Mad Gene - about that science...

Gene! (apostrophe on loan from Mr. Grady)

Point me in the right direction on your site if I missed it somewhere, but at least on the mad science retuning pages I don't see any essays on the 'how and why' of the temperaments you chose, so:

Would it be possible for you to explain a little about how you choose differing tunings for these pieces? Much of this might be beyond me, but I am certain this isn't just a random process, so it would be cool to know what musical analysis you might be doing before 'recasting' a traditional 12tet piece in a new tuning. I think, for starters, it might highlight the kind of harmonic treatments certain tunings would be 'better' suited for.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> Gene! (apostrophe on loan from Mr. Grady)

That's an exclamation point :)

> so it would be cool to know what musical analysis you might be
>doing before 'recasting' a traditional 12tet piece in a new tuning.

These examples may have been the result of sheer madness, for all I
know. But Gene has gone through quite a few examples of this kind of
thing, done quite rationally, and I think primarily on the tuning-
math list. The idea, if you're sticking to the same number of notes
per octave that are in the MIDI file you're starting with (12), is to
align the wolves of the tuning with harmonies that do not occur in
the piece in question. The harmonies that do occur in the piece, on
the other hand, will generally sound closer to JI (if possible).

However, Gene just answered Carl that he's *not* using 12-note
tunings for these pieces. In which case he has to be doing something
a lot more sophisticated than just mapping from each MIDI pitch to
the corresponding pitch in the new tuning. Which means that other
issues could and should be involved in the 'recasting' decision --
for example, a chord progression like Cmaj-Fmaj-Dmin-Gmaj-Cmaj would
drift by about a quartertone in Pajara, and that would probably not
be something agreeable to the composer . . .

Sorry to bust in, but I have a feeling I may be able to aid
communication in this particular exchange (even if I know little, as
yet, of the precise details).

-Paul

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

> However, Gene just answered Carl that he's *not* using 12-note
> tunings for these pieces.

Pajara[12] and Wreckpop are of course 12-note scales. What I was
referring to was Night on Porcupine Mountain, which permutes the
notes according to this:

! perm.scl
3-->10/3 5-->24/3 transformed Duodene permute
12
!
-200.0
600.0
400.0
500.0
300.0
1000.0
900.0
700.0
800.0
1300.0
1400.0
1200.0

and then retunes the notes to 22-equal porcupine by this (note the
doubled scale degree!):

! duopors.scl
3-->10/3 5-->24/3 sorted rotated Duodene in 22-et
12
!
54.5454545
163.636364
327.272727
381.818182
490.909091
545.454545
709.090909
818.181818
872.727273
1036.363636
1036.363636
1200.000000

In which case he has to be doing something
> a lot more sophisticated than just mapping from each MIDI pitch to
> the corresponding pitch in the new tuning.

As you see, it isn't that sophisticated, but it does seem to produce
very nice results. Examining how the harmony changes in detail will
show why. The reason for the two-step proceedure is that the pitch
bends introduced by the permuation are bogus 2^13 bends, and can be
removed without changing the result. The second step then introduces
an MTS track of the sort which will not cause Audio Compositor to act
up.

More sophisticated would be to find appropriate places to put a new
MTS track. I wasn't happy with my first attempt to put Beethoven's
4th into meantone, and am thinking of checking if I can get away with
this method with it.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> > Gene! (apostrophe on loan from Mr. Grady)
>
> That's an exclamation point :)

Nice try: the apostrophe was further down in the piece.

No, it wasn't. :) Thanks for your pre-explanation of Gene's work, which I'll follow with interest.

Cheers,
Jon "The Punctuationally Challenged Percussionist"

Hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> As you see, it isn't that sophisticated

Not all that transparent, either, but I'm willing to save it and study it!

> but it does seem to produce very nice results.

Ahem... this is a little less than scientific! I Will NOT belabor the point, but when you produce a piece (like this one) and append a commentary "nice results" or "works very well", are we truly stepping into SubjectiveLand, or do you actually mean something more theory-based?

> Examining how the harmony changes in detail will show why.

But did you examine the harmony first, to determine an appropos tuning to use, or try some, see how they tickled your fance, and then did a post-mortem?

Cheers,
Jon

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

> But did you examine the harmony first, to determine an appropos
tuning to use, or try some, see how they tickled your fance, and then
did a post-mortem?

I wanted to use certain tunings, so I looked for things which it
seemed to me the tuning I had in mind might work well for. Then fancy-
tickling comes in--you try, for example, Love-Porcupine-Death, and
perhaps find you don't think it really works too well.

Gene,

OK, stop me if I'm being pedantic, but I'm trying to get you to really hone in here, to delineate your thought process or choices. When you write the following:

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> I wanted to use certain tunings, so I looked for things which it
> seemed to me the tuning I had in mind might work well for.

...and...

> you try, for example, Love-Porcupine-Death, and
> perhaps find you don't think it really works too well.

*That* phrase comes up a lot in your posts: "works well". What makes a tuning *work*? What leads you to believe a particular tuning *isn't* working well?? Are we talking subjective intonational effects, or...?

Cheers,
Jon

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

> > you try, for example, Love-Porcupine-Death, and
> > perhaps find you don't think it really works too well.
>
> *That* phrase comes up a lot in your posts: "works well". What
makes a tuning *work*? What leads you to believe a particular tuning
*isn't* working well?? Are we talking subjective intonational
effects, or...?

By the time I get around to deciding if it "works", I've already
analyzed the chords; the "works" part is simply a "works for me"
judgment. There wasn't anything wrong with the chords in the
porcupine version of Love Death, I just found I didn't like it as
much as I hoped I would. I'm happier with Mahler #7.

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> By the time I get around to deciding if it "works", I've already
> analyzed the chords; the "works" part is simply a "works for me"
> judgment. There wasn't anything wrong with the chords in the
> porcupine version of Love Death, I just found I didn't like it as
> much as I hoped I would. I'm happier with Mahler #7.

I guess I find it... perplexing? baffling? (I don't know what the proper descriptor would be) that for all of the 'science' that has gone into the development of the various temperments/tunings you've been working on in the last few years, which (of course) contain all manner of detailed mathematic steps in their genesis (if you will)... That for all of the preceding it winds up being a grab bag of tunings that you throw against a piece to see what sticks!

I'm not using that rather flip phrase in a derogatory manner, but while I can see that it might be a more direct procedure to pick a tuning for a particular baroque piece in a certain key, I guess I had assumed that when you were generating all these retuned 'classics' there was a generalized method behind it. Mind you, I find nothing wrong with a "works for me" paradigm, but it seems to be the polar extreme from the rigor with which you have developed the tunings. Maybe it is simply the 'art' part in the art and science of music.

Cheers,
Jon

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

> I'm not using that rather flip phrase in a derogatory manner, but
while I can see that it might be a more direct procedure to pick a
tuning for a particular baroque piece in a certain key, I guess I had
assumed that when you were generating all these retuned 'classics'
there was a generalized method behind it.

There certainly is a method for the retuned classics, which is to look
which and how many chords appear. But porcupinization is not a
tuning, it is what Herman might call a warping. How can one tell if
one likes a warping without trying it on?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> There certainly is a method for the retuned classics, which is to look
> which and how many chords appear.

Right.

> But porcupinization is not a
> tuning, it is what Herman might call a warping. How can one tell if
> one likes a warping without trying it on?

I would imagine one can't, unless one really *can* imagine! But is this the only logic behind all of your retunings: try them on for fit? Somehow I thought it was more structured, but fine either way - especially if you like the retunings.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > There certainly is a method for the retuned classics, which is to
look
> > which and how many chords appear.
>
> Right.
>
> > But porcupinization is not a
> > tuning, it is what Herman might call a warping. How can one tell
if
> > one likes a warping without trying it on?
>
> I would imagine one can't, unless one really *can* imagine! But is
>this the only logic behind all of your retunings: try them on for
>fit? Somehow I thought it was more structured, but fine either way -
>especially if you like the retunings.

Hi Jon,

You may have missed where Gene told you,

'By the time I get around to deciding if it "works", I've already
analyzed the chords; the "works" part is simply a "works for me"
judgment'

Which indicates to me that the logic behind the retunings is very
precise and involved. The subjective judgment is only used as a final
filter to find the real standouts.

At least that's how I read (past tense) it.

-Paul

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> You may have missed where Gene told you,
>
> 'By the time I get around to deciding if it "works", I've already
> analyzed the chords; the "works" part is simply a "works for me"
> judgment'
>
> Which indicates to me that the logic behind the retunings is very
> precise and involved. The subjective judgment is only used as a final
> filter to find the real standouts.
>
> At least that's how I read (past tense) it.

Nope, I didn't miss it, but I was trying to get Gene to expand on *exactly* that part of this 'project'! What kind of analysis? What kind of harmonic fabrics might point to what manner of tunings?

Subjective judgements will always be just that - subjective, and therefore it pretty much invalidates any discussion beyond the original "works for me" landscape. What I was (and, I guess, still am) hoping for would be a more thorough detailing of, once years(!) of working on generating all the various temperaments/tunings have taken place, how then to utilize them in a *musical* context. I've seen all the "proper", "badness", and other metrics discussed, but I know from my perspective I've always attributed musical functions to those terms, and the people working in these areas are attributing mathematical (and other) meanings for those terms.

Again, what had picqued my curiousity was in what way did Gene apply differing tunings to pieces previously composed in 12tet.

Cheers,
Jon

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

> What I was (and, I guess, still am) hoping for would be a more
>thorough detailing of, once years(!) of working on generating all
>the various temperaments/tunings have taken place, how then to
>utilize them in a *musical* context.

Me too. This mostly lies ahead for me. Very little of it will, or
can, have to do with retuning existing music, though in some cases
that may be a nice quick way to get to have *something* to listen to
in a proposed tuning. If we can take Herman Miller's word for it, we
can look forward to some more original examples this year, and I'm
sure they'll be entertaining (musically) and enlightening (tuning-ly).

Currently, I'm hoping that the environment is ripe for Graham, Gene,
Dave, and I to come to some agreements and finally write something
up. Once that hurdle is cleared, the time will be ripe for some
unbridled musical exploration . . .

Your frustration is most understandable,
Paul

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

> Nope, I didn't miss it, but I was trying to get Gene to expand on
*exactly* that part of this 'project'! What kind of analysis? What
kind of harmonic fabrics might point to what manner of tunings?

It's often more a matter of what doesn't appear, or seldom appears,
than what does. If you find somewhere on the circle of fifths with no
major or minor triads and seventh chords at all, you don't need to
worry about the wolf fifths; if you find three places in a row with
no major chords, followed by a place with no major or minor triads or
seventh chords, followed by two places with no minor chords, you've
found a good spot to put the wolf fifths and supermajor thirds of
meantone. Otherwise you can look to see how the pattern of chords
matches tunings you have on hand. Does this set of chords fit a grail
or bifrost tuning better, for instance, and in what key?

I'm using midichord a lot; a better program for analyzing chords
would be nice, if anyone knows of one.

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

> Me too. This mostly lies ahead for me. Very little of it will, or
> can, have to do with retuning existing music, though in some cases
> that may be a nice quick way to get to have *something* to listen
to
> in a proposed tuning.

That was on my mind with this porcupinization business.

