Yahoo Tuning Groups Ultimate Backup tuning RE: Euler, Erv Wilson ..oops!!

Looks like it's time for another compendium.

Dr Richard Sanford
Fox Plaza
San Francisco
++++++++++++++++++++

What's Euler's cube?

Eulers work and Erv' s are almost a match of which he is the first to
point out, but they are not the same. .

What was Erv's work on lattices?

Original Message:
-----------------
From: tuning@yahoogroups.com
Date: 8 Mar 2005 02:28:12 -0000
To: tuning@yahoogroups.com
Subject: [tuning] Digest Number 3432

There are 25 messages in this issue.

Topics in this digest:

1. Re: new member question from a theory class
From: Kraig Grady <kraiggrady@anaphoria.com>
2. Re: Prime factorization and maqams
From: "alternativetuning" <alternativetuning@yahoo.com>
3. More lattice stuff, corrected
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
4. 53 numerology
From: novosonic productions <novosonic@yahoo.com>
5. Re: Prime factorization and maqams
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
6. monzo notation (was: Prime factorization and maqams)
From: "monz" <monz@tonalsoft.com>
7. Re: Count Chocula?
From: Pete McRae <ambassadorbob@yahoo.com>
8. Re: new member question from a theory class
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
9. Re: Prime factorization and maqams
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
10. Re: Diatonic Maqams
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
11. Re: Prime factorization and maqams
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
12. Re: new member question from a theory class
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
13. Re: Count Chocula?
From: David Beardsley <db@biink.com>
14. Re: 612-ET notation
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
15. More lattice stuff
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
16. Re: Count Chocula?
From: Pete McRae <ambassadorbob@yahoo.com>
17. Re: Count Chocula?
From: David Beardsley <db@biink.com>
18. Re: Count Chocula?
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
19. Re: Prime factorization and maqams
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
20. Re: Count Chocula?
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
21. Re: Prime factorization and maqams
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
22. RE: Digest Number 3431
From: "Yahya Abdal-Aziz" <yahya@melbpc.org.au>
23. Re: Re: Count Chocula?
From: David Beardsley <db@biink.com>
24. Re: Digest Number 3431
From: Dave Seidel <dave@superluminal.com>
25. Re: Re: 612-ET notation
From: "Daniel A. Wier" <dawiertx@sbcglobal.net>

________________________________________________________________________
________________________________________________________________________

Message: 1
Date: Mon, 07 Mar 2005 06:43:43 -0800
From: Kraig Grady <kraiggrady@anaphoria.com>
Subject: Re: new member question from a theory class

The Hexany has nothing to do with cubes, except possibly Eulers. Eulers
work and Erv' s are almost a match of which he is the first to point out,
but they are not the same. .

The stellate hexany is the union of two crossets. In two dimension it is
quite easy to by pass the hexany, as well as to miss it significance

What--that someone would independently discover something Erv found?
Erv found lots of things I didn't find, but the converse is true as
well. It's hardly surprising that there was overlap. For the record,
the Eikosany isn't something I independently discovered; I *did* find
the hexany and stellated hexany, and even wrote hexany music back
when. The geometric point of view on the hexany is a natural one, I
think.

The chord cubes, crystal balls, dwarf scales and etc. I've talked
about may not have attracted much attention, but I think they might be
of interest to the same people who find the eikosany interesting. The
stellated hexany, in fact, is the first of the chord cubes unless you
count a single tetrad, and the next chord cube of 27 chords I've
written in.

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

________________________________________________________________________
________________________________________________________________________

Message: 2
Date: Mon, 07 Mar 2005 17:15:16 -0000
From: "alternativetuning" <alternativetuning@yahoo.com>
Subject: Re: Prime factorization and maqams

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> we write the monzo of 81:80 as: [-4 4, -1>
>
> in a monzo, positive exponents denote factors of the
> numerator, and negative exponents denote factors of
> the denominator.
>

This is essential the same as in Dr. John H. Chalmers Jr.'s table in
Xenharmonikon Nr. 1. What makes it a monzo and not a chalmers?

Gabor

________________________________________________________________________
________________________________________________________________________

Message: 3
Date: Mon, 07 Mar 2005 21:07:14 -0000
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
Subject: More lattice stuff, corrected

Yahoo hasn't put it up yet, so I can't correct with a follow-up. How
it should have read is:

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

> The Hexany has nothing to do with cubes, except possibly Eulers.

