
good
> thing to keep in mind when testing claims about the unique
excellence
> of the Dodekaphone.

Other important 12-tone just scales with a prime limit of 5 include
those of De Caus and Ramos. But 12-tone 5-limit just scales were
virtually irrelevant to the history of Western music. One finds
instead Pythagorean prior to 1420, schismic between 1420 and 1470,
meantone from 1470 to 1770, and closed 12-tone temperaments
thereafter (as well as earlier with Bach, etc.) . . . Meanwhile, when
making music with computers today, we have the capacity to realize
adaptive tuning systems which bring more chords into vertical purity
than would be possible with any fixed system of tuning. I think all
these things are important to keep in mind when making such
assertions, and of course the idea that 12 is necessary -- I won't
even go there (having just performed a moving and well-received
session with an Armenian musician last night) . . .

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > Here is a comparison of Sault's Dodekaphone vs Ellis' Duodene:
> >
> > Sault: 6 6/5's 7 5/4's 9 3/2's, for a total of 22
> > Ellis: 6 6/5's 8 5/4's 9 3/2's for a total of 23
> >
> > Sault: 5 major triads 6 minor triads for a total of 11
> > Ellis: 6 major triads 6 minor triads for a total of 12
> >
> > The advantage appears to be with Ellis, and the Duodene to be a
> good
> > thing to keep in mind when testing claims about the unique
> excellence
> > of the Dodekaphone.
>
> Would you mind explaining what all that means, please? On what
basis
> are you counting and what makes you think that your criteria are
the
> only, let alone the superior ones?

Gene made no claim that these are the only or superior criteria, but
they certainly have some importance. He's counting the occurence of
the consonant dyads in each of the 12-note scales. This counting is
very easy to do when each scale is displayed on a lattice. If no one
beats me to it, I will (when I get a chance) make a lattice for each
of the following 12-tone 5-limit tunings: Sault, Ellis, De Caus,
Ramos, and the Modern Indian Gamut.

🔗Paul Erlich <paul@stretch-music.com>

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

🔗Paul Erlich <paul@stretch-music.com>

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> Here is a comparison of Sault's Dodekaphone vs Ellis' Duodene:

I'll add a couple of other CS 5-limit JI scales.

> Sault: 6 6/5's 7 5/4's 9 3/2's, for a total of 22
> Ellis: 6 6/5's 8 5/4's 9 3/2's for a total of 23
De Caus: 7 6/5's 8 5/4s 9 3/2's for a total of 23
Modern Indian Gamut: 6 6/5s 7 5/4s 9 3/2s for a total of 22

> Sault: 5 major triads 6 minor triads for a total of 11
> Ellis: 6 major triads 6 minor triads for a total of 12
De Caus: 6 major triads 6 minor triads for a total of 12
Modern Indian Gamut: 6 major triads 5 minor triads for a total of 11

> The advantage appears to be with Ellis, and the Duodene to be a
good
> thing to keep in mind when testing claims about the unique
excellence
> of the Dodekaphone.

Or De Caus, just as well -- both Ellis and De Caus are symmetric
about the 1/1-3/2 dyad.

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > > Here is a comparison of Sault's Dodekaphone vs Ellis' Duodene:
> > >
> > > Sault: 6 6/5's 7 5/4's 9 3/2's, for a total of 22
> > > Ellis: 6 6/5's 8 5/4's 9 3/2's for a total of 23
> > >
> > > Sault: 5 major triads 6 minor triads for a total of 11
> > > Ellis: 6 major triads 6 minor triads for a total of 12
> > >
> > > The advantage appears to be with Ellis, and the Duodene to be a
> > good
> > > thing to keep in mind when testing claims about the unique
> > excellence
> > > of the Dodekaphone.
> >
> > Would you mind explaining what all that means, please? On what
> basis
> > are you counting and what makes you think that your criteria are
> the
> > only, let alone the superior ones?
>
> Gene made no claim that these are the only or superior criteria,
but
> they certainly have some importance.

Dear Peter,

Let me clarify this further, in the hopes of preemptively defusing
any flame war. Gene's statment above, as I read it, was merely
setting the stage for evaluating your objective claims, whatever they
may be. In other words, if you make an objective claim (and the same
goes for Gene, me, Ellis, Pythagoras, or anyone else), it should be
admissible for anyone to attempt to either prove it or refute it, and
the latter is most easily done with a counterexample, so Gene and I
have set a few alteratives to *test* as possible counterexamples. All
Gene says above is that a certain scale is "a good thing to keep in
mind when testing" objective claims. "A good thing to keep in mind"
is very different from "superior". I hope you will keep an open mind
in case there *does* arise a counterexample you haven't previously
considered; and if you've proved that there isn't, you should sit
confident in the fact that no one will ever find a counterexample,
try as they might.

Your subjective, aesthetic claims, which may include your criteria
for choosing your scale, are of completely up to you, and no one
else, to define. However, I sincerely hope you will keep an open mind
about those as well, since there are always new and unexpected
musical experiences awaiting all of us, that can shape our aesthetic
criteria, not to mention logical insights which can help us better
express our aesthetic goals in mathematical or other more 'universal'
terms. I have learned much in my seven years on this list along all
of these lines, and it is my hope that you, a fine musician, will
stick around long enough for some true sharing and growing to occur.

Yours,
Paul

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > Here is a comparison of Sault's Dodekaphone vs Ellis' Duodene:
> >
> > Sault: 6 6/5's 7 5/4's 9 3/2's, for a total of 22
> > Ellis: 6 6/5's 8 5/4's 9 3/2's for a total of 23
> >
> > Sault: 5 major triads 6 minor triads for a total of 11
> > Ellis: 6 major triads 6 minor triads for a total of 12
> >
> > The advantage appears to be with Ellis, and the Duodene to be a
> good
> > thing to keep in mind when testing claims about the unique
> excellence
> > of the Dodekaphone.

I see what you are doing now. You are quite arbitrarily giving triads
greater importance than melodic steps. You are also only allowing for
a single 'tritone'. It is important in that respect to remember that
the tritone actually occurs only in Equal Temperament. In Just
Intonation there is theoretically a pair at that position of the
scale - the Augmented 4th and the Diminished 5th. In practice
instruments cannot be set up to play both and with continuous
spectrum instruments such as the violin no performer can accurately
play both.

Here are my counts of all correlative intervals, employing both Aug
4th and Dim 5th:-

Semitones 8
Tones 7
m3rds 6
M3rds 8
P4ths 10
+4ths 6
-5ths 6
P5ths 10
m6ths 8
M6ths 6
m7ths 7
M7ths 8

There are additionally, of course, 12 unisons and 12 P8ves. Please
also note the symmetry.

Now would you please provide a *full* set of figures for the Ellis
set of vibration ratios.

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

>
> But Peter's criterion isn't consonances, it's "correlations",
> the number of intervals that are also in the scale.
>

Quite right.

> Peter, in your application NATURAL, you seem to be insisting
> on inversion symmetry. That is, if I change the 10th degree
> from 9:16 to 9:5, the 2nd degree changes from 8:9 to 9:10.
> So you can't test scales like Ellis' Duodene.
>

Also quite right. That occurred to me while I was responding to Gene
(see 'A Recount') and I may open up the program to allow asymmetry
(in all positions) so that you can indeed test Ellis' set for
correlations.

> By the way Alexander Ellis was a great music theorist, who
> translated Helmholtz's On The Sensations of Tone into English
> and provided extensive footnotes. I'm sure you'd love this
> text. It is basically where our (in this community) literature
> starts.
>
> -Carl

I have a copy of Helmholtz' book. It is currently buried in one of
twelve boxes where it and most of my other books have been since 1998
when I moved to the USA. I came back to England as a consequence of
9/11, having watched the Towers fall, having never unpacked my books.
I really must put up some shelves...

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > Here is a comparison of Sault's Dodekaphone vs Ellis' Duodene:
> >
> > Sault: 6 6/5's 7 5/4's 9 3/2's, for a total of 22
> > Ellis: 6 6/5's 8 5/4's 9 3/2's for a total of 23
> >
> > Sault: 5 major triads 6 minor triads for a total of 11
> > Ellis: 6 major triads 6 minor triads for a total of 12
> >
> > The advantage appears to be with Ellis, and the Duodene to be a
> good
> > thing to keep in mind when testing claims about the unique
> excellence
> > of the Dodekaphone.
>
> Other important 12-tone just scales with a prime limit of 5 include
> those of De Caus and Ramos. But 12-tone 5-limit just scales were
> virtually irrelevant to the history of Western music. One finds
> instead Pythagorean prior to 1420, schismic between 1420 and 1470,
> meantone from 1470 to 1770, and closed 12-tone temperaments
> thereafter (as well as earlier with Bach, etc.) . . . Meanwhile,
when
> making music with computers today, we have the capacity to realize
> adaptive tuning systems which bring more chords into vertical
purity
> than would be possible with any fixed system of tuning. I think all
> these things are important to keep in mind when making such
> assertions, and of course the idea that 12 is necessary -- I won't
> even go there (having just performed a moving and well-received
> session with an Armenian musician last night) . . .

I have been to well-received didgeridoo concerts. However, IMHO
nothing (yet) beats a good symphony - *live*. There is no way you can
verify the lasting value of your (or any contemporary) performance
unless medical technology can keep you alive for another 100 years or
more. If people buy copies of recordings of it after that much time
then you will know you were right. This is the predicament that all
of us are in - time, lots of it, is the only judge. People used to
love Benny Goodman, but would *you* buy a recording of it?

🔗Carl Lumma <ekin@lumma.org>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

🔗Gene Ward Smith <gwsmith@svpal.org>

The first criterion--counting the number of consonant intervals--is
the very one you proposed yourself. Double 22 and you get 44 for you;
double 23 and you get 46 for Ellis. After that I do a count of
triads, which seems like a reasonable thing to want to count. The
Duodene has an extra major triad compared to the Dodekaphone.

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Carl Lumma <ekin@lumma.org>

>Oooh - yes please. I would like to see such lattices. Where did Ellis
>himself document all this? Seems to me I should read it.

I actually haven't read Ellis, though I have a copy. I'm not sure
if he did use lattices. But here's how we'd lattice his scale around
here:

5/3-------5/4------15/8------45/32
/ \ / \ / \ /
/ \ / \ / \ /
/ \ / \ / \ /
/ \ / \ / \ /
4/3-------1/1-------3/2-------9/8
/ \ / \ / \ /
/ \ / \ / \ /
/ \ / \ / \ /
/ \ / \ / \ /
16/15------8/5-------6/5-------9/5

You can see that / stands for 5:4, \ 6:5, and - 3:2. Major triads
are then point-up triangles, and minor triads are point-down.

Here's your scale:

5/3-------5/4------15/8------45/32
/ \ / \ / \ /
/ \ / \ / \ /
/ \ / \ / \ /
/ \ / \ / \ /
16/9-------4/3-------1/1-------3/2-------9/8
\ / \ / \ /
\ / \ / \ /
\ / \ / \ /
\ / \ / \ /
16/15------8/5-------6/5

Unfortunately, Yahoo's web interface doesn't display spaces
correctly. I get around this by receiving the list by e-mail.
If you don't want a flood of e-mails, you can Forward just
those messages with lattices in them from the web interface.

Cheers!

-Carl

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Carl Lumma <ekin@lumma.org>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> I see what you are doing now. You are quite arbitrarily giving
triads
> greater importance than melodic steps.

You lost me. I thought we were talking about harmony. Bt what
criterion do you propose judging melodic steps? Scala will give a lot
of scale information.

You are also only allowing for
> a single 'tritone'.

If you want two tritones, we get 13-note non-epimorphic scales, which
is another kettle of fish altogether.

It is important in that respect to remember that
> the tritone actually occurs only in Equal Temperament.

The interval of sqrt(2) occurs in any equal division with an even
number of steps--eg, 22 or 34.

In Just
> Intonation there is theoretically a pair at that position of the
> scale - the Augmented 4th and the Diminished 5th. In practice
> instruments cannot be set up to play both and with continuous
> spectrum instruments such as the violin no performer can accurately
> play both.

In which case, you must pick one and we are back to twelve notes.

> Now would you please provide a *full* set of figures for the Ellis
> set of vibration ratios.

The Duodene is a 12-note scale; it makes no sense to compare it to a
13-note scale. However you don't seem to be committing yourself to
either a 12-note scale or a 13-note scale--which is it?

🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> But Peter's criterion isn't consonances, it's "correlations",
> >> the number of intervals that are also in the scale.
> >
> >In that case I'd suggest a Pythagorean scale of 12 notes.
>
> And if we want pure 5-limit JI?

Eh? 3-limit JI is 5-limit JI.

> It seems that on the 5-limit lattice, to get the most correlations
> we want any vector between pitches to also connect 1/1 and a pitch.

I gave a list a while back of things contained in a fixed radius
under the metric making 3 and 5 symmetrical--the triangular lattice
metric. Those should be good, if you don't care about being
epimorphic.

> So what shape does that best? Any convex shape? It does seem we
> want to minimize the perimeter, and center the thing over 1/1 (which
> means inversional symmetry).

Why center on 1, and not eg 1-3-5?

🔗Carl Lumma <ekin@lumma.org>

Yes, but you know what I meant.

>> It seems that on the 5-limit lattice, to get the most correlations
>> we want any vector between pitches to also connect 1/1 and a pitch.
>
>I gave a list a while back of things contained in a fixed radius
>under the metric making 3 and 5 symmetrical--the triangular lattice
>metric. Those should be good, if you don't care about being
>epimorphic.

From monz's dictionary...

"A scale has the epimorphic property, or is epimorphic, if there is a
val h such that if qn is the nth scale degree, then h(qn)=n. The val
h is the characterizing val of the scale."

qn here is just a variable, right, not something times n?

>> So what shape does that best? Any convex shape? It does seem we
>> want to minimize the perimeter, and center the thing over 1/1 (which
>> means inversional symmetry).
>
>Why center on 1, and not eg 1-3-5?

Because the set of things you're trying to correlate with is
measured from 1/1.

-Carl

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Carl Lumma <ekin@lumma.org>

>> Some of the best 20th-century music happens to be rock.
>
>Fer example?

Most any of the stuff coming out of England in the early
70's often known as "progressive rock". It brought the
power of rock instrumentation (a chamber ensemble often
containing more than one polyphonic instrument, a bass
instrument more expressive than anything that had come
before, and a chorus singing in 2, 3, and occasionally
4-part harmony) to bear on music of a depth and complexity
equal to that of classical music. The Beatles kicked it
off with their late works, and were followed by Yes and
others, while bands like King Crimson and ELP took a harder,
less vocal approach. The Canadian band Rush took more of
a heavy metal approach (though I don't think the term
heavy metal had been invented), while American bands like
the Grateful Dead and Phish were influenced by bluegrass
and jazz. Perhaps most odd of all (and one of my favs)
were Gentle Giant, who combined early music and polyrhythms
in a psychedelic freeforall.

-Carl

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Oooh - yes please. I would like to see such lattices. Where did
Ellis
> >himself document all this? Seems to me I should read it.
>
> I actually haven't read Ellis, though I have a copy. I'm not sure
> if he did use lattices. But here's how we'd lattice his scale
around
> here:
>
> 5/3-------5/4------15/8------45/32
> / \ / \ / \ /
> / \ / \ / \ /
> / \ / \ / \ /
> / \ / \ / \ /
> 4/3-------1/1-------3/2-------9/8
> / \ / \ / \ /
> / \ / \ / \ /
> / \ / \ / \ /
> / \ / \ / \ /
> 16/15------8/5-------6/5-------9/5
>
> You can see that / stands for 5:4, \ 6:5, and - 3:2. Major triads
> are then point-up triangles, and minor triads are point-down.
>
> Here's your scale:
>
>
> 5/3-------5/4------15/8------45/32
> / \ / \ / \ /
> / \ / \ / \ /
> / \ / \ / \ /
> / \ / \ / \ /
> 16/9-------4/3-------1/1-------3/2-------9/8
> \ / \ / \ /
> \ / \ / \ /
> \ / \ / \ /
> \ / \ / \ /
> 16/15------8/5-------6/5
>
> Unfortunately, Yahoo's web interface doesn't display spaces
> correctly. I get around this by receiving the list by e-mail.
> If you don't want a flood of e-mails, you can Forward just
> those messages with lattices in them from the web interface.
>
> Cheers!
>
> -Carl

Funnily enough it displays perfectly in the 'Reply' textbox - I'm
looking at it now as it should be. So I have copied'n'pasted it into
Notepad, where I always use Courier font anyway for precisely this
reason. Now I can print it too.

I think I have a little bit of a learning curve on this one. I need
to stare at it blankly for a while. I've never seen one of these
before.

Thanks ever so for doing that.

Peter

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > >> But Peter's criterion isn't consonances, it's "correlations",
> > >> the number of intervals that are also in the scale.
> > >
> > >In that case I'd suggest a Pythagorean scale of 12 notes.
> >
> > And if we want pure 5-limit JI?
> >
> > It seems that on the 5-limit lattice, to get the most correlations
> > we want any vector between pitches to also connect 1/1 and a pitch.
> > So what shape does that best? Any convex shape? It does seem we
> > want to minimize the perimeter, and center the thing over 1/1 (which
> > means inversional symmetry).
> >
> > -Carl

> You're losing me because of unfamiliar terms. What do you mean by
> a '5-limit JI'? (I know what JI is).

We just had an argument over that very question, but in this case Carl
means intervals of the form 2^a 3^b 5^c where a,b,c are integers. The
"5-limit lattice" is what you get by reducing mod octaves. "Lattice"
is another term we argue about, but in this case Carl seems to want it
to be the equilateral triangular lattice. If 3^a1 5^a2 is one 5-limit
odd ratio and 3^b1 5^b2 is another, then we get this lattice if we
measure distances between 5-limit odd ratios according to

sqrt((a1-b1)^2 + (a1-b1)(a2-b2) + (a2-b2)^2)

> Can these lattices be extended into 3D or even 4D?

They can extend to any dimension, but since 3^2 < 11, when we go to
the 11-limit and beyond looking at them symmetrically makes less
sense. However, it is quite nice for the 5 and 7 limits.

Do they wrap?

Only if you reduce them according to some "commas"; that is, for
instance, by assuming that 81/80 counts as 1 and wrapping everything
into a cylinder.

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

> If you want two tritones, we get 13-note non-epimorphic scales,
which
> is another kettle of fish altogether.
>

Well now, fish are definitely non-epimorphic.

> It is important in that respect to remember that
> > the tritone actually occurs only in Equal Temperament.
>
> The interval of sqrt(2) occurs in any equal division with an even
> number of steps--eg, 22 or 34.
>
> In Just
> > Intonation there is theoretically a pair at that position of the
> > scale - the Augmented 4th and the Diminished 5th. In practice
> > instruments cannot be set up to play both and with continuous
> > spectrum instruments such as the violin no performer can
accurately
> > play both.
>
> In which case, you must pick one and we are back to twelve notes.
>
> > Now would you please provide a *full* set of figures for the
Ellis
> > set of vibration ratios.
>
> The Duodene is a 12-note scale; it makes no sense to compare it to
a
> 13-note scale. However you don't seem to be committing yourself to
> either a 12-note scale or a 13-note scale--which is it?

