Re: [tuning] Re: Blackjack subsets-2nd attempt

Paul Erlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > 6 notes - the 1 -3 -5 -7 hexany = A, C#[ , E, G<
>
> That's only four notes. The hexany is the six-tone scale that
> Robert Walker keeps talking about, with the wind chimes and all.

OK - disregarding my notational idiosyncracies for this hexany I get Blackjack steps 3, 7, 8, 12, 17,
19.

> > - the JI major scale with no second = can't find a good
> 5:3 starting on A.
>
> The scale doesn't start on A.

Got this one now from your lattice; here's one example, centred on step 8 :-

3 15 6

17 8 20

> > - a 4:5:6:7:9 = A, C#[ , E, G< , B[ (assuming that the :9 is
> an approximate 8:7?)
>
> This is strange notation and doesn't correspond to any of those
> proposed so far. But in any case, the chord in question doesn't
> start on A, and is within 4 cents of a pure 4:5:6:7:9.

Got this one too - 17, 8, 3, 13, 20. Or 15, 6, 1, 11, 18. And so on.

My first mistake is that I'm not using the lattices to do my basic workings. The second is that I'm not
consulting Dave Keenan's cut and paste charts.

Thanks for being patient

Kind Regards

>

>

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
>
> Paul Erlich wrote:
>
> > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> >
> > > 6 notes - the 1 -3 -5 -7 hexany = A, C#[ , E, G<
> >
> > That's only four notes. The hexany is the six-tone scale that
> > Robert Walker keeps talking about, with the wind chimes and all.
>
> OK - disregarding my notational idiosyncracies for this hexany I
get Blackjack steps 3, 7, 8, 12, 17,
> 19.

Excellent! That's one. It also appears in at least four other
positions in the Blackjack scale. Can you find them?

> > > - the JI major scale with no second = can't find a
good
> > 5:3 starting on A.
> >
> > The scale doesn't start on A.
>
> Got this one now from your lattice; here's one example, centred on
step 8 :-
>
> 3 15 6
>
> 17 8 20

Great! Can you find the other one?

Correction to my previous post: if you want one of these to have A as
tonic, then you need to center the Blackjack scale on either

G raised by 1/4 tone

or

G lowered by 1/3 tone.

Paul Erlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> >
> >
> > Paul Erlich wrote:
> >
> > > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> > >
> > > > 6 notes - the 1 -3 -5 -7 hexany = A, C#[ , E, G<
> > >
> > > That's only four notes. The hexany is the six-tone scale that
> > > Robert Walker keeps talking about, with the wind chimes and all.
> >
> > OK - disregarding my notational idiosyncracies for this hexany I
> get Blackjack steps 3, 7, 8, 12, 17,
> > 19.
>
> Excellent! That's one. It also appears in at least four other
> positions in the Blackjack scale. Can you find them?

Yes, from your multicoloured lattice I can see them popping out all over the place. For example,
there's one at G> , B[ , D> , Db^ , Ab^ , F in your notation. What an eye opener!

>
>
> > > > - the JI major scale with no second = can't find a
> good
> > > 5:3 starting on A.
> > >
> > > The scale doesn't start on A.
> >
> > Got this one now from your lattice; here's one example, centred on
> step 8 :-
> >
> > 3 15 6
> >
> > 17 8 20
>
> Great! Can you find the other one?

Yes, by scale steps I have

1 13 4

15 6 18

>
> Correction to my previous post: if you want one of these to have A as
> tonic, then you need to center the Blackjack scale on either
>
> G raised by 1/4 tone
>
> or
>
> G lowered by 1/3 tone.

Thanks again. I'd be better working from scale steps or from your notation for the moment. Then
I'll deal with notation when I have everything tuned up.

I've noticed that two adjacent hexanies share two common tones, Ab^ and F in your notation.
Consequently two of my 6 string zithers could be tuned to one hexany each, using the common tones
to modulate. As the zithers have a nice long sustain, this would work well with the kind of music
I'm writing.

Kind Regards

>

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> Kind Regards
>
Want to have another go at finding the 4:5:6:7:9 chords (remember, a
4:5:6:7 chord is a little tetrahedron on the lattice), and the
4:6:7:9:11 chords (remember, 9:11 is a neutral third)?

Paul Erlich wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> >
> > Kind Regards
> >
> Want to have another go at finding the 4:5:6:7:9 chords (remember, a
> 4:5:6:7 chord is a little tetrahedron on the lattice), and the
> 4:6:7:9:11 chords (remember, 9:11 is a neutral third)?

Yo! - 4: 5: 6: 7: 9 is 15, 1, 6, 11, 18 or, by your notation; A[ , C> , E[ , Gb^ (the
tetrahedron) and B[. With another on Bb< as a root. Now I understand the big discussions on
stellation and geometry in general. Once you understand your shapes on a lattice they remain
constant from lattice to lattice given the same axes.

4: 6: 7: 9: 11 is, for example, 9, 0, 5, 12, 18 in your notation F, C, Eb< , G, B[ . The 11 and
the 4 are at polar opposites of a hexany for my future reference.

Most gratifying and thanks for your kind guidance (assuming these are correct)

Best Wishes

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> Most gratifying and thanks for your kind guidance (assuming these
are correct)

You certainly seem to be getting the picture! It would have been even
easier to find these (and all the other examples of these chords) had
you worked from Dave's slide rule rather than my lattice (though of
course my lattice is prettier :)).

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

/tuning/topicId_29874.html#29971

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > Most gratifying and thanks for your kind guidance (assuming these
> are correct)
>
> You certainly seem to be getting the picture! It would have been
even easier to find these (and all the other examples of these
chords) had you worked from Dave's slide rule rather than my lattice
(though of course my lattice is prettier :)).

Hi Paul!

Well, since I basically have been using your lattice to find common-
tone blackjack harmonies, now I'm naturally wondering what I could be
doing with Dave's slide rules that I can't do with your lattice...

Perhaps this is an obvious question with an obvious answer, but it
isn't immediately coming to me...

JP

--- In tuning@y..., jpehrson@r... wrote:

> Hi Paul!
>
> Well, since I basically have been using your lattice to find common-
> tone blackjack harmonies, now I'm naturally wondering what I could
be
> doing with Dave's slide rules that I can't do with your lattice...
>
> Perhaps this is an obvious question with an obvious answer, but it
> isn't immediately coming to me...
>
> JP

Well, it's easy to see the 7-limit tetrads on my lattice, but what
about 9-limit and 11-limit harmonies (some of which were included in
my keyboard charts)? With the slide rule, one can immediately see
whether a given chord type will occur in Blackjack, and if it does,
where, and how many times.

The advantage of the lattice is that one can immediately see all the
possibilities for common-tone chord changes (at least between 7-limit
tetrads). To do that with the slide rule would involve having several
different "strips" and moving them around with respect to one
another -- not as elegant, and not as conducive to long-range
planning.

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

/tuning/topicId_29874.html#29991

> --- In tuning@y..., jpehrson@r... wrote:
>
> > Hi Paul!
> >
> > Well, since I basically have been using your lattice to find
common-
> > tone blackjack harmonies, now I'm naturally wondering what I
could
> be
> > doing with Dave's slide rules that I can't do with your lattice...
> >
> > Perhaps this is an obvious question with an obvious answer, but
it
> > isn't immediately coming to me...
> >
> > JP
>
> Well, it's easy to see the 7-limit tetrads on my lattice, but what
> about 9-limit and 11-limit harmonies (some of which were included
in
> my keyboard charts)? With the slide rule, one can immediately see
> whether a given chord type will occur in Blackjack, and if it does,
> where, and how many times.
>
> The advantage of the lattice is that one can immediately see all
the
> possibilities for common-tone chord changes (at least between 7-
limit
> tetrads). To do that with the slide rule would involve having
several
> different "strips" and moving them around with respect to one
> another -- not as elegant, and not as conducive to long-range
> planning.

Got it! Thanks!

JP

Hello all!

Paul Erlich wrote:

> Well, it's easy to see the 7-limit tetrads on my lattice, but what
> about 9-limit and 11-limit harmonies (some of which were included in
> my keyboard charts)? With the slide rule, one can immediately see
> whether a given chord type will occur in Blackjack, and if it does,
> where, and how many times.

Oh, are you still using the normal 7-limit lattice? I find my
7-limit/neutral third lattice much easier to use than either. If anybody
still hasn't caught on to it, the explanation starts at
<http://x31eq.com/lattice.htm> or a link from there or
something.

You could get slide rule-like behaviour on a 2-D lattice by using a
plastic sheet, writing on it, and moving it over the lattice. OHP
transparencies would probably work. Assuming you can't picture it your
head.

Graham

--- In tuning@y..., graham@m... wrote:
> Hello all!
>
> Paul Erlich wrote:
>
> > Well, it's easy to see the 7-limit tetrads on my lattice, but
what
> > about 9-limit and 11-limit harmonies (some of which were included
in
> > my keyboard charts)? With the slide rule, one can immediately see
> > whether a given chord type will occur in Blackjack, and if it
does,
> > where, and how many times.
>
> Oh, are you still using the normal 7-limit lattice? I find my
> 7-limit/neutral third lattice much easier to use than either. If
anybody
> still hasn't caught on to it, the explanation starts at
> <http://x31eq.com/lattice.htm> or a link from there or
> something.
>
> You could get slide rule-like behaviour on a 2-D lattice by using a
> plastic sheet, writing on it, and moving it over the lattice. OHP
> transparencies would probably work. Assuming you can't picture it
your
> head.

That would be great in conjunction with your lattice, Graham --
especially since many of the 11-limit connections are not shown on it.

--- In tuning@y..., graham@m... wrote:

> You could get slide rule-like behaviour on a 2-D lattice by using a
> plastic sheet, writing on it, and moving it over the lattice.

The difference is that the scale is a chain of generators, so when
laid out 1-dimensionally, you can immediately see whether a
particular chord will "fit" and if so, how many times. On a plastic
sheet, you could slide it around and potentially fail to see the
point where it "fits".

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

/tuning/topicId_29874.html#30015

> --- In tuning@y..., graham@m... wrote:
> > Hello all!
> >
> > Paul Erlich wrote:
> >
> > > Well, it's easy to see the 7-limit tetrads on my lattice, but
> what
> > > about 9-limit and 11-limit harmonies (some of which were
included
> in
> > > my keyboard charts)? With the slide rule, one can immediately
see
> > > whether a given chord type will occur in Blackjack, and if it
> does,
> > > where, and how many times.
> >
> > Oh, are you still using the normal 7-limit lattice? I find my
> > 7-limit/neutral third lattice much easier to use than either. If
> anybody
> > still hasn't caught on to it, the explanation starts at
> > <http://x31eq.com/lattice.htm> or a link from there or
> > something.
> >
> > You could get slide rule-like behaviour on a 2-D lattice by using
a
> > plastic sheet, writing on it, and moving it over the lattice.
OHP
> > transparencies would probably work. Assuming you can't picture
it
> your
> > head.
>
> That would be great in conjunction with your lattice, Graham --
> especially since many of the 11-limit connections are not shown on
it.

Ummm. If I remember correctly, Graham's 2D version of this 11-limit
lattice was a bit "scrunched up" and it was hard to work with...

Anybody have the post# on the list of that... it's someplace here in
the archive...

Maybe with the transparencies this problem would be solved.

Although, at the moment, I am busy working with Paul's 7-limit
lattices and there is much to explore here, I would enjoy trying
to "mess around" with the 11-limit ones and trasparencies.

If anyone actually *produces* this, I would be more than willing to
pay something for the trouble, including postage.

Please write to me off list if this actually happens, since I think
this could be quite valuable for future blackjack composing...

Thanks!

________ ________ ______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

> Although, at the moment, I am busy working with Paul's 7-limit
> lattices and there is much to explore here, I would enjoy trying
> to "mess around" with the 11-limit ones and trasparencies.

Well, as you may know if you've been following, Alison within the
last couple of days has been able to find 9- and 11-limit chords on
_my_ lattice.

9 is just 3*3. The 11 Odentity can be found directly below the
corresponding root -- the two are at opposite ends of a hexany. For
example, an 11/8 above F is B[. This works because 384/385 vanishes
in MIRACLE and 72-tET.

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

/tuning/topicId_29874.html#30019

> --- In tuning@y..., jpehrson@r... wrote:
>
> > Although, at the moment, I am busy working with Paul's 7-limit
> > lattices and there is much to explore here, I would enjoy trying
> > to "mess around" with the 11-limit ones and trasparencies.
>
> Well, as you may know if you've been following, Alison within the
> last couple of days has been able to find 9- and 11-limit chords on
> _my_ lattice.
>
> 9 is just 3*3. The 11 Odentity can be found directly below the
> corresponding root -- the two are at opposite ends of a hexany. For
> example, an 11/8 above F is B[. This works because 384/385 vanishes
> in MIRACLE and 72-tET.

Oh... Well, does that pattern pertain *throughout* the lattice??

Is, for example, A> the 11/8 above Ev??

JP

--- In tuning@y..., jpehrson@r... wrote:

> Oh... Well, does that pattern pertain *throughout* the lattice??

But of course!

> Is, for example, A> the 11/8 above Ev??

As you can see from the notation itself, this is a fourth plus a
quartertone, or an 11/8!

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

/tuning/topicId_29874.html#30027

> --- In tuning@y..., jpehrson@r... wrote:
>
> > Oh... Well, does that pattern pertain *throughout* the lattice??
>
> But of course!
>
> > Is, for example, A> the 11/8 above Ev??
>
> As you can see from the notation itself, this is a fourth plus a
> quartertone, or an 11/8!

Hmmm... well, then, it certainly seems like your lattice can be used
to find at least *some* 11 limit stuff.

Now a confession to make:

I've been having a very hard time making "compound" chords in
blackjack. By "compound" chords, I mean "big" chords having, let's
say, 8 notes.

The lattice works well for devising various 4-pitch "common note"
progressions and, actually, some of them are working quite well in
retrograde, too. Naturally this is all subject to taste (hopefully).

However, in the construction of these "magnum" chords, I am stymied.

In my imagination, that was the reason for putting the *two* TX81Z's
together. I was imagining glorious 8-part chords with elements
shifting in and out, all in astonishing just intonation harmony!

However, it's not quite working out that way. All the "big" chords
sound just terrible.

Any suggestions?? :)

JP

--- In tuning@y..., jpehrson@r... wrote:

> However, it's not quite working out that way. All the "big" chords
> sound just terrible.
>
> Any suggestions?? :)
>
> JP

What "big" chords are you trying???

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

/tuning/topicId_29874.html#30032

> --- In tuning@y..., jpehrson@r... wrote:
>
> > However, it's not quite working out that way. All the "big"
chords
> > sound just terrible.
> >
> > Any suggestions?? :)
> >
> > JP
>
> What "big" chords are you trying???

Well, I was trying to develop extended ones using the "common tone"
methods only extending, naturally, from more than one common tone...

None were sounding too great. I can get you some specifics later,
but maybe I should just try some others first...

Thanks!

JP

--- In tuning@y..., jpehrson@r... wrote:

> Well, I was trying to develop extended ones using the "common tone"
> methods only extending, naturally, from more than one common tone...

I don't understand. Can you elaborate?

> None were sounding too great. I can get you some specifics later,
> but maybe I should just try some others first...
>
> Thanks!
>
> JP

The first issue is voicing. A nice-sounding 8-tone chord in blackjack
is likely to require you to stretch your fingers out tremendously on
the keyboard, probably farther than physically possible :)

Now I'd guess, since you mention "'common tone' methods", that you
were probably trying to play three or more adjacent tetrads at a
time, yes?

In JI, this would tend to work best if the tetrads were in 3:2
relationships to one another. However, even then you get dissonant
intervals like 21:16 and 64:63 very early in the process. Some people
like these intervals in this kind of context . . . try a 6-note chord
like Bb< F< C< (left hand), G> D> A> (right hand). Notice the very
small "64:63" interval between Bb< and A> -- it can clash more or
less depending on how you voice it. Now complete the two Otonalities
by inserting D[ and A[ (look on the lattice to see what I mean by
that). Play around with voicing, and you have a nice big rich "JI" 8-
tone chord.

Now since we're not quite in JI, we should take advantage of certain
unison vectors, like the 225:224. You see, a lot of intervals on the
lattice that would be "dissonant" in JI become "consonant" because of
this. If you look at your own "Tuning Lab" page, you can see this
happening in some of the chords (search the page for 225:224). One
example is something I called the "magic chord" a while ago. In
Blackjack you can find it at Db^ F G Bv. Note that in order to see
all the consonant intervals in this chord (and I'm counting 9:8 as
consonant for this exercise), you have to locate at least one of the
notes in more than one place in the lattice. For example, you could
go from Db^ east-northeast to F, east to G, and northeast to Bv, but
you wouldn't see that Bv is consonant with the starting point Db^
unless you continued south-southwest from Bv to _another_ Db^.
Grouping together more notes in the vicinity, and voicing carefully,
a chord like Db^ F Ab^ G Bv Ev C might prove interesting to you, as
well as similar chords elsewhere on the lattice. 225:224 even helps
you if you try to produce some nice big 5-prime-limit chords, like
say the Ramos-inspired Eb< Bb< F< C< D[ A[ E[ B[ or D[ A[ E[ B[ C> G>
D> A>, since each of the three 45:32s is approximating 7:5 very well.

But perhaps what you really desire are 15-limit Otonalities --
8:9:10:11:12:13:14:15 chords. Then Blackjack is probably not your
answer, though 72-tET can still serve you well -- if you used a 5/72-
oct. generator instead of a 7/72-oct. generator, then a 43-tone MOS
would give you (approximations to) four 8:9:10:11:12:13:14:15 chords
and four 8:9:10:11:12:13:14:15 chords -- though 43 is more than twice
as many notes as Blackjack!

I wrote,

> if you used a 5/72-
> oct. generator instead of a 7/72-oct. generator, then a 43-tone MOS
> would give you (approximations to) four 8:9:10:11:12:13:14:15
chords
> and four 8:9:10:11:12:13:14:15 chords

Oops -- the latter line should have read

"and four 1/(8:9:10:11:12:13:14:15) chords"

Hi Joseph. I figured we could look for some simple 7- and 8-note
harmonic series chords in Blackjack, and move on to polychords and
the like later.

Let's look at Dave Keenan's slide rule again:

2 9 16 23 30 37 44 51 58 65 0 7 14 21 28 35 42 49 56 63 70
5--------------7-----1-----------------3-----------------9-------11

I'll traslate into "our" note names, and to conserve space, I'll
write them vertically:

C D E E F G G A B B C D D E F G G A A B C
> [ b v b > [ b v b > [ < b b > [ <
< ^ < ^ v ^
5---------7---1-----------3-----------9------1
1

Let's include some of the simpler composite numbers within the 11-
prime limit (the fact that they're composite means they'll
provide "extra" consonance with the lower identities and with one
another):

C D E E F G G A B B C D D E F G G A A B C
> [ b v b > [ b v b > [ < b b > [ <
< ^ < ^ v ^
2-------------5---------7-1-1-------2---3-----------9-----1-----2
5 5 1 1 7

So now, by "sliding" the slide rule, we can find some nice big
harmonic-series-based chords in 72-tET. Please voice them from lowest
to highest for best results, though you can double or even triple the
lower notes in the chord, both upward and downward by octaves.

F< C< A[ D> E[ A> C> -- this is a 1:3:5:7:15:21:25 chord

Bb< F< D[ G> C< A[ D> -- this is a 1:3:5:7:9:15:21 chord

Eb< Bb< C> F< Ab^ D[ G> C< -- a 1:3:7:9:11:15:21:27 chord

(moving between these three chords should sound really strong: "V, I,
IV")

A[ E[ C> Gb^ B[ G> Db^ -- this is another 1:3:5:7:9:15:21 chord

D[ A[ E[ G C> Gb^ B[ -- this is a 1:3:9:11:15:21:27 chord --
the 21 (Gb^) might sound especially disconnected here since there's
no 7.

(moving between these two chords should sound really strong: "V"
to "I" or "I" to "IV")

Gb^ Db^ Ev Ab^ C< F Bv -- this is a 1:3:7:9:11:15:21 chord

F C Eb< G B[ Ev Bb< -- another 1:3:7:9:11:15:21 chord

Ev Bb D[ Gbv A> Eb< A[ -- yet another 1:3:7:9:11:15:21 chord

Try these out with different timbres, pay special attention to
voicing, and let be know what you think.

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

/tuning/topicId_29874.html#30037

Well, this post sure proves that it's worth while to ask questions!
I see some more helpful posts "down the pike" which I will also get
to and experiment with. Thanks both Paul and Dave!

> The first issue is voicing. A nice-sounding 8-tone chord in
blackjack is likely to require you to stretch your fingers out
tremendously on the keyboard, probably farther than physically
possible :)
>

Well, Paul, actually the way I am working I have four notes on one
channel and four on *another* so they will be "overlaid" with the
sequencer and, hence, that's not a problem...

> Now I'd guess, since you mention "'common tone' methods", that you
> were probably trying to play three or more adjacent tetrads at a
> time, yes?
>

I was actually only trying to play a *couple* simultaneously, but I
chose some *lousy* ones right off the bat... probably I didn't do
enough thinking about what would work before I started... (That
usually might help... :) )

> In JI, this would tend to work best if the tetrads were in 3:2
> relationships to one another.

Umm, actually that came to me also after I was through with my first
experiments, but I didn't have time yet to try it out. I was also
initially "discouraged" with some of the "big chords" I found, so I
was doing other composing things with my piece for a while....

But, naturally, that would make sense, since it would be a similar
procedure to the building up of "polychords" in 12-tET... based on
the fifth...

>However, even then you get dissonant intervals like 21:16 and 64:63
>very early in the process. Some people like these intervals in this
>kind of context . . . try a 6-note chord
> like Bb< F< C< (left hand), G> D> A> (right hand). Notice the very
> small "64:63" interval between Bb< and A> -- it can clash more or
> less depending on how you voice it.

*THAT IS FANTASTIC* I *LOVE* that!! That little interval there is
really spectacular. Lots of things could be done with that!

>Now complete the two Otonalities
> by inserting D[ and A[ (look on the lattice to see what I mean by
> that). Play around with voicing, and you have a nice big rich "JI"
>8-tone chord.

This is great, too! I find adding the final A[ to be making the big
chord a bit too dissonant as a "consonant" experience... but
certainly in some contexts it could be used...

I should say right now, that this is giving me a *much* better idea
of how to find these "larger" chords on the lattice!

> Now since we're not quite in JI, we should take advantage of
certain unison vectors, like the 225:224. You see, a lot of intervals
on the lattice that would be "dissonant" in JI become "consonant"
because of this. If you look at your own "Tuning Lab" page, you can
see this
> happening in some of the chords (search the page for 225:224). One
> example is something I called the "magic chord" a while ago. In
> Blackjack you can find it at Db^ F G Bv. Note that in order to see
> all the consonant intervals in this chord (and I'm counting 9:8 as
> consonant for this exercise), you have to locate at least one of
the
> notes in more than one place in the lattice. For example, you could
> go from Db^ east-northeast to F, east to G, and northeast to Bv,
but
> you wouldn't see that Bv is consonant with the starting point Db^
> unless you continued south-southwest from Bv to _another_ Db^.