Here's yet another way to work cubic stuff into this. We can think of
7-limit intervals as represented by a cubic lattice of monzos Z4,
consisting of quadruples of integers |w x y z> with the ordinary
Euclidean metric. Suppose we decide to represent the lattice of octave
equivalence classes by means of a representative interval, with the
property that w+x+y+z=0. We can reduce an interval to its octave-class
representative by

red(q) = 2^(-ordp(q,3)-ordp(q,5)-ordp(q,7)) * 3^ordp(q,3) 5^ordp(q,5)
7^ordp(q,7)

where ordp is the p-adic valuation, meaning the monzo coordinate value
corresponding to the prime p, so that

q = 2^ordp(2,q) 3^ordp(3,q) 5^ordp(5,q) 7^ordp(7,q)

If |w x y z> is a monzo, then red(|w x y z>) = |-x-y-z x y z>.

We now find the symmetrical lattice of octave classes, with its
octahedra and tetrahedra and so forth, is just the sublattice of
reduced representatives, under the Eulicidean metric. For example the
cps {3,5,7,15,21,35} reduces to {3/2,5/2,7/2,15/4,21/4,35/4}, or in
monzo terms {|-1 1 0 0>, |-1 0 1 0>, |-1 0 0 1>, |-2 1 1 0>,
|-2 1 0 1>, |-2 0 1 1>}. It is easy to verify that these are the
verticies of an octahedron in four-dimensional space, so here you have
the hexany sitting inside of a cubic (4D) lattice.

________________________________________________________________________
________________________________________________________________________

Message: 4
Date: Mon, 7 Mar 2005 13:34:34 -0800 (PST)
From: novosonic productions <novosonic@yahoo.com>
Subject: 53 numerology

i thought i would post this, instead of trying to be
counterproductive and argue nuances.

but, i'm not sure if this plain peculiar...

BBC NEWS | Europe | Number 53 brings relief to Italy
Number 53 brings relief to Italy
The elusive number 53, blamed for several deaths and bankruptcies, has
finally
popped up in the Venice lottery after a two-year wait.
Italians had bet more than 3.5bn euros (£2.4bn), hoping that 53 would turn
up,
in what became a national obsession.
Last month a woman drowned herself in the sea off Tuscany after she bet the
family savings on 53, Reuters reports.
And police said a man living near Florence shot his wife and son and then
himself because of his number 53 debts.
The Italian national lotto invites bets of any amount on numbers from 1 to
90
in
bi-weekly draws.
The draws take place in 10 cities across the country. For each draw, 50
numbers
are picked, five in each of 10 cities.
A consumer group, Codacons, recently urged the government to ban the number
53
from the draw, to halt the country's "collective psychosis".
After 53 finally appeared on Wednesday night, it said it was delighted that
Italy's "bewitchment" had been broken.
Italy's Ansa news agency said the wins from Wednesday's draw would cost the
Italian state up to 600 million euros (£413m; $768m).
Story from BBC NEWS:
http://news.bbc.co.uk/go/pr/fr/-/2/hi/europe/4256595.stm

Published: 2005/02/11 10:26:13 GMT

***** get free microtonal mp3s here *****
http://home.comcast.net/~gregmcleod/SOUND_FILES.htm

microtonal music of buzz kimball -international lo bandwidth site
http://home.comcast.net/~gregmcleod/novosonic.html

http://www.nonoctave.com/heroes/buzz
http://psychevanhetfolk.homestead.com/expmu2.html

__________________________________________________
Do You Yahoo!?
Tired of spam? Yahoo! Mail has the best spam protection around
http://mail.yahoo.com

________________________________________________________________________
________________________________________________________________________

Message: 5
Date: Mon, 07 Mar 2005 21:31:32 -0000
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
Subject: Re: Prime factorization and maqams

--- In tuning@yahoogroups.com, "alternativetuning"
<alternativetuning@y...> wrote:

> This is essential the same as in Dr. John H. Chalmers Jr.'s table in
> Xenharmonikon Nr. 1. What makes it a monzo and not a chalmers?

It's my fault in the main. I wanted a name for my own private purposes
in my Maple programs, and I started using it in public. The reason for
the name is that while lots of people used this sort of notation, Joe
was the one who was enthusiastic about it. It gives us a name specific
to this particular use, and assoicated to the |...> notation.

________________________________________________________________________
________________________________________________________________________

Message: 6
Date: Mon, 07 Mar 2005 22:43:26 -0000
From: "monz" <monz@tonalsoft.com>
Subject: monzo notation (was: Prime factorization and maqams)

hi Gabor (and Pete, Gene, and Carl),

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

> --- In tuning@yahoogroups.com, "alternativetuning"
> <alternativetuning@y...> wrote:
>
> > This is essential the same as in Dr. John H. Chalmers Jr.'s
> > table in Xenharmonikon Nr. 1. What makes it a monzo and
> > not a chalmers?
>
> It's my fault in the main. I wanted a name for my own
> private purposes in my Maple programs, and I started using
> it in public. The reason for the name is that while lots
> of people used this sort of notation, Joe was the one who
> was enthusiastic about it. It gives us a name specific to
> this particular use, and assoicated to the |...> notation.

i advocated this notation instead of ratios, in the
first draft of my book which appeared in 1995, and in
my paper _JustMusic Prime-factor Notation_ in 1997.

i have since found out that Fokker used a similar concept
in his last papers (late 1960's) ... so AFAIK he was
the first one to use it. but also AFAIK neither Fokker
nor Chalmers ever expressly proposed to use it as a
musical notation.