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

> It's often more a matter of what doesn't appear, or seldom appears,
> than what does. If you find somewhere on the circle of fifths with no
> major or minor triads and seventh chords at all, you don't need to
> worry about the wolf fifths; if you find three places in a row with
> no major chords, followed by a place with no major or minor triads or
> seventh chords, followed by two places with no minor chords, you've
> found a good spot to put the wolf fifths and supermajor thirds of
> meantone. Otherwise you can look to see how the pattern of chords
> matches tunings you have on hand. Does this set of chords fit a grail
> or bifrost tuning better, for instance, and in what key?

Aha - Gene, thanks, it is good to see some of the thinking behind the scenes. I can see that, as a piece would become more harmonically complex, it would make this an even more difficult process. And maybe that is why you were alluding to the multiple MTS strategy.

I think that even if the 'experimentation' process goes along current lines, it may shed light on the kind of multiple-tuning schemes future composers could utilize, which would seem to be a fertile place indeed.

> I'm using midichord a lot; a better program for analyzing chords
> would be nice, if anyone knows of one.

Careful - you might get a lot of answers that don't relate to your request! :)

BTW, for anyone reading, "Mad Gene" refers to the "Mad Science" aspect of all this, not an angry Mr. Smith. Or crazed DNA, at that.

Cheers,
Jon

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Your frustration is most understandable,

Oh, moderate curiosity, not frustration, really.

Cheers,
Jon

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Currently, I'm hoping that the environment is ripe for Graham, Gene,
> Dave, and I to come to some agreements [about linear temperaments]
and finally write something
> up.

Paul,

Perhaps you and Gene should just go ahead without me. Our disagreement
on this is clear and doesn't show any signs of being bridged in the
near future. Here's a biased summary of it.

The basic problem is that there is an infinite number of these things
and any catalog or article needs to limit itself somehow to the few
"most interesting" for any given set of ratios being approximated.

I find that you and Gene place too much emphasis on temperaments with
extremes of either complexity or error, apparently based on your faith
in the purely mathematical concept of log-flat badness (important
though it is), and without enough consideration of the fact that we're
dealing with _human_ abilities and perceptions in regard to _music_.

You're unwilling to consider badness functions that would gradually
roll off these extremes in a way that might correspond roughly with
what is of musical interest to typical humans, apparently because this
is too "subjective".

But seemingly paradoxically, you are willing to apply sharp cutoffs to
both complexity and error.

At one stage I found points of agreement between our methods for both
5 and 7 limit, i.e. I found some sharp cutoffs that happened to agree
with my gradual rolloffs, not on the ranking of the temperaments, but
at least on which were in and which were out (when suitable badness
cutoffs were also applied).

But since then you seem to have thrown the gates wide again and are
including pico-temperaments only of interest to computers, and some
temperaments with errors so large that sense can only be made of them
(if at all) by using purpose-built extremely inharmonic timbres. And
you go so far as to give non-systematic non-descriptive names to these.

I figure that if people have specific unusual requirements for
temperaments such as these, they can just go and find them with
Graham's wonderful online temperament finder. There's no need to
catalog them as if they were just as lilely to find actual musical use
as say porcupine or orwell. I feel a catalog or article should include
only those temperaments that are likely to be of _general_ musical
interest (albeit to microtonalists only), not only of interest for a
specific purpose such as notation or computation or synthetic
inharmonic timbres.

I have no idea how Graham feels about this issue [of how we should
decide what to leave out], but I certainly don't find any dross in his
existing (although somewhat random) catalog.

-- Dave Keenan

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

> I find that you and Gene place too much emphasis on temperaments
with
> extremes of either complexity or error, apparently based on your
faith
> in the purely mathematical concept of log-flat badness (important
> though it is), and without enough consideration of the fact that
we're
> dealing with _human_ abilities and perceptions in regard to _music_.

I guess you haven't been reading my posts lately, Dave. No --
actually you did respond to something about epimericity.

> But since then you seem to have thrown the gates wide again and are
> including pico-temperaments only of interest to computers,

My last few lists had nothing more complex than schismic -- which
even cuts off the prized aristoxenean.

> and some
> temperaments with errors so large that sense can only be made of
them
> (if at all) by using purpose-built extremely inharmonic timbres.

Herman's examples show that even the very worst of these can sound
lovely, even "harmonic", without purpose-built timbres. Don't you
agree?

> And
> you go so far as to give non-systematic non-descriptive names to
>these.

Herman finds these easy to remember, and many of them convey much
musical meaning (like "diminished", "augmented", etc.). Let me see
your proposal for names.

-Paul

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

> You're unwilling to consider badness functions that would gradually
> roll off these extremes in a way that might correspond roughly with
> what is of musical interest to typical humans, apparently because
this
> is too "subjective".

I'm not unwilling. Let's look at the 5-limit. In my recent post (my
first here after a long break), I essentially used the blue 'badness
contour' here:

/tuning/files/Erlich/dave2.gif

Another reasonable option would be the red one, where the inclusion
of beep (27/25) and negri (16875/16384) are each negotiable by fine-
tuning the curve. If can parameterize it, perhaps Gene can prove,
using epimericity and whatnot, that no other commas lie under the
curve at higher complexities. An additional pair of options comes
from looking at the graph with linear, rather than logarithic, error
axis:

/tuning/files/Erlich/dave1.gif

The red line would make Herman unhappy, while the blue one would make
him happy, as it includes 16/15, 2187/2048, and 2109375/2097152
(though the last one is kind of buried on the chart), and he seems to
have found musical value in all three. Perhaps we should make a "for
Herman" list online but use a shorter list for our paper . . . we
still have 7-limit stuff we want to talk about . . .

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

If can parameterize it, perhaps Gene can prove,
> using epimericity and whatnot, that no other commas lie under the
> curve at higher complexities.

You could start the ball rolling by plotting epimericity curves on
your chart.

My concern with taking the lead writing is that probably no one would
follow, so I've put what I would have written on my web site.
Suggestions as to what I should put up there in connection with any
paper would be helpful.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> If can parameterize it, perhaps Gene can prove,
> > using epimericity and whatnot, that no other commas lie under the
> > curve at higher complexities.
>
> You could start the ball rolling by plotting epimericity curves on
> your chart.

I indicated epimericity with the sizes of the numbers in the ratios,
in case you didn't know that. My brain is tired -- if you can express
epimericity in terms of the quantities on the x- and y-axes, I can
probably show contours for it.

> My concern with taking the lead writing is that probably no one
would
> follow, so I've put what I would have written on my web site.
> Suggestions as to what I should put up there in connection with any
> paper would be helpful.

OK, I'll try to keep that in mind.

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

> I indicated epimericity with the sizes of the numbers in the ratios,
> in case you didn't know that. My brain is tired -- if you can express
> epimericity in terms of the quantities on the x- and y-axes, I can
> probably show contours for it.

If u = log2(n) and v = log2(d), then the x and y axes of your graph show

x = u + v
y = (u+v)/(u-v)

Solving for u and v in terms of x and y gives

u = (x + xy)/2
v = (x - xy)/2

This now gives us

n = 2^u = 2^((x + xy)/2)
d = 2^v = 2^((x - xy)/2)

From this, e = log2(n-d)/log2(d) would be

e = (2/x(y-1) log2(n-d)

which is a function of x and y. Fixing an e, you can find y in terms
of x by Newton's method.

My first reply to this seems to have vanished. Sigh.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > I find that you and Gene place too much emphasis on temperaments
> with
> > extremes of either complexity or error, apparently based on your
> faith
> > in the purely mathematical concept of log-flat badness (important
> > though it is), and without enough consideration of the fact that
> we're
> > dealing with _human_ abilities and perceptions in regard to _music_.
>
> I guess you haven't been reading my posts lately, Dave. No --
> actually you did respond to something about epimericity.

I haven't been reading everything.

> > But since then you seem to have thrown the gates wide again and are
> > including pico-temperaments only of interest to computers,
>
> My last few lists had nothing more complex than schismic -- which
> even cuts off the prized aristoxenean.

OK. I was going by our last discussion re
http://tonalsoft.com/enc/eqtemp.htm

> > and some
> > temperaments with errors so large that sense can only be made of
> them
> > (if at all) by using purpose-built extremely inharmonic timbres.
>
> Herman's examples show that even the very worst of these can sound
> lovely, even "harmonic", without purpose-built timbres. Don't you
> agree?

I didn't know he'd used them. URLs?

My guess, taking your word that they sound ok, is that any nearby MOS
(DE) would work just as well and it has little or nothing to do with
any approximation of JI.

> > And
> > you go so far as to give non-systematic non-descriptive names to
> >these.
>
> Herman finds these easy to remember, and many of them convey much
> musical meaning (like "diminished", "augmented", etc.). Let me see
> your proposal for names.

If they "convey much musical meaning (like "diminished", "augmented",
etc.)" then they are "descriptive names" and I am not objecting to
them. And I've even stopped objecting to silly names when they are for
middle-of-the-road temperaments that have actually been used in music.

It is names for extreme temps like father, beep, pirate, raider etc.
that I find pointless.

I propose not naming LTs with extreme complexity or error at all!

I'd rather have them described by their generator and period, or their
mapping.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> My first reply to this seems to have vanished. Sigh.
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> >
> > > I find that you and Gene place too much emphasis on
temperaments
> > with
> > > extremes of either complexity or error, apparently based on
your
> > faith
> > > in the purely mathematical concept of log-flat badness
(important
> > > though it is), and without enough consideration of the fact
that
> > we're
> > > dealing with _human_ abilities and perceptions in regard to
_music_.
> >
> > I guess you haven't been reading my posts lately, Dave. No --
> > actually you did respond to something about epimericity.
>
> I haven't been reading everything.
>
> > > But since then you seem to have thrown the gates wide again and
are
> > > including pico-temperaments only of interest to computers,
> >
> > My last few lists had nothing more complex than schismic -- which
> > even cuts off the prized aristoxenean.
>
> OK. I was going by our last discussion re
> http://tonalsoft.com/enc/eqtemp.htm

In that discussion, didn't I tell you that the reason that goes so
deep is because Monz already had some very high-numbered ETs
mentioned there, so it seemed sensible to connect them?

> > > and some
> > > temperaments with errors so large that sense can only be made
of
> > them
> > > (if at all) by using purpose-built extremely inharmonic timbres.
> >
> > Herman's examples show that even the very worst of these can
sound
> > lovely, even "harmonic", without purpose-built timbres. Don't you
> > agree?
>
> I didn't know he'd used them. URLs?

http://www.io.com/~hmiller/music/warped-canon.html, scroll all the
way to the bottom, and hear the 8-TET and 13-TET and "Top" father
temperament "anti-pentatonic" versions of the canon.

> My guess, taking your word that they sound ok, is that any nearby
MOS
> (DE) would work just as well and it has little or nothing to do with
> any approximation of JI.

If it's nearby, it has a similar approximation of JI. So your guess
would be hard to test. But what's the big deal about listing one or
three temperaments that have errors that may be too large according
to some as-yet unknown criterion? Five, and I'd start complaining.

> > > And
> > > you go so far as to give non-systematic non-descriptive names
to
> > >these.
> >
> > Herman finds these easy to remember, and many of them convey much
> > musical meaning (like "diminished", "augmented", etc.). Let me
see
> > your proposal for names.
>
> If they "convey much musical meaning
(like "diminished", "augmented",
> etc.)" then they are "descriptive names" and I am not objecting to
> them. And I've even stopped objecting to silly names when they are
for
> middle-of-the-road temperaments that have actually been used in
music.
>
> It is names for extreme temps like father,

Sounds like "Fourth-third", and it also "fathers" virtually all 5-
limit temperaments of interest, along with the "mother" dicot
and "third parent" beep. The "anti-pentatonic" scale associated with
it is basically Agmon's pentatonic in 8-equal, though he probably
wouldn't be happy if his name were associated with philosophies so
radically different from his own.