I see what you're saying. So because of the *temperament* we have
certain "equivalencies" here that lead to even *more* "approximate"
just harmonies!

> Grouping together more notes in the vicinity, and voicing
carefully,
> a chord like Db^ F Ab^ G Bv Ev C might prove interesting to you, as
> well as similar chords elsewhere on the lattice.

Actually, I really liked this too as a consonance until I added the
final "C." Of course, in certain contexts, that could be useful,
too... but I was basically trying for what I was hoping were
*consonances* in this 8-note chord project

225:224 even helps
> you if you try to produce some nice big 5-prime-limit chords, like
> say the Ramos-inspired Eb< Bb< F< C< D[ A[ E[ B[ or D[ A[ E[ B[ C>
G> D> A>, since each of the three 45:32s is approximating 7:5 very
well.
>

These are both quite beautiful... I'm going to try more of
these "close chainy" types of things...

> But perhaps what you really desire are 15-limit Otonalities --
> 8:9:10:11:12:13:14:15 chords. Then Blackjack is probably not your
> answer, though 72-tET can still serve you well

Well, that *may* be an ultimate destination, but my *immediate*
objective is to, obviously, find "larger" harmonies in blackjack that
will, quite frankly, take "advantage" of the temperament, as you
illustrate above.

This is really helping A LOT A LOT A LOT!!!!

JP

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

/tuning/topicId_29874.html#30044

> Hi Joseph. I figured we could look for some simple 7- and 8-note
> harmonic series chords in Blackjack, and move on to polychords and
> the like later.
>

Well, this is *fantastic* and, like I say, I'm glad I didn't sit
around here any longer trying to "invent the wheel" when all I had to
do is ask a couple of questions! I obviously made some mistakes in
my original experiments and I was getting a little discouraged about
the "big chords..." Clearly, I wasn't thinking about them in the
right way.

My objective in this was to find some really exciting "consonant"
or "semi-consonant" chords that were close to just. It seemed
blackjack should have this kind of resource, and that's why I
purchased the second synth. Clearly, I can see now that it does.

Now, the question comes up about "consonance..." I'm finding, in
first appraisal of some of the harmonies that you list below, that
I'm tempted to leave out a couple of notes here and there to make the
chords more "consonant." I figure I can *always* come up with
dissonant ones... what I was actually looking for were "special"
chords with near-consonances or certain "resonances" that just random
dissonant chords wouldn't have.

I can see, though, that, with what you are providing me, I'm clearly
on the right track at this point. The method using the "slide rule"
seems pretty clear now as well...

Now... without any implicit "criticism" of your extended chords, I
thought I would offer my initial impression... since you asked for my
opinion!

Frankly, in most of the chords, I would leave something out in order
to hear them as the "special consonances" I'm looking for:

>
> F< C< A[ D> E[ A> C> -- this is a 1:3:5:7:15:21:25 chord
>

I would leave out the E[

> Bb< F< D[ G> C< A[ D> -- this is a 1:3:5:7:9:15:21 chord
>

I want to leave out the A[

> Eb< Bb< C> F< Ab^ D[ G> C< -- a 1:3:7:9:11:15:21:27 chord
>

I feel like leaving out both the D[ and the G>

> A[ E[ C> Gb^ B[ G> Db^ -- this is another 1:3:5:7:9:15:21
chord
>

Here I want to leave out the G>

> D[ A[ E[ G C> Gb^ B[ -- this is a 1:3:9:11:15:21:27 chord --

> the 21 (Gb^) might sound especially disconnected here since there's
> no 7.
>

Yes, I want to leave out the Gb^

>
> Gb^ Db^ Ev Ab^ C< F Bv -- this is a 1:3:7:9:11:15:21 chord
>

I want to leave out the F

> F C Eb< G B[ Ev Bb< -- another 1:3:7:9:11:15:21 chord

I want to leave out both the B[ and the Ev

>
> Ev Bb D[ Gbv A> Eb< A[ -- yet another 1:3:7:9:11:15:21 chord
>

I want to leave out both the A> and the Eb<

CAVEAT:

Of course, *all* these chords could be used in certain contexts, but,
Paul, you asked me for my opinion and, frankly, I would leave a few
notes out on some of these chords.

However, after doing that, I have to admit that these are *exactly*
the kinds of extended chords I was looking for...

Of course, I could hear it all differently tomorrow... (oh, suddenly,
it's *already* tomorrow...)

Joseph

--- In tuning@y..., jpehrson@r... wrote:
>
> >However, even then you get dissonant intervals like 21:16 and
64:63
> >very early in the process. Some people like these intervals in
this
> >kind of context . . . try a 6-note chord
> > like Bb< F< C< (left hand), G> D> A> (right hand). Notice the
very
> > small "64:63" interval between Bb< and A> -- it can clash more or
> > less depending on how you voice it.
>
> *THAT IS FANTASTIC* I *LOVE* that!! That little interval there is
> really spectacular. Lots of things could be done with that!

I'd love to hear some (in music of course).
>
> >Now complete the two Otonalities
> > by inserting D[ and A[ (look on the lattice to see what I mean by
> > that). Play around with voicing, and you have a nice big
rich "JI"
> >8-tone chord.
>
> This is great, too! I find adding the final A[ to be making the
big
> chord a bit too dissonant as a "consonant" experience... but
> certainly in some contexts it could be used...

Well, at least you have a nice 7-tone chord.

> > Grouping together more notes in the vicinity, and voicing
> carefully,
> > a chord like Db^ F Ab^ G Bv Ev C might prove interesting to you,
as
> > well as similar chords elsewhere on the lattice.
>
>
> Actually, I really liked this too as a consonance until I added the
> final "C." Of course, in certain contexts, that could be useful,
> too... but I was basically trying for what I was hoping were
> *consonances* in this 8-note chord project

Well, at least this gives you another type of 6-tone chord to play
with . ..

> > Eb< Bb< F< C< D[ A[ E[ B[ or D[ A[ E[ B[ C> G> D> A>, since each
> > of the three 45:32s is approximating 7:5 very
> > well.
> >
>
> These are both quite beautiful...

Cool -- I'm glad all 8 notes sound OK together to you.

--- In tuning@y..., jpehrson@r... wrote:

> >
> > F< C< A[ D> E[ A> C> -- this is a 1:3:5:7:15:21:25 chord
> >
>
> I would leave out the E[

What if you move it up an octave, above the C>? You _did_ like both
a "seventh" and a "major seventh" in Dave Keenan's first ogdoad . . .
so maybe it's an issue of voicing.
>
> > Bb< F< D[ G> C< A[ D> -- this is a 1:3:5:7:9:15:21 chord
> >
>
> I want to leave out the A[

Again, the 15 (here A[) is your problem, so again, try transposing it
up an octave . . .

> > Eb< Bb< C> F< Ab^ D[ G> C< -- a 1:3:7:9:11:15:21:27 chord
> >
>
> I feel like leaving out both the D[ and the G>

Once gain, try transposing the 15 (here D[) up an octave . . .
>
>
>
> > A[ E[ C> Gb^ B[ G> Db^ -- this is another 1:3:5:7:9:15:21
> chord
> >
>
> Here I want to leave out the G>

Same deal.

>
>
> > D[ A[ E[ G C> Gb^ B[ -- this is a 1:3:9:11:15:21:27
chord --
>
> > the 21 (Gb^) might sound especially disconnected here since
there's
> > no 7.
> >
>
> Yes, I want to leave out the Gb^

Ok -- a nice 6-tone chord, though . . .

> >
> > Gb^ Db^ Ev Ab^ C< F Bv -- this is a 1:3:7:9:11:15:21 chord
> >
>
> I want to leave out the F

Again, the 15 is your problem, so try putting it up top.

>
>
>
> > F C Eb< G B[ Ev Bb< -- another 1:3:7:9:11:15:21 chord
>
>
> I want to leave out both the B[ and the Ev

This is the same chord as above, but now you want to leave out two
notes rather than one? Hmm . . .

> > Ev Bb D[ Gbv A> Eb< A[ -- yet another 1:3:7:9:11:15:21 chord
> >
>
> I want to leave out both the A> and the Eb<

Ditto.

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

/tuning/topicId_29874.html#30075

> --- In tuning@y..., jpehrson@r... wrote:
> >
> > >However, even then you get dissonant intervals like 21:16 and
> 64:63 very early in the process. Some people like these intervals
in this kind of context . . . try a 6-note chord like Bb< F< C< (left
hand), G> D> A> (right hand). Notice the very small "64:63" interval
between Bb< and A> -- it can clash more or less depending on how you
voice it.
> >
> > *THAT IS FANTASTIC* I *LOVE* that!! That little interval there
is really spectacular. Lots of things could be done with that!
>

> I'd love to hear some (in music of course).

[JP:]
Actually, I just started a section of my piece using this. It's
quite a spectacular little effect...

>
> > > Eb< Bb< F< C< D[ A[ E[ B[ or D[ A[ E[ B[ C> G> D> A>, since
each of the three 45:32s is approximating 7:5 very well.
> > >
> >
> > These are both quite beautiful...
>
> Cool -- I'm glad all 8 notes sound OK together to you.

[JP:]
Well, actually, as I mentioned above, the octave transpositions of
the blackjack elements really *do* make an incredible difference.
The "voicings" are more distinct than our traditional 12-tET
voicings, so it seems.

I tried transposing some of the pitches I "objected" to the first
time around, and I found them quite acceptable... so there really is
quite a bit to work with here.

Thanks again to Paul and Dave for "blackjack extended harmonic
training." I'm certainly glad I asked about it...

Joseph

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

/tuning/topicId_29874.html#30077

> --- In tuning@y..., jpehrson@r... wrote:
>
> > >
> > > F< C< A[ D> E[ A> C> -- this is a 1:3:5:7:15:21:25 chord
> > >
> >
> > I would leave out the E[
>
> What if you move it up an octave, above the C>? You _did_ like both
> a "seventh" and a "major seventh" in Dave Keenan's first
ogdoad . . . so maybe it's an issue of voicing.
> >

[JP:]
Yes, it worked much better that way. I need bigger hands, though!
As I mentioned, the voicings really do make an incredible
difference... same for the others referred to in this post.

> > > F C Eb< G B[ Ev Bb< -- another 1:3:7:9:11:15:21 chord
> >
> >
> > I want to leave out both the B[ and the Ev
>
> This is the same chord as above, but now you want to leave out two
> notes rather than one? Hmm . . .

[JP:]
That's funny. Sure they're the same... everything transposed up by
a secor. It's remarkable how many transpositions can be done that
way... as evidenced by your chord charts.

If I understand this correctly, though, the "limiting factor" is
actually in making blackjack have "octave equvalency..." otherwise
it would be totally transposable. If I understand this, blackjack is
*not* by it's nature an "octave equivalent" scale...

JP

--- In tuning@y..., jpehrson@r... wrote:

> > >
> > > *THAT IS FANTASTIC* I *LOVE* that!! That little interval
there
> is really spectacular. Lots of things could be done with that!
> >
>
>
> > I'd love to hear some (in music of course).
>
>
> [JP:]
> Actually, I just started a section of my piece using this. It's
> quite a spectacular little effect...

Besides 64:63, 49:48 and 50:49 are small intervals you can imply with
the small interval in Blackjack. Can you find chords that take
consonant advantage of this, the same way that the chord I gave you
takes consonant advantage of 64:63?

--- In tuning@y..., jpehrson@r... wrote:

> [JP:]
> That's funny. Sure they're the same... everything transposed up
by
> a secor. It's remarkable how many transpositions can be done that
> way... as evidenced by your chord charts.
>
> If I understand this correctly, though, the "limiting factor" is
> actually in making blackjack have "octave equvalency..." otherwise
> it would be totally transposable. If I understand this, blackjack
is
> *not* by it's nature an "octave equivalent" scale...
>
> JP

I wouldn't say that, any more than Pythaogean or meantone are not by
nature octave equivalent. I would say instead that to acheive full
transposability, you need to go to a full 72-tET (or 41-tET or even
31-tET if you don't mind the larger errors); but if you're willing to
give up octave equivalency (and thus most inversions of the
interesting chords, though you get some new ones), you can use a non-
octave-equivalent version of Blackjack and have full transposability
by integer numbers of secors.

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

/tuning/topicId_29874.html#30109

> Besides 64:63, 49:48 and 50:49 are small intervals you can imply
with
> the small interval in Blackjack. Can you find chords that take
> consonant advantage of this, the same way that the chord I gave you
> takes consonant advantage of 64:63?

Hi Paul!

You mean I'm supposed to figure this out?? :)

Actually, I'm composing quite a bit with that those
little "inflections" in Blackjack, so I'm sure I'm "stumbling" into
those chords...

But, how would one figure out something like that *systematically?*

By the way, I *love* my new "big chords!" They've leant a
new "dimension" to my piece, quite literally!!!

JP

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

/tuning/topicId_29874.html#30110

If I understand this, blackjack is *not* by it's nature an "octave
equivalent" scale...
> >
> > JP
>
> I wouldn't say that, any more than Pythaogean or meantone are not
by nature octave equivalent. I would say instead that to acheive full
> transposability, you need to go to a full 72-tET (or 41-tET or even
> 31-tET if you don't mind the larger errors); but if you're willing
to
> give up octave equivalency (and thus most inversions of the
> interesting chords, though you get some new ones), you can use a
non-octave-equivalent version of Blackjack and have full
transposability by integer numbers of secors.

Oh sure... I get it. Blackjack comes in various "flavors..." just
like meantone does.... some, with a larger number of
pitches, "circulating" some not ("adjusted")...

JP

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29874.html#30109
>
>
> > Besides 64:63, 49:48 and 50:49 are small intervals you can imply
> with
> > the small interval in Blackjack. Can you find chords that take
> > consonant advantage of this, the same way that the chord I gave
you
> > takes consonant advantage of 64:63?
>
>
> Hi Paul!
>
> You mean I'm supposed to figure this out?? :)

I'll get you started here, but I think I should be credited if you're
going to use these in your piece . . . so here goes . . .

Well, the chord with 64:63 in it was 1:3:9:7:21:63, or
1:3:3*3:7:7*3:7*3*3

So something similar with 50:49 would start with 1:5:7:25:35:49, or

1:5:7:5*5:7*7,

and maybe include 35 (5*7), and other notes as well.

Try F< A[ D> C C>.

Try also adding Gb^ (and try different voicings)

If you like that, try also adding Ev. Either way, try to find other
transpositions of this.

Something similar for 48:49 would begin at least with 1:3:7:7*7. You
can find this in many places on the lattice. Try adding other notes,
including 5s.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29874.html#30110
>
> If I understand this, blackjack is *not* by it's nature an "octave
> equivalent" scale...
> > >
> > > JP
> >
> > I wouldn't say that, any more than Pythaogean or meantone are not
> by nature octave equivalent. I would say instead that to acheive
full
> > transposability, you need to go to a full 72-tET (or 41-tET or
even
> > 31-tET if you don't mind the larger errors); but if you're
willing
> to
> > give up octave equivalency (and thus most inversions of the
> > interesting chords, though you get some new ones), you can use a
> non-octave-equivalent version of Blackjack and have full
> transposability by integer numbers of secors.
>
>
> Oh sure... I get it. Blackjack comes in various "flavors..." just
> like meantone does.... some, with a larger number of
> pitches, "circulating" some not ("adjusted")...

Well, I've never heard of a non-octave-equivalent version of
meantone . . .

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

/tuning/topicId_29874.html#30120
> > You mean I'm supposed to figure this out?? :)
>

> I'll get you started here, but I think I should be credited if
you're going to use these in your piece . . . so here goes . . .
>

Hi Paul!

So far, both you and Dave Keenan have been credited in every
Blackjack piece I've written!

> Well, the chord with 64:63 in it was 1:3:9:7:21:63, or
> 1:3:3*3:7:7*3:7*3*3
>
> So something similar with 50:49 would start with 1:5:7:25:35:49, or
>
> 1:5:7:5*5:7*7,
>
> and maybe include 35 (5*7), and other notes as well.
>
> Try F< A[ D> C C>.
>
> Try also adding Gb^ (and try different voicings)
>
> If you like that, try also adding Ev. Either way, try to find other
> transpositions of this.
>
>
> Something similar for 48:49 would begin at least with 1:3:7:7*7.
You can find this in many places on the lattice. Try adding other
notes, including 5s.

I'm, quite frankly, a little mystified by what you are doing here.
Is the point in factorizing these to find notes that are directly
linked by the 3, 5, 7 vectors on the lattice??

JP

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

/tuning/topicId_29874.html#30121

> >
> > Oh sure... I get it. Blackjack comes in various "flavors..."
just like meantone does.... some, with a larger number of
> > pitches, "circulating" some not ("adjusted")...
>
> Well, I've never heard of a non-octave-equivalent version of
> meantone . . .

Hi Paul...

Well, I guess considering its history, that wouldn't be too
surprising. I guess the point I was trying to affirm is that there
are, essentially, more than *one* version of Blackjack, depending
upon how one wants to set it up.... (??)

JP

I'm uploading some examples of 9 note blackjack chords.

<http://x31eq.com/miracle/big1.mp3>

1-4-7-6^-9^-2-1^-4^-7^
B[-D-F]-F<-Ab^-C<-Bb-D>-F#v

<http://x31eq.com/miracle/big2.mp3>

1-4^-7-6^-9^-2-1^-4-7^
B[-D>-F]-F<-Ab^-C<-Bb-D-F#v

<http://x31eq.com/miracle/big3.mp3>

1^-4^-7-6^-1^-4-7^-2-9^
B[-D>-F]-F<-Bb-D-F#v-Ab^-C<

<http://x31eq.com/miracle/big4.mp3>

8^-6^-9^-2-4-7^-1^-4^-0v
G-F<-Ab^-C<-D-F#v-Bb-D>-A

The absolute pitch needn't correlate with the note names, although it
might. I can't remember. I had to draw them in using the sequencer.
They don't fit on my keyboard, and I'd need three hands to play them
anyway.

Another interesting one with tiny intervals (an octave apart) is
5-1-4^-7-9^-1^-4-7^-3^, but I didn't think of it until I'd recorded the
rest. So there.

Graham

--- In tuning@y..., graham@m... wrote:

/tuning/topicId_29874.html#30133

> I'm uploading some examples of 9 note blackjack chords.
>
> <http://x31eq.com/miracle/big1.mp3>
>
> 1-4-7-6^-9^-2-1^-4^-7^
> B[-D-F]-F<-Ab^-C<-Bb-D>-F#v
>
>
> <http://x31eq.com/miracle/big2.mp3>
>
> 1-4^-7-6^-9^-2-1^-4-7^
> B[-D>-F]-F<-Ab^-C<-Bb-D-F#v
>
>
> <http://x31eq.com/miracle/big3.mp3>
>
> 1^-4^-7-6^-1^-4-7^-2-9^
> B[-D>-F]-F<-Bb-D-F#v-Ab^-C<
>
>
> <http://x31eq.com/miracle/big4.mp3>
>
> 8^-6^-9^-2-4-7^-1^-4^-0v
> G-F<-Ab^-C<-D-F#v-Bb-D>-A
>
>
> The absolute pitch needn't correlate with the note names, although
it
> might. I can't remember. I had to draw them in using the
sequencer.
> They don't fit on my keyboard, and I'd need three hands to play
them
> anyway.
>
> Another interesting one with tiny intervals (an octave apart) is
> 5-1-4^-7-9^-1^-4-7^-3^, but I didn't think of it until I'd recorded
the
> rest. So there.
>
>
> Graham

Thanks, Graham, for posting these... and just in time for Halloween,
too! These "extended" Blackjack chords are mighty spooky. I have a
section in my new Blackjack piece that is a tad reminiscent of the
Berlioz "March to the Scaffold." Very appropriate for these extended
Blackjack sounds...

Thanks again!

JP

--- In tuning@y..., graham@m... wrote:
> I'm uploading some examples of 9 note blackjack chords.
>

Hi Paul...

Graham has some interesting chords here, obviously based on his "D-
based" notation for Blackjack.

How do I convert that to "C-base" again? It's probably simple, but I
don't want to "mess up."

Thanks!!

Joseph

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29874.html#30120
> > > You mean I'm supposed to figure this out?? :)
> >
>
> > I'll get you started here, but I think I should be credited if
> you're going to use these in your piece . . . so here goes . . .
> >
>
> Hi Paul!
>
> So far, both you and Dave Keenan have been credited in every
> Blackjack piece I've written!
>
>
> > Well, the chord with 64:63 in it was 1:3:9:7:21:63, or
> > 1:3:3*3:7:7*3:7*3*3
> >
> > So something similar with 50:49 would start with 1:5:7:25:35:49,
or
> >
> > 1:5:7:5*5:7*7,
> >
> > and maybe include 35 (5*7), and other notes as well.
> >
> > Try F< A[ D> C C>.
> >
> > Try also adding Gb^ (and try different voicings)
> >
> > If you like that, try also adding Ev. Either way, try to find
other
> > transpositions of this.
> >
> >
> > Something similar for 48:49 would begin at least with 1:3:7:7*7.
> You can find this in many places on the lattice. Try adding other
> notes, including 5s.
>
>
> I'm, quite frankly, a little mystified by what you are doing here.
> Is the point in factorizing these to find notes that are directly
> linked by the 3, 5, 7 vectors on the lattice??

Yup! Don't forget the 5/3, 7/3, and 7/5 intervals also!

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29874.html#30121
>
> > >
> > > Oh sure... I get it. Blackjack comes in various "flavors..."
> just like meantone does.... some, with a larger number of
> > > pitches, "circulating" some not ("adjusted")...
> >
> > Well, I've never heard of a non-octave-equivalent version of
> > meantone . . .
>
> Hi Paul...
>
> Well, I guess considering its history, that wouldn't be too
> surprising. I guess the point I was trying to affirm is that there
> are, essentially, more than *one* version of Blackjack, depending
> upon how one wants to set it up.... (??)
>
> JP

Well, if the analogy is to varieties of meantone, then yes, you have
31-tET Blackjack at one extreme, 41-tET Blackjack at another extreme,
and 72-tET Blackjack in the middle.

I wrote:

> > > Something similar for 48:49 would begin at least with
1:3:7:7*7.
> > You can find this in many places on the lattice. Try adding other
> > notes, including 5s.

Joseph wrote,

> > I'm, quite frankly, a little mystified by what you are doing
here.
> > Is the point in factorizing these to find notes that are directly
> > linked by the 3, 5, 7 vectors on the lattice??

I wrote,

> Yup! Don't forget the 5/3, 7/3, and 7/5 intervals also!