There is a certain ambiguity, I will admit. It's arithmetically a 13-
interval scale where two of the intervals are so close, ear-wise, as
to be virtually indistinguishable. You must accept that there can
only be a single tritone in ET. Even if you only quote a single ratio
for pitch 6, you are implying two intervals whether you like it or
not. If I say that the interval from pitch 0 to pitch 6 is 45:64,
then what is the interval from pitch 6 to pitch 12? It is *not*
45:64. It is in fact the quotient of 1:2 divided by 45:64

1:2 / 45:64 = 1:2 x 64:45 = 64:90 = 32:45 Q.E.D.

This is inescapable. Let's just say it's a 12½ note scale.

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

>
> > You're losing me because of unfamiliar terms. What do you mean by
> > a '5-limit JI'? (I know what JI is).
>
> We just had an argument over that very question, but in this case
Carl
> means intervals of the form 2^a 3^b 5^c where a,b,c are integers.
The
> "5-limit lattice" is what you get by reducing mod octaves. "Lattice"
> is another term we argue about, but in this case Carl seems to want
it
> to be the equilateral triangular lattice. If 3^a1 5^a2 is one 5-
limit
> odd ratio and 3^b1 5^b2 is another, then we get this lattice if we
> measure distances between 5-limit odd ratios according to
>
> sqrt((a1-b1)^2 + (a1-b1)(a2-b2) + (a2-b2)^2)
>
> > Can these lattices be extended into 3D or even 4D?
>
> They can extend to any dimension, but since 3^2 < 11, when we go to
> the 11-limit and beyond looking at them symmetrically makes less
> sense. However, it is quite nice for the 5 and 7 limits.
>
> Do they wrap?
>
> Only if you reduce them according to some "commas"; that is, for
> instance, by assuming that 81/80 counts as 1 and wrapping everything
> into a cylinder.

Interesting. I shall have to play with these things a bit to get
familiar.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> There is a certain ambiguity, I will admit. It's arithmetically a
13-
> interval scale where two of the intervals are so close, ear-wise,
as
> to be virtually indistinguishable.

You must accept that there can
> only be a single tritone in ET.

Why must I accept that? In 19-et, a fifth is 11 steps, and so a tone
is 22-19 = 3 steps. Three of these gives a tritone of 9 steps, but we
also have 19-9 = 10 steps.

Even if you only quote a single ratio
> for pitch 6, you are implying two intervals whether you like it or
> not. If I say that the interval from pitch 0 to pitch 6 is 45:64,
> then what is the interval from pitch 6 to pitch 12? It is *not*
> 45:64. It is in fact the quotient of 1:2 divided by 45:64
>
> 1:2 / 45:64 = 1:2 x 64:45 = 64:90 = 32:45 Q.E.D.
>
> This is inescapable. Let's just say it's a 12½ note scale.

Any system where 45/32 is not the same as 65/45, which is to say any
system where the "comma" 2048/2025 is not identified with 1, will
have this property.

🔗Aaron K. Johnson <akjmicro@comcast.net>

Carl-

I love Gentle Giant!!!

We have the same taste-love Yes too. And was a "Rush head" for a while.

"Yessongs" is one of the great rock live albums.

-Aaron.

Sorry to be off topic. Oh hell-we're just talking 12-tet, that's all!

On Friday 05 December 2003 07:11 pm, Carl Lumma wrote:
> >> Some of the best 20th-century music happens to be rock.
> >
> >Fer example?
>
> Most any of the stuff coming out of England in the early
> 70's often known as "progressive rock". It brought the
> power of rock instrumentation (a chamber ensemble often
> containing more than one polyphonic instrument, a bass
> instrument more expressive than anything that had come
> before, and a chorus singing in 2, 3, and occasionally
> 4-part harmony) to bear on music of a depth and complexity
> equal to that of classical music. The Beatles kicked it
> off with their late works, and were followed by Yes and
> others, while bands like King Crimson and ELP took a harder,
> less vocal approach. The Canadian band Rush took more of
> a heavy metal approach (though I don't think the term
> heavy metal had been invented), while American bands like
> the Grateful Dead and Phish were influenced by bluegrass
> and jazz. Perhaps most odd of all (and one of my favs)
> were Gentle Giant, who combined early music and polyrhythms
> in a psychedelic freeforall.
>
> -Carl
>
>
>
> You do not need web access to participate. You may subscribe through
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--
OCEAN, n. A body of water occupying about two-thirds of a world made
for man -- who has no gills. -Ambrose Bierce 'The Devils Dictionary'

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
>
> > There is a certain ambiguity, I will admit. It's arithmetically a
> 13-
> > interval scale where two of the intervals are so close, ear-wise,
> as
> > to be virtually indistinguishable.
>
>
> You must accept that there can
> > only be a single tritone in ET.
>
> Why must I accept that? In 19-et, a fifth is 11 steps, and so a
tone
> is 22-19 = 3 steps. Three of these gives a tritone of 9 steps, but
we
> also have 19-9 = 10 steps.

Have you actually created any music using a 19 note equal-tempered
scale? If so then I would like to hear it. If not then we are
entering the realm of angels on a pinhead.

>
> Even if you only quote a single ratio
> > for pitch 6, you are implying two intervals whether you like it
or
> > not. If I say that the interval from pitch 0 to pitch 6 is 45:64,
> > then what is the interval from pitch 6 to pitch 12? It is *not*
> > 45:64. It is in fact the quotient of 1:2 divided by 45:64
> >
> > 1:2 / 45:64 = 1:2 x 64:45 = 64:90 = 32:45 Q.E.D.
> >
> > This is inescapable. Let's just say it's a 12½ note scale.
>
> Any system where 45/32 is not the same as 65/45, which is to say
any
> system where the "comma" 2048/2025 is not identified with 1, will
> have this property.

Precisely.

- Peter

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗monz <monz@attglobal.net>

hi Peter,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > >Oooh - yes please. I would like to see such lattices. Where did
> Ellis
> > >himself document all this? Seems to me I should read it.
> >
> > I actually haven't read Ellis, though I have a copy. I'm not sure
> > if he did use lattices. But here's how we'd lattice his scale
> around
> > here:
> >
> > 5/3-------5/4------15/8------45/32
> > / \ / \ / \ /
> > / \ / \ / \ /
> > / \ / \ / \ /
> > / \ / \ / \ /
> > 4/3-------1/1-------3/2-------9/8
> > / \ / \ / \ /
> > / \ / \ / \ /
> > / \ / \ / \ /
> > / \ / \ / \ /
> > 16/15------8/5-------6/5-------9/5
> >
> > You can see that / stands for 5:4, \ 6:5, and - 3:2. Major triads
> > are then point-up triangles, and minor triads are point-down.
> >
> > Here's your scale:
> >
> >
> > 5/3-------5/4------15/8------45/32
> > / \ / \ / \ /
> > / \ / \ / \ /
> > / \ / \ / \ /
> > / \ / \ / \ /
> > 16/9-------4/3-------1/1-------3/2-------9/8
> > \ / \ / \ /
> > \ / \ / \ /
> > \ / \ / \ /
> > \ / \ / \ /
> > 16/15------8/5-------6/5
> >
> > Unfortunately, Yahoo's web interface doesn't display spaces
> > correctly. I get around this by receiving the list by e-mail.
> > If you don't want a flood of e-mails, you can Forward just
> > those messages with lattices in them from the web interface.
> >
> > Cheers!
> >
> > -Carl
>
> Funnily enough it displays perfectly in the 'Reply' textbox - I'm
> looking at it now as it should be. So I have copied'n'pasted it
into
> Notepad, where I always use Courier font anyway for precisely this
> reason. Now I can print it too.
>
> I think I have a little bit of a learning curve on this one. I need
> to stare at it blankly for a while. I've never seen one of these
> before.
>
> Thanks ever so for doing that.
>
> Peter

you might want to take a look at my webpages about
lattice-diagrams:

http://sonic-arts.org/dict/lattice.htm
http://sonic-arts.org/monzo/lattices/lattices.htm

but be forwarned that i use a specific lattice formula
of my own ("Monzo lattice") in the diagrams on my webpage.
at the bottom of the Dictionary page you can see an
explanation of the kind of "triangular" ASCII lattice
that Carl used in his post.

my company (Tonalsoft) is currently developing software
for music composition (under Windows) which is based
on the use of lattice-diagrams for the tunings. it
will allow the user to create any tuning he/she wishes
and to mix different tunings in a piece.

the first release of the software will be using another
different formula for lattices, but eventually we will
incorporate all of the usual formulae.

we hope to have the beta release out around February, and
commercial release 1.0 sometime in 2004.

-monz

🔗monz <monz@attglobal.net>

🔗John A. deLaubenfels <jdl@adaptune.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Carl Lumma <ekin@lumma.org>

>> Here's your scale:
>>
>>
>> 5/3-------5/4------15/8------45/32
>> / \ / \ / \ /
>> / \ / \ / \ /
>> / \ / \ / \ /
>> / \ / \ / \ /
>> 16/9-------4/3-------1/1-------3/2-------9/8
>> \ / \ / \ /
>> \ / \ / \ /
>> \ / \ / \ /
>> \ / \ / \ /
>> 16/15------8/5-------6/5
>
>So I have copied'n'pasted it into
>Notepad, where I always use Courier font anyway for precisely this
>reason.

Good show! I do the same.

>I think I have a little bit of a learning curve on this one. I need
>to stare at it blankly for a while. I've never seen one of these
>before.

Sometimes this helps...

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

-Carl

🔗Carl Lumma <ekin@lumma.org>

>> >> But Peter's criterion isn't consonances, it's "correlations",
>> >> the number of intervals that are also in the scale.
>> >
>> >In that case I'd suggest a Pythagorean scale of 12 notes.
>>
>> And if we want pure 5-limit JI?
>>
>> It seems that on the 5-limit lattice, to get the most correlations
>> we want any vector between pitches to also connect 1/1 and a pitch.
>> So what shape does that best? Any convex shape? It does seem we
>> want to minimize the perimeter, and center the thing over 1/1 (which
>> means inversional symmetry).
>>
>> -Carl
>
>You're losing me because of unfamiliar terms.

This was mainly directed at Gene.

>What do you mean by a '5-limit JI'? (I know what JI is).

Many of the terms you'll see here have definitions in Joe Monzo's
excellent dictionary...

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

In this case, look under "limit", I think. Anyway, just before
you joined there was a huge thread here about the definition of
"limit", with the conclusion apparently being that it's a very
confusing terminology, even for experts.

>Can these lattices be extended into 3D or even 4D?

Oh yes. Usually by going above the 5-limit (admitting ratios
of 7, 11, etc. as consonances).

>Do they wrap?

Not usually, if I understand your question.

-Carl

🔗Carl Lumma <ekin@lumma.org>

>> Why must I accept that? In 19-et, a fifth is 11 steps, and so a
>> tone is 22-19 = 3 steps. Three of these gives a tritone of 9 steps,
>> but we also have 19-9 = 10 steps.
>
>Have you actually created any music using a 19 note equal-tempered
>scale? If so then I would like to hear it. If not then we are
>entering the realm of angels on a pinhead.

Peter, unbeknownst to most of the human race, there's a growing
body of staggeringly-good 19-tone music out there. I strongly
recommend Easley Blackwood's and Neil Haverstick's efforts, as
linked to from my web page...

http://lumma.org

On the internet, our own Aaron Johnson has a piece which never fails
to knock my socks off...

http://www.aaronandlorna.com/audio/juggler.mp3 (2.5mb)

Also, note that the "1/3-comma meantone" of Rameau (and popular
in Europe during the meantone era) closes very nearly after 19
tones. So nearly that 19-tET is indistinguishable from 1/3-comma
meantone (it has Just minor thirds). So what has a wolf in 12
has none in 19!

-Carl

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>

/tuning/topicId_49104.html#49153

wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > >Oooh - yes please. I would like to see such lattices. Where did
> Ellis
> > >himself document all this? Seems to me I should read it.
> >
> > I actually haven't read Ellis, though I have a copy. I'm not sure
> > if he did use lattices. But here's how we'd lattice his scale
> around
> > here:
> >
> > 5/3-------5/4------15/8------45/32
> > / \ / \ / \ /
> > / \ / \ / \ /
> > / \ / \ / \ /
> > / \ / \ / \ /
> > 4/3-------1/1-------3/2-------9/8
> > / \ / \ / \ /
> > / \ / \ / \ /
> > / \ / \ / \ /
> > / \ / \ / \ /
> > 16/15------8/5-------6/5-------9/5
> >
> > You can see that / stands for 5:4, \ 6:5, and - 3:2. Major triads
> > are then point-up triangles, and minor triads are point-down.
> >
> > Here's your scale:
> >
> >
> > 5/3-------5/4------15/8------45/32
> > / \ / \ / \ /
> > / \ / \ / \ /
> > / \ / \ / \ /
> > / \ / \ / \ /
> > 16/9-------4/3-------1/1-------3/2-------9/8
> > \ / \ / \ /
> > \ / \ / \ /
> > \ / \ / \ /
> > \ / \ / \ /
> > 16/15------8/5-------6/5
> >
> > Unfortunately, Yahoo's web interface doesn't display spaces
> > correctly. I get around this by receiving the list by e-mail.
> > If you don't want a flood of e-mails, you can Forward just
> > those messages with lattices in them from the web interface.
> >
> > Cheers!
> >
> > -Carl
>
> Funnily enough it displays perfectly in the 'Reply' textbox - I'm
> looking at it now as it should be. So I have copied'n'pasted it
into
> Notepad, where I always use Courier font anyway for precisely this
> reason. Now I can print it too.
>
> I think I have a little bit of a learning curve on this one. I need
> to stare at it blankly for a while. I've never seen one of these
> before.
>
> Thanks ever so for doing that.
>
> Peter

***Peter, you just stumbled into the perfect solution to our list
woes! We just hit *reply* and copy the text... we don't even have to
send the mail to ourselves to get the correct lattices.

Thanks so much!

Joseph Pehrson

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Peter,
>
>
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
> > --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > > >Oooh - yes please. I would like to see such lattices. Where
did
> > Ellis
> > > >himself document all this? Seems to me I should read it.
> > >
> > > I actually haven't read Ellis, though I have a copy. I'm not
sure
> > > if he did use lattices. But here's how we'd lattice his scale
> > around
> > > here:
> > >
> > > 5/3-------5/4------15/8------45/32
> > > / \ / \ / \ /
> > > / \ / \ / \ /
> > > / \ / \ / \ /
> > > / \ / \ / \ /
> > > 4/3-------1/1-------3/2-------9/8
> > > / \ / \ / \ /
> > > / \ / \ / \ /
> > > / \ / \ / \ /
> > > / \ / \ / \ /
> > > 16/15------8/5-------6/5-------9/5
> > >
> > > You can see that / stands for 5:4, \ 6:5, and - 3:2. Major
triads
> > > are then point-up triangles, and minor triads are point-down.
> > >
> > > Here's your scale:
> > >
> > >
> > > 5/3-------5/4------15/8------45/32
> > > / \ / \ / \ /
> > > / \ / \ / \ /
> > > / \ / \ / \ /
> > > / \ / \ / \ /
> > > 16/9-------4/3-------1/1-------3/2-------9/8
> > > \ / \ / \ /
> > > \ / \ / \ /
> > > \ / \ / \ /
> > > \ / \ / \ /
> > > 16/15------8/5-------6/5
> > >
> > > Unfortunately, Yahoo's web interface doesn't display spaces
> > > correctly. I get around this by receiving the list by e-mail.
> > > If you don't want a flood of e-mails, you can Forward just
> > > those messages with lattices in them from the web interface.
> > >
> > > Cheers!
> > >
> > > -Carl
> >
> > Funnily enough it displays perfectly in the 'Reply' textbox - I'm
> > looking at it now as it should be. So I have copied'n'pasted it
> into
> > Notepad, where I always use Courier font anyway for precisely
this
> > reason. Now I can print it too.
> >
> > I think I have a little bit of a learning curve on this one. I
need
> > to stare at it blankly for a while. I've never seen one of these
> > before.
> >
> > Thanks ever so for doing that.
> >
> > Peter
>
>
>
> you might want to take a look at my webpages about
> lattice-diagrams:
>
> http://sonic-arts.org/dict/lattice.htm
> http://sonic-arts.org/monzo/lattices/lattices.htm
>
> but be forwarned that i use a specific lattice formula
> of my own ("Monzo lattice") in the diagrams on my webpage.
> at the bottom of the Dictionary page you can see an
> explanation of the kind of "triangular" ASCII lattice
> that Carl used in his post.
>
>
>
> my company (Tonalsoft) is currently developing software
> for music composition (under Windows) which is based
> on the use of lattice-diagrams for the tunings. it
> will allow the user to create any tuning he/she wishes
> and to mix different tunings in a piece.
>
> the first release of the software will be using another
> different formula for lattices, but eventually we will
> incorporate all of the usual formulae.
>
> we hope to have the beta release out around February, and
> commercial release 1.0 sometime in 2004.
>
>
>
> -monz

Can I have an evaluation copy?

- Peter

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "John A. deLaubenfels" <jdl@a...>
wrote:
> >>Is deLaubenfel's algorthim spelled out precisely anywhere?
>
> >If you can get it, I can program it.
>
> It's spelled out on this list, at
/tuning/topicId_7890.html#7890 . I have forsworn
all protectionist actions (patents, etc.) and invite anyone and
everyone to use this model and to expand upon it.
>
> JdL
>
> http://www.adaptune.com

Hi John

I understand what you said in your post #7890 although I can't see
that it amounts to an algorithm for anything. You are in some way
paralleling the linear vs logarithmic (or arithmetic vs geometric)
nature of our consciousness - that a geometric progression of
vibration number gives us an arithmetic progression of pitch
sensation. And I agree with you that 'pain' is a perfectly good way
of describing the sensation of discord, although the term 'discord'
always was perfectly adequate for the purpose. Your words still make
perfect sense if 'discord' is substituted for 'pain'.

I have discovered that scales are not even needed for music per se.
Scales, like tunings, are a matter of the practicalities of playing
polytonal instruments, especially in concert with other musicians.

However, a sequence of pitches does not need a reference tone except
for dum-diddly-um-pum type melodies (please excuse my simplistic
rendition of Mozart et al.). All that is needed is that the
instantaneous experience of 'melody' relate back at least a few
seconds (abs max = 8 secs) - the duration of 'blind' memory.
Otherwise than that an aesthetic progression of notes need only
relate to the preceding notes by harmonious intervals. I will record
a sample for you to listen to as soon as I have got my old 486 out of
its box and connected up again - my ancient demo software for this
stuff is DOS-only and plays the PC speaker because that was and still
is the only way I can produce tones by frequency. Perhaps someday it
will occur to the geniuses who produce synthesizers that vibration
number is infinitely more rational than 'cents'.

As I have already announced elsewhere in my usual arrogant manner I
am not going to waste so much as a second of my life dealing
with 'cents' up or down from concert tunings. Give it to me as
vibration numbers or frequency ratios - or keep it to yourself.
That's my attitude and I'm sticking to it.