> beep,

BP, as in Bohlen-Pierce, since 27/25 is a BP interval.
Gene "fathered" this name. But nothing is set in stone.

> pirate, raider etc.

Won't be in the paper.

You know guys, both sets of names could easily appear paper,
especially if it meant keeping Dave's name off.

-Carl

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > I indicated epimericity with the sizes of the numbers in the
ratios,
> > in case you didn't know that. My brain is tired -- if you can
express
> > epimericity in terms of the quantities on the x- and y-axes, I
can
> > probably show contours for it.
>
> If u = log2(n) and v = log2(d), then the x and y axes of your graph
show
>
> x = u + v
> y = (u+v)/(u-v)
>
> Solving for u and v in terms of x and y gives
>
> u = (x + xy)/2
> v = (x - xy)/2
>
> This now gives us
>
> n = 2^u = 2^((x + xy)/2)
> d = 2^v = 2^((x - xy)/2)
>
> From this, e = log2(n-d)/log2(d) would be
>
> e = (2/x(y-1) log2(n-d)

There seems to be a parethesis missing, and . . .

> which is a function of x and y.

and n and d? No good.

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

/tuning/topicId_51065.html#51208

> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > Currently, I'm hoping that the environment is ripe for Graham,
Gene,
> > Dave, and I to come to some agreements [about linear temperaments]
> and finally write something
> > up.
>
> Paul,
>
> Perhaps you and Gene should just go ahead without me. Our
disagreement
> on this is clear and doesn't show any signs of being bridged in the
> near future. Here's a biased summary of it.
>
> The basic problem is that there is an infinite number of these
things
> and any catalog or article needs to limit itself somehow to the few
> "most interesting" for any given set of ratios being approximated.
>
> I find that you and Gene place too much emphasis on temperaments
with
> extremes of either complexity or error, apparently based on your
faith
> in the purely mathematical concept of log-flat badness (important
> though it is), and without enough consideration of the fact that
we're
> dealing with _human_ abilities and perceptions in regard to _music_.
>
> You're unwilling to consider badness functions that would gradually
> roll off these extremes in a way that might correspond roughly with
> what is of musical interest to typical humans, apparently because
this
> is too "subjective".
>
> But seemingly paradoxically, you are willing to apply sharp cutoffs
to
> both complexity and error.
>
> At one stage I found points of agreement between our methods for
both
> 5 and 7 limit, i.e. I found some sharp cutoffs that happened to
agree
> with my gradual rolloffs, not on the ranking of the temperaments,
but
> at least on which were in and which were out (when suitable badness
> cutoffs were also applied).
>
> But since then you seem to have thrown the gates wide again and are
> including pico-temperaments only of interest to computers, and some
> temperaments with errors so large that sense can only be made of
them
> (if at all) by using purpose-built extremely inharmonic timbres. And
> you go so far as to give non-systematic non-descriptive names to
these.
>
> I figure that if people have specific unusual requirements for
> temperaments such as these, they can just go and find them with
> Graham's wonderful online temperament finder. There's no need to
> catalog them as if they were just as lilely to find actual musical
use
> as say porcupine or orwell. I feel a catalog or article should
include
> only those temperaments that are likely to be of _general_ musical
> interest (albeit to microtonalists only), not only of interest for a
> specific purpose such as notation or computation or synthetic
> inharmonic timbres.
>
> I have no idea how Graham feels about this issue [of how we should
> decide what to leave out], but I certainly don't find any dross in
his
> existing (although somewhat random) catalog.
>
> -- Dave Keenan

***Personally, I *love* these kinds of *musical* Dave Keenan posts!
You go Dave! Glad you're coming back around.

Joseph

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

> x = u + v
> y = (u+v)/(u-v)

Whoops--I'm having problems looking at things sideways, I guess. Should be

x = u + v
y = (u-v)/(u+v)

However I used the right values for y in when I solved it, so the rest
is OK.

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

> > If u = log2(n) and v = log2(d), then the x and y axes of your graph
> show
> >
> > x = u + v
> > y = (u+v)/(u-v)

y = (u-v)/(u+v)

> > Solving for u and v in terms of x and y gives
> >
> > u = (x + xy)/2
> > v = (x - xy)/2
> >
> > This now gives us
> >
> > n = 2^u = 2^((x + xy)/2)
> > d = 2^v = 2^((x - xy)/2)
> >
> > From this, e = log2(n-d)/log2(d) would be
> >
> > e = (2/x(y-1) log2(n-d)
>
> There seems to be a parethesis missing, and . . .

(2/(x*(y-1))) * log2(n-d)

> > which is a function of x and y.
>
> and n and d? No good.

Yes good. I expressed them as functions of x and y, after all

n(x, y) = 2^((x + xy)/2)
d(x, y) = 2^((x - xy)/2)

Hence e is a function of x and y also

e(x, y) = (2/x(y-1)) log2(n(x,y) - d(x,y))

Hence you want to plot the lines

e(x, y) = Constant

which I presume Matlab can easily handle.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > You're unwilling to consider badness functions that would gradually
> > roll off these extremes in a way that might correspond roughly with
> > what is of musical interest to typical humans, apparently because
> this
> > is too "subjective".
>
> I'm not unwilling.

Sorry I hadn't caught up.

> Let's look at the 5-limit. In my recent post (my
> first here after a long break), I essentially used the blue 'badness
> contour' here:
>
> /tuning/files/Erlich/dave2.gif

I'm afraid I find these difficult to read because I don't know very
many LTs by their vanishing commas, but rather by their generator and
period (and to a lesser extent by their mapping), and of course the
common ones by name.

Why use these heuristics based on commas when we have the actual data
for the LTs? And I can't see this approach working once we go beyond
5-limit and have more than one comma vanishing.

The heuristics are interesting in themselves but I'd rather not
complicate an already difficult task by using them.

> The red line would make Herman unhappy, while the blue one would make
> him happy, as it includes 16/15, 2187/2048, and 2109375/2097152

I don't have a problem with including 2109375/2097152 (subminor
thirds, Orwell) but am very dubious about the other two.

My approach was to modify the badness measure and then have a
badness-only cutoff. My parameterisation was
badness = complexity * exp((error/k)**p)

When the error is RMS and the complexity is odd-limit-weighted RMS
generators per diamond interval, then I have the following values for
the parameters in the 5-limit case:
k = 7.4 cents
p = 0.5
max badness = 12. What does that look like on your diagram?

For 7-limit I have:
k = 10.7 cents
p = 0.77
max badness = 16.

> (though the last one is kind of buried on the chart), and he seems to
> have found musical value in all three.

I'm starting to think Herman can find musical value in anything. :-)

> Perhaps we should make a "for
> Herman" list online but use a shorter list for our paper . . .

Sounds like a good idea.

> we still have 7-limit stuff we want to talk about . . .

Like?

Shouldn't this discussion move to tuning-math?

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> >
> > > You're unwilling to consider badness functions that would
gradually
> > > roll off these extremes in a way that might correspond roughly
with
> > > what is of musical interest to typical humans, apparently
because
> > this
> > > is too "subjective".
> >
> > I'm not unwilling.
>
> Sorry I hadn't caught up.
>
> > Let's look at the 5-limit. In my recent post (my
> > first here after a long break), I essentially used the
blue 'badness
> > contour' here:
> >
> > /tuning/files/Erlich/dave2.gif
>
> I'm afraid I find these difficult to read because I don't know very
> many LTs by their vanishing commas, but rather by their generator
and
> period (and to a lesser extent by their mapping), and of course the
> common ones by name.
>
> Why use these heuristics based on commas when we have the actual
data
> for the LTs?

Because they agree exactly, for the Tenney-weighted minimax over
*all* intervals!! This is the other stuff we've been talking about
here and on tuning-math.

> And I can't see this approach working once we go beyond
> 5-limit and have more than one comma vanishing.

We'll have to do the same thing for "bicommas".

> The heuristics are interesting in themselves but I'd rather not
> complicate an already difficult task by using them.
>
> > The red line would make Herman unhappy, while the blue one would
make
> > him happy, as it includes 16/15, 2187/2048, and 2109375/2097152
>
> I don't have a problem with including 2109375/2097152 (subminor
> thirds, Orwell) but am very dubious about the other two.

The second was used by Blackwood in a big baroque suite. 21-equal.
And surely by now you've listened to examples of the first.

> My approach was to modify the badness measure and then have a
> badness-only cutoff. My parameterisation was
> badness = complexity * exp((error/k)**p)

I prefer looking at a graph to see where the gulfs are. I think
readers would too.

> When the error is RMS and the complexity is odd-limit-weighted RMS
> generators per diamond interval, then I have the following values
for
> the parameters in the 5-limit case:
> k = 7.4 cents
> p = 0.5
> max badness = 12. What does that look like on your diagram?

With my (Tenney) complexity and (all-interval-Tenney-minimax) error
measures?

> > we still have 7-limit stuff we want to talk about . . .
>
> Like?

You already said it, more than one comma vanishing.

> Shouldn't this discussion move to tuning-math?

Yes.

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

> Yes good. I expressed them as functions of x and y, after all
>
> n(x, y) = 2^((x + xy)/2)
> d(x, y) = 2^((x - xy)/2)
>
> Hence e is a function of x and y also
>
> e(x, y) = (2/x(y-1)) log2(n(x,y) - d(x,y))

You mean (2/(x*(y-1))) log2(n(x,y) - d(x,y)), right? I did that and
the signs seem wrong . . . I then extended the contours into negative
values and at least the magnitudes look right . . . Unfortunately,
the contours crap out at 10^-4 . . . this will be a quick look . . .
red numbers, epimericity, green numbers, cents . . .

/tuning/files/Erlich/gene1.gif

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > My first reply to this seems to have vanished. Sigh.
> >
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> > > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
> wrote:
> > >
> > > > I find that you and Gene place too much emphasis on
> temperaments
> > > with
> > > > extremes of either complexity or error, apparently based on
> your
> > > faith
> > > > in the purely mathematical concept of log-flat badness
> (important
> > > > though it is), and without enough consideration of the fact
> that
> > > we're
> > > > dealing with _human_ abilities and perceptions in regard to
> _music_.
> > >
> > > I guess you haven't been reading my posts lately, Dave. No --
> > > actually you did respond to something about epimericity.
> >
> > I haven't been reading everything.
> >
> > > > But since then you seem to have thrown the gates wide again and
> are
> > > > including pico-temperaments only of interest to computers,
> > >
> > > My last few lists had nothing more complex than schismic -- which
> > > even cuts off the prized aristoxenean.
> >
> > OK. I was going by our last discussion re
> > http://tonalsoft.com/enc/eqtemp.htm
>
> In that discussion, didn't I tell you that the reason that goes so
> deep is because Monz already had some very high-numbered ETs
> mentioned there, so it seemed sensible to connect them?

Probably. And didn't I disagree about the sense of it.

> > > Herman's examples show that even the very worst of these can
> sound
> > > lovely, even "harmonic", without purpose-built timbres. Don't you
> > > agree?
> >
> > I didn't know he'd used them. URLs?
>
> http://www.io.com/~hmiller/music/warped-canon.html, scroll all the
> way to the bottom, and hear the 8-TET and 13-TET and "Top" father
> temperament "anti-pentatonic" versions of the canon.

I agree they are perfectly lovely. But I find it hilarious that you
give the generator and period of this "temperament" to 2 decimal
places of cents, when it has errors from JI of around 50 cents and is
played using timbres whose pitches are anything but sharply defined.