How are you doing on these, Joseph? Oh, and besides 64:63, 50:49, and
49:48, the small interval in Blackjack can be interpreted as 55:54 --
once you're done with creating 49:48 examples, you can try to find a
chord that shows off the 55:54 . . .

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

/tuning/topicId_29874.html#30170

> --- In tuning@y..., jpehrson@r... wrote:
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> >
> > /tuning/topicId_29874.html#30121
> >
> > > >
> > > > Oh sure... I get it. Blackjack comes in various "flavors..."
> > just like meantone does.... some, with a larger number of
> > > > pitches, "circulating" some not ("adjusted")...
> > >
> > > Well, I've never heard of a non-octave-equivalent version of
> > > meantone . . .
> >
> > Hi Paul...
> >
> > Well, I guess considering its history, that wouldn't be too
> > surprising. I guess the point I was trying to affirm is that
there
> > are, essentially, more than *one* version of Blackjack, depending
> > upon how one wants to set it up.... (??)
> >
> > JP
>
> Well, if the analogy is to varieties of meantone, then yes, you
have 31-tET Blackjack at one extreme, 41-tET Blackjack at another
extreme, and 72-tET Blackjack in the middle.

I'm confused. Are we calling the MIRACLE cycles when they go beyond
21 pitches, Blackjack??

JP

--- In tuning@y..., jpehrson@r... wrote:

> Well, if the analogy is to varieties of meantone, then yes, you
> have 31-tET Blackjack at one extreme, 41-tET Blackjack at another
> extreme, and 72-tET Blackjack in the middle.
>
>
> I'm confused. Are we calling the MIRACLE cycles when they go
beyond
> 21 pitches, Blackjack??

No. In analogy to the varieties of meantone, we have 21-out-of-31-tET
Blackjack at one extreme, 21-out-of-41-tET Blackjack at another
extreme, and your current Blackjack tuning in the middle.

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

/tuning/topicId_29874.html#30222

> > No. In analogy to the varieties of meantone, we have 21-out-of-31-
tET Blackjack at one extreme, 21-out-of-41-tET Blackjack at another
> extreme, and your current Blackjack tuning in the middle.

Hi Paul...

Well, here is my confusion: I thought that, using the secor
generator, the first time around the cycle was Blackjack, and then
*more* notes were added leading to Canasta, and then another cycle to
41 and, finally 72-tET.

So, in *all* these cycles, the *basic* Blackjack notes are the same.

Is this wrong?

Thanks!

JP

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

/tuning/topicId_29874.html#30214

>
> How are you doing on these, Joseph? Oh, and besides 64:63, 50:49,
and 49:48, the small interval in Blackjack can be interpreted as
55:54 -- once you're done with creating 49:48 examples, you can try
to find a chord that shows off the 55:54 . . .

I'm afraid I'm going to need a little more help. I don't want to do
anything wrong!

On a positive note, though, I've been *really* enjoying and using the
new "larger" chords: the "Ramos" ones, in particular contrasted
against Dave Keenan's trumphal "optimal" Blackjack chord.

*That* one REALLY is a gem, particularly in the voicing he figured
out. It's incredibly complex and *resonant* at the same time.

It will be interesting to see if people can identify some of the
chords we have been discussing just by listening to the finished
piece. Probably this piece will be a bit longer than my "usual"
electronic ones, since there seems to really be a lot to explore
here...

And, yes, I will be giving appropriate credit for all the assistance
I've been getting...

Thanks!

JP

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29874.html#30222
>
> > > No. In analogy to the varieties of meantone, we have 21-out-of-
31-
> tET Blackjack at one extreme, 21-out-of-41-tET Blackjack at another
> > extreme, and your current Blackjack tuning in the middle.
>
> Hi Paul...
>
> Well, here is my confusion: I thought that, using the secor
> generator, the first time around the cycle was Blackjack, and then
> *more* notes were added leading to Canasta, and then another cycle
to
> 41 and, finally 72-tET.

Well, if you tune the secor generator to exactly 116 2/3 cents, then
yes, you'll get 72-tET. Otherwise, you won't.*

> So, in *all* these cycles, the *basic* Blackjack notes are the same.

Yes, as long as the precise size of the secor generator is fixed.

*If you tune the secor generator to 117.0732 cents, the cycle will
close at 41-tET. If you tune the secor generator to 116.1290 cents,
the cycle will close at 31-tET.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29874.html#30214
>
> >
> > How are you doing on these, Joseph? Oh, and besides 64:63, 50:49,
> and 49:48, the small interval in Blackjack can be interpreted as
> 55:54 -- once you're done with creating 49:48 examples, you can try
> to find a chord that shows off the 55:54 . . .
>
> I'm afraid I'm going to need a little more help. I don't want to
do
> anything wrong!

Well, give the 49:48 a shot. I practically spelled out this case for
you already (and you'll learn more my doing it yourself).

--- In tuning@y..., jpehrson@r... wrote:

> I thought that, using the secor
> generator, the first time around the cycle was Blackjack, and then
> *more* notes were added leading to Canasta, and then another cycle
to
> 41 and, finally 72-tET.

Well, I don't want to cause more confusion, but to be more precise,
using the 116 2/3 cent generator, the first time around the cycle you
get Decimal; the second time, Blackjack; the third time, Canasta; the
fourth time, MIRACLE-41; the fifth time, a 51-tone scale; the sixth
time, a 61- or 62-tone scale; and the seventh time, 72-tET.

By the way, I think the "official" value of the secor is
116.7155940982074 cents, but since you're using 72-tET, you can call
116 2/3 cents a secor and no one will blink.

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

/tuning/topicId_29874.html#30226

> --- In tuning@y..., jpehrson@r... wrote:
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> >
> > /tuning/topicId_29874.html#30214
> >
> > >
> > > How are you doing on these, Joseph? Oh, and besides 64:63,
50:49,
> > and 49:48, the small interval in Blackjack can be interpreted as
> > 55:54 -- once you're done with creating 49:48 examples, you can
try
> > to find a chord that shows off the 55:54 . . .
> >
> > I'm afraid I'm going to need a little more help. I don't want to
> do
> > anything wrong!
>
> Well, give the 49:48 a shot. I practically spelled out this case
for
> you already (and you'll learn more my doing it yourself).

Well, you're certainly right about that! First, I'll have to find
your original post in this thread. I'll see what I can do...

JP

--- In tuning@y..., jpehrson@r... wrote:

> > Well, give the 49:48 a shot. I practically spelled out this case
> for
> > you already (and you'll learn more my doing it yourself).
>
>
> Well, you're certainly right about that! First, I'll have to find
> your original post in this thread. I'll see what I can do...

Just look at the top of

/tuning/topicId_29874.html#30214

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

/tuning/topicId_29874.html#30231

> By the way, I think the "official" value of the secor is
> 116.7155940982074 cents, but since you're using 72-tET, you can
call 116 2/3 cents a secor and no one will blink.

Hmmm. Now you've made me curious again, Paul. Maybe I should
remember this, but I don't: how is it that the secor was calculated
to this precision?

JP

In-Reply-To: <9t3c8r+n72m@eGroups.com>
Joseph Pehrson wrote:

> Hmmm. Now you've made me curious again, Paul. Maybe I should
> remember this, but I don't: how is it that the secor was calculated
> to this precision?

1200*log(3.6)/log(2)/19

Graham

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

/tuning/topicId_29874.html#30247

> Just look at the top of
>
> /tuning/topicId_29874.html#30214

Hi Paul...

Well, maybe it's time to take a "fun guess..." I'm not entire sure I
know what I'm doing here... John Cage always said things were best
when he didn't know what he was doing, but it's never worked out
quite that way for me...

Let's take the very simple example of:

1:3:7: [7*7]

So I could get simply: C:G:Bb<

Now, I wouldn't know quite what to do except add another connection
of 7, which would be G>

C:G:Bb:G>

But I thought that G>:G was a *larger* interval than 49:48??

Is that it??

JP

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29874.html#30231
>
>
> > By the way, I think the "official" value of the secor is
> > 116.7155940982074 cents, but since you're using 72-tET, you can
> call 116 2/3 cents a secor and no one will blink.
>
>
> Hmmm. Now you've made me curious again, Paul. Maybe I should
> remember this, but I don't: how is it that the secor was
calculated
> to this precision?

This question should really have been posted to

tuning-math@yahoogroups.com

but what the hay.

George Secor defined it as the minimax optimum generator for the 11-
limit mapping we've been calling "MIRACLE". Minimax optimization is
harder than least-squares optimization, an example of which is
illustrated here:

/tuning/topicId_22626.html#22626

There I show that the 9-limit unweighted least-squares optimum is
116.729676636048 cents.

But Secor's minimax value, though harder to derive, is easier to
calculate. Margo posted the formula, but I can't find it now.

--- In tuning@y..., graham@m... wrote:
> In-Reply-To: <9t3c8r+n72m@e...>
> Joseph Pehrson wrote:
>
> > Hmmm. Now you've made me curious again, Paul. Maybe I should
> > remember this, but I don't: how is it that the secor was
calculated
> > to this precision?
>
> 1200*log(3.6)/log(2)/19
>
>
> Graham

Ah yes. It's exactly 1/19th of a just 18/5. That means that if you
use the "official" Secor, 18:5, 9:5, 10:9, and 20:9 will be just.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29874.html#30247
>
> > Just look at the top of
> >
> > /tuning/topicId_29874.html#30214
>
>
> Hi Paul...
>
> Well, maybe it's time to take a "fun guess..." I'm not entire sure
I
> know what I'm doing here... John Cage always said things were best
> when he didn't know what he was doing, but it's never worked out
> quite that way for me...
>
> Let's take the very simple example of:
>
> 1:3:7: [7*7]
>
> So I could get simply: C:G:Bb<
>
> Now, I wouldn't know quite what to do except add another connection
> of 7, which would be G>
>
> C:G:Bb:G>
>
> But I thought that G>:G was a *larger* interval than 49:48??

No -- remember, the smallest interval in Blackjack, the 1/6-tone,
represents the ratios 49:48, 50:49, 55:54, and 64:63.

(1/6-tone is actually a bit _smaller_ than a just 49:48, FWIW.)

> Is that it??

Yup -- now perhaps throw in a few more notes to "fortify" the
harmony -- and look for other instances in the lattice. When you're
done, move on to 55:54 (which might not be as easy to "fortify"
effectively).

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

/tuning/topicId_29874.html#30275

> >
> This question should really have been posted to
>
> tuning-math@y...
>
> but what the hay.
>

Hi Paul!

Oh sure... it's been a while since I've been over there, anyway. I'm
sure I'd understand the drift of some of the stuff over there, so
I'll try to peek over there...

> George Secor defined it as the minimax optimum generator for the 11-
> limit mapping we've been calling "MIRACLE". Minimax optimization is
> harder than least-squares optimization, an example of which is
> illustrated here:
>
> /tuning/topicId_22626.html#22626
>
> There I show that the 9-limit unweighted least-squares optimum is
> 116.729676636048 cents.
>

Of course! Now I remember entirely that process. Although I'm not
getting all the details, I get the general process, which is enough
for now...

Thanks!

JP

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

/tuning/topicId_29874.html#30277

> > But I thought that G>:G was a *larger* interval than 49:48??
>
> No -- remember, the smallest interval in Blackjack, the 1/6-tone,
> represents the ratios 49:48, 50:49, 55:54, and 64:63.
>

Hi Paul!

You know, I keep forgetting that a Blackjack interval actually
approximates several different intervals simultaneously!

Is there a chart anyplace that would show more of this multiple
relationship between just intervals and Blackjack intervals? I think
that would be *very* interesting!

> (1/6-tone is actually a bit _smaller_ than a just 49:48, FWIW.)
>
> > Is that it??
>
> Yup -- now perhaps throw in a few more notes to "fortify" the
> harmony -- and look for other instances in the lattice. When you're
> done, move on to 55:54 (which might not be as easy to "fortify"
> effectively).

I can see that this process is actually a very important part
of "Blackjack theory..." I'm going to need to practice with more of
this. Right now, I have several different chords I'd like to work
into my piece, but I can see this will be important for "chord
development..."

Thanks again!

Joseph

--- In tuning@y..., jpehrson@r... wrote:

> Hi Paul!
>
> You know, I keep forgetting that a Blackjack interval actually
> approximates several different intervals simultaneously!

Yeah . . . and I forgot to mention 45/44 and 56/55!

> Is there a chart anyplace that would show more of this multiple
> relationship between just intervals and Blackjack intervals? I
think
> that would be *very* interesting!

Well, maybe . . . For example, the 0/72 interval class represents the
ratios 1:1, 224:225, 385:384, 441:440, 540:539, 1029:1024, 1375:1372,
2401:2400, 3025:3024 . . . The 2/72 interval class represents the
ratios 45:44, 49:48, 50:49, 55:54, 56:55, 64:63, 525:512,
686:675 . . . The 5/72 interval class represents the ratios 21:20,
22:21, 81:77, 135:128, 256:245, 288:275, 360:343, 392:375, 539:512,
605:576, 825:784 . . . Perhaps Gene could complete such a chart with
a clever computer program?

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

Perhaps Gene could complete such a chart with
> a clever computer program?

Since there are an infinite number of intervals in each class, you
need to decide what "complete" means. However, you could get a 72-
note 11-limit block (perhaps from an LLL reduced basis), and then
multiply each step by some range of powers of a kernel basis, and
boot out everything above a certain height (defined for instance as
the sum of reduced numerator and denominator.) I wouldn't call that
clever, but it would work; I'm not sure if it would be good for much.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> Perhaps Gene could complete such a chart with
> > a clever computer program?
>
> Since there are an infinite number of intervals in each class, you
> need to decide what "complete" means.

Say, up to four-digit numbers.

> However, you could get a 72-
> note 11-limit block (perhaps from an LLL reduced basis), and then
> multiply each step by some range of powers of a kernel basis, and
> boot out everything above a certain height (defined for instance as
> the sum of reduced numerator and denominator.)

Well that's pretty much what I was thinking/doing.

> I wouldn't call that
> clever, but it would work; I'm not sure if it would be good for >
much.

Neither do I . . . but Joseph asked!

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> Ah yes. It's exactly 1/19th of a just 18/5. That means that if you
> use the "official" Secor, 18:5, 9:5, 10:9, and 20:9 will be just.

<pedantry>

It would be a rare context in which 9:20 would be heard as just.

I understand that what Paul means is that when calculated using the
"official" secor, the approximations to 5:18, 5:9, 9:10, 20:9 will be
exact.

When this 11-limit minimax version of the temperament is played
(asuming essentially harmonic timbres) I expect most people would find
5:9, 6:7 and 8:11 to be just, but while the 5:9 would be as exact as
the instrument could make it, the 6:7 and 8:11 approximations would
have (essentially inaudible) errors of 0.6 c.

</pedantry>

Regards,
-- Dave Keenan

In the mannner of fractional comma meantone:

I think someone once called Miracle "meansemitone". I think it might
have been Margo.

The official secor can be considered as a 15:16 widened by 1/19 of
this rather large (~95 cent!) "comma":
2^-75 * 3^21 * 5^18

Not terribly meaningful or useful I'm afraid.

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

/tuning/topicId_29874.html#30284

>
> > However, you could get a 72-
> > note 11-limit block (perhaps from an LLL reduced basis), and then
> > multiply each step by some range of powers of a kernel basis, and
> > boot out everything above a certain height (defined for instance
as the sum of reduced numerator and denominator.)
>
> Well that's pretty much what I was thinking/doing.
>
> > I wouldn't call that
> > clever, but it would work; I'm not sure if it would be good for >
> much.
>
> Neither do I . . . but Joseph asked!

Isn't it interesting, though, to see the just intervals that are
approximated by 72-tET... say out to three or four digits??

JP

Hello

I am occupied with microtonal music for almost 2 years now , but I am still totally novice .
There is so much information on the internet and on this list , that I can't find where to begin and how to connect things.
So , I am asking :
What books would you consider essential ?

Thanks

--- In tuning@y..., alex <Alexmoog@o...> wrote:

/tuning/topicId_29874.html#30321

> Hello
>
> I am occupied with microtonal music for almost 2 years now , but I
am still totally novice .
> There is so much information on the internet and on this list ,
that I can't find where to begin and how to connect things.
> So , I am asking :
> What books would you consider essential ?
>
> Thanks

Hello Alex!

Well, Paul's considerate request for "lurker-posts" is getting some
response! Well, Paul's not back yet, so I actually get to answer
even *another* question! Whoopie!

Don't worry about being a novice here. I actually occasionally get
complimentary private e-mails from "lurkers" asking me to keep up the
good work asking dumb questions. I fully intend to continue as such.

Books:

1) _On The Sensations of Tone_ by Hermann Helmholtz

2) _Genesis of a Music_ by Harry Partch

3) _The JI Intonation Primer_ by David Doty

Unlike a *lot* of wonderful books on tuning that are presently out of
print, one can *actually get these books!!!* Amazing.

And, you can get them all right here at this link, the Just
Intonation Store:

http://www.dnai.com/~jinetwk/

You should "bug" them, however, about your order by e-mail if you
don't get it right away. I've never had any problem with them in
that department, but some others have. A friendly e-mail (even to
Doty!) will help solve that situation.

After you master everything in these books... should take you at
least a whole weekend...( :) come back here and ask Paul Erlich some
questions.

Now... we live in the Internet age, and books are becoming passe...
(who every said that, don't believe it!) so here are the best
Websites:

1) John Starrett *definitely* on top. Why that (warum?) It contains
everything else!!:

http://www-math.cudenver.edu/~jstarret/microtone.html

2) However, I'll include one other important link. Joe Monzo's
dictionary (also listed on the Starrett but needs to be pointed out)

http://www.ixpres.com/interval/dict/index.htm

Well, now you already have too much to do. After you master all of
this next week, ( :) come back for further discussion!

Joseph Pehrson

--- In tuning@y..., alex <Alexmoog@o...> wrote:
> Hello
>
> I am occupied with microtonal music for almost 2 years now , but I
am
> still totally novice .
> There is so much information on the internet and on this list ,
that I
> can't find where to begin and how to connect things.

Please start by asking questions.

> So , I am asking :
> What books would you consider essential ?

Joseph suggested some good books. There are others, but these are the
most easily obtainable, and good place to start (since the "language"
spoken on this list is largely derived from these books).

> Books:
>
> 1) _On The Sensations of Tone_ by Hermann Helmholtz
>
> 2) _Genesis of a Music_ by Harry Partch
>
> 3) _The JI Intonation Primer_ by David Doty

Also, I hear Juan Roederer's 'The physics and psychophysics of music:
an introduction' is good, but I've never read it. Another good read
(and short) is Siemen Terpstra's 'A Short History of Just Intonation
Tuning Culture', which was published in 1/1 (Journal of the Just
Intonation Network) (Part 1 in vol. 10, no. 1; Part 2 in vol. 10, no.
2). Although this article contains nothing technically related to
tuning, it's a fantastic overview of the various historical
ideologies surrounding just-tuning.

Speaking of ideology, the Partch and Helmholtz are both great books
but in my view are ideologically tainted. Both seem intent on having
sound as an something exclusively physiological, "of the body"
and "of man", whereas many (from Pythagoras to La Monte Young) have
considered sound to be something fundamentally "outside the body"
and "outside man". Interesting to read if one can be aware of this
though.

Cheers,
Alex Carpenter
http://www.transparentmeans.com/

Thanks Joseph , you are great!

On Monday, November 19, 2001, at 03:36 AM, jpehrson@rcn.com wrote:

>
> Hello Alex!
>
> Well, Paul's considerate request for "lurker-posts" is getting some
> response!  Well, Paul's not back yet, so I actually get to answer
> even *another* question!  Whoopie!
>
> Don't worry about being a novice here.  I actually occasionally get
> complimentary private e-mails from "lurkers" asking me to keep up the
> good work asking dumb questions.  I fully intend to continue as such.
>
>
> Books:
>
> 1) _On The Sensations of Tone_ by Hermann Helmholtz
>
> 2) _Genesis of a Music_ by Harry Partch
>
> 3) _The JI Intonation Primer_ by David Doty
>
>
> Unlike a *lot* of wonderful books on tuning that are presently out of
> print, one can *actually get these books!!!*  Amazing.
>
> And, you can get them all right here at this link, the Just
> Intonation Store:
>
> http://www.dnai.com/~jinetwk/
>
> You should "bug" them, however, about your order by e-mail if you
> don't get it right away.  I've never had any problem with them in
> that department, but some others have.  A friendly e-mail (even to
> Doty!) will help solve that situation.
>
> After you master everything in these books... should take you at
> least a whole weekend...( :) come back here and ask Paul Erlich some
> questions.
>
> Now... we live in the Internet age, and books are becoming passe... 
> (who every said that, don't believe it!) so here are the best
> Websites:
>
> 1) John Starrett *definitely* on top.  Why that (warum?)  It contains
> everything else!!:
>
> http://www-math.cudenver.edu/~jstarret/microtone.html
>
> 2) However, I'll include one other important link.  Joe Monzo's
> dictionary (also listed on the Starrett but needs to be pointed out)
>
> http://www.ixpres.com/interval/dict/index.htm
>
> Well, now you already have too much to do.  After you master all of
> this next week, ( :)  come back for further discussion!
>
> Joseph Pehrson
>
>
>
> You do not need web access to participate.  You may subscribe through
> email.  Send an empty email to one of these addresses:
>   tuning-subscribe@yahoogroups.com - join the tuning group.
>   tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning
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>   tuning-normal@yahoogroups.com - change your subscription to
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>   tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.

--- In tuning@y..., "Alex Carpenter" <acarp@a...> wrote:

/tuning/topicId_29874.html#30337

>
> Speaking of ideology, the Partch and Helmholtz are both great books
> but in my view are ideologically tainted. Both seem intent on
having
> sound as an something exclusively physiological, "of the body"
> and "of man", whereas many (from Pythagoras to La Monte Young) have
> considered sound to be something fundamentally "outside the body"
> and "outside man". Interesting to read if one can be aware of this
> though.
>
> Cheers,
> Alex Carpenter
> http://www.transparentmeans.com/

Hello Alex!

Yes, of course, the books I listed are only a rudimentary
introduction. There are some who speak quite negatively of the
Helmholtz-Partch school, and just intonation recognition in general.
One of the most vocal is composer Brian McLaren (who is a little
eccentric... we call him the "nutty professor"). His book
_Introduction to Microtonality_ is a valuable read, although not
professionally edited. It offers a differing view of a lot of this
from the psychoacoustic perspective. However, it really is for
people already exposed to the field, and not the total newbie, in
*my* opinion. Brian McLaren can be found on the somewhat
appropriately named "Crazy Music" list:

/crazy_music/messages

Joseph Pehrson

Joseph wrote:

> There are some who speak quite negatively of the
> Helmholtz-Partch school, and just intonation recognition in
> general.
> One of the most vocal is composer Brian McLaren (who is a little
> eccentric... we call him the "nutty professor").