-monz

________________________________________________________________________
________________________________________________________________________

Message: 7
Date: Mon, 7 Mar 2005 15:40:42 -0800 (PST)
From: Pete McRae <ambassadorbob@yahoo.com>
Subject: Re: Count Chocula?

Carl Lumma <ekin@lumma.org> wrote:

>>In the bigger picture, of course, you're right. But in in this tiny
>>little window, when I hear people naming commas and temperaments and
>>such after themselves,

>Who does that?

Nevermind. They know who they are.

>>and citing their own writings,

>That's standard practice in scholarly work.

So is megalomania. I thought that was part of why the tuning list was
started...to counter some of that, and give credit where it's due.

>>it comes to seem to me like there may be a lack of humility at work
>>somewhere in the vicinity, and a need to call attention to bigger--or
>>maybe just older--people than ourselves who paid the dues and were
>>there when the real work was being done to produce art that could
>>reach ...

>Eh? Gene is no spring chicken, and he's composed considerably
>more music than Erv.

Erv Wilson is not a composer and doesn't claim to be. Gene is NOT a
composer and claims to be, if you want to look at it that way. (Sorry,
Gene) ;-)

>>But you didn't express any concern about my core statement,

>Sorry, was there a core statement? Maybe you can clarify.

My core statement was clear enough, and I think you know it to be true.
It's an awful sad day (in the puny little tuning sense?), if you do, and
won't admit it.

-Pete

You can configure your subscription by sending an empty email to one
of these addresses (from the address at which you receive the list):
tuning-subscribe@yahoogroups.com - join the tuning group.
tuning-unsubscribe@yahoogroups.com - leave the group.
tuning-nomail@yahoogroups.com - turn off mail from the group.
tuning-digest@yahoogroups.com - set group to send daily digests.
tuning-normal@yahoogroups.com - set group to send individual emails.
tuning-help@yahoogroups.com - receive general help information.

Yahoo! Groups Links

---------------------------------
Celebrate Yahoo!'s 10th Birthday!
Yahoo! Netrospective: 100 Moments of the Web

[This message contained attachments]

________________________________________________________________________
________________________________________________________________________

Message: 8
Date: Mon, 07 Mar 2005 19:34:21 -0000
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
Subject: Re: new member question from a theory class

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

> The Hexany has nothing to do with cubes, except possibly Eulers.

Sure it does. The hexany is an octahedron, and the dual polytope to
that is a cube. If you stellate the octohedron, the centers of the
tetrahedra, representing 7-limit tetrads, are in a cube. If you take
the lattice of 7-limit intervals in its symmetrical form, you get a
lattice called "A3" or "face-centered cubic". This lattice has two
sizes of hole, the "deep holes" are the octahedrons, and the "shallow
holes" tetrahedrons. If you make lattice points out of the centers of
the tetrahedrons, you are making a lattice of the 7-limit tetrads.
This is simply the cubic lattice, called "Z3". The dual lattice to A3,
A3*, is the "body-centered cubic lattice". This can be defined as the
lattice of all triples of integers (x,y,z) where either x, y and z
are all even, or they are all odd. A3 is also D3, which means it can
be thought of as triples (x,y,z) of integers such that x+y+z is even.
Hence, there are a lot of cube-related features of this.

What's Euler's cube?

Eulers work and Erv' s are almost a match of which he is the first to
point out, but they are not the same. .

What was Erv's work on lattices?

________________________________________________________________________
________________________________________________________________________

Message: 9
Date: Mon, 07 Mar 2005 23:43:06 -0000
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
Subject: Re: Prime factorization and maqams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> So sorry for that error Paul, I meant to say that I somehow hear
9801:9000

I think you mean 9801:8000?

>(not 88209/80000) to be a better substitute for 27:22, as in:
>
> 1/1 12/11 9801/8000 4/3
>
> Don't ask me why, beats me...

Hi Ozan,

I'm impressed that you're sensitive to a 3 cent change in the
intonation of one note. What means are you using to render and listen
to these intervals?

I have a bunch of questions/reactions, but let me start off with this:

(1) How do you know it's 9801/8000 and not 49/40 that your ear is
guiding you towards?