I think "fourth-thirds" is a much better name for this "temperament".

> > My guess, taking your word that they sound ok, is that any nearby
> MOS
> > (DE) would work just as well and it has little or nothing to do with
> > any approximation of JI.
>
> If it's nearby, it has a similar approximation of JI. So your guess
> would be hard to test.

So tell me what linear tuning _wouldn't_ be an approximation of JI
according to your criteria? Of course for Herman to warp the Canon
into it we have to tell him what the mapping is from 5-limit JI.

> But what's the big deal about listing one or
> three temperaments that have errors that may be too large according
> to some as-yet unknown criterion?
> Five, and I'd start complaining.

They make a mockery of the idea of temperament, which is to
approximate JI. I'm not even sure it makes sense to call pelogic an
approximation of 5-limit JI, but I've been willing to wear that one.
Worse errors and I start complaining.

But if you can somehow show me that these "temperaments" "work"
because of the 5-limit approximations you say they have, e.g. by
showing something similar that _doesn't_ work in the same way. e.g.
something with a generator midway between two of these extreme-error
"temperaments", then I'll reconsider.

And if you tell me this isn't testable then I'll tell you your
assertion that they _are_ 5-limit temperaments is meaningless.

> > It is names for extreme temps like father,
>
> Sounds like "Fourth-third",

It does!!! I would never have guessed that in a million years.

Even though I knew it was previously called "fourth-thirds", it never
once occurred to me that the name "father" might have been used
because it sounded like that.

> and it also "fathers" virtually all 5-
> limit temperaments of interest, along with the "mother" dicot
> and "third parent" beep.

This makes no sense to me whatsoever. And I would likewise never have
guessed it. Why is it any more of a "father" than the one in which
10/9 vanishes? Never mind.

> > beep,
>
> BP, as in Bohlen-Pierce, since 27/25 is a BP interval.

So are many others.

> Gene "fathered" this name. But nothing is set in stone.

Didn't that used to be called "limmal"?

I understand Gene coined both "limmal" and "fourth-thirds" too, what
was wrong with those names? Someone might actually figure out what
you're talking about?

I sometimes wonder if Gene's need to give things "clever" cryptic
names the moment they are discovered, is a kind of nervous tic.
Actually they are more than cryptic, they are encrypted. i.e. the
derivation works in the forward direction but there's no way anyone
would ever extract the claimed meaning from the final result.

--- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> You know guys, both sets of names could easily appear paper,
> especially if it meant keeping Dave's name off.

I'm afraid I can't make much sense of this sentence Carl.

What two sets of names? And why would using them keep my name off? And
would you consider this a good or bad thing?

I think I just made it clear that I don't care if my name is on it or
not. Paul is apparently still interested in my opinion regardless.

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

> > > > Herman's examples show that even the very worst of these can
> > sound
> > > > lovely, even "harmonic", without purpose-built timbres. Don't
you
> > > > agree?
> > >
> > > I didn't know he'd used them. URLs?
> >
> > http://www.io.com/~hmiller/music/warped-canon.html, scroll all
the
> > way to the bottom, and hear the 8-TET and 13-TET and "Top" father
> > temperament "anti-pentatonic" versions of the canon.
>
> I agree they are perfectly lovely. But I find it hilarious that you
> give the generator and period of this "temperament" to 2 decimal
> places of cents, when it has errors from JI of around 50 cents and
is
> played using timbres whose pitches are anything but sharply defined.

It's hilarious when you see all those 1-cent figures there, but it
seems most people actually

> I think "fourth-thirds" is a much better name for
>this "temperament".

I don't like it. Too many numbers, etc.

> > > My guess, taking your word that they sound ok, is that any
nearby
> > MOS
> > > (DE) would work just as well and it has little or nothing to do
with
> > > any approximation of JI.
> >
> > If it's nearby, it has a similar approximation of JI. So your
guess
> > would be hard to test.
>
> So tell me what linear tuning _wouldn't_ be an approximation of JI
> according to your criteria? Of course for Herman to warp the Canon
> into it we have to tell him what the mapping is from 5-limit JI.

In Herman's 8-equal and somewhat in the top-father examples, the
triads remain recognizable to me, and really seem like they're
creating a shimmery, rough-5-limit harmony. If you don't agree, I'll
gladly accept a 'badness contour' that excludes this temperament.

> > But what's the big deal about listing one or
> > three temperaments that have errors that may be too large
according
> > to some as-yet unknown criterion?
> > Five, and I'd start complaining.
>
> They make a mockery of the idea of temperament, which is to
> approximate JI. I'm not even sure it makes sense to call pelogic an
> approximation of 5-limit JI, but I've been willing to wear that one.
> Worse errors and I start complaining.

I'll concede, if your *ears* are strongly telling you this story. And
note that you still may, someday, be convinced by something new.

> But if you can somehow show me that these "temperaments" "work"
> because of the 5-limit approximations you say they have, e.g. by
> showing something similar that _doesn't_ work in the same way. e.g.
> something with a generator midway between two of these extreme-error
> "temperaments", then I'll reconsider.

Give Herman an example!

> > and it also "fathers" virtually all 5-
> > limit temperaments of interest, along with the "mother" dicot
> > and "third parent" beep.
>
> This makes no sense to me whatsoever. And I would likewise never
have
> guessed it. Why is it any more of a "father" than the one in which
> 10/9 vanishes?

That's more of a "grandfather". But look at the ET graph in the sense
of a 3-d scale tree, and you'll see that all the action is generated
by 3, 4, and 5-equal, which are connected by these three temperaments.

Never mind.
>
> > > beep,
> >
> > BP, as in Bohlen-Pierce, since 27/25 is a BP interval.
>
> So are many others.
>
> > Gene "fathered" this name. But nothing is set in stone.
>
> Didn't that used to be called "limmal"?

Asking for confusion with Blackwood (256/243 is called a "limma").

> I understand Gene coined both "limmal" and "fourth-thirds" too, what
> was wrong with those names? Someone might actually figure out what
> you're talking about?
>
> I sometimes wonder if Gene's need to give things "clever" cryptic
> names the moment they are discovered, is a kind of nervous tic.

Can we at least try to like each other if we're going to be working
together?

> Actually they are more than cryptic, they are encrypted. i.e. the
> derivation works in the forward direction but there's no way anyone
> would ever extract the claimed meaning from the final result.

I think you're talking about me, not Gene.

>I agree they are perfectly lovely. But I find it hilarious that you
>give the generator and period of this "temperament" to 2 decimal
>places of cents, when it has errors from JI of around 50 cents

Pardon me for butting in, but I think you overlook something in
this, Dave. Temperament isn't just about approximating JI with
limited resources. If it were someone like Gene, whose tools
aren't limited by key levers and the like, might simply use JI.
Rather, temperament is also valuable for the tricks its plays on
the ear, and at this one can even argue the high-error
temperaments are superior.

>They make a mockery of the idea of temperament, which is to
>approximate JI.

No, not only. For one things temperaments represent families
of periodicity blocks that can be left untempered, transformed
into one another with comma jumps, etc.

>I sometimes wonder if Gene's need to give things "clever" cryptic
>names the moment they are discovered, is a kind of nervous tic.
>Actually they are more than cryptic, they are encrypted. i.e. the
>derivation works in the forward direction but there's no way
>anyone would ever extract the claimed meaning from the final
>result.

Why do this? Haven't we already discussed the similar remarks
that can be made about your desire to name everything
systematically?

-Carl

>> You know guys, both sets of names could easily appear paper,
>> especially if it meant keeping Dave's name off.
>
>I'm afraid I can't make much sense of this sentence Carl.

Whoops, "paper" belonged at the end of the second line, not
the first.

>What two sets of names?

The systematic and the cute ones.

>And why would using them keep my name off? And
>would you consider this a good or bad thing?

If you objected to your name being on, and I certainly would
like to see your name on, if indeed said paper ever gets
written.

>I think I just made it clear that I don't care if my name is
>on it or not. Paul is apparently still interested in my
>opinion regardless.

Well ok then, carry on.

-Carl

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

> I think I just made it clear that I don't care if my name is on it
or
> not.

If you're willing to continue helping work on it, then I'd very much
like to see your name on it. If not, you'll get a real big
acknowledgement anyway..

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

> But if you can somehow show me that these "temperaments" "work"
> because of the 5-limit approximations you say they have, e.g. by
> showing something similar that _doesn't_ work in the same way. e.g.
> something with a generator midway between two of these extreme-error
> "temperaments",

That "midway generator" system probably won't be a temperament! That
is, it probably won't temper anything out, so it would have to count
as having the highest complexity.

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

> > And I can't see this approach working once we go beyond
> > 5-limit and have more than one comma vanishing.
>
> We'll have to do the same thing for "bicommas".

If my analysis on tuning-math is correct it doesn't depend on the
commas, just on the temperament, and should work fine.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > > And I can't see this approach working once we go beyond
> > > 5-limit and have more than one comma vanishing.
> >
> > We'll have to do the same thing for "bicommas".
>
> If my analysis on tuning-math is correct it doesn't depend on the
> commas, just on the temperament, and should work fine.

I don't see what distinction you're trying to make. By "bicomma" I
meant a wedgie of any pair of commas forming a basis for the kernel
of the temperament, which shouldn't depend on which pair you choose.

Please respond on tuning-math.

on 1/6/04 9:28 AM, Jon Szanto <JSZANTO@ADNC.COM> wrote:

> Gene,
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>> By the time I get around to deciding if it "works", I've already
>> analyzed the chords; the "works" part is simply a "works for me"
>> judgment. There wasn't anything wrong with the chords in the
>> porcupine version of Love Death, I just found I didn't like it as
>> much as I hoped I would. I'm happier with Mahler #7.
>
> I guess I find it... perplexing? baffling? (I don't know what the proper
> descriptor would be) that for all of the 'science' that has gone into the
> development of the various temperments/tunings you've been working on in the
> last few years, which (of course) contain all manner of detailed mathematic
> steps in their genesis (if you will)... That for all of the preceding it winds
> up being a grab bag of tunings that you throw against a piece to see what
> sticks!
>
> I'm not using that rather flip phrase in a derogatory manner, but while I can
> see that it might be a more direct procedure to pick a tuning for a particular
> baroque piece in a certain key, I guess I had assumed that when you were
> generating all these retuned 'classics' there was a generalized method behind
> it. Mind you, I find nothing wrong with a "works for me" paradigm, but it
> seems to be the polar extreme from the rigor with which you have developed the
> tunings. Maybe it is simply the 'art' part in the art and science of music.

Its great to see a person not *appearing* to be consistent in all ways.

-Kurt

>
> Cheers,
> Jon

In a message dated 2004:01:08 12:27:50 AM, sharp ol' keenan writes:

> [....]and some temperaments with errors so large that sense can only be
made of >them (if at all) by using purpose-built extremely inharmonic timbres. [.
. .]

In a message dated 2004:01:08 01:08:13 AM, paul-E writes:

>Herman's examples show that even the very worst of these can sound
>lovely, even "harmonic", without purpose-built timbres. Don't you
>agree?

Big favs with me - recently I have been "collecting" tons of data on
them. I, of course, want more data to add to my "toybox"... thus more to play
with...

>I figure that if people have specific unusual requirements for
>temperaments such as these, they can just go and find them with
>Graham's wonderful online temperament finder. There's no need to
>catalog them as if they were just as lilely to find actual musical use
>as say porcupine or orwell. I feel a catalog or article should include
>only those temperaments that are likely to be of _general_ musical
>interest (albeit to microtonalists only), not only of interest for a
>specific purpose such as notation or computation or synthetic
>inharmonic timbres.