Yes, I've heard of the infamous McLaren. I hear he's been called a
lot worse than that too!

> Yes, of course, the books I listed are only a rudimentary
> introduction.

I guess I feel they're neither rudimentary nor such a good place to
start, given their ideological bias. I just wanted to suggest to Alex
that he perhaps start with something more neutral and formulate his
own biases from there.

Cheers,
Alex C

--- In tuning@y..., "Alex Carpenter" <acarp@a...> wrote:

/tuning/topicId_29874.html#30342

> I guess I feel they're neither rudimentary nor such a good place to
> start, given their ideological bias. I just wanted to suggest to
Alex
> that he perhaps start with something more neutral and formulate his
> own biases from there.
>
> Cheers,
> Alex C

Hello Alex!

Well, that's fine, but then, besides the isolated 1/1 article, what
books that you've read and which are available would you recommend??

Joseph Pehrson

jpehrson@r... wrote:
> Hello Alex!
>
> Well, that's fine, but then, besides the isolated 1/1 article, what
> books that you've read and which are available would you recommend??

Okay, you got me! I'm not sure I know of a book that's not
ideologically tainted in some direction. But my intention was to
alert Alex to what I feel are fairly significant underlying
philosophical biases in the Partch and the Helmholtz.

I'm probably not as familiar with the tuning literature as are many
on this list - I read mainly in philosophy and cultural theory - but
I think I _am_ sensitive to how frequently musicians formulate theory
to justify their practice, as well as to how important it is for one
to avoid this style of theory while just beginning to piece the whole
puzzle together. I think any factual book on acoustic science would
be a better place to start. As for specific titles, that's a question
I'll have to throw open: what _is_ the least ideologically-tainted
book on acoustics??

Cheers,
Alex Carpenter

--- In tuning@y..., "Alex Carpenter" <acarp@a...> wrote:

> I guess I feel they're neither rudimentary nor such a good place to
> start, given their ideological bias.

Helmholtz was a scientist, so he approached the matter
scientifically; I think calling that an ideological bias is a
stretch. Partch approached things from quite a different angle, and
if you want to accuse him of bias it seems to me it would be for
those aspects which were *not* scientific, such as an almost
religious attachment to JI. I don't think you've demonstrated any
bias, and I for one have not yet figured out what you are objecting
to.

--- In tuning@y..., "Alex Carpenter" <acarp@a...> wrote:

/tuning/topicId_29874.html#30344

> jpehrson@r... wrote:
> > Hello Alex!
> >
> > Well, that's fine, but then, besides the isolated 1/1 article,
what books that you've read and which are available would you
recommend??
>
> Okay, you got me! I'm not sure I know of a book that's not
> ideologically tainted in some direction. But my intention was to
> alert Alex to what I feel are fairly significant underlying
> philosophical biases in the Partch and the Helmholtz.
>
> I'm probably not as familiar with the tuning literature as are many
> on this list - I read mainly in philosophy and cultural theory -
but I think I _am_ sensitive to how frequently musicians formulate
theory to justify their practice, as well as to how important it is
for one to avoid this style of theory while just beginning to piece
the whole puzzle together. I think any factual book on acoustic
science would be a better place to start. As for specific titles,
that's a question I'll have to throw open: what _is_ the least
ideologically-tainted book on acoustics??
>
> Cheers,
> Alex Carpenter

Hi Alex!

Well, most probably Paul Erlich will chime in (Woodstock chimes?)
with something, but of course there are several list readers who are
actually more interested in practical tunings than they are in the
acoustical basis... or at least my guess is that less than *half* of
the discussions on this forum are about acoustics.

Another problem is that several books on acoustics as related to
tuning... I'm thinking of the Backus, which I own, are substantially
out of date as far as the science goes... or at least that's what
I've been told.

On the overall, one of the sorry facts of the entire alternate tuning
field is the lack of literature *in print* about it. Even great
standards like Murray Barbour's work are out of print. Of course,
not long ago even Partch's _Genesis_ was out of print.

Some of this, I believe, has something to do with the tax code, since
publishers used to keep more older stuff around for a tax credit. I
believe it was Ronald Reagan (for sure bless his heart here) was the
one that eliminated this tax credit, and booksellers no longer keep
older inventory... or something like that...

Joseph Pehrson

--- In tuning@y..., "Alex Carpenter" <acarp@a...> wrote:
> > Books:
> >
> > 1) _On The Sensations of Tone_ by Hermann Helmholtz
> >
> > 2) _Genesis of a Music_ by Harry Partch
> >
> > 3) _The JI Intonation Primer_ by David Doty
>
>
> Also, I hear Juan Roederer's 'The physics and psychophysics of
music:
> an introduction' is good, but I've never read it.

Please do if you can. It's important to realize what has become known
about the human auditory system since Helmholtz (and therefore since
Partch). However there's virtually nothing about tuning.

> Another good read
> (and short) is Siemen Terpstra's 'A Short History of Just
Intonation
> Tuning Culture', which was published in 1/1 (Journal of the Just
> Intonation Network) (Part 1 in vol. 10, no. 1; Part 2 in vol. 10,
no.
> 2). Although this article contains nothing technically related to
> tuning, it's a fantastic overview of the various historical
> ideologies surrounding just-tuning.

Most of this is pure speculation, to my mind.

--- In tuning@y..., "Alex Carpenter" <acarp@a...> wrote:

> I guess I feel they're neither rudimentary nor such a good place to
> start, given their ideological bias. I just wanted to suggest to
Alex
> that he perhaps start with something more neutral and formulate his
> own biases from there.
>
> Cheers,
> Alex C

There isn't much "neutral" out there, even if that could be defined
in an absolute sense -- the best thing is to expose yourself to as
many ideological biases (inevitable in any individual's work) as
possible and to remain critical of all of them.

Firstly, the acheivements and essays of Margo Schulter, Dave Keenan,
Manuel op de Coul, Graham Breed, Gene Ward Smith, Paul Hahn, and
Daniel Wolf on this list are equal if not better than any published
material. Moving on to published material . . .

One book and one article to read with a very critical mind are:

Yasser, Joseph. A Theory of Evolving Tonality. American Library of
Musicology, New York, 1932. Reprint: Da Capo Press, New York, 1975,
381 pages.

Kraehenbuehl, David and Schmidt, Christopher. 1962. "On the
Development of Musical Systems." J. Music Theory vol. 6 no. 1 pp. 32-
65.

Great papers to look at are:

Krumhansl, Carol L. "General Properties of Musical Pitch Systems:
Some Psychological Considerations", in Johan Sundberg (ed.), Harmony
and Tonality. Royal Swedish Academy of Music (Publication # 54),
Stockholm, 1987, pp. 33-52.

Mathews, M. V., Pierce, J. R., and Roberts, L. A. 1987. "Harmony and
New Scales." In: Harmony and Tonality. J. Sundberg, ed. Royal Swedish
Academy of Music, Stockholm, p. 37.

Terhardt, E. 1974. "Pitch, consonance and harmony." J. Acoust. Soc.
Amer. Vol. 55 p. 1061.

as well as all of Erv Wilson's papers in Xenharmonikon.

Other books to absorb and mull over, if you can find them:

Barbour, James Murray. Tuning and Temperament: A Historical Survey.
Michigan State College Press, East Lansing, 1951. Reprint Da Capo
Press, New York, 1973, 228 pages.

Blackwood, Easley. The Structure of Recognizable Diatonic Tunings.
Princeton University Press, Princeton NJ, 1985, 318 pages.

Fokker, Adriaan D. 1975. New Music with 31 Notes. Verlag für
systematische Musikwissenschaft GmbH, Bonn.

Lindley, Mark and Ronald Turner-Smith. Mathematical Models of Musical
Scales: A New Approach. Orpheus-Schriftenreihe zu Grundfragen der
Musik vol. 66, Verlag für systematische Musikwissenschaft, Bonn-Bad
Godesberg, 1993, 308 pages.

Mann, Chester D. 1990. Analytic Study of Harmonic Intervals. Tustin,
Calif.

Parncutt, Richard. Harmony: A Psychoacoustical Approach. Springer
Series in Information Sciences vol. 19, Springer-Verlag, Berlin,
1989, 206 pages.

Sethares, William A. Tuning, Timbre, Spectrum, Scale. Springer-
Verlag, London, 1998, 345 pages. With CD.

van Eck, C. L. Van Panthaleon. 1981. J. S. Bach's Critique of Pure
Music. Princo, Culemborg, the Netherlands.

Vicentino, Nicola. L'antica musica ridotta alla moderna prattica.
Antonio Barre, Rome, 1555, 1557. English translation Ancient music
adapted to modern practice by Maria Rika Maniates (ed.), Claude V.
Palisca (ed.), Yale University Press, New Haven CT, 1996, esp. p.
xlix.

Vogel, Martin. On the Relations of Tone, translated from German by
Vincent Jean Kisselbach and edited by Carl A. Poldy, Verlag für
systematische Musikwissenschaft, Bonn-Bad Godesberg, 1993.

More articles:

Keislar, Douglas. 1991. "Six American Composers On Nonstandard
Tunings." Perspectives of New Music Vol. 29 No.1 p. 177.

Tenney, James. "John Cage and the Theory of Harmony", Soundings vol.
13, 1984, pp. 55-83.

one more book:

Chalmers, John H. Jr. The Divisions of the Tetrachord. Frog Peak
Music, Hanover NH, 1993, 234 pages.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Alex Carpenter" <acarp@a...> wrote:
>
> > I guess I feel they're neither rudimentary nor such a good place
to
> > start, given their ideological bias.
>
> Helmholtz was a scientist, so he approached the matter
> scientifically;

Much of his approach would not be considered scientific today.

> I think calling that an ideological bias is a
> stretch.

As I see it, he had a great ideological bias toward Just Intonation,
and his translator Ellis shows (perhaps going a bit too far) that
most musical cultures did not conform to Helmholtz's assumptions at
all. I think Helmholtz went too far even in equating Western music
with Just Intonation.

--- In tuning@y..., "Alex Carpenter" <acarp@a...> wrote:

> As for specific titles, that's a question
> I'll have to throw open: what _is_ the least ideologically-tainted
> book on acoustics??
>
> Cheers,
> Alex Carpenter

I posted a few in my list -- also you may want to delve deeply into
the articles on this website:

http://www.mmk.ei.tum.de/persons/ter.html

Also, the book

Pierce, John R. The Science of Musical Sound. Scientific American
books, New York, 1984, 242 pages.

is very honest -- the author recounts how his own assumptions
(ideological biases?), though based on scientific experiments, were
proved wrong (or sorely incomplete) in the course of his research.

<<Firstly, the acheivements and essays of Margo Schulter, Dave Keenan,
Manuel op de Coul, Graham Breed, Gene Ward Smith, Paul Hahn, and
Daniel Wolf on this list are equal if not better than any published
material.>>

Hi Paul,

I disagree with this. Only Margo writes essays--fifty times more than
anyone else here in fact! I think the technical tuning ideas of
yourself and some others here are often times right up there with the
big boys (and girls), but not the achievements and essays.

For the most part they're just toss offs, shop talk and works in
progress. Not that there's really anything wrong with that, and it
fits the nature of the forum well, but I think your selling the other
folks who've amassed their ideas into books and essays way, way short
(or, conversely, elevating the other folks way too high).

A book like Partch's is a many faceted and artful thing, and it would
really take quite a tuning book to stand shoulder to shoulder with
that. In fact, and I know this will endear me to one and all, I think
Brian McLaren is, with the notable exception of Margo, quite a bit
closer to what you actually said than anybody else you mentioned... by
a long shot!

--Dan Stearns

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., genewardsmith@j... wrote:

> > Helmholtz was a scientist, so he approached the matter
> > scientifically;

> Much of his approach would not be considered scientific today.

The historical material and discussion of musical theory would not be
called science back then either, but I think he approached the matter
as a scientist.

> As I see it, he had a great ideological bias toward Just
Intonation,
> and his translator Ellis shows (perhaps going a bit too far) that
> most musical cultures did not conform to Helmholtz's assumptions at
> all.

He made an instrument in the schismic temperament, and advocated it,
which suggests he was hardly a JI fanatic. He concluded, correctly,
that it sounded in better tune than meantone and in much better tune
than the 12-et.

I think Helmholtz went too far even in equating Western music
> with Just Intonation.

I don't recall him doing that.

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

> A book like Partch's is a many faceted and artful thing, and it
would
> really take quite a tuning book to stand shoulder to shoulder with
> that.

It is quite unsophisticated compared to the discussions on this list
and especially on tuning-math, however, which I think was Paul's
point.

If it were possible to magically summon into existence a perfectly
objective, scientifically verifiable book full of useful, practical
ideas, theories and their applications regarding tuning and
psychoacoustics, everyone who wanted to believe something different
from its pronouncements would say it was "ideologically tainted".

The above statement is actually a kind of valuable, important-to-
remember tautology.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "Alex Carpenter" <acarp@a...> wrote:
>
> > As for specific titles, that's a question
> > I'll have to throw open: what _is_ the least ideologically-
tainted
> > book on acoustics??
> >
> > Cheers,
> > Alex Carpenter
>

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> <<Firstly, the acheivements and essays of Margo Schulter, Dave
Keenan,
> Manuel op de Coul, Graham Breed, Gene Ward Smith, Paul Hahn, and
> Daniel Wolf on this list are equal if not better than any published
> material.>>
>
> Hi Paul,
>
> I disagree with this. Only Margo writes essays--fifty times more
than
> anyone else here in fact! I think the technical tuning ideas of
> yourself and some others here are often times right up there with
the
> big boys (and girls), but not the achievements and essays.

I think the technical tuning ideas _are_ achievements, easily
comparable to the acheivements of many of the published authors in my
list!

> For the most part they're just toss offs, shop talk and works in
> progress.

Well, if you look at these folks' webpages (except for Gene), you'll
see material that could easily be expanded into a serious
dissertation. The amount of original material is already sufficient.
Oh, that reminds me, here's another decent reference:

Mandelbaum, M. Joel. Multiple Division of the Octave and the Tonal
Resources of the 19-Tone Equal Temperament. PhD Thesis, University of
Indiana, 1961, 460 pages. University Microfilms, Ann Arbor MI, 1961.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., genewardsmith@j... wrote:
>
> > > Helmholtz was a scientist, so he approached the matter
> > > scientifically;
>
> > Much of his approach would not be considered scientific today.
>
> The historical material and discussion of musical theory would not
be
> called science back then either, but I think he approached the
matter
> as a scientist.

As a 19th century scientist, yes.
>
> > As I see it, he had a great ideological bias toward Just
> Intonation,
> > and his translator Ellis shows (perhaps going a bit too far) that
> > most musical cultures did not conform to Helmholtz's assumptions
at
> > all.
>
> He made an instrument in the schismic temperament, and advocated
it,
> which suggests he was hardly a JI fanatic. He concluded, correctly,
> that it sounded in better tune than meantone and in much better
tune
> than the 12-et.

I don't think comma shifts and drifts are preferable to the harmonic
errors of meantone. I think H., not really a musician himself,
focused far too strongly on the acoustical qualities of long-
sustained harmonies at the expense of melodic intonation factors. Of
course, Vicentino's second tuning of 1555 is preferable to both
schismic and meantone, for the type of repertoire that Helmholtz was
considering.

> > I think Helmholtz went too far even in equating Western music
> > with Just Intonation.
>
> I don't recall him doing that.

Well, then "relating" instead of "equating". The book is full of this
stuff. Even a primitive pentatonic scale, he insists on presenting as
JI: "1/1 9/8 5/4 3/2 5/3".

Hi Gene,

Technically unsophisticated, mathematically unsophisticated? Perhaps,
but that's just one piece of the presentation--and a rather
pasty-faced piece at that!

Partch's text like his music and his instruments, are works of art.
They've got backbone, depth and color in their cheeks... not to
mention more than a few technical ideas to keep most tuning enthusiast
busy for a while even today.

In fact, most of the tuning theory that I see around here that isn't
strictly acoustics or math, draws mightily from either Partch or
Wilson.

--Dan Stearns

----- Original Message -----
From: <genewardsmith@juno.com>
To: <tuning@yahoogroups.com>
Sent: Monday, November 19, 2001 2:50 PM
Subject: [tuning] Re: Essential reading about microtonal music

> --- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
>
> > A book like Partch's is a many faceted and artful thing, and it
> would
> > really take quite a tuning book to stand shoulder to shoulder with
> > that.
>
> It is quite unsophisticated compared to the discussions on this list
> and especially on tuning-math, however, which I think was Paul's
> point.
>
>
>
> ------------------------ Yahoo! Groups
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>
>

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> <<Firstly, the acheivements and essays of Margo Schulter, Dave
Keenan,
> Manuel op de Coul, Graham Breed, Gene Ward Smith, Paul Hahn, and
> Daniel Wolf on this list are equal if not better than any published
> material.>>
>
> Hi Paul,
>
> I disagree with this.

I should have put your name on there too, Dan. You've spend as much
time thinking about/working out tuning ideas as anyone, and though I
tend to be mystified by your terminology and concepts, that doesn't
say anything about the wealth of unique ideas in your posts here, and
the impressive overall philosophical framework that ties them all
together.

Sure, this falls short of a fully presented, readable account;
however, that shortcoming is much less severe in my eyes, than the
shortcomings of a certain prolific author you mentioned, namely that
the vast majority of the ideas presented are misunderstood and
misrepresented, and that the framework in which they are presented
has no coherent philosophy behind it (except, very often, the
philosophy that the author is the greatest mind in history and that
all others are ignorant fools).

Gene and Dan, what I meant by "equal if not better than any"
was "equal to any, if not even better than some". Sorry for the lax
phrasing.

Anything further on this sub-topic should be addressed to

metatuning@yahoogroups.com

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

> I don't think comma shifts and drifts are preferable to the
harmonic
> errors of meantone. I think H., not really a musician himself,
> focused far too strongly on the acoustical qualities of long-
> sustained harmonies at the expense of melodic intonation factors.

I think this is more in the nature of a limitation than a bias. Not
being a musician both helps and hurts--you can see that at work also
in Euler.

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

> Technically unsophisticated, mathematically unsophisticated?
Perhaps,
> but that's just one piece of the presentation--and a rather
> pasty-faced piece at that!

It's the only piece that interests me. I didn't get much out of
Partch's book, as opposed to his music; I could say the same about
Hindemith. Schoenberg I think is more interesting if you ignore the
serialism. I suppose I learned more from Piston's standard textbooks
than from any of them.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > I don't think comma shifts and drifts are preferable to the
> harmonic
> > errors of meantone. I think H., not really a musician himself,
> > focused far too strongly on the acoustical qualities of long-
> > sustained harmonies at the expense of melodic intonation factors.
>
> I think this is more in the nature of a limitation than a bias.

A limitation which resulted in a bias, perhaps?

Hi Paul,

Well it's your list and it should reflect the way you feel, but if
there was anyone there who seemed an omission to me, it was Joe Monzo.

He hasn't been around for a while but neither have Hahn or Wolf, and
Joe's done an awful lot for the cause.

As far as Brian goes, I don't agree with his napalm style at all and
have painfully butted heads with him over it in the past. I also find
personal correspondence to sometimes be difficult at best, but still,
he's not without merit, not by a long shot.

His essay, A Brief History of Microtonality in the Twentieth Century
was very inspiring to me. All the obscure microtonalist sounded like
endless exotic locales on a map I didn't even know existed!

It fired up my imagination in many ways and gave me added confidence
when pushing off into uncharted waters. Yes he makes mistakes, but
they never bothered me much... for example, the generalized Golden
scale algorithm and some other related ideas I've come up with were
directly inspired from a bit of McLaren text in A Brief History.

Yet he blotched the Kornerup Golden meantone example he gives... so
obviously there's sometimes more to get from a thing than precise
technical examples, and to McLaren's credit I was able to read right
through that without being any less impressed and inspired. He had
loaded just that brief presentation with more than math and tuning
theory, and in turn it was sturdy enough to absorb such a thing.
That's my take anyway, FWIW.

--Dan Stearns

----- Original Message -----
From: "Paul Erlich" <paul@stretch-music.com>
To: <tuning@yahoogroups.com>
Sent: Monday, November 19, 2001 3:34 PM
Subject: [tuning] Re: Essential reading about microtonal music

> --- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> > <<Firstly, the acheivements and essays of Margo Schulter, Dave
> Keenan,
> > Manuel op de Coul, Graham Breed, Gene Ward Smith, Paul Hahn, and
> > Daniel Wolf on this list are equal if not better than any
published
> > material.>>
> >
> > Hi Paul,
> >
> > I disagree with this.
>
> I should have put your name on there too, Dan. You've spend as much
> time thinking about/working out tuning ideas as anyone, and though I
> tend to be mystified by your terminology and concepts, that doesn't
> say anything about the wealth of unique ideas in your posts here,
and
> the impressive overall philosophical framework that ties them all
> together.
>
> Sure, this falls short of a fully presented, readable account;
> however, that shortcoming is much less severe in my eyes, than the
> shortcomings of a certain prolific author you mentioned, namely that
> the vast majority of the ideas presented are misunderstood and
> misrepresented, and that the framework in which they are presented
> has no coherent philosophy behind it (except, very often, the
> philosophy that the author is the greatest mind in history and that
> all others are ignorant fools).
>
> Gene and Dan, what I meant by "equal if not better than any"
> was "equal to any, if not even better than some". Sorry for the lax
> phrasing.
>
> Anything further on this sub-topic should be addressed to
>
> metatuning@yahoogroups.com
>
>
> ------------------------ Yahoo! Groups
Sponsor ---------------------~-->
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> --------------------------------------------------------------------
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>
> You do not need web access to participate. You may subscribe
through
> email. Send an empty email to one of these addresses:
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>
>
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>
>

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

> His essay, A Brief History of Microtonality in the Twentieth Century
> was very inspiring to me.

Well, it's by far the best thing I've seen from him.

> All the obscure microtonalist sounded like
> endless exotic locales on a map I didn't even know existed!
>
> It fired up my imagination in many ways and gave me added confidence
> when pushing off into uncharted waters.

This is exactly what I was going to tell Gene about Partch! If it
weren't for that Partch book in the library, I may have thought to
this day that trying new tuning systems was not worth my while, that
I'd have to be crazy to spend time and money on them, I wouldn't have
joined this list, etc. etc. And Partch's Tonality Diamond, while it
may be obvious to you, Gene, wasn't obvious to Dave Keenan, so there
has to be some significant originality there.

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

>And Partch's Tonality Diamond, while it
> may be obvious to you, Gene, wasn't obvious to Dave Keenan, so
there
> has to be some significant originality there.

It would be more accurate to say that I still don't understand the
point of the diamond, as opposed to a lattice. As for lattices, I got
a hint of that from Schoenberg, so thank you Arnold!