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Here's your scale:
> >>
> >>
> >> 5/3-------5/4------15/8------45/32
> >> / \ / \ / \ /
> >> / \ / \ / \ /
> >> / \ / \ / \ /
> >> / \ / \ / \ /
> >> 16/9-------4/3-------1/1-------3/2-------9/8
> >> \ / \ / \ /
> >> \ / \ / \ /
> >> \ / \ / \ /
> >> \ / \ / \ /
> >> 16/15------8/5-------6/5
> >
> >So I have copied'n'pasted it into
> >Notepad, where I always use Courier font anyway for precisely this
> >reason.
>
> Good show! I do the same.
>
> >I think I have a little bit of a learning curve on this one. I
need
> >to stare at it blankly for a while. I've never seen one of these
> >before.
>
> Sometimes this helps...
>
> >> A---------E---------B--------F#
> >> / \ / \ / \ /
> >> / \ / \ / \ /
> >> / \ / \ / \ /
> >> / \ / \ / \ /
> >> Bb---------F---------C---------G---------D
> >> \ / \ / \ /
> >> \ / \ / \ /
> >> \ / \ / \ /
> >> \ / \ / \ /
> >> Db--------Ab---------Eb
>
> -Carl

Indeed - and thankyou for it. Here is my version of the same thing:-

9---------4---------11--------6
/ \ / \ / \ /
/ \ / \ / \ /
/ \ / \ / \ /
/ \ / \ / \ /
10---------5---------0---------7---------2
\ / \ / \ /
\ / \ / \ /
\ / \ / \ /
\ / \ / \ /
1----------8---------3

I love numbers. No way can I go back to all those letters and
accidentals now.

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >> But Peter's criterion isn't consonances, it's "correlations",
> >> >> the number of intervals that are also in the scale.
> >> >
> >> >In that case I'd suggest a Pythagorean scale of 12 notes.
> >>
> >> And if we want pure 5-limit JI?
> >>
> >> It seems that on the 5-limit lattice, to get the most
correlations
> >> we want any vector between pitches to also connect 1/1 and a
pitch.
> >> So what shape does that best? Any convex shape? It does seem we
> >> want to minimize the perimeter, and center the thing over 1/1
(which
> >> means inversional symmetry).
> >>
> >> -Carl
> >
> >You're losing me because of unfamiliar terms.
>
> This was mainly directed at Gene.
>
> >What do you mean by a '5-limit JI'? (I know what JI is).
>
> Many of the terms you'll see here have definitions in Joe Monzo's
> excellent dictionary...
>
> http://sonic-arts.org/dict/

Got that. Thankyou Joe.

>
> In this case, look under "limit", I think. Anyway, just before
> you joined there was a huge thread here about the definition of
> "limit", with the conclusion apparently being that it's a very
> confusing terminology, even for experts.
>
> >Can these lattices be extended into 3D or even 4D?
>
> Oh yes. Usually by going above the 5-limit (admitting ratios
> of 7, 11, etc. as consonances).
>
> >Do they wrap?
>
> Not usually, if I understand your question.
>
> -Carl

Bet they do. Gene says so. Bet I could build polyhedral versions.
Just give me some time...

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Why must I accept that? In 19-et, a fifth is 11 steps, and so a
> >> tone is 22-19 = 3 steps. Three of these gives a tritone of 9
steps,
> >> but we also have 19-9 = 10 steps.
> >
> >Have you actually created any music using a 19 note equal-tempered
> >scale? If so then I would like to hear it. If not then we are
> >entering the realm of angels on a pinhead.
>
> Peter, unbeknownst to most of the human race, there's a growing
> body of staggeringly-good 19-tone music out there. I strongly
> recommend Easley Blackwood's and Neil Haverstick's efforts, as
> linked to from my web page...
>
> http://lumma.org
>
> On the internet, our own Aaron Johnson has a piece which never fails
> to knock my socks off...
>
> http://www.aaronandlorna.com/audio/juggler.mp3 (2.5mb)
>

Impressive! Well done Aaron. I note it is contrapuntal - is it also
possible to generate chord progressions this way?

>
> Also, note that the "1/3-comma meantone" of Rameau (and popular
> in Europe during the meantone era) closes very nearly after 19
> tones. So nearly that 19-tET is indistinguishable from 1/3-comma
> meantone (it has Just minor thirds). So what has a wolf in 12
> has none in 19!

But why 19? Why not 18 (i.e. 6 tones each divided in 3 instead of 2)?
And how can anything that is ET contain anything that is Natural?
Surely they are mutually exclusive? Either each chromatic interval is
19th root 2 (ET) or it is a ratio of whole numbers ('Natural' - I
must say I restrict my use of 'Just' to mean natural dodekaphony for
reasons which are just too long-winded to go into here and now)? And
what principle does one use to generate melodic scales? Obviously it
cannot be transposed sequences of 5ths (or can it?) because one
cannot get 2:3 (1.5) from 19th root 2.

>
> -Carl

🔗monz <monz@attglobal.net>

hi Carl,

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > Carl-
> >
> > I love Gentle Giant!!!
> >
> > We have the same taste-love Yes too. And was a "Rush head"
> > for a while.
> >
> >"Yessongs" is one of the great rock live albums.
> >
> >-Aaron.
>
> And we're in good company here. Paul Erlich is a big fan
> of prog rock, and so is monz (at least of Yes and The Beatles).

Yes and the Beatles most of all ... and also Gentle Giant!

but i also like Rush, Bill Bruford's solo albums, King Crimson
(particularly the later stuff with Adrian Belew), Emerson Lake
and Palmer's classic work, and The Band (who usually aren't
put in this category but i definitely feel they belong here).

anything else on this should go to metatuning...

-monz

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> But why 19? Why not 18 (i.e. 6 tones each divided in 3 instead of
2)?

Two reasons--19 gives triads which are much better in tune, and 19 is
a meantone system.

> And how can anything that is ET contain anything that is Natural?
> Surely they are mutually exclusive?

At some point the difference becomes inaudible. The triads of 118 et
are already hard to tell apart from JI triads; the difficulty of
doing this of course keeps on increasing as we make finer divisions.

And
> what principle does one use to generate melodic scales?

Any principle you want--Aaron found his own way, but an obvious
starting point is simply the diatonic scale.

🔗Carl Lumma <ekin@lumma.org>

>> http://www.aaronandlorna.com/audio/juggler.mp3 (2.5mb)
>>
>
>Impressive! Well done Aaron. I note it is contrapuntal - is it also
>possible to generate chord progressions this way?

Oh yes. I'm sure you'll love Neil Haverstick's album Acoustic Stick.

>> Also, note that the "1/3-comma meantone" of Rameau (and popular
>> in Europe during the meantone era) closes very nearly after 19
>> tones. So nearly that 19-tET is indistinguishable from 1/3-comma
>> meantone (it has Just minor thirds). So what has a wolf in 12
>> has none in 19!
>
>But why 19? Why not 18 (i.e. 6 tones each divided in 3 instead of 2)?

It's this sort of question we have very good answers for around
here. It's 19 for the same reasons it's 12 and not 11 or 13.
Namely, good approximations to low-numbered Just ratios. This
doesn't mean fantastic music can't be written in 18. But if you
want to approximate Just intonation, it isn't as good of a choice
as 19.

>And how can anything that is ET contain anything that is Natural?

Define "Natural".

>Surely they are mutually exclusive? Either each chromatic interval
>is 19th root 2 (ET) or it is a ratio of whole numbers ('Natural' -
>I must say I restrict my use of 'Just' to mean natural dodekaphony
>for reasons which are just too long-winded to go into here and now)?

19-tET certainly involves irrational intervals, and it certainly
doesn't have 12 tones, so it fails your definition of Natural
completely. However, it better approximates (by most measures)
ratios through 5 than does 12-tET. In fact it has minor thirds
(6:5) that are aurally indistinguishable from Just under any
circumstances that matter.

You've mentioned several times on this list the term "ufology".
Forgive me if I find the practice of defining irrational numbers
to be less "natural" than rational ones to be pure ufology.

>And what principle does one use to generate melodic scales?

Generally any principle one likes. The diatonic scale exists in
19-tET in all its glory (indeed, this tuning of the diatonic scale
*predates* its tuning in 12-tET in Western music by a few hundred
years). Your path-finding method as used in your piece "Odeion
Natural No. 1-003" would certainly work in a Just system based on
19 tones instead of 12.

19 also contains many other interesting scales, including an
8-tone one discovered by yours truly, based on a chain of minor
thirds instead of a chain of fifths.

>Obviously it cannot be transposed sequences of 5ths (or can it?)
>because one cannot get 2:3 (1.5) from 19th root 2.

The 3:2 ratio measures very nearly 702 cents. Its nearest
approximation in 12-tET measures exactly 700 cents. Its nearest
approx. in 19-tET measures 695 cents. I miss the better fifths
of 12-tET when playing in 19, and the 9:8 is truly miserable (since
the error is compounded), but the major and minor thirds are quite
nice. And if you go out to 31-tET you get *really* nice triads.
And in 34-tET the major and minor triads sound completely Just in
most circumstances.

-Carl

🔗monz <monz@attglobal.net>

hi Peter,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> >
> > my company (Tonalsoft) is currently developing software
> > for music composition (under Windows) which is based
> > on the use of lattice-diagrams for the tunings. it
> > will allow the user to create any tuning he/she wishes
> > and to mix different tunings in a piece.
> >
> > the first release of the software will be using another
> > different formula for lattices, but eventually we will
> > incorporate all of the usual formulae.
> >
> > we hope to have the beta release out around February, and
> > commercial release 1.0 sometime in 2004.
> >
> >
> >
> > -monz
>
> Can I have an evaluation copy?
>
> - Peter

we have a very small handful of potential beta-testers in
mind, so i can't give you much hope for that ... but anyway,
it's still too early. all we have done so far is the tuning
and lattice stuff. we're only now beginning the music
composition coding.

-monz

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

> Define "Natural".

Ratios of whole numbers. Common harmonics. Birdsong. None of which
need be dodekaphonic, unlike (strictly speaking) JI.

>
> >Surely they are mutually exclusive? Either each chromatic interval
> >is 19th root 2 (ET) or it is a ratio of whole numbers ('Natural' -
> >I must say I restrict my use of 'Just' to mean natural dodekaphony
> >for reasons which are just too long-winded to go into here and
now)?
>
> 19-tET certainly involves irrational intervals, and it certainly
> doesn't have 12 tones, so it fails your definition of Natural
> completely. However, it better approximates (by most measures)
> ratios through 5 than does 12-tET. In fact it has minor thirds
> (6:5) that are aurally indistinguishable from Just under any
> circumstances that matter.
>
> You've mentioned several times on this list the term "ufology".
> Forgive me if I find the practice of defining irrational numbers
> to be less "natural" than rational ones to be pure ufology.

'Ufology', as it relates to music, is the business of tuning yourself
to phases of the Moon divided by the golden mean. You know the sort
of thing, I am sure.

>
> >And what principle does one use to generate melodic scales?
>
> Generally any principle one likes. The diatonic scale exists in
> 19-tET in all its glory (indeed, this tuning of the diatonic scale
> *predates* its tuning in 12-tET in Western music by a few hundred
> years). Your path-finding method as used in your piece "Odeion
> Natural No. 1-003" would certainly work in a Just system based on
> 19 tones instead of 12.
>
> 19 also contains many other interesting scales, including an
> 8-tone one discovered by yours truly, based on a chain of minor
> thirds instead of a chain of fifths.
>
> >Obviously it cannot be transposed sequences of 5ths (or can it?)
> >because one cannot get 2:3 (1.5) from 19th root 2.
>
> The 3:2 ratio measures very nearly 702 cents. Its nearest
> approximation in 12-tET measures exactly 700 cents. Its nearest
> approx. in 19-tET measures 695 cents. I miss the better fifths
> of 12-tET when playing in 19, and the 9:8 is truly miserable (since
> the error is compounded), but the major and minor thirds are quite
> nice. And if you go out to 31-tET you get *really* nice triads.
> And in 34-tET the major and minor triads sound completely Just in
> most circumstances.
>
> -Carl

Thanks for the explanation, Carl. That all makes perfect sense, if
not perfect 7s (ok, '5ths' if you must).

🔗Kurt Bigler <kkb@breathsense.com>

on 12/7/03 10:02 PM, Peter Wakefield Sault <sault@cyberware.co.uk> wrote:

> As I have already announced elsewhere in my usual arrogant manner I
> am not going to waste so much as a second of my life dealing
> with 'cents' up or down from concert tunings. Give it to me as
> vibration numbers or frequency ratios - or keep it to yourself.
> That's my attitude and I'm sticking to it.

Everyone is welcome to the atttitude they choose. However you may be making
a bigger thing out of it in advance of an actual *particular* need to
communicate in a specific focused area. When an actual need to communicate
comes up, the terms used will end up being negotiated on the fly. If one
person won't give, the other one perhaps will. If this becomes impractical
then the communication ends. This is something that may happen. It need
not be announced in advance with a lot of show. If it involves a genuine
difficulty on your part then everyone will be most glad to help you
translate things to terms you are familiar with. If you simply refuse to
experience difficulty while everyone else around you picks up the slack,
then you simply end relationship, and that is your choice. Relationships
where one side does all the work tend to be short-lived, except under
exceptional conditions.

All of us have similar preferences in various areas of terminology and ways
of thinking about things, though perhaps most of us feel in advance more
willingness to work on our side of the translation, rather than require
others to do all the translation for us. Nonetheless in many cases these
individual preferences can go almost unnoticed when things to communicate
are simply dealt with as they come up.

So I'm saying that arrogance is merely a style, which is perhaps what you
are also saying. When push comes to shove everyone will see how it turns
out. And it won't matter one whit to anyone here whether you forget
yourself one day and find that for some unforseen reason it suddenly becomes
worthwhile to know what cents means! ;) Heck have you ever incorrectly
predited your future choices? If not, then I suppose that means you never
learned anything. Perhaps in that case you were already born knowing what
you know now.

-Kurt

🔗Kurt Bigler <kkb@breathsense.com>

on 12/8/03 12:20 AM, Gene Ward Smith <gwsmith@svpal.org> wrote:

> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
>
>> But why 19? Why not 18 (i.e. 6 tones each divided in 3 instead of
> 2)?
>
> Two reasons--19 gives triads which are much better in tune, and 19 is
> a meantone system.
>
>> And how can anything that is ET contain anything that is Natural?
>> Surely they are mutually exclusive?
>
> At some point the difference becomes inaudible. The triads of 118 et
> are already hard to tell apart from JI triads; the difficulty of
> doing this of course keeps on increasing as we make finer divisions.
>
> And
>> what principle does one use to generate melodic scales?
>
> Any principle you want--Aaron found his own way, but an obvious
> starting point is simply the diatonic scale.

His original question might have been seen as a question for how to
construct a diatonic scale in 19-et. This is not something that everyone
knows about. (Personally I haven't learned it yet.) Perhaps it does have
to do with the circle of (tempered) 5ths after all, or perhaps only because
19-et is meantone?

-Kurt

🔗Carl Lumma <ekin@lumma.org>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Peter,
>
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
> > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > >
> > > my company (Tonalsoft) is currently developing software
> > > for music composition (under Windows) which is based
> > > on the use of lattice-diagrams for the tunings. it
> > > will allow the user to create any tuning he/she wishes
> > > and to mix different tunings in a piece.
> > >
> > > the first release of the software will be using another
> > > different formula for lattices, but eventually we will
> > > incorporate all of the usual formulae.
> > >
> > > we hope to have the beta release out around February, and
> > > commercial release 1.0 sometime in 2004.
> > >
> > >
> > >
> > > -monz
> >
> > Can I have an evaluation copy?
> >
> > - Peter
>
>
>
> we have a very small handful of potential beta-testers in
> mind, so i can't give you much hope for that ... but anyway,
> it's still too early. all we have done so far is the tuning
> and lattice stuff. we're only now beginning the music
> composition coding.
>

Have you heard the stuff pumped out by my software (which is now
nearly 20 years old)? Go to http://www.odeion.org/music and look for
ODEION Natural No.1-003

>
>
> -monz

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> /tuning/topicId_49104.html#49185
>
>
> > --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
<sault@c...>
> wrote:
> >
> > > Have you actually created any music using a 19 note equal-
> tempered
> > > scale? If so then I would like to hear it. If not then we are
> > > entering the realm of angels on a pinhead.
> >
> > There's plently of it available; in fact a url for nice piece was
> > posted here recently.
>
> ***Neil Haverstick is really the 19-tET maestro. There's no music
on
> his website, though, since he's very busy *SELLING* records.
> However, I found some mp3s here:
>
> http://www.guitar9.com/acousticstick.html
>
> J. Pehrson

Thanks for the link Joseph but I can't make any use of it. Can't
download anything because Mr. Haverstick is just too tight-arsed
about his stuff. Can't stream it because I'm on a dial-up connection
(I live in a remote English village - we might get broadband here by
the year 2103 - we're lucky to have telephone lines and electricity
and we probably have those only because of the USAF base up the road).

Can't make much of Johnny Reinhard's 'Ravening' - it's just a bit too
je ne sais quoi for my taste. I think I prefer Aaron's effort
('Juggler') - now that *is* good, despite the unfamiliar dissonances.

🔗Graham Breed <graham@microtonal.co.uk>

Peter Wakefield Sault wrote:

<snip>
> relate to the preceding notes by harmonious intervals. I will record > a sample for you to listen to as soon as I have got my old 486 out of > its box and connected up again - my ancient demo software for this > stuff is DOS-only and plays the PC speaker because that was and still > is the only way I can produce tones by frequency. Perhaps someday it > will occur to the geniuses who produce synthesizers that vibration > number is infinitely more rational than 'cents'.

If it uses the PC speaker, why were you talking about Sound Blaster dependency? Whatever, DOSEMU can use or emulate both:

http://dosemu.sourceforge.net/docs/README-tech/1.2/config.html#AEN885

http://dosemu.sourceforge.net/docs/README-tech/1.2/config.html#AEN989

http://dosemu.sourceforge.net/docs/HOWTO/x500.html#AEN534

Of course, the only way to know if it'll work with your program is to give it a try. Let me have your code and I'll see what I can do.

Graham

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

Carl wrote:
>I see nothing in the scale archive under wing* or
>chalmers*wing*.

load/all *wing* will do.

Peter wrote:
>Care to expand on that? What are the constituent vibration ratios?

Chalmers' Major Wing:
25/24 9/8 6/5 5/4 4/3 3/2 25/16 8/5 5/3 9/5 15/8 2/1
Chalmers' Minor Wing:
9/8 6/5 5/4 4/3 36/25 3/2 8/5 5/3 9/5 15/8 48/25 2/1

The music page of your website mentions that you'd like to
have your midi files in just intonation. You could retune them
with Scala. If you also install the scale archive, in C:\ for
example, then the Scala commands are like these:

load c:\scl\malcolm
example/midi myfile.mid myfile-ji.mid

But you can also use the menus.
See http://www.xs4all.nl/~huygensf/scala

Manuel

🔗Aaron K. Johnson <akjmicro@comcast.net>

On Monday 08 December 2003 01:28 am, Peter Wakefield Sault wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > >> Why must I accept that? In 19-et, a fifth is 11 steps, and so a
> > >> tone is 22-19 = 3 steps. Three of these gives a tritone of 9
>
> steps,
>
> > >> but we also have 19-9 = 10 steps.
> > >
> > >Have you actually created any music using a 19 note equal-tempered
> > >scale? If so then I would like to hear it. If not then we are
> > >entering the realm of angels on a pinhead.
> >
> > Peter, unbeknownst to most of the human race, there's a growing
> > body of staggeringly-good 19-tone music out there. I strongly
> > recommend Easley Blackwood's and Neil Haverstick's efforts, as
> > linked to from my web page...
> >
> > http://lumma.org
> >
> > On the internet, our own Aaron Johnson has a piece which never fails
> > to knock my socks off...
> >
> > http://www.aaronandlorna.com/audio/juggler.mp3 (2.5mb)
>
> Impressive! Well done Aaron. I note it is contrapuntal - is it also
> possible to generate chord progressions this way?