Eh? "Actual musical use"? Do I detect a subtle "Euro-tonality/theory
bias" here?
Or what? ::just wantin' some clarification of this above statement/opin....::
See how our linguistic jargon/arcana messes with our heads?

>I have no idea how Graham feels about this issue [of how we should
>decide what to leave out], but I certainly don't find any dross in his
>existing (although somewhat random) catalog.

LMAOROTF I think Breed's randomness is actually "poetic"... If it was
more orderly, I think his website wouldn't be that intriguing... or colourful,
esp'ly since he is not tryin' to be "encyclopedic" like Monz's. And Herman
Miler's pages are sorta like the Middle Path...

---|-----|--------|-------------|---------------------|
Hanuman Zhang, musical mad scientist

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

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

/tuning/topicId_51065.html#51248

> I sometimes wonder if Gene's need to give things "clever" cryptic
> names the moment they are discovered, is a kind of nervous tic.
> Actually they are more than cryptic, they are encrypted. i.e. the
> derivation works in the forward direction but there's no way anyone
> would ever extract the claimed meaning from the final result.

***Personally, I just feel Gene is having fun with this. There is
no problem with that, but if we are developing terms to be seriously
used in practical microtonality, maybe we should think twice (or
come to a vote... :)

And, I used the title _Beepy_ for my Bohlen-Pierce piece of a couple
of years ago.

:)

J. Pehrson

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

> ***Personally, I just feel Gene is having fun with this.

My main consideration is coming up with names I can remember.

Dave Keenan wrote:

> I have no idea how Graham feels about this issue [of how we should
> decide what to leave out], but I certainly don't find any dross in his
> existing (although somewhat random) catalog.

I thought at the time it was better to write something up instead of spending all that time deciding which temperaments should be listed or not. And the fact that years have gone by with still no paper suggests I was right to be concerned. I wonder if the new Xenharmonikon will continue to be postponed long enough for us to get our act together.

My own write up does have to be improved, because last time people did point out things that weren't clear.

I'm all for teaching a man how to fish, instead of giving him a choice of 100 different freshwater fish that you've selected as being possibly interesting. Especially if the only one he's ever eaten before is trout, which he didn't like much anyway, and he has no idea about the other ones. So he's probably more interested in an excuse to sit by the river than actually eating fish.

Not that I encourage blood sports, but I hope that clears up my position.

Graham

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

>> I sometimes wonder if Gene's need to give things "clever" cryptic
>> names the moment they are discovered, is a kind of nervous tic.

>> Actually they are more than cryptic, they are encrypted. i.e. the
>> derivation works in the forward direction but there's no way anyone
>> would ever extract the claimed meaning from the final result.

I think they are not only poetic, but mnemonic and nice&short -
additionally - for some of them, somehow appropriate.

... and before I even get done with this email, Gene - the Man of the Hour -
sends his confession:

>My main consideration is coming up with names I can remember.

LOL

In a message dated 2004:01:08 02:53:18 PM, joe p. writes:

>***Personally, I just feel Gene is having fun with this. There is
>no problem with that, but if we are developing terms to be seriously
>used in practical microtonality, maybe we should think twice (or
>come to a vote... :)

Well, belle in hell!, if the quantum phys boys (& grrlies) can get away
with addin' a lil _flavour_ and _colour_ to their _quarks_ , _charms_ and
general _strangeness_ , we already do much more so than they! HiphipHuRRaH!

Yes yes I think Gene is having waaaay too much fun. (gimme some that,
you...)

OBTUNING: Throbbing Cthonic Bleu [TCB] (my name for 2nd root of 8/7)
Notice the mutated iconism of the 3 lettres _TCB_ and
mathophobe's nightmare of _2nd root of 8/7_... (Oh just squint your eyes, insomniac
unimaginative ones...)

--- º°`°º ø,¸¸,ø º°`°º ø,¸¸,ø º°`°º ø,¸¸,ø º°`°º º°`°º ø,¸~->

Hanuman "Mister Sinister" Zhang, Sloth-Style Gungfu Typist
- "the sloth is a chinese poet upsidedown" --- Jack Kerouac {1922-69}

"One thing foreigners, computers, and poets have in common
is that they make unexpected linguistic associations." --- Jasia Reichardt

"There is no reason for the poet to be limited to words, and in fact the
poet is most poetic when inventing languages. Hence the concept of the poet as
'language designer'." --- O. B. Hardison, Jr.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > ***Personally, I just feel Gene is having fun with this.
>
> My main consideration is coming up with names I can remember.

I think that's the key point. Herman is wanting to work with names,
not concatenated sets of numbers like "fourth-thirds" or anything
like that. We all know what meantone is. What's porcupine? You can
ascribe a set of numbers to it to describe it, but that won't help
you remember it. It's just a cute name in a long undifferentiated
list of cute names, basically meaningless. But work with it for a
while for composing/improvising, and you'll have a *musical* image of
the tuning to associate with the word "porcupine". The name becomes a
reminder of the *sound* (including chord progressions, etc.) of the
tuning, and it's much harder to get confused, once you've done this,
than if all you have are a bunch of similar-sounding, numerically-
oriented names for the different tunings. Especially for most people
I've met, who are much worse at remembering numbers (such as phone
numbers) than I am, but have an easier time remembering people's
names after first meeting them.

Of course, that's just my little itty-bitty humble opinion.

--- In tuning@yahoogroups.com, Graham Breed <graham@m...> wrote:

> I'm all for teaching a man how to fish, instead of giving him a
choice
> of 100 different freshwater fish that you've selected as being
possibly
> interesting. Especially if the only one he's ever eaten before is
> trout, which he didn't like much anyway, and he has no idea about
the
> other ones. So he's probably more interested in an excuse to sit
by the
> river than actually eating fish.
>
> Not that I encourage blood sports, but I hope that clears up my
position.
>
>
> Graham

How about teaching a man how to fish *and* giving him trout plus 12
or so other kinds of fish?

--- In tuning@yahoogroups.com, czhang23@a... wrote:

> Well, belle in hell!, if the quantum phys boys (& grrlies)

my former classmates!

> can get away
> with addin' a lil _flavour_ and _colour_ to their _quarks_ ,
>_charms_ and
> general _strangeness_ , we already do much more so than they!
>HiphipHuRRaH!

That's the spirit. And (off topic) I, an avid reader of Scientific
American, had to wait 6 months for that freakin' rag Discover to come
out with their recap-of-2003 issue before I found out about the
pentaquark:
http://news.bbc.co.uk/1/hi/sci/tech/3034754.stm

wallyesterpaulrus wrote:

> How about teaching a man how to fish *and* giving him trout plus 12 > or so other kinds of fish?

Yes, but the poor man's been waiting for a couple of years now and he still doesn't have either! Whereas he's had plenty of opportunities to further his interest in hamburgers.

Graham

>> How about teaching a man how to fish *and* giving him trout plus 12
>> or so other kinds of fish?
>
>Yes, but the poor man's been waiting for a couple of years now and he
>still doesn't have either! Whereas he's had plenty of opportunities to
>further his interest in hamburgers.

Paul's 5-limit database constitutes 5-limit fish, with a little
explanatory stuff that's mostly been written. The teaching-how-to-fish,
however, is clearly much more work. Nobody's yet come close.

In any case, it seems that this TOP business has to settle somewhat
before anything else. And if I were you guys I'd at least consider
journals other than XH.

-Carl

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

> Paul's 5-limit database constitutes 5-limit fish, with a little
> explanatory stuff that's mostly been written. The teaching-how-to-
fish,
> however, is clearly much more work. Nobody's yet come close.

What did you have in mind?

> In any case, it seems that this TOP business has to settle somewhat
> before anything else. And if I were you guys I'd at least consider
> journals other than XH.

Yes, it seems that the XH era is ending, and even 1/1 always got more
circulation anyway. I'd like the co-authors to think big, and check
out as many issues of the Journal of Music Theory as they can, as
nauseating as it might be.

>> Paul's 5-limit database constitutes 5-limit fish, with a little
>> explanatory stuff that's mostly been written. The teaching-how-to-
>fish,
>> however, is clearly much more work. Nobody's yet come close.
>
>What did you have in mind?

A 'for-dummies' how-to identify, search for and optimize temperaments
and turn them in to scales. Definitions of epimericity, epimorphic,
how to use wedgies, etc. Probably a Grassman algebra primer for
total dummies would have to be a subset.

>> In any case, it seems that this TOP business has to settle somewhat
>> before anything else. And if I were you guys I'd at least consider
>> journals other than XH.
>
>Yes, it seems that the XH era is ending,

It is? I love XH, it's art to me. I have a complete set plus some
dupes. There are issues I'd like to hang on the wall. In fact, I
think I'll do that...

>I'd like the co-authors to think big, and check
>out as many issues of the Journal of Music Theory as they can, as
>nauseating as it might be.

Indeed. If the paper referenced a XH article or two and was published
in say, the Journal of Music Theory, it would be wonderful.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Paul's 5-limit database constitutes 5-limit fish, with a little
> >> explanatory stuff that's mostly been written. The teaching-how-
to-
> >fish,
> >> however, is clearly much more work. Nobody's yet come close.
> >
> >What did you have in mind?
>
> A 'for-dummies' how-to identify, search for and optimize
temperaments
> and turn them in to scales. Definitions of epimericity, epimorphic,
> how to use wedgies, etc. Probably a Grassman algebra primer for
> total dummies would have to be a subset.

Ouch -- I think you're talking about a book, not an article. I see no
reason for most of this stuff.

> Indeed. If the paper referenced a XH article or two and was
published
> in say, the Journal of Music Theory, it would be wonderful.

XH has been referenced in PNM, at least (Bob Gilmore's article) . . .

>> >What did you have in mind?
>>
>> A 'for-dummies' how-to identify, search for and optimize
>> temperaments and turn them in to scales. Definitions of
>> epimericity, epimorphic, how to use wedgies, etc. Probably
>> a Grassman algebra primer for total dummies would have
>> to be a subset.
>
>Ouch -- I think you're talking about a book, not an article. I see no
>reason for most of this stuff.

Most? The Grassman Algebra primer is the only part I see as
optional. And perhaps "working with matrices" would be a better
title for the scope I had in mind for that -- something that shows
briefly, with examples, how to represent a temperament as a bunch
of vals, wedge them, find monzos, etc. It seems fairly necessary
if you want people to be able to "fish".

A book, an article, it's all the same in pdf.

-Carl

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

> Paul's 5-limit database constitutes 5-limit fish, with a little
> explanatory stuff that's mostly been written. The teaching-how-to-fish,
> however, is clearly much more work. Nobody's yet come close.

No one likes my explanations for things, so I think I can't be the one
to kick the ball off. However, if I get some feedback on my web site
stuff from the point of view of a potential article it would help.

If Paul wrote a draft, that would be a beginning.

> In any case, it seems that this TOP business has to settle somewhat
> before anything else. And if I were you guys I'd at least consider
> journals other than XH.

I agree; I'd like something mainstream theorists would at least see,
if not understand.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >What did you have in mind?
> >>
> >> A 'for-dummies' how-to identify, search for and optimize
> >> temperaments and turn them in to scales. Definitions of
> >> epimericity, epimorphic, how to use wedgies, etc. Probably
> >> a Grassman algebra primer for total dummies would have
> >> to be a subset.
> >
> >Ouch -- I think you're talking about a book, not an article. I see
no
> >reason for most of this stuff.
>
> Most? The Grassman Algebra primer is the only part I see as
> optional. And perhaps "working with matrices" would be a better
> title for the scope I had in mind for that -- something that shows
> briefly, with examples, how to represent a temperament as a bunch
> of vals, wedge them, find monzos, etc. It seems fairly necessary
> if you want people to be able to "fish".