--- In tuning@y..., genewardsmith@j... wrote:

/tuning/topicId_29874.html#30368

> --- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
>
> > Technically unsophisticated, mathematically unsophisticated?
> Perhaps,
> > but that's just one piece of the presentation--and a rather
> > pasty-faced piece at that!
>
> It's the only piece that interests me. I didn't get much out of
> Partch's book, as opposed to his music; I could say the same about
> Hindemith. Schoenberg I think is more interesting if you ignore the
> serialism. I suppose I learned more from Piston's standard
textbooks than from any of them.

Hello Gene!

Schoenberg's _Harmonielehre_ is really a terrible book. (Please
forgive me, Schoenberg fans!) He even makes excuses for it right *in
the book!* It's really amazing.

He obviously *had* to write that thing as part of his teaching
curriculum. _Structural Functions of Harmony_ is, admittedly, quite
a bit better... and it seems that he actually *wanted* to write that
one.

Piston's standard _Harmony_ text is also pretty bad. I *always*
hated that book. Talk about *definitions!* Definition, statement
and *poof*... there's really little thinking in it! I find Allen
Forte's _Tonal Harmony_ book quite superior.

Piston's _Counterpoint_ book is just adequate... pretty good
for "invertible" counterpoint... and, curiously enough, his
_ORCHESTRATION_ book is *outstanding!* I still use it.

Probably, being a composer, he was most take with *that* one of all,
and, for me, anyway, it really shows!

JP

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

/tuning/topicId_29874.html#30369

> --- In tuning@y..., genewardsmith@j... wrote:
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> >
> > > I don't think comma shifts and drifts are preferable to the
> > harmonic
> > > errors of meantone. I think H., not really a musician himself,
> > > focused far too strongly on the acoustical qualities of long-
> > > sustained harmonies at the expense of melodic intonation
factors.
> >
> > I think this is more in the nature of a limitation than a bias.
>
> A limitation which resulted in a bias, perhaps?

If I recall correctly, Helmholtz really *does* try to pidgeon-hole a
good part of Western Harmony into a just intonational acoustical
mold... even moreso than Heinrich Schenker...

But, still, as a classic compendium, I would think that most students
of tuning would want to read through that book, if even with a few
caveats...

JP

--- In tuning@y..., jpehrson@r... wrote:

> Piston's standard _Harmony_ text is also pretty bad.

Agreed.

> I *always*
> hated that book. Talk about *definitions!* Definition, statement
> and *poof*... there's really little thinking in it! I find Allen
> Forte's _Tonal Harmony_ book quite superior.

Yes, really quite superior. Gene, check it out if you haven't yet.

--- In tuning@y..., jpehrson@r... wrote:

> But, still, as a classic compendium, I would think that most
students
> of tuning would want to read through that book, if even with a few
> caveats...
>
> JP

Well that's what I was trying to get at in reply to Alex. If you
eliminated everything that had any bias in it (even if that could be
objectively determined), you'd be left with virtually nothing! Better
by far is to read _everything_ (except for glaring misinformation) --
then at least you'll be in a position to speak the language of
whatever interested parties you may encounter, and then to argue
against the very positions that you feel are biased in a way that
these parties can understand.

genewardsmith@juno.com wrote:
--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

> A book like Partch's is a many faceted and artful thing, and it
would
> really take quite a tuning book to stand shoulder to shoulder with
> that.

It is quite unsophisticated compared to the discussions on this list
and especially on tuning-math, however, which I think was Paul's
point.

Hello, Gene,

But Partch was quite clear to me in his observation that JI just isn't very interesting to a mathmatician, which I ain't...but I wish I could be...Now I'll read the rest of the stuff.

Thanks,

Pete

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jpehrson@rcn.com wrote:
--- In tuning@y..., "Alex Carpenter" <acarp@a...> wrote:

/tuning/topicId_29874.html#30344

> jpehrson@r... wrote:
> > Hello Alex!
> >
> > Well, that's fine, but then, besides the isolated 1/1 article,
what books that you've read and which are available would you
recommend??
>
> Okay, you got me! I'm not sure I know of a book that's not
> ideologically tainted in some direction. But my intention was to
> alert Alex to what I feel are fairly significant underlying
> philosophical biases in the Partch and the Helmholtz.
>
> I'm probably not as familiar with the tuning literature as are many
> on this list - I read mainly in philosophy and cultural theory -
but I think I _am_ sensitive to how frequently musicians formulate
theory to justify their practice, as well as to how important it is
for one to avoid this style of theory while just beginning to piece
the whole puzzle together. I think any factual book on acoustic
science would be a better place to start. As for specific titles,
that's a question I'll have to throw open: what _is_ the least
ideologically-tainted book on acoustics??
>
> Cheers,
> Alex Carpenter

Hi Alex!

Well, most probably Paul Erlich will chime in (Woodstock chimes?)
with something, but of course there are several list readers who are
actually more interested in practical tunings than they are in the
acoustical basis... or at least my guess is that less than *half* of
the discussions on this forum are about acoustics.

Another problem is that several books on acoustics as related to
tuning... I'm thinking of the Backus, which I own, are substantially
out of date as far as the science goes... or at least that's what
I've been told.

On the overall, one of the sorry facts of the entire alternate tuning
field is the lack of literature *in print* about it. Even great
standards like Murray Barbour's work are out of print. Of course,
not long ago even Partch's _Genesis_ was out of print.

Some of this, I believe, has something to do with the tax code, since
publishers used to keep more older stuff around for a tax credit. I
believe it was Ronald Reagan (for sure bless his heart here) was the
one that eliminated this tax credit, and booksellers no longer keep
older inventory... or something like that...

Joseph Pehrson

Hey, you guys (a form of address I detest, but...)!

I corresponded with Backus and perused his book many years ago, and found him to be a 12t-ET fascist of the most ardent stripe. I can only hope that things have changed recenty.

Yours,

Pete
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The Pythag Sourcebook would not be considered microtonal readin round these
parts
maybe Nichomachus

Try barbara heros "the bead game"
www.lambdoma.com

and add
Music and the Power of sound
alain Danielou

or some Mathieu for a smile

Pat Pagano, Director
South East Just Intonation Society
http://www.screwmusicforever.com/SHREESWIFT/
> Duckworth, William, et al., ed. _Sound and Light: La Monte Young
> Marian Zazeela_. Lewisburg: Bucknell University Press, 1996.
>
> Guthrie, Kenneth Sylvan, ed. _The Pythagorean Sourcebook and
> Library_. Grand Rapids: Phanes Press, 1987. (Revised since.)
>
> James, Jamie. _The Music of the Spheres_. Rev. ed. London: Abacus,
> 1994.
>
> Anderson, Warren D. _Music and Musicians in Ancient Greece_. Ithaca:
> Cornell University Press, 1994.
>
> Best wishes,
> Alex Carpenter
> http://www.transparentmeans.com
>
>
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning group.
> tuning-nomail@yahoogroups.com - put your email message delivery on hold
for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to daily digest
mode.
> tuning-normal@yahoogroups.com - change your subscription to individual
emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>

In-Reply-To: <005601c1723b$333f2de0$847dd63f@stearns>
I haven't seen Ivor Darreg mentioned yet. Some of the files at
<http://www.ixpres.com/interval/darreg/contents.htm> work well as a call
to arms, and also help to redress the pro JI bias. And could it be that
Mathieu's "Harmonic Experience" got squeezed out by heavier texts?

Graham

--- In tuning@y..., graham@m... wrote:

> In-Reply-To: <005601c1723b$333f2de0$847dd63f@stearns>
> I haven't seen Ivor Darreg mentioned yet. Some of the files at
> <http://www.ixpres.com/interval/darreg/contents.htm> work well as a
call
> to arms, and also help to redress the pro JI bias.

Thanks for this link; I don't know if anyone will be greatly
informed, but they will certainly be amused. Fun stuff!

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> >And Partch's Tonality Diamond, while it
> > may be obvious to you, Gene, wasn't obvious to Dave Keenan, so
> there
> > has to be some significant originality there.
>
> It would be more accurate to say that I still don't understand the
> point of the diamond, as opposed to a lattice. As for lattices, I
got
> a hint of that from Schoenberg, so thank you Arnold!

Gene,

In case it helps, here's my
'Tonality diamonds understood (at last!)'
/tuning/topicId_7680.html#7680

Regards,
-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

> In case it helps, here's my
> 'Tonality diamonds understood (at last!)'
> /tuning/topicId_7680.html#7680

It confirms I understood what a Tonality Diamond is, and I like the
shuffling part, as it makes it seem there may be some rhyme or reason
to the order. It doesn't answer my basic question, which is so what?
What good is it? Arranging things so that nearby tones are together
suggests that it might be used as a practial arrangment in
performance, but that's different than saying it leads to any kind of
theoretical insight such as a lattice brings.

genewardsmith!
I am passing through and thought i would throw in my 4.5 cents.
The tonality Diamond can also be seen as the common tone modulations, in this case a harmonic
hexad which also generates its reciprocal.
Common tone modulations have been useful to quite alot of composers for quite a period of
time.
Now if you also look at http://www.anaphoria.com/lamb.PDF you will notice that the diamond,
being a version of a lambdoma generates super particular ratios between adjacent ratios (in ex.
high to low). Now going all the way back to the greeks, it was noticed that there is something
special about super particular ratios.
Also with Partch's Diamond you have the basis of a 41 tone moment of Symmetry.
As for the actual layout of the diamond you can see quickly which tones ar related by them
occurring in the row the pitch of interest is in.

genewardsmith@juno.com wrote:

> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
>
> > In case it helps, here's my
> > 'Tonality diamonds understood (at last!)'
> > /tuning/topicId_7680.html#7680
>
> It confirms I understood what a Tonality Diamond is, and I like the
> shuffling part, as it makes it seem there may be some rhyme or reason
> to the order. It doesn't answer my basic question, which is so what?
> What good is it? Arranging things so that nearby tones are together
> suggests that it might be used as a practial arrangment in
> performance, but that's different than saying it leads to any kind of
> theoretical insight such as a lattice brings.
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> Now if you also look at http://www.anaphoria.com/lamb.PDF you
will notice that the diamond,
> being a version of a lambdoma generates super particular ratios
between adjacent ratios (in ex.
> high to low). Now going all the way back to the greeks, it was
noticed that there is something
> special about super particular ratios.

If you want superparticular ratios in massive amounts you could look
at my stuff about "jacks" on the math list, as well as at the proof
that there are only a finite number in any p-limit. I don't see that
the diamond helps here; the Farey sequence is more to the point.

> Also with Partch's Diamond you have the basis of a 41 tone
moment of Symmetry.

This does not seem to me to be a good method for producing MOS.

> As for the actual layout of the diamond you can see quickly
which tones ar related by them
> occurring in the row the pitch of interest is in.

That's more like it. The defect of lattices is that they may be in
more than two dimensions, though you can project them as a la Monzo.

Hi Gene,

> From: Dave Keenan <D.KEENAN@UQ.NET.AU>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, November 20, 2001 6:08 PM
> Subject: [tuning] Re: Essential reading about microtonal music
>
>
> --- In tuning@y..., genewardsmith@j... wrote:
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> >
> > > And Partch's Tonality Diamond, while it may be obvious
> > > to you, Gene, wasn't obvious to Dave Keenan, so there
> > > has to be some significant originality there.
> >
> > It would be more accurate to say that I still don't
> > understand the point of the diamond, as opposed to a
> > lattice. As for lattices, I got a hint of that from
> > Schoenberg, so thank you Arnold!
>
> Gene,
>
> In case it helps, here's my
> 'Tonality diamonds understood (at last!)'
> /tuning/topicId_7680.html#7680
>
> Regards,
> -- Dave Keenan

And since you mentioned my favorite "cult hero",
Schoenberg, you may be interested in this if you
missed it before:

From: "monz" <joemonz@y...>
Date: Wed Jul 18, 2001 9:16 am
Subject: lattices of Schoenberg's rational implications
/tuning-math/message/516

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

Hello again, Gene,

> From: <genewardsmith@juno.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, November 20, 2001 7:59 PM
> Subject: [tuning] Re: Essential reading about microtonal music
>
>
> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
>
> > In case it helps, here's my
> > 'Tonality diamonds understood (at last!)'
> > /tuning/topicId_7680.html#7680
>
> It confirms I understood what a Tonality Diamond is, and I like the
> shuffling part, as it makes it seem there may be some rhyme or reason
> to the order. It doesn't answer my basic question, which is so what?
> What good is it? Arranging things so that nearby tones are together
> suggests that it might be used as a practial arrangment in
> performance, but that's different than saying it leads to any kind of
> theoretical insight such as a lattice brings.

A lattice is generally constructed according to
prime-factorization, whereas the Partch (by way of
Novaro) Tonality Diamond is based on *odd*-factoring.

Partch saw the odd-number series as the one manifesting
the important harmonic information in a multi-tone chord.

Also, as he himself said, the diamond "constitutes
_prima facie_ proof of the at-least-dual identity of
each ratio". (I'm paraphrasing, despite the quotes.)

O-/U-tonal (i.e., harmonic/subharmonic) Dualism is a
very important aspect of Partch's theories, and these
relationships are laid bare on the Diamond.

On the other hand, I tend to agree with you that the
prime-factor lattice conveys the same information in
a simpler (i.e, further reduced) format.

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

genewardsmith!
The Lambdoma is related to the Farey series as my link points out in the title. Anyway to have
your most closely related notes is a very musical feature.
If all you want is an MOS obviously not the best method. But MOS are only a solution to having
melodic integrity, the diamond solves the other question, harmonic.

genewardsmith@juno.com wrote:

> If you want superparticular ratios in massive amounts you could look
> at my stuff about "jacks" on the math list, as well as at the proof
> that there are only a finite number in any p-limit. I don't see that
> the diamond helps here; the Farey sequence is more to the point.
>
> > Also with Partch's Diamond you have the basis of a 41 tone
> moment of Symmetry.
>
> This does not seem to me to be a good method for producing MOS.

>
>
> > As for the actual layout of the diamond you can see quickly
> which tones ar related by them
> > occurring in the row the pitch of interest is in.
>
> That's more like it. The defect of lattices is that they may be in
> more than two dimensions, though you can project them as a la Monzo.
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> A lattice is generally constructed according to
> prime-factorization, whereas the Partch (by way of
> Novaro) Tonality Diamond is based on *odd*-factoring.

I wouldn't call it factoring--it's a product set. There is not of
course unique factorization for odd numbers.

> Also, as he himself said, the diamond "constitutes
> _prima facie_ proof of the at-least-dual identity of
> each ratio". (I'm paraphrasing, despite the quotes.)

The "dual identity" is completely obvious from the reciprocal map
x |--> 1/x.

> On the other hand, I tend to agree with you that the
> prime-factor lattice conveys the same information in
> a simpler (i.e, further reduced) format.

It doesn't convey the *same* information, but it conveys a lot more
information, it seems to me.

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> On the other hand, I tend to agree with you that the
> prime-factor lattice conveys the same information in
> a simpler (i.e, further reduced) format.

So Monz or Gene,

Draw us up a prime-factor lattice for the 11-limit diamond and let's
see if it's as intelligible as the diamond layout itself. The lattice
will be four dimensional and will treat ratios of 9's as second-class
citizens. Compare this to the diamond's viewable and playable two
dimensionality and all-odds-are-equal, at a cost of only 7 redundant
vertices.

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

> Draw us up a prime-factor lattice for the 11-limit diamond and
let's
> see if it's as intelligible as the diamond layout itself.

Drawing is not the point so far as I am concered.

The lattice
> will be four dimensional and will treat ratios of 9's as second-
class
> citizens.

The lattice will show 9 = 3^2, which is correct; the diamond will
obscure that.

Compare this to the diamond's viewable and playable two
> dimensionality and all-odds-are-equal, at a cost of only 7
redundant
> vertices.

But what does it tell you?

In-Reply-To: <9tf8q7+ilkh@eGroups.com>
Gene wrote:

> What good is it? Arranging things so that nearby tones are together
> suggests that it might be used as a practial arrangment in
> performance, but that's different than saying it leads to any kind of
> theoretical insight such as a lattice brings.

I think this shows a philosophical difference. If something works in
practice, but not in theory, I'd always try to correct the theory.

Graham

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

/tuning/topicId_29874.html#30425

> genewardsmith!
> I am passing through and thought i would throw in my 4.5 cents.
> The tonality Diamond can also be seen as the common tone
modulations, in this case a harmonic hexad which also generates its
reciprocal.
> Common tone modulations have been useful to quite alot of
composers for quite a period of time.

Hi Kraig!

Welcome back, for however how long... I just wanted to add
that "common tone modulations" have become quite important to my
current "Blackjack" composing as I work my way through the Blackjack
lattice...

Joseph Pehrson

--- In tuning@y..., graham@m... wrote:

> I think this shows a philosophical difference. If something works
in
> practice, but not in theory, I'd always try to correct the theory.

It hardly makes sense to correct the theory when theory, not
practice, was the issue. I wasn't suggesting the diamond wasn't neat,
I was asking what insight it gives.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
>
> > In case it helps, here's my
> > 'Tonality diamonds understood (at last!)'
> > /tuning/topicId_7680.html#7680
>
> It confirms I understood what a Tonality Diamond is, and I like the
> shuffling part, as it makes it seem there may be some rhyme or
reason
> to the order. It doesn't answer my basic question, which is so
what?
> What good is it? Arranging things so that nearby tones are together
> suggests that it might be used as a practial arrangment in
> performance, but that's different than saying it leads to any kind
of
> theoretical insight such as a lattice brings.

Gene -- until Wilson, I don't think any musician could draw and
comprehend an 11-limit lattice -- so failing that, Partch's 6-by-6
arrangement shows off as many of the properties of the Diamond as
possible.

--- In tuning@y..., genewardsmith@j... wrote:

> > Also with Partch's Diamond you have the basis of a 41 tone
> > moment of Symmetry.
>
> This does not seem to me to be a good method for producing MOS.

Kraig often says MOS when he means CS (which can be thought of as a
circle of modified fifths). 11/10 and 10/9 must be considered
equivalent for this to work.

> > As for the actual layout of the diamond you can see quickly
> which tones ar related by them
> > occurring in the row the pitch of interest is in.
>
> That's more like it. The defect of lattices is that they may be in
> more than two dimensions, though you can project them as a la Monzo.

Wilson's 11-limit lattices are far more enlightening than Monz's --
in Wilson's, the Diamond has a decagonal symmetry, with all the
hexads appearing as regular pentagons (Otonals pointing up, Utonals
pointing down), with their 1 Identity in their centers. But yes, the
6-by-6 arrangement makes this simpler by using only 2 dimensions
(works great for the Diamond pitch set; wouldn't work for others).

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> A lattice is generally constructed according to
> prime-factorization, whereas the Partch (by way of
> Novaro) Tonality Diamond is based on *odd*-factoring.

Partch's lattice isn't based on factoring at all! Notice how 1/1,
3/3, 5/5, etc, all appear in different places! Meanwhile, Wilson's
lattices _are_ based on odd-factoring.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > A lattice is generally constructed according to
> > prime-factorization, whereas the Partch (by way of
> > Novaro) Tonality Diamond is based on *odd*-factoring.
>
> I wouldn't call it factoring--it's a product set.

Right.

> There is not of
> course unique factorization for odd numbers.

In Wilson's lattices, the same note often appears in more than one
place.

> > Also, as he himself said, the diamond "constitutes
> > _prima facie_ proof of the at-least-dual identity of
> > each ratio". (I'm paraphrasing, despite the quotes.)
>
> The "dual identity" is completely obvious from the reciprocal map
> x |--> 1/x.

Completely obvious to a mathematician, not to a non-mathematical
musician.

> > On the other hand, I tend to agree with you that the
> > prime-factor lattice conveys the same information in
> > a simpler (i.e, further reduced) format.
>
> It doesn't convey the *same* information, but it conveys a lot more
> information, it seems to me.

For the case of the Diamond, a prime-factor lattice might fail to
show "consonances" like 9:5, while Partch's 6-by-6 arrangement
manages to convey _all_ the important information, as far as I can
see. However, once you start adding more notes, the flat arragement
is toast.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> /tuning/topicId_29874.html#30425
>
> > genewardsmith!
> > I am passing through and thought i would throw in my 4.5
cents.
> > The tonality Diamond can also be seen as the common tone
> modulations, in this case a harmonic hexad which also generates its
> reciprocal.

Kraig, Gene understands the coolness of the tonality diamond as a
pitch set -- in fact he came up with the same concept independently --
he just thinks that depicting it on a lattice tells you more than
depicting it Partch's way.

> > Common tone modulations have been useful to quite alot of
> composers for quite a period of time.
>
> Hi Kraig!
>
> Welcome back, for however how long... I just wanted to add
> that "common tone modulations" have become quite important to my
> current "Blackjack" composing as I work my way through the
Blackjack
> lattice...
>
> Joseph Pehrson

Yes, a lattice is a perfect way of viewing pitch sets if one is
interested in "common tone modulations".

Paul E.!

Paul Erlich wrote:

> Kraig often says MOS when he means CS (which can be thought of as a
> circle of modified fifths). 11/10 and 10/9 must be considered
> equivalent for this to work.

Stand corrected, since more scales I tend to work with are CS than MOS, yes i do this.
In reference below i would just like to add that Wilson will generate more than one lattice for
any system when he feels it shows properties that are apparent in others. As one can see in
http://www.anaphoria.com/dal.PDF

>
> Wilson's 11-limit lattices are far more enlightening than Monz's --
> in Wilson's, the Diamond has a decagonal symmetry, with all the
> hexads appearing as regular pentagons (Otonals pointing up, Utonals
> pointing down), with their 1 Identity in their centers. But yes, the
> 6-by-6 arrangement makes this simpler by using only 2 dimensions
> (works great for the Diamond pitch set; wouldn't work for others).
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Paul E.!
Wilson tends to think of the 9 as kind of a musical "prime". in other words an independent
musical existence from being a mere 3 x 3

Paul Erlich wrote:

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > A lattice is generally constructed according to
> > prime-factorization, whereas the Partch (by way of
> > Novaro) Tonality Diamond is based on *odd*-factoring.
>
> Partch's lattice isn't based on factoring at all! Notice how 1/1,
> 3/3, 5/5, etc, all appear in different places! Meanwhile, Wilson's
> lattices _are_ based on odd-factoring.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Paul E.!
> Wilson tends to think of the 9 as kind of a musical "prime". in
other words an independent
> musical existence from being a mere 3 x 3

Exactly! Even if one is skeptical of this "independent musical
existence", one must admit that Wilson's lattices make dyads which
are ratios of 9 look like "consonances" just like ratios of 7 and
ratios of 11 (as they should be), while a true prime lattice will
tend to obscure the consonance of the ratios of 9.

We shouldn't equate the words "theory" or "theoretical"
with "impractical" and treat theory and practice as mutually
exclusive or as having an intrinsically adversarial relationship.
This perception of these terms has obscured communications here.