>> It takes a little algebra to find the generators, which is why I
>> copied them from Gene's post :) But as you can see, I verified
>>that
>> these generators do satisfy the condition that 4000:3993 be
tempered
>> out . . . and it seems, from the below, that you may now
understand
>> this verification -- but let me know if I need to clarify further.
>
>
> But that is the crux of the issue! I want to know how to find the
>generators, so that I can manage to temper any interval I choose
>after that.

Kalle has just posted basically the same question here. I hope you
and Kalle will both post your questions on tuning-math, since that's
where this has been discussed in the past, particularly by Gene and
Graham.

> The generators are given in cents, which is a logarithm-of-ratio
> measure of interval size. A basic property of logarithms is that
>
> log(a^b) = b*log(a)
>
> So if we say that g1=1200 cents represents prime 2 = 2:1, then
> 2*g1=2400 cents represents 2^2 = 4:1, 3*g1=3600 cents represents
2^3
> = 8:1, 4*g1=4800 cents represents 2^4 = 16:1, and 5*g1=6000 cents
> represents 2^5 = 32:1, etc. And if g3=2786 cents represents prime 5
> = 5:1, then 2*g1=5572 cents represents 5^2 = 25:1, and 3*g1=8358
> cents represents 5^3 = 125:1.
>
> Making sense?
>
>
> I'm sure it does to math-people like yourself, but give me some
>more time to understand the relationships.

OK . . . let's take a step back. Do you normally consider interval
sizes in cents? Or in some other system of units? Would you agree
than an octave is a 2:1 ratio, and that a triple-octave is an 8:1
ratio? Or does this mystify you?

> BTW, how do you feel about tempered octaves? If you approve of
them,
> I might use the TOP temperament of 4000:3993 alone, whose
> approximations to the primes can be calculated with the formulas in
> the paper I sent you.
>
>
> That would be swell Paul. You mean widening the octaves of course,
>don't you? Otherwise I would hear them to be unduly dissonant. My
>Bechstein grand has the octaves stretched by a few cents you know (I
>instructed the tuners myself). That creates a brilliant effect in
>fff passages.

I wasn't thinking of a piano, because the scale in question will have
too many notes per octave to be expressible on a piano. A piano has
stretched overtones, which is why stretched octaves sound great on
it. However, many other instruments, such as bowed strings,
brass/wind instruments, and the human voice have harmonic overtones.
For such instruments, a stretched octave won't sound much less
discordant than a similarly compressed octave, based on my experience
and knowledge. But perhaps you have found otherwise? Perhaps you're
only speaking of *melodic* octaves, not harmonic (simultaneously-
sounding) ones?

>> Hopefully the first case above is now equally clear to you. Let me
>> know if it isn't. Also, I'd encourage you to write a similar
>> paragraph explaining how 81:80 vanishes in meantone temperament --
I
>> think you'd learn something about both the general idea of
>> temperament and about the specific example in which Western common
>> practice music arose.
>
>
>> Urm... Let's see... For 81:80 to vanish, I need the numerator of
>this interval to be equal to the denumerator. Since the syntonic
>comma is a 5-limit interval, the system will have the primes 2,3 and
>5, making this a three dimensional system of tuning. Right?

Most likely, though for your example of 4000:3993, which is an 11-
limit interval, I was thinking, instead of letting

>Tempering out the syntonic comma will result in the upper-most
>dimension (prime) to collapse,

What do you mean uppermost? The largest? How do you know this? What
is it about the syntonic comma that allows you to reach this
conclusion?

>creating a temperament of 2 dimensions. So, the first dimension is
>the octave with 2:1 which will remain untouched for my purposes, and
>the second dimension is the tempered perfect fifth with the ratio
>3:2 and the third dimension is the tempered pure third with the
>ratio 5:4.

I thought you said 2 dimensions?

> Prime factorizing 81:80 gives me
>
> 3*3*3*3 (3^4) for the numerator
>
> and
>
> 2*2*2*2*5 (2^4 * 5^1) for the denumerator.
>
> So, will you help me figure out the rest?

You seem to have left out some of your reasoning above. Perhaps it
was valid, perhaps it wasn't . . . I'm not sure unless you fill it in
for me.

________________________________________________________________________
________________________________________________________________________

Message: 10
Date: Mon, 07 Mar 2005 23:50:54 -0000
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
Subject: Re: Diatonic Maqams

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...> wrote:

> I entertained the idea that ditonic scales (beginning with 9:8+9:8)
>form the backbone of diatonic scales Paul. The most renown is the
>Pythagorean 7-tone ditonic-diatonic scale. I'm sure that not all 7-
>note scales are diatonic (let alone ditonic), but is there some
>algebraic process that can help us distinguish those which are, and
>those which are not?

Yes, if you mean which are diatonic and which aren't. Simply
speaking, if the scale is diatonic, it will be "correctly" spelled
with all 7 letter names, one letter per note . . . Of course, things
can be fuzzy if you're dealing with a "real" scale and an unfamiliar
musical usage . . . but I think my paper _The Forms Of Tonality: A
Preview_, which I think you've read, will help you see what I mean
by "diatonic".