I'm not yet convinced of that. But this discussion belongs on tuning-
math anyway, since that's where this was all spawned (pun partially
intended).

> A book, an article, it's all the same in pdf.

It's easier to get an article than book published to reach more of
the people that we aren't reaching on the internet.

On Thu, 08 Jan 2004 04:10:17 -0000, "Dave Keenan" <d.keenan@bigpond.net.au>
wrote:

>> The red line would make Herman unhappy, while the blue one would make
>> him happy, as it includes 16/15, 2187/2048, and 2109375/2097152
>
>I don't have a problem with including 2109375/2097152 (subminor
>thirds, Orwell) but am very dubious about the other two.

I wouldn't put too much effort into trying to accommodate Orwell (I prefer
the Monzo notation [-21 3 7] over the impossible to remember ratios of
large integers) or Negri [-14 3 4] as far as the 5-limit list goes. As far
as the other two, 16/15 has its uses, but it's more of interest for its
exotic melodic properties than its questionable harmonies; 27/25, which is
next to it on the graph, doesn't have much to recommend it, although it
does have a sort of pelog approximation. 2187/2048 [-11 7] is probably of
more general interest, especially considering its use in Blackwood's 21-ET
etude, and fits between meantone and pelogic on the temperament chart. It's
only marginally better than pelogic, but the circle of fifths closing after
7 steps is a really nice property, and it's a much more natural progression
in traditional harmony than other commas of a similar level of complexity.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

On Thu, 08 Jan 2004 02:58:29 -0000, "Dave Keenan" <d.keenan@bigpond.net.au>
wrote:

>If they "convey much musical meaning (like "diminished", "augmented",
>etc.)" then they are "descriptive names" and I am not objecting to
>them. And I've even stopped objecting to silly names when they are for
>middle-of-the-road temperaments that have actually been used in music.
>
>It is names for extreme temps like father, beep, pirate, raider etc.
>that I find pointless.
>
>I propose not naming LTs with extreme complexity or error at all!
>
>I'd rather have them described by their generator and period, or their
>mapping.

As far as "father" and "dicot", the commas are simple enough (16;15, 25;24)
that it might be easiest to refer to them by the commas (or in the case of
"dicot", the more useful name "neutral thirds"). But if for instance
someone mentions the "442.2 cent generator" temperament, that doesn't seem
to convey much useful information (beyond what's necessary to tune it in
Scala). How is that different from a temperament with a 442.9 cent
generator? It's not immediately apparent. The mapping [(1, 0), (2, -1), (2,
1)] might be more useful as a general naming convention for linear
temperaments. It's clear that this isn't very similar to the [(1, 0), (-1,
7), (-1, 9)] temperament (which is "semisixths" with a generator around
442.9 cents and a [2 9 -7] comma) even though the generator is about the
same size.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

Could you (and Dave) give a list of desired commas?

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> On Thu, 08 Jan 2004 02:58:29 -0000, "Dave Keenan" <d.keenan@b...>
> wrote:
> >I propose not naming LTs with extreme complexity or error at all!
> >
> >I'd rather have them described by their generator and period, or their
> >mapping.
>
> As far as "father" and "dicot", the commas are simple enough (16;15,
25;24)
> that it might be easiest to refer to them by the commas (or in the
case of
> "dicot", the more useful name "neutral thirds").

It used to be called "neutral thirds". Why was it changed? It might
also be called "minor major thirds" in the same sense in which
"father" could be (and was) called "fourth thirds". Incidentally,
these are not numbers but names of intervals. (Paul said it was
changed to father because "fourth thirds" had too many numbers).

> But if for instance
> someone mentions the "442.2 cent generator" temperament, that
doesn't seem
> to convey much useful information (beyond what's necessary to tune it in
> Scala).

I think you'd have to admit that is pretty useful information. It's
not much good if you can't tune it.

But I would generally not use decimal places of cents here, and I
would not bother with the word "generator". So I might say "442 cent
temperament". But actually, I would only use cents here as a last
resort. I prefer to describe the generator in terms of the just
interval it approximates _according_to_the_mapping_. In this case we
find it represents both the major third and the perfect fourth, which
is why "fourth thirds" is such an appropriate name.

If the period isn't mentioned then it is the octave and if it is a
fraction of an octave then the appropriate multiple word is used
first: twin (or double), triple, quadruple etc.

> How is that different from a temperament with a 442.9 cent
> generator?

I agree that merely calling it the 443 cent temperament isn't much
help in distinguishing it if the above is called the 442 cent
temperament. However, even if they were both 443 to the nearest cent,
one of them clearly has much lower badness than the other. I propose
that the best one gets the unqualified name and the other gets
qualified according to whether it is more complex than the other e.g.
"the complex 443 cent temperament", or in this case less accurate than
the other "the inaccurate 443 cent temperament". I think I found a
better word than "inaccurate" once, but I've forgotten it. I suppose
you could say "the simple 443 cent temperament".

But once again I'd prefer to name it after what just interval the
generator approximates _according_to_the_mapping_.

>It's not immediately apparent. The mapping [(1, 0), (2, -1), (2,
> 1)] might be more useful as a general naming convention for linear
> temperaments.

Only if you shortened it to the octave-equivalent [-1, 1] ...

> It's clear that this isn't very similar to the [(1, 0), (-1,
> 7), (-1, 9)]

... and [7, 9].

> temperament (which is "semisixths" with a generator around
> 442.9 cents and a [2 9 -7] comma) even though the generator is about the
> same size.

Here we find that a single generator does not approximate any 5-limit
consonance. i.e. When we look at the coefficients in the
octave-equivalent mapping, and the difference between any pair, we
find the smallest absolute value we can get is 2 (= 9-7) and we figure
out (octave specifically now) that two generators approximates a major
sixth (3:5), which is why we call it "semisixths".

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >I agree they are perfectly lovely. But I find it hilarious that you
> >give the generator and period of this "temperament" to 2 decimal
> >places of cents, when it has errors from JI of around 50 cents
>
> Pardon me for butting in, but I think you overlook something in
> this, Dave. Temperament isn't just about approximating JI with
> limited resources. If it were someone like Gene, whose tools
> aren't limited by key levers and the like, might simply use JI.
> Rather, temperament is also valuable for the tricks its plays on
> the ear,

I totally agree with the above, but not the following.

> and at this one can even argue the high-error
> temperaments are superior.

My ears don't find any such tricks in Herman's Warped Canon in the
"fourth thirds" linear tuning. I just hear intrigueing simultaneous
melodies, not approximations of familiar harmonies (or any harmonies).
They are intrigueing because they are in an unfamiliar scale. I hear
no puns.

> >They make a mockery of the idea of temperament, which is to
> >approximate JI.
>
> No, not only. For one things temperaments represent families
> of periodicity blocks that can be left untempered, transformed
> into one another with comma jumps, etc.

So something that isn't tempered can be called a temperament? That
reminds me of the guy who proved black was white, and got killed on
the next zebra-crossing. -- Douglas Adams

> >I sometimes wonder if Gene's need to give things "clever" cryptic
> >names the moment they are discovered, is a kind of nervous tic.
> >Actually they are more than cryptic, they are encrypted. i.e. the
> >derivation works in the forward direction but there's no way
> >anyone would ever extract the claimed meaning from the final
> >result.
>
> Why do this? Haven't we already discussed the similar remarks
> that can be made about your desire to name everything
> systematically?

I don't think you just discussed remarks that can be made, I think you
_made_ them, and I took them to heart and have eased off on promoting
systematic naming of extreme temperaments (extreme in either error or
complexity) and I am now just suggesting we hold off naming them until
it actually becomes necessary.

We already have a bunch of temperaments that were named (by Gene) when
they were first discovered, and now they have been renamed (by Gene)
apparently because people have learnt more now and found some problems
with the first names. I'm having trouble keeping up.

IMHO, the best time for standardisation is after the research is
fairly complete, and just before it starts being used in earnest.

As I've pointed out elsewhere, 3 years elapsed between describing the
"chain of minor thirds" temperament and giving it the name "kleismic".

But I do need to watch my acid wit (or "exquisite arrogance" :-), and
I'm sorry if you found the "nervous tic" remark hurtful Gene.

Gene, There are many things I admire about you. Your mathematical
brilliance, your tenacity and your stand for peace and tolerance in
the world. (I read some pieces in other forums that I assume were by
the same Gene Ward Smith).

Also, I must say that I now understand that you had no expectation
that anyone be able to unpack the meaning from the names you give
(which is what I would prefer) but rather you expect to have to
explain the cryptic derivation of each one, and you only hope that
this will serve as a mnemonic. In that case, it would be useful if, in
any table of temperaments that uses such names, you include a column
giving these mnemonic derivations.

-- Dave Keenan

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > So tell me what linear tuning _wouldn't_ be an approximation of JI
> > according to your criteria? Of course for Herman to warp the Canon
> > into it we have to tell him what the mapping is from 5-limit JI.
...
> > But if you can somehow show me that these "temperaments" "work"
> > because of the 5-limit approximations you say they have, e.g. by
> > showing something similar that _doesn't_ work in the same way. e.g.
> > something with a generator midway between two of these extreme-error
> > "temperaments", then I'll reconsider.
>
> Give Herman an example!

I don't know how to. And I think the onus is on you to provide
examples of linear tunings which do _not_ sound like 5-limit
temperaments to you when treated in the same was as the "father" examples.

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

> We already have a bunch of temperaments that were named (by Gene)
when
> they were first discovered, and now they have been renamed (by Gene)
> apparently because people have learnt more now and found some
problems
> with the first names. I'm having trouble keeping up.

I'm not responsible for all temperament names and even less for new
names.

> Also, I must say that I now understand that you had no expectation
> that anyone be able to unpack the meaning from the names you give
> (which is what I would prefer) but rather you expect to have to
> explain the cryptic derivation of each one, and you only hope that
> this will serve as a mnemonic.

Right. They are supposed to be names, not formulas.

In that case, it would be useful if, in
> any table of temperaments that uses such names, you include a column
> giving these mnemonic derivations.

That's a thought, but they don't always have a mnemomic derivation.

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

> My ears don't find any such tricks in Herman's Warped Canon in the
> "fourth thirds" linear tuning. I just hear intrigueing simultaneous
> melodies, not approximations of familiar harmonies (or any
harmonies).
> They are intrigueing because they are in an unfamiliar scale. I hear
> no puns.

What do "puns" sound like? When the diatonic scale is reduced to only
5 notes, and previously different notes in the tune become the same,
are there any criteria for "punning" that are not audibly satisfied?

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> > On Thu, 08 Jan 2004 02:58:29 -0000, "Dave Keenan" <d.keenan@b...>
> > wrote:
> > >I propose not naming LTs with extreme complexity or error at all!
> > >
> > >I'd rather have them described by their generator and period, or
their
> > >mapping.
> >
> > As far as "father" and "dicot", the commas are simple enough
(16;15,
> 25;24)
> > that it might be easiest to refer to them by the commas (or in the
> case of
> > "dicot", the more useful name "neutral thirds").
>
> It used to be called "neutral thirds". Why was it changed? It might
> also be called "minor major thirds" in the same sense in which
> "father" could be (and was) called "fourth thirds". Incidentally,
> these are not numbers but names of intervals. (Paul said it was
> changed to father because "fourth thirds" had too many numbers).