Thank you! Yes, chord progressions are possible....

> > Also, note that the "1/3-comma meantone" of Rameau (and popular
> > in Europe during the meantone era) closes very nearly after 19
> > tones. So nearly that 19-tET is indistinguishable from 1/3-comma
> > meantone (it has Just minor thirds). So what has a wolf in 12
> > has none in 19!
>
> But why 19? Why not 18 (i.e. 6 tones each divided in 3 instead of 2)?

19-tet has a very nearly pure minor third, a better approximation to a major
3rd than 12-tet, and a flatter fifth than et, but still functions and is
recognizable as such, just a bit more active.

18-tet has a 12-tet major third, a very much sharp minor third, and an
unusable for traditional harmony perfect fifth.

take your pick....if you want to do alien music, 18 works well ;)

> And how can anything that is ET contain anything that is Natural?

Hmm....it seems elsewhere that you defend 12-tet concerts and music.
'Naturalness' doesn't come in to your argument there! Or do I misunderstand
you?

> Surely they are mutually exclusive? Either each chromatic interval is
> 19th root 2 (ET) or it is a ratio of whole numbers ('Natural' - I
> must say I restrict my use of 'Just' to mean natural dodekaphony for
> reasons which are just too long-winded to go into here and now)? And
> what principle does one use to generate melodic scales? Obviously it
> cannot be transposed sequences of 5ths (or can it?) because one
> cannot get 2:3 (1.5) from 19th root 2.

Neither does one have 2:3 in 12-tet!!! each ET will have different
approximations to various important Just intervals....19-tet has a fifth with
a ratio of 1.49375896165449 as opposed to 1.5...perfectly listenable and
recognizable as a 'fifth', though a bit more active and insistent due to its
faster beating. It stands at 694.7368 cents as opposed to 700 cents for the
12-tet fifth (BTW, cents are a very good measure of the relative perceptual
fatness and sharpness of intervals, you plea for a ratios only approach
aside)

For the metaphysician, 19-tet is also justifiable as a being very closely
approximated by a chain of 19 just minor thirds. Try it! You could tune it by
ear...is that 'natural' enough for you? ;)

Best,
Aaron.

🔗Paul Erlich <paul@stretch-music.com>

🔗John A. deLaubenfels <jdl@adaptune.com>

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
wrote:

> Carl-
>
> I love Gentle Giant!!!
>
> We have the same taste-love Yes too.

I can sympathize completely.

You might like the current band Spock's Beard, influenced by both
bands. I'm not too crazy about them . . .

? And was a "Rush head" for a while.
>
> "Yessongs" is one of the great rock live albums.
>
> -Aaron.
>
> Sorry to be off topic. Oh hell-we're just talking 12-tet, that's
>all!

I confess to being a sometime prog-head myself. Dan Stearns, a list
member known for forward-thinking musical tastes, recommended the
current band Thinking Plague's _In Extremis_, influenced by Yes and
Henry Cow. It's challenging but I liked in on last listen.

Mostly I can't listen to prog-rock these days, too much jazz and
Eastern music in my input and output, but I must say no prog-rock fan
should go without checking out Gong and Focus. Egg is even more
obscure but worth it to seek out.

🔗Aaron K. Johnson <akjmicro@comcast.net>

On Monday 08 December 2003 09:22 am, Paul Erlich wrote:
> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
>
> wrote:
> > Carl-
> >
> > I love Gentle Giant!!!
> >
> > We have the same taste-love Yes too.
>
> I can sympathize completely.
>
> You might like the current band Spock's Beard, influenced by both
> bands. I'm not too crazy about them . . .
>
> ? And was a "Rush head" for a while.
>
> > "Yessongs" is one of the great rock live albums.
> >
> > -Aaron.
> >
> > Sorry to be off topic. Oh hell-we're just talking 12-tet, that's
> >all!
>
> I confess to being a sometime prog-head myself. Dan Stearns, a list
> member known for forward-thinking musical tastes, recommended the
> current band Thinking Plague's _In Extremis_, influenced by Yes and
> Henry Cow. It's challenging but I liked in on last listen.
>
> Mostly I can't listen to prog-rock these days, too much jazz and
> Eastern music in my input and output, but I must say no prog-rock fan
> should go without checking out Gong and Focus. Egg is even more
> obscure but worth it to seek out.

I love the names-very evocative !!!!

Maybe this should go to meta-tuning?

-Aaron.

🔗Aaron K. Johnson <akjmicro@comcast.net>

On Monday 08 December 2003 03:08 am, Kurt Bigler wrote:
> on 12/7/03 10:02 PM, Peter Wakefield Sault <sault@cyberware.co.uk> wrote:
> > As I have already announced elsewhere in my usual arrogant manner I
> > am not going to waste so much as a second of my life dealing
> > with 'cents' up or down from concert tunings. Give it to me as
> > vibration numbers or frequency ratios - or keep it to yourself.
> > That's my attitude and I'm sticking to it.
>
> Everyone is welcome to the atttitude they choose. However you may be
> making a bigger thing out of it in advance of an actual *particular* need
> to communicate in a specific focused area. When an actual need to
> communicate comes up, the terms used will end up being negotiated on the
> fly. If one person won't give, the other one perhaps will. If this
> becomes impractical then the communication ends. This is something that
> may happen. It need not be announced in advance with a lot of show. If it
> involves a genuine difficulty on your part then everyone will be most glad
> to help you translate things to terms you are familiar with. If you simply
> refuse to experience difficulty while everyone else around you picks up the
> slack, then you simply end relationship, and that is your choice.
> Relationships where one side does all the work tend to be short-lived,
> except under exceptional conditions.
>
> All of us have similar preferences in various areas of terminology and ways
> of thinking about things, though perhaps most of us feel in advance more
> willingness to work on our side of the translation, rather than require
> others to do all the translation for us. Nonetheless in many cases these
> individual preferences can go almost unnoticed when things to communicate
> are simply dealt with as they come up.
>
> So I'm saying that arrogance is merely a style, which is perhaps what you
> are also saying. When push comes to shove everyone will see how it turns
> out. And it won't matter one whit to anyone here whether you forget
> yourself one day and find that for some unforseen reason it suddenly
> becomes worthwhile to know what cents means! ;) Heck have you ever
> incorrectly predited your future choices? If not, then I suppose that
> means you never learned anything. Perhaps in that case you were already
> born knowing what you know now.
>
> -Kurt

Beautifully said, Kurt !!!

-Aaron

🔗Paul Erlich <paul@stretch-music.com>

🔗Aaron K. Johnson <akjmicro@comcast.net>

On Monday 08 December 2003 03:33 am, Peter Wakefield Sault wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > hi Peter,
> >
> > --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> >
> > wrote:
> > > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > > > my company (Tonalsoft) is currently developing software
> > > > for music composition (under Windows) which is based
> > > > on the use of lattice-diagrams for the tunings. it
> > > > will allow the user to create any tuning he/she wishes
> > > > and to mix different tunings in a piece.
> > > >
> > > > the first release of the software will be using another
> > > > different formula for lattices, but eventually we will
> > > > incorporate all of the usual formulae.
> > > >
> > > > we hope to have the beta release out around February, and
> > > > commercial release 1.0 sometime in 2004.
> > > >
> > > >
> > > >
> > > > -monz
> > >
> > > Can I have an evaluation copy?
> > >
> > > - Peter
> >
> > we have a very small handful of potential beta-testers in
> > mind, so i can't give you much hope for that ... but anyway,
> > it's still too early. all we have done so far is the tuning
> > and lattice stuff. we're only now beginning the music
> > composition coding.
>
> Have you heard the stuff pumped out by my software (which is now
> nearly 20 years old)? Go to http://www.odeion.org/music and look for
> ODEION Natural No.1-003

Peter-

I just listened to you 'Odeion Natural No.1-003' for the first time. Wow! It's
some of the most impressive algorithmic composition I've heard yet!

I can understand why you feel that there is something magical going on here-it
has that sort of expressive yet objective quality of Bach textures. I'd be
interested to see what you could cook up with rhythmic algorithms--although
my instinct is to think that the intersection of tonal functioning with
rhythmic grammers is ultimately non-algorithmic when a composition can be
considered artistically satisfying. The closest I've heard is David Cope's
experiments with a LISP programmed-composition environment, which still
requires human input, because it is statistically base, using Markov chains,
etc. But perhaps humans do the same thing anyway (you have to hear x number
of symphonies before you write one, or know what makes a symphony a symphony)

Now, I definately want to see you code, and Pythonize it!!! I guarantee that
we could implement a JI version of Odeion quite easily (i.e. after my big
'Messiah' performance--say early January?) using some midi and JI function
libraries for Python that I've developed.....

Or, I could send some Python code to you, and you could start....

Best,
Aaron.

🔗David Beardsley <db@biink.com>

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> >
> > >If no one
> > > beats me to it, I will (when I get a chance) make a lattice for
> > each
> > > of the following 12-tone 5-limit tunings: Sault, Ellis, De
Caus,
> > > Ramos, and the Modern Indian Gamut.
> >
> > I hope you do. Looking at which ones are Fokker blocks might be
> > interesting also.
>
> They all are -- only the chalmers "wing" scale isn't, of those
> mentioned so far (still catching up, though) . . .

Sorry, the Modern Indian Gamut is not a Fokker periodicity block, but
it is a periodicity block -- see the second link below.

I screwed up De Caus -- De Caus is actually identical to Ellis. What
I meant was Marpurg's 'monochord number 1' tuning, which is certainly
the equal of Ellis in terms of the criteria Gene was looking at.

Please examine carefully this, which spells out both scales:

http://www.sonic-arts.org/td/erlich/intropblock2.htm

and this, which has Modern Indian Gamut:

http://www.sonic-arts.org/td/erlich/intropblockex.htm

Really, we need triangular lattice versions of these . . .

🔗Aaron K. Johnson <akjmicro@comcast.net>

On Monday 08 December 2003 09:25 am, Paul Erlich wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
>
> wrote:
> > Have you actually created any music using a 19 note equal-tempered
> > scale? If so then I would like to hear it.
>
> Aaron K. Johnson recently posted a wonderful 19-note equal-tempered
> composition to this list, currently my top candidate for "piece of
> the year". Would Aaron kindly repost the link?

Sure-http://www.aaronandlorna.com/audio/juggler.mp3

I think Peter has already heard it though.....

Boy, I feel great that everyone loves this piece, but I also feel like I need
to get back to writing more soon-especially in 19-tet !! I'm a bit afraid
that I'm going to have to constantly out-do 'Juggler' to stay compositionally
relevant. And to have a larger work or body of works. But, one just must
write and hope for the best, no? Unfortunately, I feel dry right now ;(

I am really thankful and thrilled that people have recieved it so warmly,
though :)

Best,
Aaron.

🔗Paul Erlich <paul@stretch-music.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
> > His original question might have been seen as a question for how
to
> > construct a diatonic scale in 19-et. This is not something that
> everyone
> > knows about. (Personally I haven't learned it yet.) Perhaps it
> does have
> > to do with the circle of (tempered) 5ths after all, or perhaps
only
> because
> > 19-et is meantone?
>
> A diatonic scale is a scale of seven notes of meantone, what I
would
> call meantone[7], derived from a chain of six meantone fifths. The
> fifths in practice need not be all the same size, though that is
the
> easiest to consider and would be the case in 19-et.

Unless you say the harmony is to be triadic, "the diatonic scale"
could also apply to 3-limit constructions (e.g., Pythagorean diatonic
scale) or temperaments thereof (in 22-equal, "Pythagorean diatonic"
becomes "septimal diatonic" because 64:63 vanishes) . . .

For a slightly more JI-friendly view of the diatonic scale, see

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

🔗Carl Lumma <ekin@lumma.org>

>You might like the current band Spock's Beard, influenced by both
>bands. I'm not too crazy about them . . .

Or for an ELP/Yes mix, Glass Hammer. The problem with these modern-
day (Phish excepted) prog bands: CHEESE-EEE. And so unoriginal.
Spock's Beard did a tune that was a virtual duplicate of GG's "knots",
which I never cared much for anyway.

>I confess to being a sometime prog-head myself. Dan Stearns, a list
>member known for forward-thinking musical tastes, recommended the
>current band Thinking Plague's _In Extremis_, influenced by Yes and
>Henry Cow. It's challenging but I liked in on last listen.
>
>Mostly I can't listen to prog-rock these days, too much jazz and
>Eastern music in my input and output, but I must say no prog-rock fan
>should go without checking out Gong and Focus. Egg is even more
>obscure but worth it to seek out.

Thanks for passing on the Thinking Plague name. I've been avoiding
listening to Yes for many years now, to avoid burning out on them.
I only bring it out for special occasions. I can still handle
Gentle Giant now and again, and I've really been into Phish lately.

Actually I rarely listen to music outside of my car these days, and
when I do it's usually something eclectic I'm checking out... at the
moment, Fleck's Outward Bound, some piano music by Charles Koechlin,
South Park The Movie soundtrack and the complete symphonies of
Honegger.

By the way Paul, I was able to get The Polite Force on cd, and it
has a different cover than yours (perhaps the original UK jacket).

-Carl

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, Graham Breed <graham@m...> wrote:
> Peter Wakefield Sault wrote:
>
> <snip>
> > relate to the preceding notes by harmonious intervals. I will
record
> > a sample for you to listen to as soon as I have got my old 486
out of
> > its box and connected up again - my ancient demo software for
this
> > stuff is DOS-only and plays the PC speaker because that was and
still
> > is the only way I can produce tones by frequency. Perhaps someday
it
> > will occur to the geniuses who produce synthesizers that
vibration
> > number is infinitely more rational than 'cents'.
>
> If it uses the PC speaker, why were you talking about Sound Blaster
> dependency? Whatever, DOSEMU can use or emulate both:
>
> http://dosemu.sourceforge.net/docs/README-
tech/1.2/config.html#AEN885
>
> http://dosemu.sourceforge.net/docs/README-
tech/1.2/config.html#AEN989
>
> http://dosemu.sourceforge.net/docs/HOWTO/x500.html#AEN534
>
> Of course, the only way to know if it'll work with your program is
to
> give it a try. Let me have your code and I'll see what I can do.
>
>
> Graham

Hi Graham

There are two ODEION programs. One produces MIDI streams and files
and the other plays the PC speaker.

The MIDI streamer could not address Creative Soundblaster cards for
the simple reason that the control codes were not published and did
not correspond to the Roland MPU-401 standard. Creative wanted a ton
of money from developers for the info, which was never guaranteed to
be the actual control codes (it wasn't as it happens). So this
version of ODEION could only be used with an actual Roland MPU-401
and an external MIDI synthesizer. Roland later produced a MPU-401
variant which took a Roland wavetable synth daughterboard and would
send audio direct to PC speakers, and I still possess it.

The PC speaker version directly programs the PC timer chip in order
to produce a continuous sound spectrum. Winduhs does not like this
and tends to lock up pretty quickly if it is tried in its pseudo-DOS
window. The purpose of the PC speaker version was to enable
modulation by dynamic retuning of Justly Intonated scales relative to
the modulation bridge note.

Hope that clarifies the matter. As for providing the source code, it
comprises a high-level shell written in BASIC for the IBM BASIC
Compiler v1.00 which links assembly-language object library to create
an EXE file. All the action takes place in the assembly language. For
either program to even work on the computer on which it was all put
together, an original IBM PC-XT (I owned the first one delivered in
the UK, as it happens) with a 4MHz 8088 processor, many tricks were
necessary. For example, I do not pass variables in the usual manner,
as parameters. Instead their segment:offset addresses are passed as
parameters once-only at program initialization and thereafter the
data is referenced directly at its fixed address by both the caller
and the routines. This is single-thread programming, remember.

Also, all scales are defined as 12-bits of 16-bit integers, with a
one-to-one bit-to-pitchnumber mapping. Thus modes of scales are
produced by in-register rotations of these integers.

These are just examples. Still think you can port it?

- Peter

🔗Paul Erlich <paul@stretch-music.com>

As usual, the lattices will look "messed up" except when you
hit "reply".

So here's Marpurg's Monochord #1:

25/24-----25/16
/ \ / \
/ \ / \
/ \ / \
/ \ / \
5/3-------5/4------15/8------45/32
/ \ / \ / \ /
/ \ / \ / \ /
/ \ / \ / \ /
/ \ / \ / \ /
4/3-------1/1-------3/2-------9/8
\ / \ /
\ / \ /
\ / \ /
\ / \ /
6/5-------9/5

and here's the Modern Indian Gamut:

5/4------15/8------45/32
/ \ / \ / \
/ \ / \ / \
/ \ / \ / \
/ \ / \ / \
4/3-------1/1-------3/2-------9/8------27/16
/ \ / \ / \ /
/ \ / \ / \ /
/ \ / \ / \ /
/ \ / \ / \ /
16/15------8/5-------6/5-------9/5

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:
>
> Carl wrote:
> >I see nothing in the scale archive under wing* or
> >chalmers*wing*.
>
> load/all *wing* will do.
>
> Peter wrote:
> >Care to expand on that? What are the constituent vibration ratios?
>
> Chalmers' Major Wing:
> 25/24 9/8 6/5 5/4 4/3 3/2 25/16 8/5 5/3 9/5 15/8 2/1
> Chalmers' Minor Wing:
> 9/8 6/5 5/4 4/3 36/25 3/2 8/5 5/3 9/5 15/8 48/25 2/1
>
> The music page of your website mentions that you'd like to
> have your midi files in just intonation. You could retune them
> with Scala. If you also install the scale archive, in C:\ for
> example, then the Scala commands are like these:
>
> load c:\scl\malcolm
> example/midi myfile.mid myfile-ji.mid
>
> But you can also use the menus.
> See http://www.xs4all.nl/~huygensf/scala
>
> Manuel

But can I dynamically retune relative to a modulation bridge note
with Scala? You see MIDI is a clunky old piece of crap and one vital
piece of information has always been missing from its specification.
The KEY of each note. I had to design special data files for ODEION
where each note is defined as a tonic pitch number (0-128) plus
offset (0-11). MIDI is incapable of this - and therefore useless for
my purposes. My ODEION files are translated to MIDI only for the
purpose of final performance. To work with the tonic + offset data,
ODEION contains its own editor. Also please note once again that a
modulation bridge note may not be the tonic of either the preceding
or subsequent key, so it is no good retuning relative to the new
tonic. The retuning absolutely has to be relative to the bridge note.