> I took a glance at Blackwood's work, but the techno-babble is
>beyond me.

Oh dear, then surely my own techno-babble can only be
incomprehensible to you. Is there a passage in Blackwood's book that
you'd like me to try "laymanizing" for you?

> I have read your paper, though I'm still in the dark as to some of
>the concepts you have produced.

Allow me to shed light! Ask, ask, ask away . . .

>Nevertheless, the nice sloping lines
>tell me that there are certain zones within tolerable boundaries
>representing consonant dyads which equate to simple integer ratios
>as perceived by the human ear. Am I right?

Which chart are you looking at? Is this in _The Forms Of Tonality_,
or in a different paper?

________________________________________________________________________
________________________________________________________________________

Message: 11
Date: Tue, 08 Mar 2005 00:03:31 -0000
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
Subject: Re: Prime factorization and maqams

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@c...>
wrote:
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@s...>
wrote:
>
> > It takes a little algebra to find the generators, which is why I
> > copied them from Gene's post :) But as you can see, I verified
that
> > these generators do satisfy the condition that 4000:3993 be
tempered
> > out . . . and it seems, from the below, that you may now
understand
> > this verification -- but let me know if I need to clarify further.
>
> > But that is the crux of the issue! I want to know how to find the
> generators, so that I can manage to temper any interval I choose
after
> that.
>
> You might go over to tuning-math, give an example of what you want
to
> find generators for, and we could take it from there. In general,
> however, finding generators depends on how you want to optimize--you
> define what you mean by "best", and then calculate the tuning which
is
> "best" in that sense.

Gene, I might express the situation a bit differently.

You can express the generators, for example, in terms of ratios which
they represent in the temperament, in which case the question of
optimization or what is "best" is moot. The set of generators will
not be unique, but different optimizations don't change this; they
simply tell you the precise tuning of a given set of generators that
will be "best" under various criteria.

Isn't it true that when *you* determine the generators of a
temperament, your software first determines them abstractly of any
specific optimization criterion?

________________________________________________________________________
________________________________________________________________________

Message: 12
Date: Tue, 08 Mar 2005 00:25:23 -0000
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
Subject: Re: new member question from a theory class

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

> so restating my observation with that assumption given:
> i find that a fairly small 11-limit periodicity-block
> contains sounds which audibly approximate ratios of any
> higher prime-limit.
>
> (i'm happy to hone this statement to something more precise.)

Let's get happy :)

________________________________________________________________________
________________________________________________________________________

Message: 13
Date: Mon, 07 Mar 2005 18:50:18 -0500
From: David Beardsley <db@biink.com>
Subject: Re: Count Chocula?

Pete McRae wrote:

> So is megalomania. I thought that was part of why the tuning list
> was started...to counter some of that, and give credit where it's due.
>

Yooze new 'round here. Ain't you?

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

________________________________________________________________________
________________________________________________________________________

Message: 14
Date: Tue, 08 Mar 2005 00:29:48 -0000
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
Subject: Re: 612-ET notation

--- In tuning@yahoogroups.com, "Daniel A. Wier" <dawiertx@s...> wrote:
> From: "monz": (after I wrote)
>
> >> (I use numeric notation for my own work, like [4 -1 1] for
> >> the 5/4 major third and [10 -1 -2] for 7/4.)
> >
> > exactly how does this numeric notation work? it looks like
> > the first number in each set is the generator "5th" number ...
> > what are the other two?
>
> The first number is the number of Pythagorean semitones from 1/1
> (C/Do/Rast):
>
> 1/1 [0 0 0]
> 256/243 [1 0 0]
> 9/8 [2 0 0]

This seems like a problematic choice for a numeric notation, because
you're equating two different "Pythagorean semitones" with a single
vector, [1 0 0]. Wouldn't you instead want a notation where a chain
of two superimposed [1 0 0]s yields a [2 0 0]? Otherwise it seems
you'd tie yourself in knots.

________________________________________________________________________
________________________________________________________________________

Message: 15
Date: Mon, 07 Mar 2005 20:31:27 -0000
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
Subject: More lattice stuff

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

> The Hexany has nothing to do with cubes, except possibly Eulers.

red(q) = 2^(-ordp(q,3)-ordp(q,5)-ordp(q,7))*q

where ordp is the p-adic valuation, meaning the monzo coordinate value
corresponding to the prime p, so that

q = 2^ordp(2,q) 3^ordp(3,q) 5^ordp(5,q) 7^ordp(7,q)

Then the symmetrical lattice of octave classes, with its octahedra and
tetrahedra and so forth, is just the sublattice of reduced
representatives, under the Eulicidean metric. For example the cps
{3,5,7,15,21,35} reduces to {3/2,5/2,7/2,15/4,21/4,35/4}, or in monzo
terms {|-1 1 0 0>, |-1 0 1 0>, |-1 0 0 1>, |-2 1 1 0>, |-2 1 0 1>,
|-2 0 1 1>}. It is easy to verify that these are the verticies of an
octahedron in four-dimensional space, so here you have the hexany
sitting inside of a cubic (4D) lattice.