Paul knew all too well that they were names of intervals --
*diatonic* names of intervals, in fact -- but they were numbers
nonetheless.

Besides, all these generators are only defined once you impose octave
repetition on the temperament. If we're talking about naming the
temperament in general, without an assumption of octave repetition,
then the choice of generators is not unique, and it's an even worse
idea to attempt to name the temperaments after them.

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

> I don't know how to. And I think the onus is on you to provide
> examples of linear tunings which do _not_ sound like 5-limit
> temperaments to you when treated in the same was as the "father"
>examples.

The treatment was a mapping from 5-limit JI to the temperament; how
are you supposed to do this if the tuning you want to use is not a
temperament?

>But I would generally not use decimal places of cents here, and I
>would not bother with the word "generator". So I might say "442 cent
>temperament". But actually, I would only use cents here as a last
>resort. I prefer to describe the generator in terms of the just
>interval it approximates _according_to_the_mapping_. In this case we
>find it represents both the major third and the perfect fourth, which
>is why "fourth thirds" is such an appropriate name.
>
>If the period isn't mentioned then it is the octave and if it is a
>fraction of an octave then the appropriate multiple word is used
>first: twin (or double), triple, quadruple etc.

What about planar temperaments? And how do you distinguish between
different maps with the same size generator?

>But once again I'd prefer to name it after what just interval the
>generator approximates _according_to_the_mapping_.

You mean what diatonic interval?

-Carl

>> Pardon me for butting in, but I think you overlook something in
>> this, Dave. Temperament isn't just about approximating JI with
>> limited resources. If it were someone like Gene, whose tools
>> aren't limited by key levers and the like, might simply use JI.
>> Rather, temperament is also valuable for the tricks its plays on
>> the ear,
>
>I totally agree with the above, but not the following.
>
>> and at this one can even argue the high-error
>> temperaments are superior.
>
>My ears don't find any such tricks in Herman's Warped Canon in the
>"fourth thirds" linear tuning. I just hear intrigueing simultaneous
>melodies, not approximations of familiar harmonies (or any harmonies).
>They are intrigueing because they are in an unfamiliar scale. I hear
>no puns.

Nor do I. But retuning an arbitrary piece (and how? I wonder if
he's going through the map or just doing a 12-tone substitution...)
isn't a good test. To justify my statement, consider super-accurate temperaments like 612. I don't think you'd discern any puns at all.
There has to be some error to get a pun (or the pun can be turned
into a shift and the vertical tuning left just).

>> >They make a mockery of the idea of temperament, which is to
>> >approximate JI.
>>
>> No, not only. For one things temperaments represent families
>> of periodicity blocks that can be left untempered, transformed
>> into one another with comma jumps, etc.
>
>So something that isn't tempered can be called a temperament? That
>reminds me of the guy who proved black was white, and got killed on
>the next zebra-crossing. -- Douglas Adams

I *love* Adams by the way. No, something that isn't tempered
shouldn't be called a temperament. I said *family* of periodicity
blocks. You wouldn't call any one of them temperament, or even
the practice of morphing between them. But you could say a
temperament governed such a practice.

>> >I sometimes wonder if Gene's need to give things "clever" cryptic
>> >names the moment they are discovered, is a kind of nervous tic.
>> >Actually they are more than cryptic, they are encrypted. i.e. the
>> >derivation works in the forward direction but there's no way
>> >anyone would ever extract the claimed meaning from the final
>> >result.
>>
>> Why do this? Haven't we already discussed the similar remarks
>> that can be made about your desire to name everything
>> systematically?
>
>I don't think you just discussed remarks that can be made, I think you
>_made_ them, and I took them to heart and have eased off on promoting
>systematic naming of extreme temperaments (extreme in either error or
>complexity) and I am now just suggesting we hold off naming them until
>it actually becomes necessary.

Just for the record, in that thread I first made those remarks about
*myself*, but I wrote ambiguously and you thought I was talking
about you (which I was, indirectly).

>We already have a bunch of temperaments that were named (by Gene) when
>they were first discovered, and now they have been renamed (by Gene)
>apparently because people have learnt more now and found some problems
>with the first names. I'm having trouble keeping up.

I've had that trouble too, but that's ok because I'm essentially
peaking into a pre-publication process.

-Carl

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > I don't know how to. And I think the onus is on you to provide
> > examples of linear tunings which do _not_ sound like 5-limit
> > temperaments to you when treated in the same was as the "father"
> >examples.
>
> The treatment was a mapping from 5-limit JI to the temperament; how
> are you supposed to do this if the tuning you want to use is not a
> temperament?

Good question? Does this mean your claim is untestable and therefore
vacuous?

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> What about planar temperaments?

I'd probably name these after the two best linear temps that produce
it. I also suggested calling the most important one (miracle-meantone)
"byzantine". But lets not get ahead of ourselves.

> And how do you distinguish between
> different maps with the same size generator?

I explained that here.
/tuning/topicId_51065.html#51338

The one with the lowest badness gets the unqualified name and the
others get "complex" or "simple" prepended depending on their
complexity relative to the lowest badness one, and if more such
qualifiers are needed, then supercomplex, hypercomplex, ultracomplex
and supersimple, hypersimple, ultrasimple. Any reasonable badness
measure will work for this since they usually differ widely.

> >But once again I'd prefer to name it after what just interval the
> >generator approximates _according_to_the_mapping_.
>
> You mean what diatonic interval?

No, I name after the just interval, or at least the diamond interval,
that is approximated by the fewest generators. I prefer to use the
extended-diatonic names for these intervals, after Fokker, because it
is basically the only game in town. Possibly further extending these
using the miracle/72-ET-based scheme outlined here.
http://dkeenan.com/Music/Miracle/MiracleIntervalNaming.txt
Or simply using the ratio if the words "wide" or "narrow" would
otherwise need to be used in the miracle/72-ET scheme, or if the ratio
is outside the 11-limit diamond.

For me these extended-diatonic interval names long ago ceased to refer
to numbers of steps (plus one - yuck) and are merely names of
particular dyadic _sounds_. I think that is true for most microtonalists.

I know you (and Paul?) want to redefine these terms (e.g. third,
fourth, fifth, octave) in other linear temperaments so that they refer
to the number-of-steps-plus-one in the 5-to-10-note MOS (or "natural"
nominals) of that temperament, but I think this is doomed to failure.
I just can't see people calling an approximate 1:2 a fifth in some
cases and a tenth in others, and everything in between.

I think an approximate 1:2 will always be an octave. I think we're
just going to have to come up with some other way of referring to the
number of steps in the "natural MOS" of a non-diatonic temperament,
and while we're at it we might fix the off-by-one problem so the
arithmetic works properly.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > What about planar temperaments?
>
> I'd probably name these after the two best linear temps that produce
> it.

Two linear temperaments don't necessarily produce a planar
temperament. Three linearly independent vals will do so.

I also suggested calling the most important one (miracle-meantone)
> "byzantine". But lets not get ahead of ourselves.

And people objected. I've proposed "marvel" as a name. What do you
think?

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Nor do I. But retuning an arbitrary piece (and how? I wonder if
> he's going through the map or just doing a 12-tone substitution...)
> isn't a good test.

Not entirely arbitrary, it is a piece that uses 5-limit harmony and
works in strict 5-limit JI. I assumed he was going thru the map, at
least in the cases of these claimed 5-limit linear temperaments.

> To justify my statement, consider super-accurate temperaments like
612. I don't think you'd discern any puns at all.
> There has to be some error to get a pun (or the pun can be turned
> into a shift and the vertical tuning left just).

Agreed, but I think that with increasing error there comes a point
where the ear/brain can no longer bend things to fit the familiar
frameworks (even when we assist it by using inharmonic timbres to make
the "implied fundamentals" vague), and so any possibility of "double
meanings" is lost.

> >> >They make a mockery of the idea of temperament, which is to
> >> >approximate JI.
> >>
> >> No, not only. For one things temperaments represent families
> >> of periodicity blocks that can be left untempered, transformed
> >> into one another with comma jumps, etc.
> >
> >So something that isn't tempered can be called a temperament? That
> >reminds me of the guy who proved black was white, and got killed on
> >the next zebra-crossing. -- Douglas Adams
>
> I *love* Adams by the way. No, something that isn't tempered
> shouldn't be called a temperament. I said *family* of periodicity
> blocks. You wouldn't call any one of them temperament, or even
> the practice of morphing between them. But you could say a
> temperament governed such a practice.

I have a feeling there's another word you can use here besides
"temperament". Maybe Paul can help?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > > What about planar temperaments?
> >
> > I'd probably name these after the two best linear temps that produce
> > it.
>
> Two linear temperaments don't necessarily produce a planar
> temperament. Three linearly independent vals will do so.
>
> I also suggested calling the most important one (miracle-meantone)
> > "byzantine". But lets not get ahead of ourselves.
>
> And people objected. I've proposed "marvel" as a name. What do you
> think?

I don't think there's any need for a name other than
"miracle-meantone" or "miracle/meantone" at this stage (or maybe ever).

>> To justify my statement, consider super-accurate temperaments like
>> 612. I don't think you'd discern any puns at all.
>> There has to be some error to get a pun (or the pun can be turned
>> into a shift and the vertical tuning left just).
>
>Agreed, but I think that with increasing error there comes a point
>where the ear/brain can no longer bend things to fit the familiar
>frameworks (even when we assist it by using inharmonic timbres to make
>the "implied fundamentals" vague), and so any possibility of "double
>meanings" is lost.

One of the things about the kleismic progressions I made that
disappointed me a bit is that they didn't sound weird enough.

-Carl

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

> I don't think there's any need for a name other than
> "miracle-meantone" or "miracle/meantone" at this stage (or maybe
ever).

Miracle-meantone is a terrible name. Marvel it is.

On Fri, 09 Jan 2004 05:53:36 -0000, "Gene Ward Smith" <gwsmith@svpal.org>
wrote:

>--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
>
>Could you (and Dave) give a list of desired commas?

I'm pretty much in agreement with Paul's original list, with the addition
of the [-11 7] 2187;2048 temperament, and not necessarily including "beep"
or "father". "Beep" [0 3 -2], as I've mentioned, doesn't seem particularly
useful with its large 133.2 cent comma, except as an alternative pelog
scale; "father" [4 -1 -1] has the nice anti-pentatonic scale and the 8-note
MOS that corresponds with the 13-ET mode Blackwood calls "subminor" (which
could also be taken to imply a 7-limit temperament involving three 7/6
subminor thirds plus a major third), but its 5-limit harmonies are
questionable at best.