Gene said the lattice promotes "theoretical insight", which is always
good. You can't play either the diamond or the lattice diagrams, so
the apparent "practicality" of the pitch order is only a conditioned
perception based on musical practice that creates the comfortable
illusion of understanding and little more.

Theoretical insight translates to everyday language as greater depth
of comprehension and consequently more ability to handle larger
amounts of interacting information with greater ease and
simplicity...and THAT has GREAT practical value. Theories that don't
work to unify and simplify to a comparitively few elements the
comprehensive range of specific possibilities under consideration
don't count. They're just bad theories. So people should stop dumping
on theory as impractical simply because some theories are bad. I
still eat apples, even though rotten apples do indeed exist.

--- In tuning@y..., graham@m... wrote:
> In-Reply-To: <9tf8q7+ilkh@e...>
> Gene wrote:
>
> > What good is it? Arranging things so that nearby tones are
together
> > suggests that it might be used as a practial arrangment in
> > performance, but that's different than saying it leads to any
kind of
> > theoretical insight such as a lattice brings.
>
> I think this shows a philosophical difference. If something works
in
> practice, but not in theory, I'd always try to correct the theory.
>
>
> Graham

--- In tuning@y..., BobWendell@t... wrote:
> We shouldn't equate the words "theory" or "theoretical"
> with "impractical" and treat theory and practice as mutually
> exclusive or as having an intrinsically adversarial relationship.
> This perception of these terms has obscured communications here.
>
> Gene said the lattice promotes "theoretical insight", which is
always
> good. You can't play either the diamond or the lattice diagrams,

When you're playing Partch's Diamond Marimba, you _are_ playing the
diamond diagram.

I wrote,

> --- In tuning@y..., BobWendell@t... wrote:

> > Gene said the lattice promotes "theoretical insight", which is
> always
> > good. You can't play either the diamond or the lattice diagrams,
>
> When you're playing Partch's Diamond Marimba, you _are_ playing the
> diamond diagram.

Similarly, in Monz's virtual reality JustMusic program, you _are_
playing Monz's lattice diagram.

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

/tuning/topicId_29874.html#30460

> Paul E.!
>
> Paul Erlich wrote:
>
> > Kraig often says MOS when he means CS (which can be thought of as
a
> > circle of modified fifths). 11/10 and 10/9 must be considered
> > equivalent for this to work.
>
> Stand corrected, since more scales I tend to work with are CS than
MOS, yes i do this.
> In reference below i would just like to add that Wilson will
generate more than one lattice for
> any system when he feels it shows properties that are apparent in
others. As one can see in
> http://www.anaphoria.com/dal.PDF
>

Hi Kraig!

These .pdfs really work much better than the "old days," that's for
sure. I'm curious: what do you use to create the .pdfs... is it the
Adobe software? That's rather expensive, isn't it??

JP

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

/tuning/topicId_29874.html#30464

> --- In tuning@y..., BobWendell@t... wrote:
> > We shouldn't equate the words "theory" or "theoretical"
> > with "impractical" and treat theory and practice as mutually
> > exclusive or as having an intrinsically adversarial relationship.
> > This perception of these terms has obscured communications here.
> >
> > Gene said the lattice promotes "theoretical insight", which is
> always
> > good. You can't play either the diamond or the lattice diagrams,
>
> When you're playing Partch's Diamond Marimba, you _are_ playing the
> diamond diagram.

And Bill Sethares has it set up so that one can actually play it on
line, provided one has java installed...!

http://members.home.net/prodgers13/DiamondMarimba.html

Got to admit, it makes a really impressive music, especially when the
bars are played diagonally...

Joseph Pehrson

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> I wrote,
>
> > --- In tuning@y..., BobWendell@t... wrote:
>
> > > Gene said the lattice promotes "theoretical insight", which is
> > always
> > > good. You can't play either the diamond or the lattice diagrams,
> >
Paul wrote:
> > When you're playing Partch's Diamond Marimba, you _are_ playing
the
> > diamond diagram.
>
Paul wrote:
> Similarly, in Monz's virtual reality JustMusic program, you _are_
> playing Monz's lattice diagram.

Bob replies:
Yes, I half expected someone to answer with that. It's obviously a
possibility, but has little to do with the point of my reply. I was
referring to the hard copy or screen dislplay of the diagrams, which
are not playable, and whose purpose is manifestly simply to
communicate information in as effective a manner as possible. This
might be aided by playability although that is not essential to
comprehension of the information displayed.

The ONE and ONLY purpose of theory is to elucidate and facilitate
practice. It is essential to practicality and not antithetical to it.
So I would love to see an end to this "practical" posturing that puts
down the vital role of theory as if "theoretical" were an antonym
for "practical". This latter perception is a very popular idea based
on a complete misunderstanding of both the nature and purpose of
theory.

Yes, undoubtedly theory must be born out by practice, and in this
regard, practical utility is the ultimate criterion for the value of
any theory and is therefore king. Even so, without the unifying power
of coherent, comprehensive theory, practice becomes lame.

The theoretical insight to which Gene refers often leads to renewed
creativity and important new discoveries. One of the good things
about this list is that theories get proposed and theories get
challenged. Also theories that have long been proposed get aired and
challenged (and illuminated for better or worse). Hopefully only the
good ones will survive.

Respectfully,

Bob

--- In tuning@y..., jpehrson@r... wrote:

/tuning/topicId_29874.html#30468
>
> http://members.home.net/prodgers13/DiamondMarimba.html
>
> Got to admit, it makes a really impressive music, especially when
the bars are played diagonally...
>
> Joseph Pehrson

Of course, I meant not Bill Sethares, but Prent Rodgers.

Bill Sethares has many wonders of his own:

http://eceserv0.ece.wisc.edu/~sethares/

Hi JP!
Yes i tried to find someone with Adobe Acrobat for Mac some times ago. I had to shell out the
$250 to put all the Wilson stuff up.
Let me remind you that all those on this list can contribute to North American Embassy of
Anaphoria island since we are a non profit and tax deductible. Considering how much many on these
lists benefit from this it seems some others could lessen the burden on myself as my income is
sporadic at best. If interested please see http://www.anaphoria.com/nonprof.html
Joe Has already contributed, it's time some of the rest of you do, :)

jpehrson@rcn.com wrote:

> Hi Kraig!
>
> These .pdfs really work much better than the "old days," that's for
> sure. I'm curious: what do you use to create the .pdfs... is it the
> Adobe software? That's rather expensive, isn't it??
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

I have no idea why or if it is common but I can write Acrobat files from MS Word 97. They come out fine, though I am sure there are a lot more options with Acrobat. Tis a fine piece of software.

ammegand
----- Original Message -----
From: Kraig Grady
To: tuning@yahoogroups.com
Sent: Wednesday, November 21, 2001 7:45 PM
Subject: Re: [tuning] Re: Essential reading about microtonal music

Hi JP!
Yes i tried to find someone with Adobe Acrobat for Mac some times ago. I had to shell out the
$250 to put all the Wilson stuff up.
Let me remind you that all those on this list can contribute to North American Embassy of
Anaphoria island since we are a non profit and tax deductible. Considering how much many on these
lists benefit from this it seems some others could lessen the burden on myself as my income is
sporadic at best. If interested please see http://www.anaphoria.com/nonprof.html
Joe Has already contributed, it's time some of the rest of you do, :)

jpehrson@rcn.com wrote:

> Hi Kraig!
>
> These .pdfs really work much better than the "old days," that's for
> sure. I'm curious: what do you use to create the .pdfs... is it the
> Adobe software? That's rather expensive, isn't it??
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

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--- In tuning@y..., BobWendell@t... wrote:

> The ONE and ONLY purpose of theory is to elucidate and facilitate
> practice. It is essential to practicality and not antithetical to
it.
> So I would love to see an end to this "practical" posturing that
puts
> down the vital role of theory as if "theoretical" were an antonym
> for "practical". This latter perception is a very popular idea
based
> on a complete misunderstanding of both the nature and purpose of
> theory.

I agree completely, but I think you're targeting the wrong person.
You were reacting to Graham Breed, theoretician extraordinaire!

--- In tuning@y..., "ammegand" <ammegand@c...> wrote:

> I have no idea why or if it is common but I can write Acrobat files
from MS Word 97.

Really? I'll have to try this when I get back to the office! I've
been having .pdf headaches for years.

--- In tuning@y..., BobWendell@t... wrote:
> The ONE and ONLY purpose of theory is to elucidate and facilitate
> practice. It is essential to practicality and not antithetical to
> it.

Antithetical, no. Essential? Hubris maximus. Please, someone talk
about the theoretical background that Howlin Wolf absorbed before he
developed his eminently 'practical' blues renditions. Including
microtones.

More on this later - it's been an interesting thread, especially
since the subject line asked for reading about "microtonal music",
the author said he had been involved in "microtonal music" for some
time, and in addition to the 'usual suspect' books (which garnered
their traditional support and raspberries) was treated to books on
acoustics and other extrapolated topics.

But I'm grabbing my one day off with my teeth, so everyone have a
great Thursday... in theory.

Cheers,
Jon

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "ammegand" <ammegand@c...> wrote:
>
> > I have no idea why or if it is common but I can write Acrobat
files
> from MS Word 97.
>
> Really? I'll have to try this when I get back to the office! I've
> been having .pdf headaches for years.

Somewhere, at some point, there was a free plug-in *from* Adobe *for*
MS Word, and I've used it ever since (my most recent version is still
Word 97.

I'll do a search and see if it's still available, and if not check to
see if I still have the installable for the plugin...

Cheers,
Jon (nice pickup on the Diamond stuff, Paul...)

In-Reply-To: <9thbtd+ln1e@eGroups.com>
> > http://members.home.net/prodgers13/DiamondMarimba.html
> >
> > Got to admit, it makes a really impressive music, especially when
> the bars are played diagonally...
> >
> > Joseph Pehrson
>
> Of course, I meant not Bill Sethares, but Prent Rodgers.

This is excellent! I didn't know about it. By clicking on multiple
notes, you can get some great rhythms set up. Which means there is a
point in having all those 1/1 repetitions.

Graham

In-Reply-To: <9thbhk+o5sb@eGroups.com>
Bob Wendell wrote:

> The ONE and ONLY purpose of theory is to elucidate and facilitate
> practice. It is essential to practicality and not antithetical to it.
> So I would love to see an end to this "practical" posturing that puts
> down the vital role of theory as if "theoretical" were an antonym
> for "practical". This latter perception is a very popular idea based
> on a complete misunderstanding of both the nature and purpose of
> theory.

Quite right. That's pretty much what I meant to say, but you seem to
think you're disagreeing with me. I was pulling Gene up on his (roughly
paraphrased) "it works in practice but not in theory" which I consider to
be bogus. I'm sure he didn't really intend it to come out like that, but
his clarification is still somewhat ambiguous.

> Yes, undoubtedly theory must be born out by practice, and in this
> regard, practical utility is the ultimate criterion for the value of
> any theory and is therefore king. Even so, without the unifying power
> of coherent, comprehensive theory, practice becomes lame.

I'm with you on the first sentence. But ISTM that alot of practical
musicians can get by fine with very little theory. Let's not give
ourselves delusions of grandeur.

> The theoretical insight to which Gene refers often leads to renewed
> creativity and important new discoveries. One of the good things
> about this list is that theories get proposed and theories get
> challenged. Also theories that have long been proposed get aired and
> challenged (and illuminated for better or worse). Hopefully only the
> good ones will survive.

Yes, I expect that's what he was thinking. But in the interests of good
theory, it is a mistake to ignore the practical benefits of a diamond
layout. It's a theoretical construct that has practical advantages. So
it must be good theory.

Erv Wilson's CPS diagrams are the theoretical advance that builds on the
diamond layout's advantages. I don't think I could have made that step,
but Wilson did and it looks like so much numerology until you consider the
practical benefits. Once you do understand it, all the theoretical
treatises about the impracticality of just intonation suddenly begin to
resemble a steaming pile of bovine ordure. Perhaps there's another
breakthrough around the corner, and we won't be able to find it if we
can't see beyond those regular lattices.

And to drag this thread back on topic, the reason Partch stands as a
towering figure of 20th Century music theory is that he was the one who
showed that high-limit JI could be of practical, musical benefit. Even if
he didn't make much use of the JI harmonies, that's the path he took and
to understand it you could try to read his book.

I don't think there's any "essential reading" about microtonality. You
could stay on this list and learn from the rest of us who are trying make
sense of it. But mostly you have to learn for yourself by tuning up some
scales and, if necessary, working out some ideas on a spreadsheet. Not
enough people have done this and made great music as a result for us to
have a set of key ideas that can be written up and taught to newcomers.
Almost by definition, anything well understood and appreciated isn't
"microtonal". So many good ideas are sitting in journals, and there are
so many different approaches you'll have to work out for yourself what you
need to know.

Still, Partch and Darreg are good places to start. Then Wilson and
Sethares.

Okay, I'll get off my soap box now ...

Graham

Hi Gene,

> From: <genewardsmith@juno.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, November 20, 2001 11:01 PM
> Subject: [tuning] Re: Essential reading about microtonal music
>
>

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> > A lattice is generally constructed according to
> > prime-factorization, whereas the Partch (by way of
> > Novaro) Tonality Diamond is based on *odd*-factoring.
>
> I wouldn't call it factoring--it's a product set. There is not of
> course unique factorization for odd numbers.
>
> > Also, as he himself said, the diamond "constitutes
> > _prima facie_ proof of the at-least-dual identity of
> > each ratio". (I'm paraphrasing, despite the quotes.)
>
> The "dual identity" is completely obvious from the reciprocal map
> x |--> 1/x.
>
> > On the other hand, I tend to agree with you that the
> > prime-factor lattice conveys the same information in
> > a simpler (i.e, further reduced) format.
>
> It doesn't convey the *same* information, but it conveys a lot more
> information, it seems to me.

You understand the math of all this far, far better
than I do. But essentially, I agree with you.
Lattices are supreme.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

Thanks Graham,

Ivor's definitely another person to mention (along with Margo and
Brian) when it comes to microtonal essay writing.

--Dan Stearns

----- Original Message -----
From: <graham@microtonal.co.uk>
To: <tuning@yahoogroups.com>
Sent: Tuesday, November 20, 2001 2:30 AM
Subject: [tuning] Re: Essential reading about microtonal music

> In-Reply-To: <005601c1723b$333f2de0$847dd63f@stearns>
> I haven't seen Ivor Darreg mentioned yet. Some of the files at
> <http://www.ixpres.com/interval/darreg/contents.htm> work well as a
call
> to arms, and also help to redress the pro JI bias. And could it be
that
> Mathieu's "Harmonic Experience" got squeezed out by heavier texts?
>
>
> Graham
>
>
>
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I almost forgot . . .

The best single piece of reading you can do to get you up to speed on
acoustics, psychoacoustics, musical tuning (including experimental
microtonality) and synthesis, are Dave Benson's course notes, which
you can download here:

ftp://byrd.math.uga.edu/pub/html/math-music.html

--- In tuning@y..., graham@m... wrote:

> Quite right. That's pretty much what I meant to say, but you seem
to
> think you're disagreeing with me. I was pulling Gene up on his
(roughly
> paraphrased) "it works in practice but not in theory" which I
consider to
> be bogus.

I don't recall saying that. I also don't recall learning anything of
*theoretical* significance from Partch; this is unlike the case with
Helmholtz, Euler, Barbour, or, incidentally, Graham Breed.

> Yes, I expect that's what he was thinking. But in the interests of
good
> theory, it is a mistake to ignore the practical benefits of a
diamond
> layout. It's a theoretical construct that has practical
advantages. So
> it must be good theory.

It don't think a diamond layout can be called a theoretical
construct; it's not a product set, which *is* a theoretical construct.

> Erv Wilson's CPS diagrams are the theoretical advance that builds
on the
> diamond layout's advantages. I don't think I could have made that
step,
> but Wilson did and it looks like so much numerology until you
consider the
> practical benefits.

I'd be more impressed with this argument but for the fact that I knew
about these before I even read Partch--from lattices. And lattices I
got, more or less, from Schoenberg. That is not to say that reading
Partch is not a reasonable route to the same place, but I think it
would be a terrible idea to go only as far as the diamond in your
understanding and then stop.

Paul,

Knowing your love for voicing the alternate viewpoint, in fostering
dialogue, let me ask this:

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> The best single piece of reading you can do to get you up to speed
> on acoustics, psychoacoustics, musical tuning (including
> experimental microtonality) and synthesis

So he asks about _essential_ reading about "microtonal music", and
you choose to send him to Math and Music, with the above breakdown of
subjects. I downloaded that .pdf the first time you posted it and
spent an hour or so 'thumbing' through it.

Are we so poor in this area, that we have no book to point to that
uses *music* as the starting point, and brings in the other subjects
as necessary parts of the scheme? Is microtonal music going to be
always doomed to start it's life with a calculator, an oscilliscope,
and an anechoic chamber?

[You know me well enough to imagine my tongue-in-cheek, but the basic
thrust is there: not everyone who wants to find an alternative to the
12tET prison is going to approach it from the science side - some
will come from the music side, no? We need resources for them!]

And, frankly, I wish I *could* recommend a 'one' book.

Cheers,
Jon

Thread drift now at warp speed...

--- In tuning@y..., genewardsmith@j... wrote:
> That is not to say that reading
> Partch is not a reasonable route to the same place, but I think it
> would be a terrible idea to go only as far as the diamond in your
> understanding and then stop.

Yep, that lame diamond concept, limiting as it is, surely must have
been the reason that Partch was only able to create 50 years worth of
unique works, wide-ranging in style and manner, including an entire
orchestra of instruments well-sprung from that paltry source. Some
people just know when to stop speculating and calculating and get on
with it.

Cheers,
Jon

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

> So he asks about _essential_ reading about "microtonal music", and
> you choose to send him to Math and Music, with the above breakdown
of
> subjects.

There's an idea. I think I'll add an undergraduate text on linear
algebra and abstract algebra to the list, and maybe the first part of
Jacobson's "Basic Algebra" to make sure you didn't miss anything
basic. Then some elementary number theory, such as Hardy and Wright
or Niven and Zuckerman, something on diophantine approximation, and
something which at least defines valuations.

I'm not sure if I'm kidding or not; I'll think about it. :)

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

> Yep, that lame diamond concept, limiting as it is, surely must have
> been the reason that Partch was only able to create 50 years worth
of
> unique works, wide-ranging in style and manner, including an entire
> orchestra of instruments well-sprung from that paltry source. Some
> people just know when to stop speculating and calculating and get
on
> with it.

Partch never really took full advantage of his own ideas, it seems to
me. As for the diamond, I'm afraid when I read it it struck me that
Partch had gotten half-way to understanding things, and then got
stuck. So sue me.

In-Reply-To: <9tksho+kf3k@eGroups.com>
Me:
> > Quite right. That's pretty much what I meant to say, but you seem
> to
> > think you're disagreeing with me. I was pulling Gene up on his
> (roughly
> > paraphrased) "it works in practice but not in theory" which I
> consider to
> > be bogus.

Gene:
> I don't recall saying that. I also don't recall learning anything of
> *theoretical* significance from Partch; this is unlike the case with
> Helmholtz, Euler, Barbour, or, incidentally, Graham Breed.

What you said is "Arranging things so that nearby tones are together
suggests that it might be used as a practical arrangement in
performance, but that's different than saying it leads to any kind of
theoretical insight such as a lattice brings." And also "It hardly makes
sense to correct the theory when theory, not practice, was the issue."

Gene:
> It don't think a diamond layout can be called a theoretical
> construct; it's not a product set, which *is* a theoretical construct.

You can write a diamond on paper, and there are general rules for
constructing it, so it must be theoretical.

Me:
> > Erv Wilson's CPS diagrams are the theoretical advance that builds
> on the
> > diamond layout's advantages. I don't think I could have made that
> step,
> > but Wilson did and it looks like so much numerology until you
> consider the
> > practical benefits.

Gene:
> I'd be more impressed with this argument but for the fact that I knew
> about these before I even read Partch--from lattices. And lattices I
> got, more or less, from Schoenberg. That is not to say that reading
> Partch is not a reasonable route to the same place, but I think it
> would be a terrible idea to go only as far as the diamond in your
> understanding and then stop.

You knew about CPS scales or the way Wilson draws them? Did you get as
far as D'Alessandro, and do you have an alternative that works with
Canasta? I knew about lattices before I read Schoenberg, if that means
anything.

Of course, if something's of theoretical interest you don't stop with it.
Now I'm thinking about the reordered diamond, it's the same principle as
my 9-limit lattice <http://x31eq.com/lattice.htm#9limit> where
4:5:6:7:9 is set to increase in pitch from left to right.

Graham

Partch's ear took advantage of things within the diamond that most here only find by number
crunching. BTW since you have so little interest in the diamond just what do you have to have
musicians to play upon.

genewardsmith@juno.com wrote:

>
> Partch never really took full advantage of his own ideas, it seems to
> me. As for the diamond, I'm afraid when I read it it struck me that
> Partch had gotten half-way to understanding things, and then got
> stuck. So sue me.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Gene,

--- In tuning@y..., genewardsmith@j... wrote:
> Partch never really took full advantage of his own ideas, it
> seems to me.

I have no idea if you like or are interested in Partchs 'end
product'. I don't care, because musical tastes are very personal. But
your comment is, "it seems to me", further documentation of the gap
between those who would endlessly 'experiment' and those that find
resources to make something, and then make it. You completely gloss
over an entire body of work to focus on the small aspect of what
could have been. One way of looking at the world, I suppose, but
pretty limiting.

> As for the diamond, I'm afraid when I read it it struck me that
> Partch had gotten half-way to understanding things, and then got
> stuck. So sue me.

He wasn't a theorist, he was a composer, and he went as far as he
*needed* to - he found materials to base his composition on, and used
them. That he found even that much concept, essentially working alone
with little precident, is pretty striking. But the fact that he
didn't end up endlessly refining and refocusing the underlying fabric
of the intonation system he chose is meaningless in light of the
compositional accomplishments.

Except to some mathematicians and theorists, apparantly.

Regards,
Jon

Bob had written:
> Yes, undoubtedly theory must be born out by practice, and in this
> regard, practical utility is the ultimate criterion for the value
of
> any theory and is therefore king. Even so, without the unifying
power
> of coherent, comprehensive theory, practice becomes lame.

Graham replied:
I'm with you on the first sentence. But ISTM that alot of practical
musicians can get by fine with very little theory. Let's not give
ourselves delusions of grandeur.

Bob answers:
Why "delusions of grandeur"? The musicians you refer to are standing
on the shouders of those whose theoretical work laid the practical
foundation and generated the fundamental musical resources for
everything those musicians do. These musical resources, whether they
understand them theoretically or not, are what they manipulate to
produce their music.

That this manipulation is intuitive detracts nothing from the
value of the theoretical foundations upon which their musical
resources are based. Without these pre-existent resources and no
theoretical understanding of their own, they could do little. Don't
forget that the understanding of generations of musicians is embodied
in many of our instruments, most especially those well-adapted to
microtonal performance.