Peter

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
wrote:
> On Monday 08 December 2003 01:28 am, Peter Wakefield Sault wrote:
> > --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > > >> Why must I accept that? In 19-et, a fifth is 11 steps, and
so a
> > > >> tone is 22-19 = 3 steps. Three of these gives a tritone of 9
> >
> > steps,
> >
> > > >> but we also have 19-9 = 10 steps.
> > > >
> > > >Have you actually created any music using a 19 note equal-
tempered
> > > >scale? If so then I would like to hear it. If not then we are
> > > >entering the realm of angels on a pinhead.
> > >
> > > Peter, unbeknownst to most of the human race, there's a growing
> > > body of staggeringly-good 19-tone music out there. I strongly
> > > recommend Easley Blackwood's and Neil Haverstick's efforts, as
> > > linked to from my web page...
> > >
> > > http://lumma.org
> > >
> > > On the internet, our own Aaron Johnson has a piece which never
fails
> > > to knock my socks off...
> > >
> > > http://www.aaronandlorna.com/audio/juggler.mp3 (2.5mb)
> >
> > Impressive! Well done Aaron. I note it is contrapuntal - is it
also
> > possible to generate chord progressions this way?
>
> Thank you! Yes, chord progressions are possible....
>
> > > Also, note that the "1/3-comma meantone" of Rameau (and popular
> > > in Europe during the meantone era) closes very nearly after 19
> > > tones. So nearly that 19-tET is indistinguishable from 1/3-
comma
> > > meantone (it has Just minor thirds). So what has a wolf in 12
> > > has none in 19!
> >
> > But why 19? Why not 18 (i.e. 6 tones each divided in 3 instead of
2)?
>
> 19-tet has a very nearly pure minor third, a better approximation
to a major
> 3rd than 12-tet, and a flatter fifth than et, but still functions
and is
> recognizable as such, just a bit more active.
>
> 18-tet has a 12-tet major third, a very much sharp minor third, and
an
> unusable for traditional harmony perfect fifth.
>
> take your pick....if you want to do alien music, 18 works well ;)
>
> > And how can anything that is ET contain anything that is Natural?
>
> Hmm....it seems elsewhere that you defend 12-tet concerts and
music.
> 'Naturalness' doesn't come in to your argument there! Or do I
misunderstand
> you?
>
> > Surely they are mutually exclusive? Either each chromatic
interval is
> > 19th root 2 (ET) or it is a ratio of whole numbers ('Natural' - I
> > must say I restrict my use of 'Just' to mean natural dodekaphony
for
> > reasons which are just too long-winded to go into here and now)?
And
> > what principle does one use to generate melodic scales? Obviously
it
> > cannot be transposed sequences of 5ths (or can it?) because one
> > cannot get 2:3 (1.5) from 19th root 2.
>
> Neither does one have 2:3 in 12-tet!!! each ET will have different
> approximations to various important Just intervals....19-tet has a
fifth with
> a ratio of 1.49375896165449 as opposed to 1.5...perfectly
listenable and
> recognizable as a 'fifth', though a bit more active and insistent
due to its
> faster beating. It stands at 694.7368 cents as opposed to 700 cents
for the
> 12-tet fifth (BTW, cents are a very good measure of the relative
perceptual
> fatness and sharpness of intervals, you plea for a ratios only
approach
> aside)
>
> For the metaphysician, 19-tet is also justifiable as a being very
closely
> approximated by a chain of 19 just minor thirds. Try it! You could
tune it by
> ear...is that 'natural' enough for you? ;)
>
> Best,
> Aaron.

Ummm - doesn't a 'chain' of 4 minor 3rds return me to the tonic???

What kind of minor 3rds are we talking about here?

Peter

🔗Paul Erlich <paul@stretch-music.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗John A. deLaubenfels <jdl@adaptune.com>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
>
> > There is no way you can
> > verify the lasting value of your (or any contemporary)
performance
> > unless medical technology can keep you alive for another 100
years
> or
> > more.
>
> Who cares. My performances give me and the people present far more
> meaningful fulfillment than the best intellectual internet
> discussions.
>
> > People used to
> > love Benny Goodman, but would *you* buy a recording of it?
>
> Yes (though I haven't). What's the relevance? Non-western cultures
> have been using their respective non-dodecaphonic scales for
> centuries, and these musics indisputably have lasting value within
> their cultures. That's the only point I was making.

Once again, scientific verification of your claim involves waiting
for longer than the maximum outstanding duration of our little lives.
As it happens dodekaphony is slowly but surely displacing traditional
tribal systems the same way that the English language is displacing
the Navajo language and many others. It is only a matter of time
before the sitar and Chinese bells and hammered harps are museum
pieces. It may be cultural imperialism but it is real and all the
petty nationalists in the world cannot stop it. As it happens I think
that musicians dump their local tribal chants in favour of western
symphonies simply because the sophistication and aesthetic content of
a good symphony is more powerful than any conquering army. I feel
that you are surrendering to a romanticism about 'noble savages' and
the suchlike that has no substance in reality.

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:
> --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
<sault@c...>
> > wrote:
> >
> > > There is no way you can
> > > verify the lasting value of your (or any contemporary)
> performance
> > > unless medical technology can keep you alive for another 100
> years
> > or
> > > more.
> >
> > Who cares. My performances give me and the people present far
more
> > meaningful fulfillment than the best intellectual internet
> > discussions.
> >
> > > People used to
> > > love Benny Goodman, but would *you* buy a recording of it?
> >
> > Yes (though I haven't). What's the relevance? Non-western
cultures
> > have been using their respective non-dodecaphonic scales for
> > centuries, and these musics indisputably have lasting value
within
> > their cultures. That's the only point I was making.
>
> Once again, scientific verification of your claim involves waiting
> for longer than the maximum outstanding duration of our little
lives.
> As it happens dodekaphony is slowly but surely displacing
traditional
> tribal systems the same way that the English language is displacing
> the Navajo language and many others.

And this is a good thing?

> It is only a matter of time
> before the sitar and Chinese bells and hammered harps are museum
> pieces.

I find that a truly vile sentiment.

> It may be cultural imperialism but it is real and all the
> petty nationalists in the world cannot stop it. As it happens I
think
> that musicians dump their local tribal chants in favour of western
> symphonies simply because the sophistication and aesthetic content
of
> a good symphony is more powerful than any conquering army.

The sophistication and aesthetic content of non-Western musics is
evidently not something you're willing to consider. Based on what
experience do you make this vast, genocidal dismissal?

And where are these symphonies being performed, anyway? If anything,
electronic music (very international by nature) is displacing
symphonies, rather than symphonies displacing music of other
cultures, and in electronic music today we hear a *humungous*
rejection of dodecaphony, tonality, and traditional notions of
timbre, melody, etc. Dodecaphony will be nothing but a minor footnote
in the history of world music.

> I feel
> that you are surrendering to a romanticism about 'noble savages'
and
> the suchlike that has no substance in reality.

I don't call my musician collaborators, let along true masters, from
other cultures 'noble savages' -- how insulting! This is getting
absolutely disgusting . . .

🔗Jon Szanto <JSZANTO@ADNC.COM>

Peter,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...> wrote:
> As it happens dodekaphony is slowly but surely displacing traditional
> tribal systems the same way that the English language is displacing
> the Navajo language and many others. It is only a matter of time
> before the sitar and Chinese bells and hammered harps are museum
> pieces. It may be cultural imperialism but it is real and all the
> petty nationalists in the world cannot stop it. As it happens I think
> that musicians dump their local tribal chants in favour of western
> symphonies simply because the sophistication and aesthetic content of
> a good symphony is more powerful than any conquering army. I feel
> that you are surrendering to a romanticism about 'noble savages' and
> the suchlike that has no substance in reality.

I'm not participating in the list much at the moment, but when scanning a couple of days posts this really caught my eye.

As someone who not only has spent the better part of his 50 years on the planet in classical music, and moreover has been playing in professional symphony orchestras for the last 30, and continually seeks out great performances of same (most recent: Berlin/Rattle/New Disney Hall), I can only say that I find your above opinions unbelievably arrogant, naive, and fairly repulsive.

Maybe that is a bit strong, I'm not sure. But I can't let it pass without a fairly strong reaction.

I've seen espousals of cultural superiority before, but this one takes the cake! As much as I'm committed artistically to the symphonic literature of Western tradition, I'd fight nearly to the death with anyone that actively tried to do away with the great musical traditions of Java, India, Africa, etc, etc.

I'm glad you've found your particular Holy Grail. I hope at some point you'd be enlightened enough to recognize the beauty deeply held in the many world music traditions that *don't* happen to fit your mold.

Cheers,
Jon (who semi-enjoyed your algo-comp piece this morning...)

🔗Aaron K. Johnson <akjmicro@comcast.net>

On Monday 08 December 2003 02:59 pm, Peter Wakefield Sault wrote:
> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
> > For the metaphysician, 19-tet is also justifiable as a being very
> > closely approximated by a chain of 19 just minor thirds. Try it! You could
> > tune it by
> > ear...is that 'natural' enough for you? ;)
> >
> > Best,
> > Aaron.
>
> Ummm - doesn't a 'chain' of 4 minor 3rds return me to the tonic???
>
> What kind of minor 3rds are we talking about here?
>

We are talking about 6:5 minor thirds. Four of these doesn't bring one to 2
(the octave), but to a sharp octave of 2.0736 !!!!

19 of them bring one to 1.99674999606639, which is about 3 cents shy of a
perfect octave.

Hence, 19-tet.

Q.E.D.

-Aaron.

--
OCEAN, n. A body of water occupying about two-thirds of a world made
for man -- who has no gills. -Ambrose Bierce 'The Devils Dictionary'

🔗Kurt Bigler <kkb@breathsense.com>

on 12/8/03 7:43 AM, Aaron K. Johnson <akjmicro@comcast.net> wrote:

> On Monday 08 December 2003 09:25 am, Paul Erlich wrote:
>> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
>>
>> wrote:
>>> Have you actually created any music using a 19 note equal-tempered
>>> scale? If so then I would like to hear it.
>>
>> Aaron K. Johnson recently posted a wonderful 19-note equal-tempered
>> composition to this list, currently my top candidate for "piece of
>> the year". Would Aaron kindly repost the link?
>
> Sure-http://www.aaronandlorna.com/audio/juggler.mp3
>
> I think Peter has already heard it though.....
>
> Boy, I feel great that everyone loves this piece, but I also feel like I need
> to get back to writing more soon-especially in 19-tet !! I'm a bit afraid
> that I'm going to have to constantly out-do 'Juggler' to stay compositionally
> relevant. And to have a larger work or body of works. But, one just must
> write and hope for the best, no? Unfortunately, I feel dry right now ;(
>
> I am really thankful and thrilled that people have recieved it so warmly,
> though :)
>
> Best,
> Aaron.

Hey. I like the piece a lot myself, yet as is often the case, I have to
"suspend" my dislike for the synthesized medium in order to try to hear the
music. But I am able to do this. Partly because I very much *want* to do
this. My significant-other does not want to do this - so she does not like
the piece much and feels unable to hear what 19-et might offer, as a result.

I'd like to see a midi file for the piece, and try to come up with a way of
rendering it to make it palatable to those with different tastes. Any
chance?

Thanks,
Kurt

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
> >
> > >
> > > But Peter's own scale doesn't have inversion symmetry because
of
> > the
> > > tritone, while Ellis' Duodene happens to inversion symmetry
about
> > the
> > > *dyad* 1/1-3/2.
> > >
> >
> > Actually there is no tritone in my scale (nor can there be in any
> > natural scale based on vibration ratios of whole numbers). There
is
> > an Aug 4th and a Dim 5th in the theoretical scale. I reduce this
to
> a
> > Dim 5th (45:64) for the practical scale. In the program the Aug
4th
> > can be switched on or off with the Aug 4th button. I also refer
to
> > these as 6a (the Dim 5th) and 6b (the Aug 4th).
> >
> > So you see it does have inversion symmetry throughout.
> >
> > Peter
>
> So it's not 12 notes at all, but rather 11 or 13?

Whatever you do in terms of natural tunings, you will get 13
*intervals* (not notes) and not 12 in a dodekaphonic scale. There is,
of course and contrary to what I said earlier, a natural tritone =
8^3:9^3 = 512:729 but this implies another interval of the same class
(6) but different size from the note formed by the interval 512:729
up to the octave note, i.e.:-

1:2 / 512:729 = 1:2 x 729:512 = 729:1024

I have been over this before and it is utterly inescapable. For
practical purposes one of these can be ignored, but the theoretical
arithmetic demands both.

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

🔗John A. deLaubenfels <jdl@adaptune.com>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
wrote:
> On Monday 08 December 2003 03:08 am, Kurt Bigler wrote:
> > on 12/7/03 10:02 PM, Peter Wakefield Sault <sault@c...> wrote:
> > > As I have already announced elsewhere in my usual arrogant
manner I
> > > am not going to waste so much as a second of my life dealing
> > > with 'cents' up or down from concert tunings. Give it to me as
> > > vibration numbers or frequency ratios - or keep it to yourself.
> > > That's my attitude and I'm sticking to it.
> >
> > Everyone is welcome to the atttitude they choose. However you
may be
> > making a bigger thing out of it in advance of an actual
*particular* need
> > to communicate in a specific focused area. When an actual need to
> > communicate comes up, the terms used will end up being negotiated
on the
> > fly. If one person won't give, the other one perhaps will. If
this
> > becomes impractical then the communication ends. This is
something that
> > may happen. It need not be announced in advance with a lot of
show. If it
> > involves a genuine difficulty on your part then everyone will be
most glad
> > to help you translate things to terms you are familiar with. If
you simply
> > refuse to experience difficulty while everyone else around you
picks up the
> > slack, then you simply end relationship, and that is your choice.
> > Relationships where one side does all the work tend to be short-
lived,
> > except under exceptional conditions.
> >
> > All of us have similar preferences in various areas of
terminology and ways
> > of thinking about things, though perhaps most of us feel in
advance more
> > willingness to work on our side of the translation, rather than
require
> > others to do all the translation for us. Nonetheless in many
cases these
> > individual preferences can go almost unnoticed when things to
communicate
> > are simply dealt with as they come up.
> >
> > So I'm saying that arrogance is merely a style, which is perhaps
what you
> > are also saying. When push comes to shove everyone will see how
it turns
> > out. And it won't matter one whit to anyone here whether you
forget
> > yourself one day and find that for some unforseen reason it
suddenly
> > becomes worthwhile to know what cents means! ;) Heck have you
ever
> > incorrectly predited your future choices? If not, then I suppose
that
> > means you never learned anything. Perhaps in that case you were
already
> > born knowing what you know now.
> >
> > -Kurt
>
> Beautifully said, Kurt !!!
>
> -Aaron

And I confess I was overly tired when I made my original statement.
However, I will continue to champion the more rational system. It
took me years to unlearn all those clunky letters and accidentals and
replace my previous thinking with numerical interval and pitch
classifications. You should try it.

Peter

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> Whatever you do in terms of natural tunings, you will get 13
> *intervals* (not notes) and not 12 in a dodekaphonic scale.

Actually I count more than 13 *intervals* in every 12-note JI scale.
For example, the Ellis 12-note JI scale

1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 (2/1)

has the following intervals:

1
25:24
135:128
16:15
27:25
10:9
9:8
256:225
75:64
32:27
6:5
5:4
32:25
675:512
4:3
27:20
25:18
45:32
64:45
36:25
40:27
3:2
25:16
8:5
5:3
27:16
225:128
16:9
9:5
15:8
(2)

> I have been over this before and it is utterly inescapable. For
> practical purposes one of these can be ignored, but the theoretical
> arithmetic demands both.

There's no especial difficulty if you align your theory more closely
to practice, and consistently distinguish *pitch-ratios* from
*interval-ratios*.

🔗Paul Erlich <paul@stretch-music.com>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

I quote from the 'Oxford Companion to Music', since you are now
demanding citations:-
"The diatonic scales are the major and minor, made up of tones and
semitones (in the case of the harmonic minor scale, also an augmented
second), as distinct from the chromatic, made up entirely of
semitones. The modes are diatonic in structure."

I don't see anything about meantones there.

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
> > --- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
> > wrote:
>
> > > For the metaphysician, 19-tet is also justifiable as a being
very
> > closely
> > > approximated by a chain of 19 just minor thirds. Try it! You
> could
> > tune it by
> > > ear...is that 'natural' enough for you? ;)
> > >
> > > Best,
> > > Aaron.
> >
> > Ummm - doesn't a 'chain' of 4 minor 3rds return me to the tonic???
> >
> > What kind of minor 3rds are we talking about here?
> >
> > Peter
>
> We're talking "just" minor 3rds with frequency ratio almost exactly
> 6/5 = 1.2 -- in the case of 19-equal, it's 2^(5/19) = 1.2001. But
> anyway, before the advent of closed 12-tone tunings and the
> assumption of octave equivalence, and even in notated tonal music
> today, 4 minor 3rds add up to a diminished 9th, not an octave.

Wait a moment. A Just minor third is *exactly* 5:6, not "almost
exactly". 4 of these give me an 'octave' of 2.0736, so you could be
right in calling it a "diminished 9th". However, 19 of these minor
thirds leads us to 31.948, which transposes down to 1.9967 which is
no more of an octave than 2.0736. Following your logic it is an
augmented seventh.

🔗Carl Lumma <ekin@lumma.org>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

> > As it happens dodekaphony is slowly but surely displacing
> traditional
> > tribal systems the same way that the English language is
displacing
> > the Navajo language and many others.
>
> And this is a good thing?
>

I was not making a value judgment but stating a fact of life.

> > It is only a matter of time
> > before the sitar and Chinese bells and hammered harps are museum
> > pieces.
>
> I find that a truly vile sentiment.
>

Again - it is a fact of life. Live with it.

> > It may be cultural imperialism but it is real and all the
> > petty nationalists in the world cannot stop it. As it happens I
> think
> > that musicians dump their local tribal chants in favour of
western
> > symphonies simply because the sophistication and aesthetic
content
> of
> > a good symphony is more powerful than any conquering army.
>
> The sophistication and aesthetic content of non-Western musics is
> evidently not something you're willing to consider. Based on what
> experience do you make this vast, genocidal dismissal?
>

You are evidently unwilling to accept reality. That is your problem,
not mine.

> And where are these symphonies being performed, anyway? If
anything,
> electronic music (very international by nature) is displacing
> symphonies, rather than symphonies displacing music of other
> cultures, and in electronic music today we hear a *humungous*
> rejection of dodecaphony, tonality, and traditional notions of
> timbre, melody, etc. Dodecaphony will be nothing but a minor
footnote
> in the history of world music.
>

Once again you are making assertions that cannot be tested by us
because of the brevity of our lives. The simple fact is that we will
never know. What is your problem with that?

> > I feel
> > that you are surrendering to a romanticism about 'noble savages'
> and
> > the suchlike that has no substance in reality.
>
> I don't call my musician collaborators, let along true masters,
from
> other cultures 'noble savages' -- how insulting! This is getting
> absolutely disgusting . . .

I use the term simply to illustrate my point, which you are obtusely
refusing to see while gayly making unfounded predictions that cannot
be verified. Perhaps you have consulted an oracle. Was it a fortune
cookie or a tarot kook?