________________________________________________________________________
________________________________________________________________________

Message: 16
Date: Mon, 7 Mar 2005 16:56:51 -0800 (PST)
From: Pete McRae <ambassadorbob@yahoo.com>
Subject: Re: Count Chocula?

I gotta give it to you, DB, you've come up with some FUNNY ones, lately!

Salud,

David Beardsley <db@biink.com> wrote:

Pete McRae wrote:

> So is megalomania. I thought that was part of why the tuning list
> was started...to counter some of that, and give credit where it's due.
>

Yooze new 'round here. Ain't you?

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

Yahoo! Groups Links

__________________________________________________
Do You Yahoo!?
Tired of spam? Yahoo! Mail has the best spam protection around
http://mail.yahoo.com

[This message contained attachments]

________________________________________________________________________
________________________________________________________________________

Message: 17
Date: Mon, 07 Mar 2005 20:01:46 -0500
From: David Beardsley <db@biink.com>
Subject: Re: Count Chocula?

grin.

Pete McRae wrote:

> I gotta give it to you, DB, you've come up with some FUNNY ones, lately!
>
> Salud,
>
> P
>
> */David Beardsley <db@biink.com>/* wrote:
>
>
> Pete McRae wrote:
>
> > So is megalomania. I thought that was part of why the tuning list
> > was started...to counter some of that, and give credit where
> it's due.
> >
>
> Yooze new 'round here. Ain't you?
>
> :0
>
>

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

________________________________________________________________________
________________________________________________________________________

Message: 18
Date: Tue, 08 Mar 2005 01:03:49 -0000
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
Subject: Re: Count Chocula?

--- In tuning@yahoogroups.com, Pete McRae <ambassadorbob@y...> wrote:

> Erv Wilson is not a composer and doesn't claim to be. Gene is NOT a
composer and claims to be, if you want to look at it that way.

What, besides composing, in your view is required in order to be a
composer? Did you come to the conclusion I was not a composer after
listening to things I wrote which weren't music, and if so, what things?

________________________________________________________________________
________________________________________________________________________

Message: 19
Date: Tue, 08 Mar 2005 01:00:41 -0000
From: "Gene Ward Smith" <genewardsmith@coolgoose.com>
Subject: Re: Prime factorization and maqams

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> You can express the generators, for example, in terms of ratios which
> they represent in the temperament, in which case the question of
> optimization or what is "best" is moot.

I thought that by "finding the generators" he simply meant finding the
tuning.

> Isn't it true that when *you* determine the generators of a
> temperament, your software first determines them abstractly of any
> specific optimization criterion?

"Finding the generators" in what sense? You can use Hermite normal
form, and "find" the generators of 225/224-planar in the sense of
saying that
some tuning of 2, 3, and 5 will work; but you also could, for
instance, find TOP tunings for 2, 3, 5, and 7. Most of the time people
are talking about linear temperaments, in which case you find the
period and, perhaps, the smallest generator > 1 according to some
optimization.

________________________________________________________________________
________________________________________________________________________

Message: 20
Date: Tue, 08 Mar 2005 01:34:56 -0000
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
Subject: Re: Count Chocula?

>So is megalomania. I thought that was part of why the tuning list
>was started...to counter some of that, and give credit where it's
>due.

I like giving credit where it's due whenever I know it's due someone
(see all the personal names in my new paper). But I thought this list
was about discussing tuning and helping people to grasp tuning
concepts for themselves, so that (for example) they can (if they
wish) climb the same mountains and view the same vistas that have
been viewed before, and perhaps also see something that no human has
seen before. To me, the climb relevant in this particular case is a
pretty straightforward one, that anyone with enough interest can
pursue. And many such climbs have been ventured on these lists and in
my private conversations with others. I always mention Erv Wilson and
his work wherever it's relevant.

Suggesting megalomania in this connection seems to imply something
that disturbs me. It suggests that the average reader of this list
can't formulate thoughts with enough depth or clarity to come to the
same concepts themselves. This discourages both independent thought
and thought within a thinking group, and encourages "cultism" where
only an "elite" are entitled to dictate the "sacred cow" concepts,
and anyone outside this elite is an "infidel" who surely can't have
thought of the same concepts themselves.