Finally, to say that practice without theory becomes lame (or
perhapes better, blind) DOES NOT HAVE TO IMPLY that any particular
musician must understand theory in order to practice or even to
astound. So why take this as if it were the only possible
interpretation? On the contrary, theory is by nature global and
practice, local. So it runs counter to the very nature of theoretical
discussion to interpret such a statement about theoretical
understanding as necessarily applying to individual practitioners.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Jon Szanto" <JSZANTO@A...> wrote:
>
> > So he asks about _essential_ reading about "microtonal music",
and
> > you choose to send him to Math and Music, with the above
breakdown
> of
> > subjects.
>
> There's an idea. I think I'll add an undergraduate text on linear
> algebra and abstract algebra to the list, and maybe the first part
of
> Jacobson's "Basic Algebra" to make sure you didn't miss anything
> basic. Then some elementary number theory, such as Hardy and Wright
> or Niven and Zuckerman, something on diophantine approximation, and
> something which at least defines valuations.
>
> I'm not sure if I'm kidding or not; I'll think about it. :)

Bob:
No! Do it! Some of us would love that even if others would prefer to
take another route.

--- In tuning@y..., genewardsmith@j... wrote:

> It don't think a diamond layout can be called a theoretical
> construct; it's not a product set, which *is* a theoretical
construct.

Why not?

--- In tuning@y..., "Jon Szanto" <JSZANTO@A...> wrote:
> Paul,
>
> Knowing your love for voicing the alternate viewpoint, in fostering
> dialogue, let me ask this:
>
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > The best single piece of reading you can do to get you up to
speed
> > on acoustics, psychoacoustics, musical tuning (including
> > experimental microtonality) and synthesis
>
> So he asks about _essential_ reading about "microtonal music", and
> you choose to send him to Math and Music, with the above breakdown
of
> subjects. I downloaded that .pdf the first time you posted it and
> spent an hour or so 'thumbing' through it.
>
> Are we so poor in this area, that we have no book to point to that
> uses *music* as the starting point, and brings in the other
subjects
> as necessary parts of the scheme?

I'm presuming that someone coming to this list is already familiar
with the basics of music. Dave Benson's article traces the
development of Western music, with plenty of listening requirements
cited. It then directs you to recordings of Harry Partch, Wendy
Carlos, and other microtonal greats, while discussing a bit about
their theories; hence I would say that it uses music as a primary
reference around which everything else is geared.

--- In tuning@y..., graham@m... wrote:

> You knew about CPS scales or the way Wilson draws them? Did you
get as
> far as D'Alessandro,

D'Alessandro has lower symmetry than any of the CPS scales it is
constructed from -- in fact D'Alessandro is simply the [3 5 7 9 11]
Euler genus.

Paul!
Euler failed to recognize 1 as an element causing him to fail to see the Hexany, Dekany and
Eikosany, which are the more interesting aspects of this set. The structural symmetry, hence the
musical meaning is different. It is quite possible to construct a Full CPS out of a set without 1
of course. D'Alessandro fits well on a 31-tone Bosanquet Keyboard. If one wanted the full
symmetrical set, you add a harmonic hexad on the square of the other 5 elements plus their
reciprocals pitches.

Wilson has hunted high and low for a predecessor of Combination product sets so if you or any
of these others can refer us to a mathematician that did this before, outside of themselves seeing
this obvious while in high school we would be truly interested.

Paul Erlich wrote:

> --- In tuning@y..., graham@m... wrote:
>
> > You knew about CPS scales or the way Wilson draws them? Did you
> get as
> > far as D'Alessandro,
>
> D'Alessandro has lower symmetry than any of the CPS scales it is
> constructed from -- in fact D'Alessandro is simply the [3 5 7 9 11]
> Euler genus.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Hey Paul,

[re-ordering your comments...]

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> Dave Benson's article

Are we talking about the same thing? What I downloaded wasn't an
article, it was a whole book!

> traces the
> development of Western music, with plenty of listening requirements
> cited. It then directs you to recordings of Harry Partch, Wendy
> Carlos, and other microtonal greats, while discussing a bit about
> their theories; hence I would say that it uses music as a primary
> reference around which everything else is geared.

Fairly big apologies if I missed that in the big .pdf file I was
scanning through. I must admit that my eyes glazed over a bit during
a lot of the math presentations, but the book leads the title
with "Math" so it certainly didn't bother me at all...

> I'm presuming that someone coming to this list is already familiar
> with the basics of music.

That's funny, because I see quite a bit of stuff on the list that
doesn't have anything to do with music. And I don't even remotely
mean that as an insult.

Cheers,
Jon

--- In tuning@y..., graham@m... wrote:

> You knew about CPS scales or the way Wilson draws them? Did you
get as
> far as D'Alessandro, and do you have an alternative that works with
> Canasta?

Well, you've got me, pal. I don't know how Wilson draws them, I know
nothing of D'Alessandro, and I don't see what any of it has to do
with Canasta. Of course any comma induces an equivalency on a
lattice, which includes the commas of miracle.

I knew about lattices before I read Schoenberg, if that means
> anything.

Did you think them up from something else, or get it somewhere else?
I got lattices from Schoenberg rather indirectly, passing through a
stage of the dual tiling of chords, which was related to Schoenberg's
tonal regions. It would be interesting to know how this business
evolved, and from where.

> Of course, if something's of theoretical interest you don't stop
with it.
> Now I'm thinking about the reordered diamond, it's the same
principle as
> my 9-limit lattice <http://x31eq.com/lattice.htm#9limit>
where
> 4:5:6:7:9 is set to increase in pitch from left to right.

I've looked at that, and don't get the point of it either. Maybe I'm
sunk. :)

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:

> Partch's ear took advantage of things within the diamond that most
here only find by number
> crunching. BTW since you have so little interest in the diamond
just what do you have to have
> musicians to play upon.

Computers. I'm sorry if I stepped on your corns, but people are
allowed to have opinions. People are also allowed to attempt to
refute those opinions, and it would make more sense for you to try
than to go on like this.

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

> I have no idea if you like or are interested in Partchs 'end
> product'.

I like Partch, but I think harmony plays less of a role in his music
than one might expect.

>You completely gloss
> over an entire body of work to focus on the small aspect of what
> could have been. One way of looking at the world, I suppose, but
> pretty limiting.

Sorry, but this is nonsense. The diamond was put forward as a
theoretical innovation by Partch of some importance; I did not bring
it up.

> He wasn't a theorist, he was a composer, and he went as far as he
> *needed* to - he found materials to base his composition on, and
used
> them.

I never claimed he was a theorist, which in fact seems to be why you
are mad at me. Does this make sense to you? It doesn't to me.

Genewardsmith!
Computers! I have no objection to computers but they are not a tuning system.
Just what is it that i am not trying.
weather Partch overlooked the implication of the diamond it seems might be more than an opinion.
Listen i don't use the diamond, but if i had been brought up in a culture that had it for its
tuning I would be a hard pressed to do what i do now.

genewardsmith@juno.com wrote:

> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
>
> > Partch's ear took advantage of things within the diamond that most
> here only find by number
> > crunching. BTW since you have so little interest in the diamond
> just what do you have to have
> > musicians to play upon.
>
> Computers. I'm sorry if I stepped on your corns, but people are

> allowed to have opinions. People are also allowed to attempt to
> refute those opinions, and it would make more sense for you to try
> than to go on like this.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., genewardsmith@j... wrote:
>
> > It don't think a diamond layout can be called a theoretical
> > construct; it's not a product set, which *is* a theoretical
> construct.
>
> Why not?

It's not as abstract; but we're splitting hairs.

> Well, you've got me, pal. I don't know how Wilson draws them, I know
> nothing of D'Alessandro, and I don't see what any of it has to do
> with Canasta. Of course any comma induces an equivalency on a
> lattice, which includes the commas of miracle.

D'Alessandro is the 3.5.7.9.11 Euler genus with some notes added to fill a
meantone keyboard designed for 31 notes plus some duplicates. It means the
keyboard functions melodically like meantone, but it's all JI. There are two
problems with converting it to Canasta. Firstly, pairs like 3 and 11.5.7
can't both be represented because 385:384 is tempered out. Secondly, it
overspills the 41 note MOS instead of the 31 note one.

The genus was chosen because it contains all the CPSes. There may be a
similar Miracle-unique scale which also has a lot of CPS subsets.

You need so many Miracle notes because factors of 27 come up as 3.9. In
meantone or schismic that's good, because it encourages modulation by fifths
and fifths are cheap. In Miracle, they're 6 Secors, so it pays to be more
frugal with them. As 9 is already 3.3 you can probably get by without 3.9 as
well, but I don't have a modifiied CPS that takes account of this.

If these problems could be worked around, it would lead to a just tuning of a
Miracle keyboard.

Me:
> I knew about lattices before I read Schoenberg, if that means
> > anything.

Gene:
> Did you think them up from something else, or get it somewhere else?
> I got lattices from Schoenberg rather indirectly, passing through a
> stage of the dual tiling of chords, which was related to Schoenberg's
> tonal regions. It would be interesting to know how this business
> evolved, and from where.

I was working with elementary music theory. Triads and keys. I drew a
triangular and square lattice to make the relationships easier. All part of
fumbling towards the realisation that a 5-limit scale has to be founded on
two basic intervals, but there's no uniquely privileged pair that does the
job. At that time, I didn't see how to diagram the 7-limit in two
dimensions, so switched to numbers for everything.

Me:
> > Now I'm thinking about the reordered diamond, it's the same
> principle as
> > my 9-limit lattice <http://x31eq.com/lattice.htm#9limit>
> where
> > 4:5:6:7:9 is set to increase in pitch from left to right.

Gene:
> I've looked at that, and don't get the point of it either. Maybe I'm
> sunk. :)

If you take a major third and stretch it a bit, you get 9:7. But 5:4 and 9:7
aren't particularly close on the usual 7-limit lattice. The same with 7:6
and 6:5. So the 9-limit lattice gives you four different triads where the
third gets higher as the middle note gets higher up the lattice. 9-limit
chords are no more complex than on the 7-limit lattice, but you get some of
the melodic advantages of a generalized keyboard.

Graham

Gene,

--- In tuning@y..., genewardsmith@j... wrote:
> I like Partch, but I think harmony plays less of a role in his
> music than one might expect.

Then it is your expectations, and not the work(s) in question, that
are askew. You see the Diamond, and you assume that every avenue
should have been explored; he looked at (and heard) the Diamond, and
he used it for musical expression.

> >You completely gloss
> > over an entire body of work to focus on the small aspect of what
> > could have been. One way of looking at the world, I suppose, but
> > pretty limiting.
>
> Sorry, but this is nonsense.

Eloquently put. Does all your dialogue run along these lines?

> The diamond was put forward as a theoretical innovation by Partch
> of some importance; I did not bring it up.

At the time, it was; it still has some staying power, as other
composers are still utilizing it's resources. But you have chosen to
place an importance on it that was not his, looking at the glass as
half-full ("not fully realized"); others find that same glass
brimming with opportunity.

Not to mention his reasoning behind writing "Genesis of a Music",
where the Tonality Diamond rears it's ugly head:

"It is addressed to those who are searching for more than
intellectual openings into the mysteries of music and intonation. I
have written it for those with a musically creative attitude: (1) for
composers; (2) for those who expect to compose; (3) for anyone, even
without a knowldege of ordinary music theory, who has this creative
attitude."

The book, and the theories, have flaws, biases, and areas that have
been superceded in the years since. But it also stands that it is
about a lot more than theory, which, unfortunately, is how many
approach it.

> I never claimed he was a theorist, which in fact seems to be why
> you are mad at me.

I am not mad. I save that for important moments, and avoid it when
possible.

> Does this make sense to you? It doesn't to me.

You look at the theory first, the work second, and find it lacking
(somehow, somewhere). You find his 'fault' in not fulfilling the
promise of the diamond, and I say you've got it bass-ackwards. *That*
doesn't make sense to me, but I see it a lot.

Neither does describing as "garbage" and "well-written ignorance" a
book you haven't even read. Sorry, I expect a little more...

Regards,
Jon

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Paul!
> Euler failed to recognize 1 as an element causing him to fail
to see the Hexany, Dekany and
> Eikosany, which are the more interesting aspects of this set.

I agree with you that they are the more interesting aspects of this
set, and that Euler failed to recognize them. But it's not because he
failed to recognize 1. Instead, Euler Geni and CPS scales are very
different in their symmetries, whether 1 is included or not.

>If one wanted the full
> symmetrical set, you add a harmonic hexad on the square of the
other 5 elements plus their
> reciprocals pitches.

I'd like to understand better what you mean here (by "square", for
example), and I'm sure you are correct, but if you're going to end up
accusing me of "intellectual imperialism", maybe you better keep it
to yourself.

>
> Wilson has hunted high and low for a predecessor of Combination
product sets so if you or any
> of these others can refer us to a mathematician that did this
before, outside of themselves seeing
> this obvious while in high school we would be truly interested.

All I know is that Gene came up with at least the octahedron
visualization of the hexany about 25 years ago, and we had to inform
him that he was not alone!

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

> > I'm presuming that someone coming to this list is already
familiar
> > with the basics of music.
>
> That's funny, because I see quite a bit of stuff on the list that
> doesn't have anything to do with music.

Whether that's true or not, I don't see what that has to do with my
presumption above.

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

> All I know is that Gene came up with at least the octahedron
> visualization of the hexany about 25 years ago, and we had to
inform
> him that he was not alone!

Wilson took a combinatorial approach, and I took a geometric one.
There is a wide area of overlap, but not an identity, and I think a
discussion and comparison of the two approaches might be interesting.
I was going to launch into some theory when you told me that I was
talking about hexanies. I thought I'd better go read up on hexanies
first, but having done that I think both points of view are valid and
could both benefit by being tied together.

Hi Paul,

> From: Paul Erlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, November 23, 2001 5:22 PM
> Subject: [tuning] Re: Essential reading about microtonal music
>

> ... Euler Geni and CPS scales are very
> different in their symmetries ...

The plural of "genus" is "genera".

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

Hi Gene,

> From: <genewardsmith@juno.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, November 23, 2001 12:55 PM
> Subject: [tuning] Re: Essential reading about microtonal music
>
>
> --- In tuning@y..., graham@m... wrote:
>
> > I knew about lattices before I read Schoenberg, if that means
> > anything.
>
> Did you think them up from something else, or get it somewhere else?
> I got lattices from Schoenberg rather indirectly, passing through a
> stage of the dual tiling of chords, which was related to Schoenberg's
> tonal regions. It would be interesting to know how this business
> evolved, and from where.

I'm not totally clear on what you're asking there, but if
it's concerning the history of tonal lattices, I can offer
this: the big pre-Tuning-List names are Euler, Riemann,
Tanaka, Fokker, and Wilson.

The 5-limit triangular lattice, under the name of Riemann's
"Tonnetz", was employed quite a bit in theoretical literature
(especially German) of the 1800s.

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

Paul,

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "Jon Szanto" <JSZANTO@A...> wrote:
> > That's funny, because I see quite a bit of stuff on the list that
> > doesn't have anything to do with music.
>
> Whether that's true or not, I don't see what that has to do with my
> presumption above.

You assumed someone would know about music. I seem to recall that
Pierre Lamouthe (sp?) claimed he was not involved in music in the
least. Other people have professed the love of numbers all by
themselves.

I suppose this is what I was referring to.

Jon

--- In tuning@y..., genewardsmith@j... wrote:

> It would be interesting to know how this business
> evolved, and from where.

I came up with lattices through the tetrahedral-octahedral lattice
independently on my own. I wasn't optimistic about being able to
visualize higher dimensions. When John Chalmers showed me Wilson's
lattices for the 9-, 11-, 13- . . . limits, I was impressed -- yes, a
little bit of symmetry had to be broken, but not much!

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., genewardsmith@j... wrote:
> >
> > > It don't think a diamond layout can be called a theoretical
> > > construct; it's not a product set, which *is* a theoretical
> > construct.
> >
> > Why not?
>
> It's not as abstract; but we're splitting hairs.

Well, isn't it the product set of the 11-limit hexad with its
inverse? Doesn't the diamond layout show this most clearly? And what
of your lattice -- if you don't include an axis for 9, won't you be
obscuring the diamond's symmetry?

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

>Other people have professed the love of numbers all by
> themselves.

I'm a number theorist. By thesis advisors were Ken Ribet, of Fermat
Last Theorem fame, and Hendrick Lenstra, known for LLL among other
things. So sue me again.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., genewardsmith@j... wrote:
> >
> > > It don't think a diamond layout can be called a theoretical
> > > construct; it's not a product set, which *is* a theoretical
> > construct.
> >
> > Why not?
>
> It's not as abstract; but we're splitting hairs.

Partch clearly presented the diamond as a generalization -- specific
examples include the 5-limit lattice, the 11-limit lattice, and the
13-limit lattice. Similarly, CPSs have specific examples. How is one
more abstract than the other?

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

> Neither does describing as "garbage" and "well-written ignorance" a
> book you haven't even read. Sorry, I expect a little more...

I qualifed it by saying *if* the review was on target in suggesting
that those who promoted systems other than 12-et were the Bad Guys,
then it "sounded" like garbage. But you are in danger of
contradicting yourself here--if not supporting 12-et is evil, what
are we to make of Partch, for whom even the likes of 53-et was not
good enough? You knew the man--what do you think he would have
thought of this attitude?

Paul!

Paul Erlich wrote:

> >If one wanted the full
> > symmetrical set, you add a harmonic hexad on the square of the
> other 5 elements plus their
> > reciprocals pitches.
>
> I'd like to understand better what you mean here (by "square", for
> example), and I'm sure you are correct, but if you're going to end up
> accusing me of "intellectual imperialism", maybe you better keep it
> to yourself.
>

in this case 3^2 5^2 7^2 9^2 11^2

>
> >
> > Wilson has hunted high and low for a predecessor of Combination
> product sets so if you or any
> > of these others can refer us to a mathematician that did this
> before, outside of themselves seeing
> > this obvious while in high school we would be truly interested.
>
> All I know is that Gene came up with at least the octahedron
> visualization of the hexany about 25 years ago, and we had to inform
> him that he was not alone!

it is possible to map other things to the octahedron besides the 2)4 hexany

>
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

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

> If you take a major third and stretch it a bit, you get 9:7. But
5:4 and 9:7
> aren't particularly close on the usual 7-limit lattice. The same
with 7:6
> and 6:5. So the 9-limit lattice gives you four different triads
where the
> third gets higher as the middle note gets higher up the lattice. 9-
limit
> chords are no more complex than on the 7-limit lattice, but you get
some of
> the melodic advantages of a generalized keyboard.
>
>
> Graham

Graham (and Gene),

Are you familiar with the fact that the Tenney lattice has a built-in
pitch axis? What about Canright's 2-d lattices which also have a
pitch axis built in? If we're interested in seeing pitch height on
our lattices, these types of approaches would seem preferable . . .

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > All I know is that Gene came up with at least the octahedron
> > visualization of the hexany about 25 years ago, and we had to
> inform
> > him that he was not alone!
>
> Wilson took a combinatorial approach, and I took a geometric one.

His approach was geometric as well, and also resulted in an
octahedron. I too thought I had come up with it first, as the
octahedron in the tetrahedral-octahedral lattice, but John Chalmers
informed me of Wilson's precedence. Something I'd be mildly
interested to know (and perhaps Kraig would too) is if anyone before
Wilson realized the correspondence between larger CPSs and higher-
dimensional symmetrical figures, analogous to the octahedron.

--- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> Hi Gene,
>
>
> > From: <genewardsmith@j...>
> > To: <tuning@y...>
> > Sent: Friday, November 23, 2001 12:55 PM
> > Subject: [tuning] Re: Essential reading about microtonal music
> >
> >
> > --- In tuning@y..., graham@m... wrote:
> >
> > > I knew about lattices before I read Schoenberg, if that means
> > > anything.
> >
> > Did you think them up from something else, or get it somewhere
else?
> > I got lattices from Schoenberg rather indirectly, passing through
a
> > stage of the dual tiling of chords, which was related to
Schoenberg's
> > tonal regions. It would be interesting to know how this business
> > evolved, and from where.
>
>
> I'm not totally clear on what you're asking there, but if
> it's concerning the history of tonal lattices, I can offer
> this: the big pre-Tuning-List names are Euler, Riemann,
> Tanaka, Fokker, and Wilson.
>
> The 5-limit triangular lattice, under the name of Riemann's
> "Tonnetz", was employed quite a bit in theoretical literature
> (especially German) of the 1800s.
>
Don't forget the "Duodenarium" in Helmholtz-Ellis; Barbour's
lattices, which did have the triangular arragement; and Donald Hall's
nice hexagonal tuning lattices (also the triangular arrangement but
allowing for the display of the error in each interval).

--- In tuning@y..., "Jon Szanto" <JSZANTO@A...> wrote:
> Paul,
>
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., "Jon Szanto" <JSZANTO@A...> wrote:
> > > That's funny, because I see quite a bit of stuff on the list
that
> > > doesn't have anything to do with music.
> >
> > Whether that's true or not, I don't see what that has to do with
my
> > presumption above.
>
> You assumed someone would know about music. I seem to recall that
> Pierre Lamouthe (sp?) claimed he was not involved in music in the
> least.

Lamothe . . . yes, this was very odd, as he had clearly read tomes
upon tomes on musics of various cultures and time periods.

> Other people have professed the love of numbers all by
> themselves.

Gene pled guilty to this -- yet he's been trying to understand music
for some 25 years now, and proved himself to be a good composer in
his own right.
>
> I suppose this is what I was referring to.
>
> Jon

Well, OK, so let's say someone came to this list not knowing much
about music. What do you find lacking in Dave Benson's article/book
for the needs of such an individual, and what would you suggest as a
means to fill that gap?

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Paul!
>
> Paul Erlich wrote:
>
> > >If one wanted the full
> > > symmetrical set, you add a harmonic hexad on the square of the
> > other 5 elements plus their
> > > reciprocals pitches.
> >
> > I'd like to understand better what you mean here (by "square", for
> > example), and I'm sure you are correct, but if you're going to
end up
> > accusing me of "intellectual imperialism", maybe you better keep
it
> > to yourself.
> >
>
> in this case 3^2 5^2 7^2 9^2 11^2

You mean this Euler genus? I wouldn't consider that to have the full
symmmetry of the Eikosany or Diamond -- it has lower symmetry. Or do
you mean that this set would _contain_ some highly-symmetrical set as
a subset?

> it is possible to map other things to the octahedron besides the 2)
> 4 hexany

Interesting . . . would you like to give some examples? (again, no
pressure -- I'm sure some things are better kept secret until
publication, though personally, I always spill the beans)

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> Partch clearly presented the diamond as a generalization --
> specific examples include the 5-limit lattice, the 11-limit
> lattice, and the 13-limit lattice.