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> Peter,
>
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:
> > As it happens dodekaphony is slowly but surely displacing
traditional
> > tribal systems the same way that the English language is
displacing
> > the Navajo language and many others. It is only a matter of time
> > before the sitar and Chinese bells and hammered harps are museum
> > pieces. It may be cultural imperialism but it is real and all the
> > petty nationalists in the world cannot stop it. As it happens I
think
> > that musicians dump their local tribal chants in favour of
western
> > symphonies simply because the sophistication and aesthetic
content of
> > a good symphony is more powerful than any conquering army. I feel
> > that you are surrendering to a romanticism about 'noble savages'
and
> > the suchlike that has no substance in reality.
>
> I'm not participating in the list much at the moment, but when
scanning a couple of days posts this really caught my eye.
>
> As someone who not only has spent the better part of his 50 years
on the planet in classical music, and moreover has been playing in
professional symphony orchestras for the last 30, and continually
seeks out great performances of same (most recent: Berlin/Rattle/New
Disney Hall), I can only say that I find your above opinions
unbelievably arrogant, naive, and fairly repulsive.
>
> Maybe that is a bit strong, I'm not sure. But I can't let it pass
without a fairly strong reaction.
>
> I've seen espousals of cultural superiority before, but this one
takes the cake! As much as I'm committed artistically to the
symphonic literature of Western tradition, I'd fight nearly to the
death with anyone that actively tried to do away with the great
musical traditions of Java, India, Africa, etc, etc.
>
> I'm glad you've found your particular Holy Grail. I hope at some
point you'd be enlightened enough to recognize the beauty deeply held
in the many world music traditions that *don't* happen to fit your
mold.
>
> Cheers,
> Jon (who semi-enjoyed your algo-comp piece this morning...)

Why don't you try *thinking* for a bit before firing off your overly
emotional responses? I am not espousing any "cultural superiority"
but simply stating the facts of life. Maybe you don't like them but
you have no right to attack me for reporting them. I am not trying to
suppress anyone's cultural traditions. It is *YOU* who are trying to
keep the people of these cultures in a primitive state so that *YOU*
can indulge *YOUR* overweening patronization of them

Insofar as dodekaphony is *NOT* a 'western' invention, we in
the 'western' culture are no more than the first to have been
conquered by it. Why do you play in an orchestra? By doing so you are
betraying your own ancient cultural traditions and should instead
return to banging pots and pans around an open fire.

Can you say "hypocrite"?

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
>
> > Whatever you do in terms of natural tunings, you will get 13
> > *intervals* (not notes) and not 12 in a dodekaphonic scale.
>
> Actually I count more than 13 *intervals* in every 12-note JI
scale.
> For example, the Ellis 12-note JI scale
>
> 1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 (2/1)
>
> has the following intervals:
>
> 1
> 25:24
> 135:128
> 16:15
> 27:25
> 10:9
> 9:8
> 256:225
> 75:64
> 32:27
> 6:5
> 5:4
> 32:25
> 675:512
> 4:3
> 27:20
> 25:18
> 45:32
> 64:45
> 36:25
> 40:27
> 3:2
> 25:16
> 8:5
> 5:3
> 27:16
> 225:128
> 16:9
> 9:5
> 15:8
> (2)
>
> > I have been over this before and it is utterly inescapable. For
> > practical purposes one of these can be ignored, but the
theoretical
> > arithmetic demands both.
>
> There's no especial difficulty if you align your theory more
closely
> to practice, and consistently distinguish *pitch-ratios* from
> *interval-ratios*.

There is no such thing as a "pitch ratio".

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:
> --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
<sault@c...>
> > wrote:
> > > --- In tuning@yahoogroups.com, "Aaron K. Johnson"
<akjmicro@c...>
> > > wrote:
> >
> > > > For the metaphysician, 19-tet is also justifiable as a being
> very
> > > closely
> > > > approximated by a chain of 19 just minor thirds. Try it! You
> > could
> > > tune it by
> > > > ear...is that 'natural' enough for you? ;)
> > > >
> > > > Best,
> > > > Aaron.
> > >
> > > Ummm - doesn't a 'chain' of 4 minor 3rds return me to the
tonic???
> > >
> > > What kind of minor 3rds are we talking about here?
> > >
> > > Peter
> >
> > We're talking "just" minor 3rds with frequency ratio almost
exactly
> > 6/5 = 1.2 -- in the case of 19-equal, it's 2^(5/19) = 1.2001. But
> > anyway, before the advent of closed 12-tone tunings and the
> > assumption of octave equivalence, and even in notated tonal music
> > today, 4 minor 3rds add up to a diminished 9th, not an octave.
>
> Wait a moment. A Just minor third is *exactly* 5:6, not "almost
> exactly". 4 of these give me an 'octave' of 2.0736, so you could be
> right in calling it a "diminished 9th". However, 19 of these minor
> thirds leads us to 31.948, which transposes down to 1.9967 which is
> no more of an octave than 2.0736.

*Listen* to both and tell me one isn't more of an octave than the
other! Really, now!

> Following your logic it is an
> augmented seventh.

No, it's not an augmented seventh following this logic at all --
observe:

Bx-Dx-Fx-A#-C#-E-G-Bb-Db-Fb-Abb-Cbb-Ebbb-Gbbb-Bbbbb-Dbbbb-Fbbbb-
Abbbbb-Cbbbbb-Ebbbbbb

So technically, it's an octuply-diminished eleventh!

But one would be very unlikely to use diatonic spelling for all the
minor thirds in such a chain. Regardless, the last note is
*enharmonically equivalent* to the first in 19-tone equal
temperament, just as in 12-tone equal temperament, a chain of 12
perfect fifths leads to a note enharmonically equivalent to the first
note. That's the important point here.

🔗Jon Szanto <JSZANTO@ADNC.COM>

Peter,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...> wrote:
> Why don't you try *thinking* for a bit before firing off your
> overly emotional responses?

Thanks. I tend to think quite a bit before I respond. However, your self-centered and ill-informed pronouncements on the state of world music didn't take a lot of it.

> I am not espousing any "cultural superiority" but simply stating
> the facts of life.

You aren't coming close to "stating facts of life". Sitars, and the study of them, are alive and well, as with the other traditions you are predicting will wind up in museums or dust-bins. The amazing thing is that while you opine that symphonic music will outlive and outlast them all, I am actively watching the symphonic world slowly shrink and die - unless your future simply includes amateur groups. No problem with that for me, but the composers won't get the performances they deserve, and the literature will suffer for it.

> It is *YOU* who are trying to keep the people of these cultures in
> a primitive state so that *YOU* can indulge *YOUR* overweening
> patronization of them

Man, you can sure stretch things - where do you get patronization? This is nuts. The Javanese culture of art, as an intrinsic part of their society, far exceeds that of the West, where art is merely (most often) an 'entertainment', and not a compelling part of everyday life. It appears that your knowledge of these cultures is pitifully small, leading you to the small-minded belief in your "facts".

> Insofar as dodekaphony is *NOT* a 'western' invention...

At this point, I'm not buying into your dedekaphony sales pitch.

> Why do you play in an orchestra? By doing so you are
> betraying your own ancient cultural traditions and should instead
> return to banging pots and pans around an open fire.

So you revere the symphonic form, and the forces that play it, but show complete disrespect for someone who actually *does* it?

> Can you say "hypocrite"?

Sure - it's easy to call names.

I'll let the group take it from here, as this tunnel-vision view of the musical world is a complete waste of my time.

Jon

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> > > It is only a matter of time
> > > before the sitar and Chinese bells and hammered harps are
museum
> > > pieces.
> >
> > I find that a truly vile sentiment.
> >
>
> Again - it is a fact of life. Live with it.

In response to this, let me quote you:

"> Once again you are making assertions that cannot be tested by us
> because of the brevity of our lives. The simple fact is that we
will
> never know. What is your problem with that?"

Now who's the hypocrite?

> > The sophistication and aesthetic content of non-Western musics is
> > evidently not something you're willing to consider. Based on what
> > experience do you make this vast, genocidal dismissal?
> >
>
> You are evidently unwilling to accept reality. That is your
problem,
> not mine.

OK, then I'm endlessly grateful to the universe for this 'problem' of
having my aesthetic, emotional, intellectual, and spiritual vistas --
not to mention my musicianship -- continually opened by contact with
previously unfamiliar (and yes, perhaps initially to someone from a
different culture, 'primitive' and 'out-of-tune' sounding), but
endlessly deep and rich, musics. For the fact that you don't have
this 'problem', I can only feel sorry for you.
> >
> > > I feel
> > > that you are surrendering to a romanticism about 'noble
savages'
> > and
> > > the suchlike that has no substance in reality.
> >
> > I don't call my musician collaborators, let along true masters,
> from
> > other cultures 'noble savages' -- how insulting! This is getting
> > absolutely disgusting . . .
>
> I use the term simply to illustrate my point, which you are
obtusely
> refusing to see while gayly making unfounded predictions that
cannot
> be verified.

I know very well what the 'noble savage' myth imp[ies, but let me
assure you that I subscribe to no such demeaning mythology. So your
use of the term, and your attempt to apply it to me, illustrate what
point exactly?

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:
> --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> > Corrected list of intervals, assuming the scale is octave-
repeating:
> >
> > --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> >
> > > For example, the Ellis 12-note JI scale
> > >
> > > 1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 (2/1)

These can be called *pitch-ratios*, Peter.

> > > has the following intervals:
> >
> > 1
> > 25:24
> > 135:128
> > 16:15
> > 27:25
> > 10:9
> > 9:8
> > 256:225
> > 75:64
> > 32:27
> > 6:5
> > 5:4
> > 32:25
> > 675:512
> > 4:3
> > 27:20
> > 25:18
> > 45:32
> > 64:45
> > 36:25
> > 40:27
> > 3:2
> > 1024:675
> > 25:16
> > 8:5
> > 5:3
> > 27:16
> > 128:75
> > 225:128
> > 16:9
> > 9:5
> > 50:27
> > 15:8
> > 256:135
> > 48:25
> > (2)
>
> You are getting closer to an understanding of ODEION which
constrains
> melodic steps to the intervals of the defining set. Thus all those
> secondary 'irrelative' intervals which crop up throughout the scale
> are cast out and never occur in an ODEION composition.

OK, great. But one thing at a time. Clearly there are not 13
intervals here, no matter how you count them. Do you want to amend
your earlier statement somehow, then?

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
> > --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> > > Corrected list of intervals, assuming the scale is octave-
> repeating:
> > >
> > > --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> > >
> > > > For example, the Ellis 12-note JI scale
> > > >
> > > > 1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 (2/1)
>
> These can be called *pitch-ratios*, Peter.

They are vibration ratios. Pitch is a subjective response.

>
> > > > has the following intervals:
> > >
> > > 1
> > > 25:24
> > > 135:128
> > > 16:15
> > > 27:25
> > > 10:9
> > > 9:8
> > > 256:225
> > > 75:64
> > > 32:27
> > > 6:5
> > > 5:4
> > > 32:25
> > > 675:512
> > > 4:3
> > > 27:20
> > > 25:18
> > > 45:32
> > > 64:45
> > > 36:25
> > > 40:27
> > > 3:2
> > > 1024:675
> > > 25:16
> > > 8:5
> > > 5:3
> > > 27:16
> > > 128:75
> > > 225:128
> > > 16:9
> > > 9:5
> > > 50:27
> > > 15:8
> > > 256:135
> > > 48:25
> > > (2)
> >
> > You are getting closer to an understanding of ODEION which
> constrains
> > melodic steps to the intervals of the defining set. Thus all
those
> > secondary 'irrelative' intervals which crop up throughout the
scale
> > are cast out and never occur in an ODEION composition.
>
> OK, great. But one thing at a time. Clearly there are not 13
> intervals here, no matter how you count them. Do you want to amend
> your earlier statement somehow, then?

🔗Kurt Bigler <kkb@breathsense.com>

on 12/8/03 12:55 PM, Peter Wakefield Sault <sault@cyberware.co.uk> wrote:

> --- In tuning@yahoogroups.com, "Manuel Op de Coul"
> <manuel.op.de.coul@e...> wrote:
>>
>> Carl wrote:
>>> I see nothing in the scale archive under wing* or
>>> chalmers*wing*.
>>
>> load/all *wing* will do.
>>
>> Peter wrote:
>>> Care to expand on that? What are the constituent vibration ratios?
>>
>> Chalmers' Major Wing:
>> 25/24 9/8 6/5 5/4 4/3 3/2 25/16 8/5 5/3 9/5 15/8 2/1
>> Chalmers' Minor Wing:
>> 9/8 6/5 5/4 4/3 36/25 3/2 8/5 5/3 9/5 15/8 48/25 2/1
>>
>> The music page of your website mentions that you'd like to
>> have your midi files in just intonation. You could retune them
>> with Scala. If you also install the scale archive, in C:\ for
>> example, then the Scala commands are like these:
>>
>> load c:\scl\malcolm
>> example/midi myfile.mid myfile-ji.mid
>>
>> But you can also use the menus.
>> See http://www.xs4all.nl/~huygensf/scala
>>
>> Manuel
>
> But can I dynamically retune relative to a modulation bridge note
> with Scala? You see MIDI is a clunky old piece of crap and one vital
> piece of information has always been missing from its specification.
> The KEY of each note. I had to design special data files for ODEION
> where each note is defined as a tonic pitch number (0-128) plus
> offset (0-11). MIDI is incapable of this - and therefore useless for
> my purposes. My ODEION files are translated to MIDI only for the
> purpose of final performance. To work with the tonic + offset data,
> ODEION contains its own editor. Also please note once again that a
> modulation bridge note may not be the tonic of either the preceding
> or subsequent key, so it is no good retuning relative to the new
> tonic. The retuning absolutely has to be relative to the bridge note.
>
> Peter

Carl, please take note - Peter agrees with me about the bridge note.

Meanwhile for some purposes I may relax that requirement tentatively
trusting people's experience that staying near to a fixed tuning (perhaps
but not necessarily 12et) may yield audibly indistinguishable results.
(This does not mean that what is not audibly noticed does not end up having
an effect on the experience of the listener, so I reserve judgement about
that for the moment.)

For a certain set of compositional possibilities that I am currently
interested in the flexible choice of bridge note will be essential. This is
something I can not quite do with "xmw" (xenharmonic moving windows) as it
currently stands.

This is not to say that dynamic retuning methods currently under discussion
do not address the need for static bridge notes. Instead as I understand
it, they depend on there being places in a piece where there are either
rests, and either a lack of any bridge notes, or an over-determination of
common notes, so that the "spring" back towards the overall tuning center
can "relax".

-Kurt

🔗Paul Erlich <paul@stretch-music.com>

🔗Kurt Bigler <kkb@breathsense.com>

on 12/8/03 2:00 PM, Peter Wakefield Sault <sault@cyberware.co.uk> wrote:

> And I confess I was overly tired when I made my original statement.
> However, I will continue to champion the more rational system. It
> took me years to unlearn all those clunky letters and accidentals and
> replace my previous thinking with numerical interval and pitch
> classifications. You should try it.

I did, actually. I never had any motivation to learn harmony theory based
on classical descriptions of function. It always seemed so awkward to me
that I ended up pursuing it. So I was always at a loss in a lot of
contexts. Nonetheless I managed to learn a lot without reference to an
external language of theory. But as soon as I got exposed to the harmonic
scale and got a little experience with its relation to other things (such as
12et) I suddenly was able to understand composition in a way I had never
before. I am much more at home with "approximation to 4:5:6:7" than I have
ever been with any other way of naming such chords, involving roman numerals
and words like "dominant".

But that is my particular experience and different from yours.

In addition to the above which applies to composition and music theory, I
have found cents an incredibly useful aid to communication which has allowed
me (for example) to easily load the better part of a hundred different
temperaments into my own synthesis software. This has been incredibly
rewarding for me. Not one single source of the temperaments in question
used anything besides cents. Thus, I was motivated. Also, I disliked it a
little, and would rather see log-base-2 values being used directly, so that
I wouldn't have to always multiply by 1200 on my calculator. But the pain
of this is relatively small compared to all the other things that take time
in the process.

And nonethelss when people use cents to describe intervals, I still haven't
learned the translation. I have to get out my calculator, and I do not do
that to read every email. Nonethless I intend to eventually learn this, so
that I can understand what is being said, not because the system is good,
but because so many people are using it that it becomes simply useful for me
to know it.

As I originally said, I have no disagreement with you regarding chosing
one's own ways of thinking that weave together well with one's own unique
ways of experiencing, or having access to experiences. But if you publicly
claim less that may *seem* to restrict your future choices, you will be more
free to discover things "in public". You are very proud I take it, and if
you are like many of us, pride may make it more uncomfortable for you to
change your mind after having made a public statement. Sufficient pride
sometimes entirely prevents such changes of mind, it appears. Some things
are best "contained" until a feeling for the ways of relating to a
particular community are better understood. This particular community is
truly amazing in its tolerance. You will *rarely* find such a thing in a
mailing list.

-Kurt

🔗Carl Lumma <ekin@lumma.org>

>> But can I dynamically retune relative to a modulation bridge note
>> with Scala? You see MIDI is a clunky old piece of crap and one vital
>> piece of information has always been missing from its specification.
>> The KEY of each note. I had to design special data files for ODEION
>> where each note is defined as a tonic pitch number (0-128) plus
>> offset (0-11). MIDI is incapable of this - and therefore useless for
>> my purposes. My ODEION files are translated to MIDI only for the
>> purpose of final performance. To work with the tonic + offset data,
>> ODEION contains its own editor. Also please note once again that a
>> modulation bridge note may not be the tonic of either the preceding
>> or subsequent key, so it is no good retuning relative to the new
>> tonic. The retuning absolutely has to be relative to the bridge note.
>>
>> Peter
>
>Carl, please take note - Peter agrees with me about the bridge note.

And what is a bridge note?

-Carl

🔗Kurt Bigler <kkb@breathsense.com>

on 12/8/03 5:44 PM, Paul Erlich <paul@stretch-music.com> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
>> This is not to say that dynamic retuning methods currently under
> discussion
>> do not address the need for static bridge notes. Instead as I
> understand
>> it, they depend on there being places in a piece where there are
> either
>> rests, and either a lack of any bridge notes, or an over-
> determination of
>> common notes, so that the "spring" back towards the overall tuning
> center
>> can "relax".
>>
>> -Kurt
>
> There is of course no explicit dependence of this sort. What makes
> you think there's an implicit one?

Well, I figure it goes without saying that tied notes for example, should
not be retuned, and immediately-repeated notes also should probably not be.
Thus you could "tie up" an entire piece into a situation where no dynamic
retuning toward a reference "center" could take place.

Does that make sense?

-Kurt

🔗Kurt Bigler <kkb@breathsense.com>

on 12/8/03 6:02 PM, Carl Lumma <ekin@lumma.org> wrote:

>>> But can I dynamically retune relative to a modulation bridge note
>>> with Scala? You see MIDI is a clunky old piece of crap and one vital
>>> piece of information has always been missing from its specification.
>>> The KEY of each note. I had to design special data files for ODEION
>>> where each note is defined as a tonic pitch number (0-128) plus
>>> offset (0-11). MIDI is incapable of this - and therefore useless for
>>> my purposes. My ODEION files are translated to MIDI only for the
>>> purpose of final performance. To work with the tonic + offset data,
>>> ODEION contains its own editor. Also please note once again that a
>>> modulation bridge note may not be the tonic of either the preceding
>>> or subsequent key, so it is no good retuning relative to the new
>>> tonic. The retuning absolutely has to be relative to the bridge note.
>>>
>>> Peter
>>
>> Carl, please take note - Peter agrees with me about the bridge note.
>
> And what is a bridge note?
>
> -Carl

I'm making the assumption from a lot of consistent context that a bridge
note is a common pitch in a modulation. For example, in a scale of the form
8:9:11:16 to keep it simple, if a modulation assigned 11 to a held note
previously assigned to the 9, then that modulation would have as its bridge
note a note that was not the tonic (8) in either key.