Pete, the reason this came up is because you brought up "science" on
this list, I didn't know if you meant "math" but certain ways of
applying math to the question of tuning lead directly to constructs
like the CPS scales. I believe that if you, or anyone else on this
list, pursues certain theoretical questions, such as how to display
all the consonances in a tuning system at a glance, perhaps getting
help from others if they need some math they haven't learned,
you/they will naturally see how the CPS scales arise. Perhaps this
kind of theoretical thinking doesn't interest you, and (like many
people) it is painful for you to engage in. I see nothing wrong with
that. But . . . oops I have to run to rehearsal right now, let's
continue this later, OK? Maybe on another list. On this list, maybe
we can instead discuss the relevant tuning concepts and constructs
themselves, as has been done in the past, such as in 2000:

http://sonic-arts.org/td/erlich/paul-cps.htm

where I gave Erv Wilson credit for "best single illustration of the
CPS concept" among other things . . .

P.S. Sorry I remembered wrong. It appears that Erv Wilson is indeed
the earliest we know of to write down any Eikosany scales. But it
would be sad indeed if someone who claimed precedence had to be
accused of "megalomania". Anyway, we'll have to continue this at some
point in the near future . . .

--- In tuning@yahoogroups.com, Pete McRae <ambassadorbob@y...> wrote:
>
>
> Carl Lumma <ekin@l...> wrote:
>
> >>In the bigger picture, of course, you're right. But in in this
tiny
> >>little window, when I hear people naming commas and temperaments
and
> >>such after themselves,
>
> >Who does that?
>
> Nevermind. They know who they are.
>
> >>and citing their own writings,
>
> >That's standard practice in scholarly work.
>
> So is megalomania. I thought that was part of why the tuning list
was started...to counter some of that, and give credit where it's due.
>
> >>it comes to seem to me like there may be a lack of humility at
work
> >>somewhere in the vicinity, and a need to call attention to bigger-
-or
> >>maybe just older--people than ourselves who paid the dues and were
> >>there when the real work was being done to produce art that could
> >>reach ...
>
> >Eh? Gene is no spring chicken, and he's composed considerably
> >more music than Erv.
>
> Erv Wilson is not a composer and doesn't claim to be. Gene is NOT
a composer and claims to be, if you want to look at it that way.
(Sorry, Gene) ;-)
>
> >>But you didn't express any concern about my core statement,
>
> >Sorry, was there a core statement? Maybe you can clarify.
>
> My core statement was clear enough, and I think you know it to be
true. It's an awful sad day (in the puny little tuning sense?), if
you do, and won't admit it.
>
> -Pete
>
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>
>
>
>
>
>
>
>
>
> ---------------------------------
> Celebrate Yahoo!'s 10th Birthday!
> Yahoo! Netrospective: 100 Moments of the Web

________________________________________________________________________
________________________________________________________________________

Message: 21
Date: Tue, 08 Mar 2005 01:44:06 -0000
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
Subject: Re: Prime factorization and maqams

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@c...>
wrote:
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> > You can express the generators, for example, in terms of ratios
which
> > they represent in the temperament, in which case the question of
> > optimization or what is "best" is moot.
>
> I thought that by "finding the generators" he simply meant finding
the
> tuning.
>
> > Isn't it true that when *you* determine the generators of a
> > temperament, your software first determines them abstractly of
any
> > specific optimization criterion?
>
> "Finding the generators" in what sense? You can use Hermite normal
> form, and "find" the generators of 225/224-planar in the sense of
> saying that
> some tuning of 2, 3, and 5 will work; but you also could, for
> instance, find TOP tunings for 2, 3, 5, and 7.

I could have easily told Ozan how the primes would be tuned by TOP
for the temperament in question. But finding a set of generators
(even abstractly) brings you a step closer to actually constructing a
reasonable scale in that temperament. And for that I relied on your
post. Now I'm asking you a question about your methods, but as far as
I can tell, you're not answering.

> Most of the time people
> are talking about linear temperaments,

I never use that term anymore, and George Secor agrees with my new
usage. It partly came down to, believe it or not Pete, respect for
Erv Wilson's original usage of and meaning for the term, which we
believe would not encompass a lot of the systems where the octave is
more than one period that we used to call "linear temperaments."

> in which case you find the
> period and, perhaps, the smallest generator > 1 according to some
> optimization.

________________________________________________________________________
________________________________________________________________________

Message: 22
Date: Tue, 8 Mar 2005 12:49:49 +1100
From: "Yahya Abdal-Aziz" <yahya@melbpc.org.au>
Subject: RE: Digest Number 3431

Dave,

Great title! :-)

I'll have another go at downloading some of your work. Perhaps
GetRight is causing my problems downloading from your site? If
it doesn't work this time, I'll try downloading without using it.