He actually even diagrammed and plotted out a diamond to the 17-
limit, but it existed on paper only. The materials were given to Ben
Johnston in the late 40's or early 50's, I believe...

Cheers,
Jon

--- In tuning@y..., genewardsmith@j... wrote:
> I'm a number theorist. [...] So sue me again.

Frivolous litigation doesn't interest me, but it's always nice to
know the built-in biases. I have nothing against love of numbers, per
se.

Best,
Jon

--- In tuning@y..., genewardsmith@j... wrote:
> I qualifed it by saying *if* the review was on target in suggesting
> that those who promoted systems other than 12-et were the Bad Guys,
> then it "sounded" like garbage.

Oh, that your linquistics were as crystaline as your calculations.
Your garbage statement seemed very much without qualification, and
the second post buried it in syntax. But I'll take you at your word
that you'd never judge a book by it's review...

> But you are in danger of
> contradicting yourself here--if not supporting 12-et is evil, what
> are we to make of Partch, for whom even the likes of 53-et was not
> good enough? You knew the man--what do you think he would have
> thought of this attitude?

What attitude? I have *no* opinion on the book at this point; I'll
hazard a guess at Harry's thoughts (get Dion Warwick on the line) if
you'll phrase the question clearly.

Cheers,
Jon

Paul,

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> Lamothe . . . yes, this was very odd, as he had clearly read tomes
> upon tomes on musics of various cultures and time periods.

I'll hazard there have been a lot that passed through, looked for
musical guidance, and spun around on their heels. I don't necessarily
think that's bad, in that sometimes the extra effort is rewarded. But
we're back to the old music<>math debate, which is tired. For both
sides...

> Gene pled guilty to this -- yet he's been trying to understand
> music for some 25 years now, and proved himself to be a good
> composer in his own right.

Remember: we are allowed to pull apart all manner of diagrams,
lattices, spreadsheets, theories, historical treatises -- but we
can't talk about the strengths and weaknesses of composers and
compositions presented here. It Just Doesn't Work. Way too much
crying, which is why other lists have formed.

> Well, OK, so let's say someone came to this list not knowing much
> about music. What do you find lacking in Dave Benson's article/book
> for the needs of such an individual, and what would you suggest as
> a means to fill that gap?

Maybe you missed something in one of my posts to you: I tried to say
that I'll give the book another glance/read, but (1) I *can't*
recommend a better suggestion right now, and (2) I think there is a
Critical Need for a book on the subject of alternate tunings and
microtonal music that comes from the music first, and works in the
tunings bit by bit.

As Dan so perfectly explained, and politely too, those who are very
well-inclined with the math end of our world very often do *not* see
how much of a barrier it can be to many musicians, and how intensely
valuable it would be to find a text that didn't simply present the
material, but presented it *well* - to the 'layman'.

I'd be the first name on the pre-order list.

Bestest,
Jon

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

> As Dan so perfectly explained, and politely too, those who are very
> well-inclined with the math end of our world very often do *not*
see
> how much of a barrier it can be to many musicians, and how
intensely
> valuable it would be to find a text that didn't simply present the
> material, but presented it *well* - to the 'layman'.

This is a reasonable request, but it can only be taken so far.
Creation and evaluation of tuning systems is partly a matter of art,
but it really is more a sort of engineering problem. Like so many
engineering problems, math comes into the picture. The problem is
that artists usually don't think in this way, and probably some
people winced when they read the word "engineering". Sometimes they
do, and it is not an accident that perspective was invented by one
artist-engineer, Bruneschelli, and developed by another, Leonardo. I
think a Leonardo point of view would help anyone trying to explore
this mostly uncharted territory. Fainting in coils is not painting in
oils.

Paul!
This will be easier to illustrate once Erv's letter to John Chalmers is up on this subject. It
50 pages which i just haven't had time to PDF this up. from it you can see a 12 fold Symmetry.

Paul Erlich wrote:

> > in this case 3^2 5^2 7^2 9^2 11^2
>
> You mean this Euler genus? I wouldn't consider that to have the full
> symmmetry of the Eikosany or Diamond -- it has lower symmetry. Or do
> you mean that this set would _contain_ some highly-symmetrical set as
> a subset?

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Was it Fuller first who showed how tetrahedrons can be used to make octahedron?

Paul Erlich wrote:

> --- In tuning@y..., genewardsmith@j... wrote:
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> >
> > > All I know is that Gene came up with at least the octahedron
> > > visualization of the hexany about 25 years ago, and we had to
> > inform
> > > him that he was not alone!
> >
> > Wilson took a combinatorial approach, and I took a geometric one.
>
> His approach was geometric as well, and also resulted in an
> octahedron. I too thought I had come up with it first, as the
> octahedron in the tetrahedral-octahedral lattice, but John Chalmers
> informed me of Wilson's precedence. Something I'd be mildly
> interested to know (and perhaps Kraig would too) is if anyone before
> Wilson realized the correspondence between larger CPSs and higher-
> dimensional symmetrical figures, analogous to the octahedron.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

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

> As Dan so perfectly explained, and politely too, those who are very
> well-inclined with the math end of our world very often do *not*
see
> how much of a barrier it can be to many musicians,

Too true -- I've been guilty of this in the past, and Gene currently.

> and how intensely
> valuable it would be to find a text that didn't simply present the
> material, but presented it *well* - to the 'layman'.

You really think Dave Benson's course falls short in this respect? It
looks to me like the kind of course you would take if you hated math,
were really bad at it, but needed one course with math content to
fulfill your college requirements. Plus it manages to give a complete
novice to the subject enough information to understand virtually
everything on this list, and much more. Just skip the sections that
don't interest you or look too hard -- each section is self-contained.

Cheers,
Paul

--- In tuning@y..., genewardsmith@j... wrote:

> This is a reasonable request, but it can only be taken so far.

Well, Gene, you have to admit that Dan Stearns had a point in his
last post!

> Creation and evaluation of tuning systems is partly a matter of
art,
> but it really is more a sort of engineering problem. Like so many
> engineering problems, math comes into the picture.

I said exactly the same thing to Joseph Pehrson a few months ago, in
response to some talk about "science" and tuning. It's not science, I
replied, but it's very often engineering, and hence can get quite
mathematical.

> The problem is
> that artists usually don't think in this way,

That's right -- they pick up the 12-tET guitar and keyboard and
proceed to make music on it. They don't appreciate that the
mathematicians/engineers who came up with the tuning system they're
using had to solve "music's greatest riddle"!

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Paul!
> This will be easier to illustrate once Erv's letter to John
Chalmers is up on this subject. It
> 50 pages which i just haven't had time to PDF this up. from it you
can see a 12 fold Symmetry.

I look forward to it, but note that we're talking about far more than
just 12-fold symmetry. For example, in the 5-limit, the [3 5] Euler
genus has four axes of reflectional symmetry and four angles of
rotational symmetry, while the 5-limit diamond has six axes of
reflectional symmetry and six angles of rotational symmetry. In the
11-limit these numbers are in the hundreds.

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Was it Fuller first who showed how tetrahedrons can be used to make
octahedron?

You mean in the tetrahedral-octahedral lattice? He popularized it,
but it was well known, for example to crystallographers, much
earlier. I'd guess that the ancients were well aware of it -- I
wouldn't be surprised if it turned up in one of Euclid's proofs. Gene?

Paul,

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> Too true -- I've been guilty of this in the past, and Gene
> currently.

It's not a matter of guilt or innocence <g>, but it would sure make
for better relations around here if people could wise up about
effectively communicating (or at least attempting) basics of their
*own* chosen field.

> You really think Dave Benson's course falls short in this respect?
> It looks to me like the kind of course you would take if you hated
> math, were really bad at it, but needed one course with math
> content to fulfill your college requirements.

The second and third sentences from the *Introduction*:

"The prerequisites for this course consist of differential and
integral calculus, and either calculus of several variables or
ordinary differential equations, as well as an elementary knowledge
of music notation. Parts of the notes require a little more
mathematical background."

Guilty again, Paul. Look, I'm not a mathematical illiterate,
especially since my second degree (in software engineering) included
a fair amount of catching up on math subjects I had earnestly avoided
(including 'slaying the dragon', which was how we referred to the
Calculus classes...). And while people might be willing to bash me
for bringing up this Hatfield vs. the McCoys subject again, don't say
I don't try: I still have the .pdfs of the book, but I went back and
downloaded not only the Postscript files but the Ghostscript
environment and previewer as well, all to try and *read* the thing
better.

When I have some time.

But if this dog still has mainly mathematical fleas on it, I'm coming
back here and demand that you quit your job and write a proper book
on the subject, coming *from* the musical angle that you claim as
your main residence.

Going to bed,
Jon

Paul wrote:

> Are you familiar with the fact that the Tenney lattice has a built-in
> pitch axis? What about Canright's 2-d lattices which also have a
> pitch axis built in? If we're interested in seeing pitch height on
> our lattices, these types of approaches would seem preferable . . .

I've always thought of Tenney as a 3-dimensional square lattice person. But,
sure enough, the lattice in CMJ11.1 is similar to my 9-limit one. David
Canright's lattices do their own thing, but aren't optimized to show
particular chords. The disadvantage of those approaches is that they can't
be shown in ASCII. Another difference with mine is that they only order
pitch height horizontally, whereas I look at the vertical as well.

Graham

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

> The second and third sentences from the *Introduction*:
>
> "The prerequisites for this course consist of differential and
> integral calculus, and either calculus of several variables or
> ordinary differential equations, as well as an elementary knowledge
> of music notation. Parts of the notes require a little more
> mathematical background."

I'm surprised, but I can assure you that the sections related to
tuning require no such mathematical background.

--- In tuning@y..., Graham Breed <graham@m...> wrote:
> Another difference with mine is that they only order
> pitch height horizontally, whereas I look at the vertical as well.

I don't get it. Pitch is a 1-dimensional quantity, so mapping it to
one axis is perfect. What do you mean, then?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "Jon Szanto" <JSZANTO@A...> wrote:
>
> > The second and third sentences from the *Introduction*:
> >
> > "The prerequisites for this course consist of differential and
> > integral calculus, and either calculus of several variables or
> > ordinary differential equations, as well as an elementary
knowledge
> > of music notation. Parts of the notes require a little more
> > mathematical background."

> I'm surprised, but I can assure you that the sections related to
> tuning require no such mathematical background.

It's standard math department boiler plate which basically means the
calculus sequence is considered a prerequisite for anything, whether
it makes sense or not.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> I'm surprised, but I can assure you that the sections related to
> tuning require no such mathematical background.

Surprised? That means you recommended it without being familiar
enough? <g> Hey, all chiding aside, I *did* end up staying awake
until about 3:00 am, and I would recommend people - no, musicians
wanting to get a grip on tuning when being less than stellar
mathematicians - can very much go to chapters 4, 5, and 6 (I think
those were the ones). I'm going to hunt up a Postscript printer to
print them out (there is an especially funny cartoon to post to this
list, BTW...).

But honestly, take a look at Chaps 1, 2, or 3. Take them around to a
bevy of practicing musicians, and watch what happens. THAT is what I
meant by needing a guide that starts out with music as the FIRST
principle understanding, and goes the other direction. The world
waits...

Cheers,
Jon

> From: Jon Szanto <JSZANTO@ADNC.COM>
> To: <tuning@yahoogroups.com>
> Sent: Friday, November 23, 2001 10:13 PM
> Subject: [tuning] Re: Essential reading about microtonal music
>
>
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > Partch clearly presented the diamond as a generalization --
> > specific examples include the 5-limit lattice, the 11-limit
> > lattice, and the 13-limit lattice.
>
> He actually even diagrammed and plotted out a diamond to the 17-
> limit, but it existed on paper only. The materials were given to Ben
> Johnston in the late 40's or early 50's, I believe...

Yup... Ben showed it to me when I met him.
(because he knew that I'd really be able to appreciate it)

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

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

/tuning/topicId_29874.html#30525

> Thread drift now at warp speed...
>
> --- In tuning@y..., genewardsmith@j... wrote:
> > That is not to say that reading
> > Partch is not a reasonable route to the same place, but I think
it
> > would be a terrible idea to go only as far as the diamond in your
> > understanding and then stop.
>
> Yep, that lame diamond concept, limiting as it is, surely must have
> been the reason that Partch was only able to create 50 years worth
of
> unique works, wide-ranging in style and manner, including an entire
> orchestra of instruments well-sprung from that paltry source. Some
> people just know when to stop speculating and calculating and get
on
> with it.
>
> Cheers,
> Jon

I wholeheartedly agree with Jon here and, in fact, it's *exactly* how
I feel about the new "Blackjack conversion!..."

JP

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

/tuning/topicId_29874.html#30524

> Paul,
>
> Knowing your love for voicing the alternate viewpoint, in fostering
> dialogue, let me ask this:
>
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > The best single piece of reading you can do to get you up to
speed on acoustics, psychoacoustics, musical tuning (including
> > experimental microtonality) and synthesis
>
> So he asks about _essential_ reading about "microtonal music", and
> you choose to send him to Math and Music, with the above breakdown
of subjects. I downloaded that .pdf the first time you posted it and
> spent an hour or so 'thumbing' through it.
>
> Are we so poor in this area, that we have no book to point to that
> uses *music* as the starting point, and brings in the other
subjects as necessary parts of the scheme? Is microtonal music going
to be always doomed to start it's life with a calculator, an
oscilliscope, and an anechoic chamber?
>

Hello Jon!

I believe, if I remember correctly, that there were a *couple* of
different people who requested basic information on microtonal
music. I believe one of them was particularly interested in the
*acoustics* of it all, and that was the person Paul was addressing.

I *thought* I remember this, but don't have time or interest in
searching up these posts. Anybody else have the same hallucination?

JP

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

/tuning/topicId_29874.html#30525

> Thread drift now at warp speed...
>
> --- In tuning@y..., genewardsmith@j... wrote:
> > That is not to say that reading
> > Partch is not a reasonable route to the same place, but I think
it
> > would be a terrible idea to go only as far as the diamond in your
> > understanding and then stop.
>
> Yep, that lame diamond concept, limiting as it is, surely must have
> been the reason that Partch was only able to create 50 years worth
of unique works, wide-ranging in style and manner, including an
entire orchestra of instruments well-sprung from that paltry source.
Some people just know when to stop speculating and calculating and
get on with it.
>
> Cheers,
> Jon

This is a very, very interesting topic, and I'm not much of an
authoritative source on it... :)

However... it's really interesting, since we have Gene who is
unimpressed with the intellectual rigor of Partch's theorizing and
Paul Erlich who was so "bowled over" by Partch's book that it got him
started in alternate tuning. Paul's not really all *that* stupid, is
he?? :)

My point is that (hopefully I'll not be too simplistic) art has a way
of communicating that is *not necessarily* the path of the greatest
intellectual rigor.

I suppose it differs from science and mathematics in this respect.
Frequently pieces of music that are created strictly by rules of
science and math can be boring or repetitive. (Please don't ask me to
name the names of the composers... :) )

However, other less "rigorous" methods, such as those of Partch or,
maybe, Varese, create products that engage and inspire deeply.

So, in short, _Genesis of a Music_ is an *art* book, not a rigorous
science or math text.

I guess that's pretty obvious... but it seems to be slightly
forgotten momentarily in this debate... or so it seems to me..

Joseph Pehrson

Paul Erlich wrote:

<< Pitch is a 1-dimensional quantity, so mapping it to one axis is perfect. >>

Pitch is only a sensation parametred by log (frequency).

The few I read about perception phenomenology (Merleau-Ponty) convinced me that sense investment is possible only by mean of differentiation ; and the unconscious part tends to be organized in systems.

What keeps trace of sense with pitches is the field of intervals : differences of pitch height. This field is not, perceptively, only linear. There exist a planar topological invariance in the auditive field : a complete width order combined with an harmonic preorder which are correlable, strictly by perception, in the begining portion of the Stern-Brocot tree. The Tenny's distance is simply a complete order idealization of that, but useful in context of lattice having few low primes.

The harmonic dimension is not an algebraic dimension. Differences of sonance are not composable. The formal algebraic structures of musical modes concern only width differences, but there exist an harmonic order in the space of well-formed tonal structures. I would say that time tends to respect the simplest among them.

There is a problem with the harmonic entropy approach until date. Rather than to refine a categorical perception model, it tends to reduce all at a sensitive perception model. Without showing how its particular differences are integrated to a contextualized perception, I think it brings nothing to the essential questions.

Pierre

--- In tuning@y..., "Pierre Lamothe" <plamothe@a...> wrote:
> Paul Erlich wrote:
>
> << Pitch is a 1-dimensional quantity, so mapping it to one axis
is perfect. >>
>
> Pitch is only a sensation parametred by log (frequency).

So it is. So what? Pierre, you're jumping in here with all this, some
of which I agree with, but do you even understand the context of the
discussion in which this statement came up? And to what degree that
context actually _supports_, rather than contradicts, many of the
claims you're making?

Again, I do not appreciate having statements of mine taken out of
context like this. If you'd like to participate in our discussion,
Pierre, I would like nothing better. But what you are doing here is
very intellectually dishonest -- you go away for a long time, come
back and pick up on a tag line you'd like to run with, and use it as
a launching point for a criticism that seems (superficially) to paint
your intellectual superiority.

I have a suggestion for you -- cut it out, and help us understand
your axiom system over at tuning-math. Gene (if I may speak for him)
and I are all ears. Gene has been creating all kinds of interesting
structures based on the way I think about tuning -- no doubt he can
develop much of interest from your way of thinking about things too.
You and I are blessed to have such a fine mathematician involved with
interest in our speculations!

Paul Erlich wrote:

<< I do not appreciate having statements of mine taken out of context like this. >>

I apologize for that. The intention was not to say you make there a mistake. I wanted only to force an occasion to talk about my conceptions.

In many posts you affirm we have a great distance in our philosophy, leaving to think that your's is well founded in your musical competence while I would manipulate only unsubstantial symbolism. I would like to say that my thoughts are not enclosed in math objects and English words.

I cut it out, but I don't return now in tuning-math discussing only axioms. I'll take time to write, forcely in French, about my founding principles.

For Gene, I suggest he takes first a look on the math message Sur le théorème des accords.

http://www.ircam.fr/listes/archives/mamuphi/msg00248.html

Pierre

Paul Erlich wrote:

> I don't get it. Pitch is a 1-dimensional quantity, so mapping it to
> one axis is perfect. What do you mean, then?

You have pitch ordered in two dimensions on a guitar fretboard, so why not
a lattice? In fact, as you have a 22-equal guitar you can get close to
that lattice by tuning the open strings F-A-C-E-G-B with 5-limit thirds.

Graham

I wrote,

> --- In tuning@y..., jpehrson@r... wrote:
> > Is there a chart anyplace that would show more of this multiple
> > relationship between just intervals and Blackjack intervals? I
> think
> > that would be *very* interesting!
>
> Well, maybe . . . For example, the 0/72 interval class represents
the
> ratios 1:1, 224:225, 385:384, 441:440, 540:539, 1029:1024,
1375:1372,
> 2401:2400, 3025:3024 . . .

Joseph! I left out 243:242 here! How could I!

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

/tuning/topicId_29874.html#30837

> I wrote,
>
> > --- In tuning@y..., jpehrson@r... wrote:
> > > Is there a chart anyplace that would show more of this multiple
> > > relationship between just intervals and Blackjack intervals? I
> > think
> > > that would be *very* interesting!
> >
> > Well, maybe . . . For example, the 0/72 interval class represents
> the ratios 1:1, 224:225, 385:384, 441:440, 540:539, 1029:1024,
> 1375:1372, 2401:2400, 3025:3024 . . .
>
> Joseph! I left out 243:242 here! How could I!

Thanks, Paul! Obviously nobody else noticed it... or at least they
didn't comment!

JP

--- In tuning@y..., jpehrson@r... wrote:

> > Joseph! I left out 243:242 here! How could I!
>
> Thanks, Paul! Obviously nobody else noticed it... or at least they
> didn't comment!
>
> JP

In terms of the unison vectors we've discussed most frequently, it's

243/242 = (2401/2400) * (225/224) * (225/224) * (384/385) * (384/385)

This is probably why no one found or mentioned it before!

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> In terms of the unison vectors we've discussed most frequently, it's
>
> 243/242 = (2401/2400) * (225/224) * (225/224) * (384/385) *
(384/385)
>
> This is probably why no one found or mentioned it before!

What do you mean? See
/tuning/topicId_26488.html#26511
and I expect Graham Breed mentioned it in relation to Blackjack long
before that, since it is the neutral third comma, the difference
between a 2:3 perfect fifth and a stack of two 9:11 neutral thirds.

In-Reply-To: <9u6i5p+ufbq@eGroups.com>
Paul E:
> > In terms of the unison vectors we've discussed most frequently, it's
> >
> > 243/242 = (2401/2400) * (225/224) * (225/224) * (384/385) *
> (384/385)
> >
> > This is probably why no one found or mentioned it before!

Dave K:
> What do you mean? See
> /tuning/topicId_26488.html#26511
> and I expect Graham Breed mentioned it in relation to Blackjack long
> before that, since it is the neutral third comma, the difference
> between a 2:3 perfect fifth and a stack of two 9:11 neutral thirds.

What? Yes. Here: </tuning/topicId_21957.html#21985>.
225:224 is the interval between 16:15 and 15:14, and 385:384 is what stops
a 6:5 minor third and an 8:7 supermajor second making an 11:8 sub fourth.
Approximate them all away, and you get Miracle temperament.

2401:2400 is only important if you want a 7-prime limit system. It means
two 5:4 major thirds and a 3:2 perfect fifth approximate the same as a
string of 7:4 subminor sevenths.

For some other notable equivalences, an 8:7 supermajor second followed by
a 15:14 semitone is sharp of an 11:9 neutral third by 540:539. If you
used a 16:15 semitone instead, you'd need to temper out 385:384 again.
The 441:440 unison vector makes an 8:7 supermajor second plus a 10:9 major
second the same as 14:11 supermajor third.

The best way of showing all these relationships is a lattice or
generalised keyboard, not a list of numbers.

Graham

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_29874.html#30837
>
> > I wrote,
> >
> > > --- In tuning@y..., jpehrson@r... wrote:
> > > > Is there a chart anyplace that would show more of this
multiple
> > > > relationship between just intervals and Blackjack intervals?
I
> > > think
> > > > that would be *very* interesting!
> > >
> > > Well, maybe . . . For example, the 0/72 interval class
represents
> > the ratios 1:1, 224:225, 385:384, 441:440, 540:539, 1029:1024,
> > 1375:1372, 2401:2400, 3025:3024 . . .
> >
> > Joseph! I left out 243:242 here! How could I!
>
> Thanks, Paul! Obviously nobody else noticed it... or at least they
> didn't comment!
>
> JP

Well, they commented _preemptively_. And Graham is right, these
things are best understood on the lattice, rather than numerically.