-Kurt

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 12/8/03 5:44 PM, Paul Erlich <paul@s...> wrote:
>
> > --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> >
> >> This is not to say that dynamic retuning methods currently under
> > discussion
> >> do not address the need for static bridge notes. Instead as I
> > understand
> >> it, they depend on there being places in a piece where there are
> > either
> >> rests, and either a lack of any bridge notes, or an over-
> > determination of
> >> common notes, so that the "spring" back towards the overall
tuning
> > center
> >> can "relax".
> >>
> >> -Kurt
> >
> > There is of course no explicit dependence of this sort. What makes
> > you think there's an implicit one?
>
> Well, I figure it goes without saying that tied notes for example,
>should
> not be retuned,

Though there might be a tiny bit of sliding involved -- I'm not sure
if John's current software supports this . . .

> and immediately-repeated notes also should probably not be.

Well, there's a spring connecting immediately-repeated notes, to
minimize the retuning motion, but yes, they can be retuned. In fact,
a great deal of the dialogue between John deL. and me in the archives
concerns just these retuning motions, and my motivation to reduce
them to inaudible levels was the driving force for some significant
improvements in the program.

The classic example of adaptive JI -- where the vertical springs are
very strong so that the harmonies (simultaneities) are just wherever
possible -- is the "comma pump" progression. It's near the bottom of
this page:

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

Without these small (1/4-comma, 5.4 cents) retuning motions in
repeated notes, none of the benefits of adaptive JI could be
realized -- the piece would either drift by a full comma, or some
sonority would have to be a full comma off. John's program initially
rendered this progression with some retuning motions around 11 cents,
which I found disturbing. Currently it approaches the ideal solution
above.

🔗monz <monz@attglobal.net>

hi Peter,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> I quote from the 'Oxford Companion to Music', since you are
> now demanding citations:-
> "The diatonic scales are the major and minor, made up of
> tones and semitones (in the case of the harmonic minor scale,
> also an augmented second), as distinct from the chromatic,
> made up entirely of semitones. The modes are diatonic in
> structure."
>
> I don't see anything about meantones there.

and i don't see anything about dodekaphony.

you're simply projecting dodekaphony and 12edo onto that
Oxford definition, which does not specify any tuning whatsoever.

tones, semitones, augmented-2nds, diatonic scales, and
chromatic scales all exist within the contexts of both
12-tone equal-temperament *and* meantone ... and after all,
12edo *is* a meantone too.

... if you don't believe me, read this:
http://sonic-arts.org/dict/12-eq.htm

-monz

🔗monz <monz@attglobal.net>

hi Peter,

[in response to Jon Szanto:]
>
> Why don't you try *thinking* for a bit before firing
> off your overly emotional responses? I am not espousing
> any "cultural superiority" but simply stating the facts of life.
> Maybe you don't like them but you have no right to attack
> me for reporting them. I am not trying to suppress anyone's
> cultural traditions. It is *YOU* who are trying to keep
> the people of these cultures in a primitive state so that
> *YOU* can indulge *YOUR* overweening patronization of them
>
> Insofar as dodekaphony is *NOT* a 'western' invention,
> we in the 'western' culture are no more than the first
> to have been conquered by it. Why do you play in an
> orchestra? By doing so you are betraying your own ancient
> cultural traditions and should instead return to banging
> pots and pans around an open fire.
>
> Can you say "hypocrite"?

i don't know if you've been lurking here for a long time
without posting, or if you've just suddenly appeared on
the tuning list. based on the volume of posts you've
suddenly started submitting, i'll guess the latter.

in any case, like many here who feel the need to make a
big splash when they first discover the tuning list
(myself included, around March 1998), you're stating
your own opinions as tho they are gospel and deriding
the opinions of all who disagree with you.

there's nothing intrinsically wrong with that, but
unfortunately, as usually happens, in the face of a large
amount of criticism, your tone has now taken on an arrogance
which will be more likely to start flame-wars than to
encourage constructive discourse.

i suggest that you please re-read carefully and thoughtfully
every response that has been sent to you over the past
few days (and there have been very many), before responding
to anything else. please.

and please don't take this post too personally. it's
happened so many times before, there's just no need for
it to happen again. and i'm a pacifist and prefer to see
this list maintain a diplomatic exchange of ideas and not
just overblown opinions.

we all have our dogmas, and the list is here so that we
can make them public. but there's no need to overdo it
in the face of obvious resistance. we can see that as a
newcomer to this forum you have a need to make your position
plain.

but we also are all very familiar with the territory,
and would rather that you just state succintly what it
is that you want to say, and let us derive any new value
that we may find in it thru our probing questions of
whatever of your ideas we find intriguing.

becoming a bully will only make you unpopular, no matter
how great the worth of your ideas. it's happened before,
in at least one glaring example that shall remain unspecified
(but everyone here will remember it).

take it easy, relax, enjoy the tremendous wealth of
knowledge and insight that can be found in the archives
of this list, and groove to the music.

-monz

🔗monz <monz@attglobal.net>

hi Peter,

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

> > [Peter Wakefield Sault:]
> >
> > Following your logic it is an
> > augmented seventh.
>
> No, it's not an augmented seventh following this logic
> at all -- observe:
>
> Bx-Dx-Fx-A#-C#-E-G-Bb-Db-Fb-Abb-Cbb-Ebbb-Gbbb-Bbbbb-
> Dbbbb-Fbbbb-Abbbbb-Cbbbbb-Ebbbbbb
>
> So technically, it's an octuply-diminished eleventh!
>
> But one would be very unlikely to use diatonic spelling
> for all the minor thirds in such a chain. Regardless,
> the last note is *enharmonically equivalent* to the first
> in 19-tone equal temperament, just as in 12-tone equal
> temperament, a chain of 12 perfect fifths leads to a note
> enharmonically equivalent to the first note. That's the
> important point here.

i can see from what you write that you are thinking of the
pitch universe entirely in 12edo/12-tET/dodekaphonic terms.

from that perspective, what paul wrote probably makes
absolutely no sense to you.

in hopes that a careful reading of it will help in your
comprehension of what paul is saying, try:

http://sonic-arts.org/dict/19edo.htm

i wish i had the time to make a mouse-over applet that
lets you hear the pitches that are on the graphs.

-monz

🔗monz <monz@attglobal.net>

hi Peter,

hey, if you espouse dodekaphony and no other tuning,
then exactly *why* are you reading and posting to the
*Alternative Tunings Mailing List*? !!!!!!!!

and please don't write some clever/sarcastic remark,
but rather, be sincere and give me a good explanation.

consider it a challenge if you must, but i honestly
want to know what you're doing here with this attitude.
it's _a priori_ going to provoke negative response
from the community, so why are you here pursuing it?

-monz

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
>
> > > > It is only a matter of time before the sitar
> > > > and Chinese bells and hammered harps are museum
> > > > pieces.
> > >
> > > I find that a truly vile sentiment.
> > >
> >
> > Again - it is a fact of life. Live with it.
>
> In response to this, let me quote you:
>
> > "Once again you are making assertions that cannot be
> > tested by us because of the brevity of our lives. The
> > simple fact is that we will never know. What is your
> > problem with that?"
>
> Now who's the hypocrite?
>
> > > The sophistication and aesthetic content of
> > > non-Western musics is evidently not something
> > > you're willing to consider. Based on what
> > > experience do you make this vast, genocidal dismissal?
> > >
> >
> > You are evidently unwilling to accept reality.
> > That is your problem, not mine.

and that's simply another dismissal, of paul's question.

> OK, then I'm endlessly grateful to the universe
> for this 'problem' of having my aesthetic, emotional,
> intellectual, and spiritual vistas -- not to mention
> my musicianship -- continually opened by contact with
> previously unfamiliar (and yes, perhaps initially to
> someone from a different culture, 'primitive' and
> 'out-of-tune' sounding), but endlessly deep and rich,
> musics. For the fact that you don't have this 'problem',
> I can only feel sorry for you.
>
> > >
> > > > I feel that you are surrendering to a romanticism
> > > > about 'noble savages' and the suchlike that has no
> > > > substance in reality.
> > >
> > > I don't call my musician collaborators, let alone
> > > true masters, from other cultures 'noble savages'
> > > -- how insulting! This is getting absolutely disgusting . . .
> >
> > I use the term simply to illustrate my point, which you
> > are obtusely refusing to see while gayly making unfounded
> > predictions that cannot be verified.
>
> I know very well what the 'noble savage' myth implies,
> but let me assure you that I subscribe to no such
> demeaning mythology. So your use of the term, and your
> attempt to apply it to me, illustrate what point exactly?

🔗Carl Lumma <ekin@lumma.org>

🔗John A. deLaubenfels <jdl@adaptune.com>

[Kurt Bigler:]
>>Well, I figure it goes without saying that tied notes for example, should not be retuned...

[Paul E:]
>Though there might be a tiny bit of sliding involved -- I'm not sure if John's current software supports this . . .

Yes, there are horizontal springs which allow a continuously sounding note to retune on the fly; they are stiffer, of course, than horizontal springs which join a pitch degree across a span of time in which it does not sound. Consider the "comma pump" sequence:

C,E,G -> C,E,A -> D,F,A -> D,G,B -> C,E,G [repeat ad nauseum]

with notes tied wherever possible. Every chord change has at least one tied note, so if we disallow tuning motion within a continuous note, we must either accept permanent drift or a fixed-tuning meantone-like solution. The spring matrix can of course be adjusted to squeeze horizontal motion to nearly nothing, or to go to the other extreme with JI intervals everywhere and lots of horizontal motion, or even to accept drift by assigning negligible stiffness to the grounding springs.

Your ear (Paul E) is quite a bit more sensitive to horizontal motion than mine: you object to tunings where I can't even HEAR a change. So I would often follow up one tuning example with another having stiffer horizontal springs, which in general pleased your ear better.

JdL

http://www.adaptune.com

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

🔗Haresh BAKSHI <hareshbakshi@hotmail.com>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Peter,
>
>
> hey, if you espouse dodekaphony and no other tuning,
> then exactly *why* are you reading and posting to the
> *Alternative Tunings Mailing List*? !!!!!!!!
>
> and please don't write some clever/sarcastic remark,
> but rather, be sincere and give me a good explanation.
>
> consider it a challenge if you must, but i honestly
> want to know what you're doing here with this attitude.
> it's _a priori_ going to provoke negative response
> from the community, so why are you here pursuing it?
>
>
> -monz
>
>

I think you must have missed my post about atonality. Everything here
seems to devolve from an obsession with scales that divide the
octave, following Aristotle's dictum that the octave is supreme. That
is only the case for music playing communally on manual instruments
with fixed tunings. I have created melodies that proceed simply by
consonant vibration ratios without any reference whatever to a fixed
tonic.

Please don't repeat the stuff about no fixed notes on viols. To play
a viol along with a clavier require the viol to submit to the tuning
of the clavier. That is what playing communally with another musician
is all about. The players must agree beforehand the rules that govern
their playing together.

🔗monz <monz@attglobal.net>

hi Peter,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > hi Peter,
> >
> > --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
<sault@c...>
> > wrote:
> >
> >
> > > I quote from the 'Oxford Companion to Music', since you are
> > > now demanding citations:-
> > > "The diatonic scales are the major and minor, made up of
> > > tones and semitones (in the case of the harmonic minor scale,
> > > also an augmented second), as distinct from the chromatic,
> > > made up entirely of semitones. The modes are diatonic in
> > > structure."
> > >
> > > I don't see anything about meantones there.
> >
> >
> >
> > and i don't see anything about dodekaphony.
> >
> > you're simply projecting dodekaphony and 12edo onto that
> > Oxford definition, which does not specify any tuning whatsoever.
> >
>
> No. I was simply refuting whoever it was who claimed that
> the definition of 'diatonic' somehow involves 'meantone',

i think that was Gene who said that.

> which it does not.

well, often "diatonic" most certainly *does* involve meantone.
but "diatonic" may also refer to Pythagorean, or in the case
of 12edo, both simultaneously.

-monz

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Peter,
>
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
> > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > > hi Peter,
> > >
> > > --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
> <sault@c...>
> > > wrote:
> > >
> > >
> > > > I quote from the 'Oxford Companion to Music', since you are
> > > > now demanding citations:-
> > > > "The diatonic scales are the major and minor, made up of
> > > > tones and semitones (in the case of the harmonic minor scale,
> > > > also an augmented second), as distinct from the chromatic,
> > > > made up entirely of semitones. The modes are diatonic in
> > > > structure."
> > > >
> > > > I don't see anything about meantones there.
> > >
> > >
> > >
> > > and i don't see anything about dodekaphony.
> > >
> > > you're simply projecting dodekaphony and 12edo onto that
> > > Oxford definition, which does not specify any tuning whatsoever.
> > >
> >
> > No. I was simply refuting whoever it was who claimed that
> > the definition of 'diatonic' somehow involves 'meantone',
>
>
> i think that was Gene who said that.
>
>
> > which it does not.
>
>
> well, often "diatonic" most certainly *does* involve meantone.
> but "diatonic" may also refer to Pythagorean, or in the case
> of 12edo, both simultaneously.
>
>
> -monz

Well now. I already quoted the definition of 'diatonic' from
the 'Oxford Companion to Music', which does not mention 'meantone'.
Here is a link http://dictionary.reference.com/search?q=diatonic to
another definition, which also does not include any reference
to 'meantone'. What is your reference?

🔗monz <monz@attglobal.net>

hi Peter,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > hi Peter,
> >
> >
> > hey, if you espouse dodekaphony and no other tuning,
> > then exactly *why* are you reading and posting to the
> > *Alternative Tunings Mailing List*? !!!!!!!!
> >
> > and please don't write some clever/sarcastic remark,
> > but rather, be sincere and give me a good explanation.
> >
> > consider it a challenge if you must, but i honestly
> > want to know what you're doing here with this attitude.
> > it's _a priori_ going to provoke negative response
> > from the community, so why are you here pursuing it?
> >
> >
> > -monz
> >
> >
>
> I think you must have missed my post about atonality.

yes, i did.

> Everything here seems to devolve from an obsession with
> scales that divide the octave, following Aristotle's dictum
> that the octave is supreme.

it only seems that way to you. i guess you haven't been
reading the list for very long.

of course, most of the tunings and scales discussed here
do involve "8ve-equivalence" ... but we certainly have
very often discussed tunings that don't, sometimes going
into some very deep research about them.

*no* interval is sacred on this list !!!! ;-)

> That is only the case for
> music playing communally on manual instruments with fixed
> tunings. I have created melodies that proceed simply by
> consonant vibration ratios without any reference whatever
> to a fixed tonic.
>
>
> Please don't repeat the stuff about no fixed notes on
> viols. To play a viol along with a clavier require the
> viol to submit to the tuning of the clavier. That is
> what playing communally with another musician is all
> about. The players must agree beforehand the rules that
> govern their playing together.

ah, yes, what you say here is true.

but what about communal music-making in which there are
*no* instruments with fixed tuning? ... such as:
string quartets, or barbershop quartet singing.

the only notes that will be present in that music are
those which the performers hear as being "in tune"
... whatever that means in those particular cases.

and the *string quartet* is the specific example i used
earlier.

-monz

🔗monz <monz@attglobal.net>

hi Peter,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> > well, often "diatonic" most certainly *does* involve
> > meantone. but "diatonic" may also refer to Pythagorean,
> > or in the case of 12edo, both simultaneously.
>
>
> Well now. I already quoted the definition of 'diatonic'
> from the 'Oxford Companion to Music', which does not
> mention 'meantone'. Here is a link
http://dictionary.reference.com/search?q=diatonic
> to another definition, which also does not include any
> reference to 'meantone'. What is your reference?

i'm *SO* glad you asked *ME* that !!!!

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

;-)

the point i was making was that the Oxford stayed neutral
by not mentioning *anything* about tuning except generic
interval-sizes, which exist in many, many different actual
sizes.

historically, the diatonic scale arose within the context
of Pythagorean tuning. later, as European musical culture
evolved to predominantly a meantone paradigm, the nature
of the diatonic scale shifted to accomodate meantone tuning,
but it was still diatonic.

-monz

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Peter,
>
>
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
> > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > > well, often "diatonic" most certainly *does* involve
> > > meantone. but "diatonic" may also refer to Pythagorean,
> > > or in the case of 12edo, both simultaneously.
> >
> >
> > Well now. I already quoted the definition of 'diatonic'
> > from the 'Oxford Companion to Music', which does not
> > mention 'meantone'. Here is a link
> http://dictionary.reference.com/search?q=diatonic
> > to another definition, which also does not include any
> > reference to 'meantone'. What is your reference?
>
> i'm *SO* glad you asked *ME* that !!!!
>
> http://sonic-arts.org/dict/diatonic.htm
>
> ;-)
>
> the point i was making was that the Oxford stayed neutral
> by not mentioning *anything* about tuning except generic
> interval-sizes, which exist in many, many different actual
> sizes.
>
> historically, the diatonic scale arose within the context
> of Pythagorean tuning. later, as European musical culture
> evolved to predominantly a meantone paradigm, the nature
> of the diatonic scale shifted to accomodate meantone tuning,
> but it was still diatonic.

It would appear that you are agreeing with me. The diatonic nature of
a scale has nothing whatever to do with the precise values of the
tones and semitones constituting it.

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
>
> > I quote from the 'Oxford Companion to Music', since you are now
> > demanding citations:-
> > "The diatonic scales are the major and minor, made up of tones
and
> > semitones (in the case of the harmonic minor scale, also an
> augmented
> > second), as distinct from the chromatic, made up entirely of
> > semitones. The modes are diatonic in structure."
> >
> > I don't see anything about meantones there.
>
> It's there if you carefully read between the lines, since it
> says "tones", not "major tones" and "minor tones". Two distinct
kinds
> of tones are not being assumed. Unless you assume two semitones
must
> make up a tone, which historically one cannot do, we are left with
> meantone.

I think you are reading into it something which is not there. Can you
provide an independent reference for your terms "major tone"
and "minor tone"? On this side of the Atlantic a 'tone' is a class of
interval equal to two successive semitones. The exact size of it is
neither here nor there. Whether a particular 'tone' evaluates to 8:9,
9:10, 1:1.1225 or what have you, it is still a 'tone' and is never
a 'semitone'. I am beginning to suspect that you are indulging in
pure sophistry, Gene. I too love a good debate but always hope that
something constructive will emerge out of it. It seems to me that on
this issue we are going around a fruitloop, of benefit to nobody let
alone you or I.

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > hey, if you espouse dodekaphony and no other tuning,
> > then exactly *why* are you reading and posting to the
> > *Alternative Tunings Mailing List*? !!!!!!!!
>
> His tuning certainly counts as alternate. I'm not so sure it counts
> as dodekaphony, since there seems to be an extra tritone lurking in
> the underbrush.

I just don't sweep it under the carpet as others seem to do. Every
natural scale that has a single central pitch class has a
complementary pair at that position. Perhaps I am just the first to
acknowledge this rather than trying to skate around the issue. For
practical purposes on traditional fixed pitch instruments (i.e. not
viols etc) only one can be used. But in the theoretical arithmetic I
can see two. I doubt very strongly that many, if any, musicians can
distinguish between 32:45 and 45:64. It is a proven fact of
perception that, despite the presence of an audible beat, when two
notes get close enough together it is impossible to tell which is the
higher and which is the lower. The technique used by piano tuners in
this situation is always to back off a bit (i.e. to detune) and then
to bring the two together again, repeatedly until no beat can be
detected.