Regards,
Yahya

-----Original Message-----
________________________________________________________________________

Message: 1
From: Dave Seidel <dave@superluminal.com>
Subject: New piece: Passacaglia and Fugue State

I have just published a new piece called "Passacaglia and Fugue State"
to http://mysterybear.net/articles/10.

This is third of three pieces inspired by La Monte Young's work with
sine-tone installations based on prime-numbered harmonics. I used Scala
to make a 31-tone "scale" base on LMY's "The Base 9:7:4 Symmetry...",
and then used this within Steven Yi's blue with Csound on the back end.

MP3 and Ogg versions are available on the page. Comments are welcome,
as always! Hope you enjoy it.

- Dave

--
Dave Seidel
[blog] http://superluminal.com/dave/weblog
[music] http://mysterybear.net

________________________________________________________________________

--
No virus found in this outgoing message.
Checked by AVG Anti-Virus.
Version: 7.0.300 / Virus Database: 266.6.0 - Release Date: 2/3/05

________________________________________________________________________
________________________________________________________________________

Message: 23
Date: Mon, 07 Mar 2005 20:50:56 -0500
From: David Beardsley <db@biink.com>
Subject: Re: Re: Count Chocula?

wallyesterpaulrus wrote:

>Suggesting megalomania in this connection seems to imply something
>that disturbs me. It suggests that the average reader of this list
>can't formulate thoughts with enough depth or clarity to come to the
>same concepts themselves. This discourages both independent thought
>and thought within a thinking group, and encourages "cultism" where
>only an "elite" are entitled to dictate the "sacred cow" concepts,
>and anyone outside this elite is an "infidel" who surely can't have
>thought of the same concepts themselves.
>
>
*you doth protest too loudly.*

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

________________________________________________________________________
________________________________________________________________________

Message: 24
Date: Mon, 07 Mar 2005 21:19:58 -0500
From: Dave Seidel <dave@superluminal.com>
Subject: Re: Digest Number 3431

Hi Yahya,

I hope you're able to download the file -- I haven't had any other
reports of download problems from anybody, so maybe it is GetRight.
BTW, I use Free Download Manager (http://www.freedownloadmanager.org/)
and it works very nicely.

- Dave

Yahya Abdal-Aziz wrote:
>
> Dave,
>
> Great title! :-)
>
> I'll have another go at downloading some of your work. Perhaps
> GetRight is causing my problems downloading from your site? If
> it doesn't work this time, I'll try downloading without using it.
>
> Regards,
> Yahya
>
>
> -----Original Message-----
> ________________________________________________________________________
>
> Message: 1
> From: Dave Seidel <dave@superluminal.com>
> Subject: New piece: Passacaglia and Fugue State
>
> I have just published a new piece called "Passacaglia and Fugue State"
> to http://mysterybear.net/articles/10.
>
> This is third of three pieces inspired by La Monte Young's work with
> sine-tone installations based on prime-numbered harmonics. I used Scala
> to make a 31-tone "scale" base on LMY's "The Base 9:7:4 Symmetry...",
> and then used this within Steven Yi's blue with Csound on the back end.
>
> MP3 and Ogg versions are available on the page. Comments are welcome,
> as always! Hope you enjoy it.
>
> - Dave
>

________________________________________________________________________
________________________________________________________________________

Message: 25
Date: Mon, 7 Mar 2005 20:28:07 -0600
From: "Daniel A. Wier" <dawiertx@sbcglobal.net>
Subject: Re: Re: 612-ET notation

From: "wallyesterpaulrus":

>> The first number is the number of Pythagorean semitones from 1/1
>> (C/Do/Rast):
>>
>> 1/1 [0 0 0]
>> 256/243 [1 0 0]
>> 9/8 [2 0 0]
>
> This seems like a problematic choice for a numeric notation, because
> you're equating two different "Pythagorean semitones" with a single
> vector, [1 0 0]. Wouldn't you instead want a notation where a chain
> of two superimposed [1 0 0]s yields a [2 0 0]? Otherwise it seems
> you'd tie yourself in knots.

I probably need to use a different symbol than brackets then, since I mean
to simply draw a "Pythagorean roadmap" rather than indicate a vector.

There are alternative systems, one of them having the first number indicate
12-TET steps. I just thought of another that has the first number actually
indicate 9/8 major seconds, then a flat or sharp could be placed next to it
if you want to shift the note up or down by 2187/2048. But that would make
a
perfect fifth [b3 0 0] and a perfect octave [6 -1 0], which looks odd to
me.

________________________________________________________________________
________________________________________________________________________

------------------------------------------------------------------------
Yahoo! Groups Links

------------------------------------------------------------------------

--------------------------------------------------------------------
mail2web - Check your email from the web at
http://mail2web.com/ .

RE: Euler, Erv Wilson ..oops!!

🔗bractea@earthlink.net