🔗Kurt Bigler <kkb@breathsense.com>

on 12/9/03 9:10 PM, Peter Wakefield Sault <sault@cyberware.co.uk> wrote:

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
>> wrote:
>>
>>> I quote from the 'Oxford Companion to Music', since you are now
>>> demanding citations:-
>>> "The diatonic scales are the major and minor, made up of tones
> and
>>> semitones (in the case of the harmonic minor scale, also an
>> augmented
>>> second), as distinct from the chromatic, made up entirely of
>>> semitones. The modes are diatonic in structure."
>>>
>>> I don't see anything about meantones there.
>>
>> It's there if you carefully read between the lines, since it
>> says "tones", not "major tones" and "minor tones". Two distinct
> kinds
>> of tones are not being assumed. Unless you assume two semitones
> must
>> make up a tone, which historically one cannot do, we are left with
>> meantone.
>
> I think you are reading into it something which is not there. Can you
> provide an independent reference for your terms "major tone"
> and "minor tone"? On this side of the Atlantic a 'tone' is a class of
> interval equal to two successive semitones. The exact size of it is
> neither here nor there. Whether a particular 'tone' evaluates to 8:9,
> 9:10, 1:1.1225 or what have you, it is still a 'tone' and is never
> a 'semitone'. I am beginning to suspect that you are indulging in
> pure sophistry, Gene. I too love a good debate but always hope that
> something constructive will emerge out of it. It seems to me that on
> this issue we are going around a fruitloop, of benefit to nobody let
> alone you or I.

You spent three sentences carefully elucidating personally subjective
subtlties of how communication appears to you to be failing. An equal
number of questions that redirect things to the point would assure that you
keep up your end, and help with the communication, such that you might
receive a response that *you* experience as direct to your point. This is a
process. Communication will never happen to one person's specifications.
It is the existence of a continuing process, not the form it takes, which
characterizes communication, as I understand it.

I suspect Gene has good reason for saying that one can not assume two
semitones make up a tone, but has not revealed it. I understand this also
as a "style": Gene does not assume something needs explaining until he is
asked for the explanation. Knowing that, what do you have to ask?

I would like to know whether there is any implicit reference to the circle
of fifths in all of this. I was assuming so when I originally mentioned
meantone. If so, then a generalized sense of meantone as I understand it
from usage here, becomes relevant. As knowledge unfolds, existing meanings
change. A lot of unfolding of knowledge has occured here over several
years. As a result, terms like "meantone" are changing somewhat in their
meaning. This is a natural occurrence within a culture, and something that
is accelerated in subcultures such as this one.

However in this case I see diatonic as needing to include temperaments, thus
leaving the strict meantone territory. A tempered 12-tone scale is a
diatonic scale, no? So what is the constant? I am guessing it is either
the circle of fifths or it is something in the development process by which
sharps/flats are added to a scale which originally didn't have them.

-Kurt

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

🔗monz <monz@attglobal.net>

hi Peter and Gene,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

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

> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > >
> > > --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
> <sault@c...>
> > > wrote:
> > >
> > > > It would appear that you are agreeing with me.
> > > > The diatonic nature of a scale has nothing whatever
> > > > to do with the precise values of the tones and
> > > > semitones constituting it.

Peter, i'm not quite sure yet how much i agree with *you*,
since to my mind you haven't made that much effort to
clarify what i'm having trouble understanding in your posts.
however, yes, i do agree with *this* statement.

as you should have gleaned from my own definition of
"diatonic", the word itself simply refers to a type of
scale which contains mostly "whole-tones". that's
what the ancient Greeks meant when they used that word,
and that is still what characterizes what any of us here
would think of as a "diatonic scale".

later, a more specific idea of "the diatonic scale" came
to mean a 7-note scale which was composed of 5 "whole-steps"
and 2 "half-steps".

but it doesn't really mean anything more specific than
that ... unless, of course, the writer specifies a certain
tuning.

> > > Meantone does not refer to a precise value, or at
> > > least not on this list.
> >
> > In particular, it is quite reasonable in my book
> > to consider Pythagoran to be a version of meantone,
> > along with 12-equal, of course.
>
> WHAT?!?!?! I'm leaving this thread.

come on, don't wimp out and become a girly-man now!

Gene is primarily an algebraist, and he has his own
mathematical reasons for wanting to "consider Pythagorean
to be a version of meantone". that needn't bother us.

-monz

🔗monz <monz@attglobal.net>

guys (Peter, Gene, Kurt),

(Peter, in this post i use a common convention around here:
the tilde ~ means "approximately")

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

> on 12/9/03 9:10 PM, Peter Wakefield Sault <sault@c...> wrote:
>
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> >> --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
<sault@c...>
> >> wrote:

> >>
> >>> I quote from the 'Oxford Companion to Music', since
> >>> you are now demanding citations:-
> >>> "The diatonic scales are the major and minor, made
> >>> up of tones and semitones (in the case of the
> >>> harmonic minor scale, also an augmented second),
> >>> as distinct from the chromatic, made up entirely of
> >>> semitones. The modes are diatonic in structure."
> >>>
> >>> I don't see anything about meantones there.
> >>
> >> It's there if you carefully read between the lines,
> >> since it says "tones", not "major tones" and
> >> "minor tones". Two distinct kinds of tones are
> >> not being assumed. Unless you assume two semitones
> >> must make up a tone, which historically one cannot do,
> >> we are left with meantone.

bravo, Gene. a very good and *very perceptive* point.

> > I think you are reading into it something which is not
> > there. Can you provide an independent reference for your
> > terms "major tone" and "minor tone"? On this side of
> > the Atlantic a 'tone' is a class of interval equal to
> > two successive semitones. The exact size of it is
> > neither here nor there. Whether a particular 'tone'
> > evaluates to 8:9, 9:10, 1:1.1225 or what have you,
> > it is still a 'tone' and is never a 'semitone'. I am
> > beginning to suspect that you are indulging in pure
> > sophistry, Gene. I too love a good debate but always
> > hope that something constructive will emerge out of it.
> > It seems to me that on this issue we are going around a
> > fruitloop, of benefit to nobody let alone you or I.

Peter, Gene does not need any "independent reference" for
the terms "major tone" and "minor tone" -- they both arise
simply as a result of using just-intonation. the "major tone"
is the 9:8 ratio, the "minor tone" is the 10:9 ratio.

> However in this case I see diatonic as needing to include
> temperaments, thus leaving the strict meantone territory.
> A tempered 12-tone scale is a diatonic scale, no? So what
> is the constant? I am guessing it is either the circle
> of fifths or it is something in the development process by
> which sharps/flats are added to a scale which originally
> didn't have them.

Kurt, sharps and flats really have nothing to do with it.

the word "diatonic" was originally used by the ancient Greeks
to indicate a type of scale which was composed mostly of
"whole tones", and this is still what it means.

during the so-called "common-practice" era (c. 1600-1900)
"diatonic" came to refer to a specific type of scale
construction composed of 5 "whole steps" and 2 "half-steps",
with "8ve-equivalence".

as i thought i already belabored, this arose first in
Pythagorean (3-limit) tuning, so that the "whole step"
was a 9:8 ratio (~204 cents) and the "half step" was a
256:243 ratio (~90 cents).

(5*~204) + (2*~90) = ~1020 + ~180 = ~1200 cents, the "8ve".

the basic diatonic scale was what we would now call the
"A natural minor scale", using only the white keys of the piano.

this is the basis of our "A B C D E F G A ..." nomenclature,
as well as lines and spaces of the regular staff notation.

when the European tuning paradigm shifted to 1/4-comma
meantone c. 1500, the diatonic scale was retained, with
its 5+2 format, but now the "whole step" was the true
"mean tone" of ~193 cents, and the "half step" was still
the difference between a "perfect 4th" and 2 "whole steps"
as it had always been in Pythagorean, only now the "half step"
was ~117 cents.

(5*~193) + (2*~117) = ~965 + ~234 = ~1200 cents, the "8ve".

around 1900, the tuning paradigm again shifted, this time
to the 12edo which is still our nearly-universal standard.
in this tuning, a "whole step" is 200 cents and a "half step"
is 100 cents.

obviously, (5*200) + (2*100) = 1000 + 200 = 1200 cents, the "8ve".

-monz

🔗monz <monz@attglobal.net>

hi Peter,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> >
> > Meantone does not refer to a precise value, or at least
> > not on this list.
>
> I understand 'meantone' to mean a whole class of tunings
> where the major thirds are accurate and other intervals
> adapted.

"meantone" in its specific sense refers to the single tuning
where each "perfect-5th" is narrowed by 1/4 syntonic comma,
so that four "perfect-5ths", reduced by two "8ves", results
in precisely the JI "major-3rd" with 5:4 ratio.

in its generic sense, "meantone" refers to the whole family
of tunings in which the syntonic comma disappears (because
it is tempered out) and four "5ths" give the best approximation
to the "major-3rd".

see my Dictionary entry on "meantone" for more:

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

you might also want to look at my "bingo-card lattices" for
such equal-tempered meantones as 12, 19, 26, 31, 43, 50, and 55:

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

these diagrams show at a glance which "commas" are tempered out.
all of the above temper out the syntonic comma (prime-factored
as 3^4 * 5^-1) and thus they are all meantones (in the generic
sense).

> The organs of Bach's day were tuned in some or other version
> of the meantone system. Some of Bach's organ music may have
> been written to be compatible with such instruments. His
> 'Well-tempered Clavier' of 1722 was, however, created for
> Equal Temperament, not meantone.

wrong. see my last post.

the _Well-Tempered Klavier_ was intended to be tuned in
a 12-note circulating temperament, not equal-temperament.

-monz

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> I think you are reading into it something which is not there. Can
you
> provide an independent reference for your terms "major tone"
> and "minor tone"?

http://www.xs4all.nl/~huygensf/doc/intervals.html

On this side of the Atlantic a 'tone' is a class of
> interval equal to two successive semitones.

On any side of the Atlantic a useful interval to know about is the
(minor) diesis, which is also on the list above. It is
(16/15)/(25/24) = 128/125. The diatonic semitone of 16/15 and the
chromatic semitone of 25/24 are of course not equal in just
intonation, but they are also not equal in, eg, 1/4 comma meantone.
In other words C#', which is a major third above A, is a chromatic
semitone above C'; whereas Db, a major third below F, is a diatonic
semitone above C. The two are equal in the 12-et version of meantone,
or in any system where the major third is equated to the cube root of
two, but 16/15 is larger than 25/24 in just intonation, and in the
more authentic meantone systems with fifths flatter than those of 12-
et we also have that major thirds are flatter than those of 12-et and
the chromatic semitone smaller than the diatonic semitone.

For instance if we divide the octave into 31 parts, then
a fifth is 18 parts and a major third 10 parts. The diatonic semitone
corresponds to 2*(2/3)*(4/5), so it is 31-18-10=3 parts. The
chromatic semitone corresponds to (1/2)*(5/3)*(5/4), and
5/3 = 2*(2/3)*(5/4), so it has 31-18+10=23 parts, and so the chromatc
semitone has -31+23+10=2 parts. The two semitones taken together
produce the single full tone, which is neither a 9/8 or a 10/9 but
about half-way between--ie, a *mean* tone. This has been an important
fact of music life on your side of the Atlantic for hundreds of
years, and is a key thing to bear in mind for anyone performing early
music.

The exact size of it is
> neither here nor there. Whether a particular 'tone' evaluates to
8:9,
> 9:10, 1:1.1225 or what have you, it is still a 'tone' and is never
> a 'semitone'. I am beginning to suspect that you are indulging in
> pure sophistry, Gene.

Listen and learn.

🔗Graham Breed <graham@microtonal.co.uk>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Aaron K. Johnson <akjmicro@comcast.net>

Tuners,

It seems to me that argument for the Bach keyboard oeuvre being in 12-tet
because of the existence of fretted lutes and guitars in the 16th century,
etc. are faulty. After all, these fretted, 12-tet instruments co-existed with
centuries of keyboards tuned in several varieties of meantone, which
indicates that there was no neccessary synchrony between fretted and keyboard
instruments with regards to a temperament bearing plan.

12-tet is wholly unsuited to the color of either harpsichord or fortepiano,
with their bright spectrum and longer decay time than a lute, which has a
gentler spectra.

On a subjective level, having tuned the WTC on harpsichord to a Neidhardt or
Werckmeister temperament, I'm won over by the play of the different moods of
each key--Bach knew just what to write for each key color intimately and
appropriately.

Yes, the WTC works in 12-tet, but I prefer the earthier colors and shadings,
and the contrast between calmer triads closer to C major, and the active
thirds of the distant triads.

Another piece of evidence that Bachs tuning was not 12-tet--he was reputedly
able to tune his clavier in 10 minutes!!!!

Best,
Aaron.

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

🔗Carl Lumma <ekin@lumma.org>

🔗Aaron K. Johnson <akjmicro@comcast.net>

On Friday 12 December 2003 12:17 am, Peter Wakefield Sault wrote:
> > Another piece of evidence that Bachs tuning was not 12-tet--he was
>
> reputedly
>
> > able to tune his clavier in 10 minutes!!!!
>
> Isn't that a bit of a non-sequitur? In his day musicians and tuners
> were one and the same - those with a musical ear. He came from a
> family of professional musicians of just this sort. He learned his
> art at the same time and pace as he learned to speak. We, in our
> uniformly mediocre world which forcibly, by law, delegates education
> to institutionalized 'professionals' whose primary task is political
> indoctrination, do not have a hope in hell of ever achieving such
> excellence. He could very probably tune his claviers in any one of a
> dozen different ways in ten minutes and all by ear alone.

You forget the fact that his contemporaries found this fact remarkable enough
to note it.......

-A.

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
wrote:
> On Friday 12 December 2003 12:17 am, Peter Wakefield Sault wrote:
> > > Another piece of evidence that Bachs tuning was not 12-tet--he
was
> >
> > reputedly
> >
> > > able to tune his clavier in 10 minutes!!!!
> >
> > Isn't that a bit of a non-sequitur? In his day musicians and
tuners
> > were one and the same - those with a musical ear. He came from a
> > family of professional musicians of just this sort. He learned his
> > art at the same time and pace as he learned to speak. We, in our
> > uniformly mediocre world which forcibly, by law, delegates
education
> > to institutionalized 'professionals' whose primary task is
political
> > indoctrination, do not have a hope in hell of ever achieving such
> > excellence. He could very probably tune his claviers in any one
of a
> > dozen different ways in ten minutes and all by ear alone.
>
> You forget the fact that his contemporaries found this fact
remarkable enough
> to note it.......
>
> -A.

True but what's that got to do with whether or not he could tune ET
by ear? I just cannot accept that a man of his intellect would spend
his whole life immersed in music and tuning and never consider or
experiment with ET - especially in view of the fact that ET
instruments, albeit not claviers, had been around for nearly 200
years and that ET had first been proposed 2000 years earlier.

Peter

🔗Werner Mohrlok <wmohrlok@hermode.com>

-----Ursprï¿½ngliche Nachricht-----
Von: Aaron K. Johnson [mailto:akjmicro@comcast.net]
Gesendet: Freitag, 12. Dezember 2003 15:20
An: tuning@yahoogroups.com
Betreff: Re: [tuning] Re: Bach - Fretted vs. Keyboard tunings

You forget the fact that his contemporaries found this fact remarkable
enough
to note it.......

-A.

I know harpsichord players who can do so. But not by retuning all tones as
it should be done when creating different "well tempered" tuning models.
This would be impossible. Impossible, too, for Bach.
They handle it as follows:
The tuning model is a meantone temperament. For instance in the standard
line from Eb to G#, which means: The major chords beginning with Eb-G-Bb
and ending with E-G#-B are tuned to good frequency ratios. With this model
music in the the keys Bb major, F major, C major and so on, ending with
A-major (and their minor parallels) can be performed.
If they want to change to a piece in Ab major they tune upwards the G# to
an Ab and the C# to a Db.
Inverse, to a piece in E major they tune downwards the Eb to a D#.
Indeed, retuning one tone in all octaves required less than ten minutes.
Is there no well educated harpsichord player beyond us?
Werner Mohrlok

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🔗kraig grady <kraiggrady@anaphoria.com>

Hello Aaron!
I am sure you are right about this but have you tried tuning the well temperment starting on another pitch to see if the pieces sounded right or wrong. or is it possible to
find a key where it is really bad sounding

Regardless it seems when we look at measurements done in the field, we fine a preferance for scales with uneqaul sized steps. Rameau says something along these lines also

>
> From: "Aaron K. Johnson" <akjmicro@comcast.net>
> Subject:
>
>
> On a subjective level, having tuned the WTC on harpsichord to a Neidhardt or
> Werckmeister temperament, I'm won over by the play of the different moods of
> each key--Bach knew just what to write for each key color intimately and
> appropriately.
>
> Yes, the WTC works in 12-tet, but I prefer the earthier colors and shadings,
> and the contrast between calmer triads closer to C major, and the active
> thirds of the distant triads.
>
> Another piece of evidence that Bachs tuning was not 12-tet--he was reputedly
> able to tune his clavier in 10 minutes!!!!
>
> Best,
> Aaron.
>
>

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

🔗Kurt Bigler <kkb@breathsense.com>

on 12/12/03 8:00 PM, Peter Wakefield Sault <sault@cyberware.co.uk> wrote:

> --- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
> wrote:
>> On Friday 12 December 2003 12:17 am, Peter Wakefield Sault wrote:
>>>> Another piece of evidence that Bachs tuning was not 12-tet--he
> was
>>>
>>> reputedly
>>>
>>>> able to tune his clavier in 10 minutes!!!!
>>>
>>> Isn't that a bit of a non-sequitur? In his day musicians and
> tuners
>>> were one and the same - those with a musical ear. He came from a
>>> family of professional musicians of just this sort. He learned his
>>> art at the same time and pace as he learned to speak. We, in our
>>> uniformly mediocre world which forcibly, by law, delegates
> education
>>> to institutionalized 'professionals' whose primary task is
> political
>>> indoctrination, do not have a hope in hell of ever achieving such
>>> excellence. He could very probably tune his claviers in any one
> of a
>>> dozen different ways in ten minutes and all by ear alone.
>>
>> You forget the fact that his contemporaries found this fact
> remarkable enough
>> to note it.......
>>
>> -A.
>
> True but what's that got to do with whether or not he could tune ET
> by ear? I just cannot accept that a man of his intellect would spend
> his whole life immersed in music and tuning and never consider or
> experiment with ET - especially in view of the fact that ET
> instruments, albeit not claviers, had been around for nearly 200
> years and that ET had first been proposed 2000 years earlier.
>
> Peter

Even the most brilliant have assumptions, and in spite of the bad
connotation of "assumption", some of those assumptions might have been good
anyway. Bach might have intuitiviely/unconsciously realized that 12et was
just a bad idea (to him), that is he might never have even considered
thinking about it for longer than a millisecond. So for him it would have
been a sporadic neural firing that disappeared into the noise. ;)

I'm not really saying 12et is all bad. It is quite good for octatonic, for
example. My recent experiences indicate that 12et may be a *particularly*
bad choice for piano though, i.e. if you were looking for what tuning would
create the most unpleasant attack transients 12et would be ideal. I'll have
more to say about that at another time.

-Kurt