So that leaves:
unnamed [-11 7] possibly relevant to Thai music (7-ET)
"dicot" [-3 -1 2] Arabic neutral third scale
"pelogic" [-7 3 1]
"blackwood" [8 -5] Easley Blackwood's decatonic
"diminished" [3 4 -4] familiar octatonic scale
"porcupine" [1 -5 3]
"augmented" [7 0 -3] used by Beethoven, many others
"meantone" [-4 4 -1] THE classic linear temperament
"magic" [-10 -1 5]
"diaschismic" [11 -4 -2] Paul Erlich's decatonic
"kleismic" [-6 -5 6]
"schismic" [-15 8 1] very well known and useful temperament

Kleismic-11 and kleismic-15 are the basis of some of my more recent
experimentation with Zireen music, and seems to be useful. You can play
Ernesto Lecuona's _Malagueña_ in kleismic, and it mostly fits. I've also
done some recent experiments with pelogic, and I used a porcupine harmonic
progression in my _Mizarian Porcupine Overture_. Paul Erlich has explored
the melodic properties of the porcupine MOS in his _Glassic_. I haven't
done much with magic, but it shows up on Graham Breed's list, and is simple
enough that it's probably worth mentioning. Negri [-14 3 4] and orwell [-21
3 7] are marginally almost good enough to mention; others such as tetracot
[5 -9 4] or amity [9 -13 5] are probably of very limited use. But the above
list will probably cover the vast majority of uses for 5-limit
temperaments.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

>> I don't think there's any need for a name other than
>> "miracle-meantone" or "miracle/meantone" at this stage (or maybe
>ever).
>
>Miracle-meantone is a terrible name. Marvel it is.

I love Marvel. It reminds me of the Marvel Universe, which is
definitely good. It also goes with our other m* superlatives,
miracle and magic.

-Carl

On Fri, 09 Jan 2004 12:57:57 -0800, Carl Lumma <ekin@lumma.org> wrote:

>What about planar temperaments? And how do you distinguish between
>different maps with the same size generator?

Planar temperaments could be tricky to identify by their generators since
they don't have a unique mapping. "Starling", for instance, was originally
the name for a specific tuning with generators of 312 and 388 cents and a
period of an octave, but it could just as well have had generators of 76
and 236 cents, or any other combination that adds up to the same values.
"Empire" is a scale with approximate 6/5 and 7/5 generators, but it could
just as well have been 6/5 and 7/6.

Another way to identify linear temperaments is as a combination of two
ET's; meantone could be the "5&7" temperament (as on Graham Breed's page
http://x31eq.com/temper/method.html). This might be the best way
to identify complex temperaments like vulture [24 -21 4] (5&48) or escapade
[32 -7 -9] (22&43). You can see the usefulness of this by locating these
temperaments on the chart (at http://tonalsoft.com/enc/eqtemp.htm). Could
the same technique be applied to planar temperaments? So "marvel" [-5 2 2
-1] could be the 9&10&12 temperament, "starling" [1 2 -3 1] could be
12&15&16, the 64;63 temperament could be 5&7&10, and so on.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

>Another way to identify linear temperaments is as a combination of two
>ET's; meantone could be the "5&7" temperament (as on Graham Breed's page
>http://x31eq.com/temper/method.html). This might be the best
>way to identify complex temperaments like vulture [24 -21 4] (5&48) or
>escapade [32 -7 -9] (22&43). You can see the usefulness of this by
>locating these temperaments on the chart (at
>http://tonalsoft.com/enc/eqtemp.htm). Could the same technique be applied
>to planar temperaments? So "marvel" [-5 2 2 -1] could be the 9&10&12
>temperament, "starling" [1 2 -3 1] could be 12&15&16, the 64;63
>temperament could be 5&7&10, and so on.

I believe you need 2 complete vals in the case of a linear
temperament -- Graham's probably assuming the standard val, or similar
when you give him an ET. For planar temperamants 3 vals are required,
according to Gene.

If you want precise names that map 1:1 to temperaments, I think wedgies
fit the bill, and I don't think anything less fits the bill. Since
wedgies generally make terrible names, further mapping them to cute and
Intriguing names like "vulture" seems to fit the bill.

-Carl

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> Another way to identify linear temperaments is as a combination of
two
> ET's; meantone could be the "5&7" temperament (as on Graham Breed's
page
> http://x31eq.com/temper/method.html). This might be the
best way
> to identify complex temperaments like vulture [24 -21 4] (5&48) or
escapade
> [32 -7 -9] (22&43).

It doesn't make much sense to do this for 5-limit temperaments, since
the comma identifies them exactly, and them two vals have these
defects:

(1) There are two of them, versus one comma

(2) There is only one comma for a temperament, but an infinite number
of possible pairs of vals

(3) If the vals are given by numbers ("48") there is sometimes a
question as to which val is meant.

On the other hand, for higher limits two vals still always work to
define a linear temperament, whereas we keep need ever more commas.

You can see the usefulness of this by locating these
> temperaments on the chart (at http://tonalsoft.com/enc/eqtemp.htm).
Could
> the same technique be applied to planar temperaments? So "marvel" [-
5 2 2
> -1] could be the 9&10&12 temperament, "starling" [1 2 -3 1] could be
> 12&15&16, the 64;63 temperament could be 5&7&10, and so on.

I hate 12&15&16 for Starling, and 9&10&12 is even worse for Marvel!
Anyone would think these were low-precision temperaments from this;
moreover, the question of which val you are talking about has become
acute. Larger, more precise vals might help suggest what the higher
prime limit versions might be, but I wouldn't trust these small ones
to be helpful.

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

> If you want precise names that map 1:1 to temperaments, I think
wedgies
> fit the bill, and I don't think anything less fits the bill.

Other possiblies are the TM comma basis and some kind of standard
reduction of the mapping, such as Hermite.

Since
> wedgies generally make terrible names, further mapping them to cute
and
> Intriguing names like "vulture" seems to fit the bill.

That's a 5-limit comma, which means it more or less is a wedgie
already. Lucky bird. Like Dave and his generator sizes, I associate
wedgies mentally to temperaments but I agree they make rotten names.

on 1/9/04 5:11 PM, Dave Keenan <d.keenan@bigpond.net.au> wrote:

> I know you (and Paul?) want to redefine these terms (e.g. third,
> fourth, fifth, octave) in other linear temperaments so that they refer
> to the number-of-steps-plus-one in the 5-to-10-note MOS (or "natural"
> nominals) of that temperament, but I think this is doomed to failure.
> I just can't see people calling an approximate 1:2 a fifth in some
> cases and a tenth in others, and everything in between.
>
> I think an approximate 1:2 will always be an octave. I think we're
> just going to have to come up with some other way of referring to the
> number of steps in the "natural MOS" of a non-diatonic temperament,
> and while we're at it we might fix the off-by-one problem so the
> arithmetic works properly.

Well how about meta-third and meta-fifth, etc.? That's not too much harder
to type. Within a given document or page it can always be noted that all
intervals are "meta" so that shorthand notations can be used throughout.

This may be a slight stretch of the meaning of "meta". Perhaps Gene can
come up with a prefix that really reflects the mathematical truth of how
this relates to the "normal" sense of third/fifth, etc.

-Kurt

Gene Ward Smith wrote:

> It doesn't make much sense to do this for 5-limit temperaments, since > the comma identifies them exactly, and them two vals have these > defects:
> > (1) There are two of them, versus one comma
> > (2) There is only one comma for a temperament, but an infinite number > of possible pairs of vals
> > (3) If the vals are given by numbers ("48") there is sometimes a > question as to which val is meant.

But then again, a comma is two integers, usually larger than the number of notes to the octave for an equal temperament.

(And, BTW, these really are temperaments -- we don't have to abstract them as vals.)

When giving only the numbers, you should always try to label consistent ETs with them, so then there won't be any confusion.

> On the other hand, for higher limits two vals still always work to > define a linear temperament, whereas we keep need ever more commas.

Yes, that's where the real advantage arises. And although wedgies are unique and unambiguous, they aren't human readable. At least for most of us. Whereas constituent ETs give you an idea of the melodic properties, and vanishing commas the harmonic.

> I hate 12&15&16 for Starling, and 9&10&12 is even worse for Marvel! > Anyone would think these were low-precision temperaments from this; > moreover, the question of which val you are talking about has become > acute. Larger, more precise vals might help suggest what the higher > prime limit versions might be, but I wouldn't trust these small ones > to be helpful.

Yes. Not only are they inconsistent, and so ambiguous, they don't give you much idea of the temperament either. Who would have guessed that 9-equal tempers out 225:224? Better is 12&19&22, or 29&31&41 if you want it to look more accurate.

12&19&27 are the simplest consistent ETs for this Starling. For the next step up, 31&46&50, or 58.

If you're specifying a higher limit temperament, you can choose your octave sizes accordingly. 29&41&72 and 41&72&94 are both distinct in the 15-limit, and 225:224 vanish in both. I don't know if either of them are any good.

It also happens that 31, 41, 58, 72, 89, 113 and 130-equal all temper out both 243:242 and 2401:2400. So 41&58&72 defines a 13-limit temperament that fits my 7-limit neutral-third lattice! And also includes 130-equal. 31&41&58 also tempers out 144:143, taking the nearest approximation to 31-equal.

It's likely to be in the higher limits that planar temperaments come into their own, and this is the most efficient way of specifying one. There will also be fewer different ways of specifying it with consistent ETs.

It is worth giving the 225:224 planar temperament a name, because it covers a lot of linear temperaments (meantone, miracle, schismic, magic, orwell) so we're likely to talk about it a fair bit. And some music written in any of these linear temperaments will likely translate to the planar temperament. So Marvel's a good name, and ties in with the "M" theory. But can you still specify it some other way the first time you mention it, for the benefit of those of us who can't remember all the names?

As for other planar temperaments, what do we have to say about them, beyond listing a few numbers?

Graham

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

/tuning/topicId_51065.html#51403

> Another way to identify linear temperaments is as a combination of
two
> ET's; meantone could be the "5&7" temperament (as on Graham Breed's
page
> http://x31eq.com/temper/method.html).

***I may be getting a glimmer of this. So, in other words, these two
ETs provide a kind of intersection that defines the temperament: as
in the wonderful new horagrams that Paul Erlich made, where the
pentatonic and diatonic are, quite obviously, sharing the same
pitches.

Sounds like a much better way of describing these things to *me* than
inventing new terminology...

J. Pehrson

On Fri, 09 Jan 2004 21:23:45 -0800, Carl Lumma <ekin@lumma.org> wrote:

>If you want precise names that map 1:1 to temperaments, I think wedgies
>fit the bill, and I don't think anything less fits the bill. Since
>wedgies generally make terrible names, further mapping them to cute and
>Intriguing names like "vulture" seems to fit the bill.

Unfortunately, I was away from tuning-math precisely when the wedgie
discussion was taking place, and I've never had a full understanding of
much of what's been going on since then. The so-called "definitions" of
wedge product have been unhelpful, and exactly how they relate to tuning is
still a mystery to me -- you put some commas into a black box and end up
with a wedgie, and it's not obvious looking at a wedgie what commas might
pop out of it. I'm a computer programmer and deal with quaternions and
matrices on a regular basis, but I just haven't had the time to absorb the
theoretical algebra background for understanding wedge products.

There's nothing much wrong with "vulture" as a name, but it doesn't help
you to locate it on Paul Erlich's chart (the one on Joe Monzo's equal
temperament page). Knowing that it passes through 5 and 48 does tell you
where you can find it (if you've stared at this chart as long as I have, it
shouldn't be a problem finding 48, although more obscure ones like 73 might
be harder to locate). Some names are better than others: "dicot" and
"tetracot" are clearly related, and you can see that "dicot" divides the
fifth into two parts while "tetracot" divides it into four parts.
"Ennealimmal" clearly has something to do with nine (the period is 1/9
octave), and something to do with some kind of limma (1/9 octave is about
the size of the large limma 27/25). "Parakleismic" is quite transparently
"next to kleismic" on the chart. Others, like "misty", are less obvious (an
acronym?).

When it comes to planar temperaments, it would be hard to visualize without
a stereogram of a chart like this, but you could still get an idea of what
it could be useful for; "9&10&12" could be seen as a combination of the
"9&10" (Negri) and "10&12" (diaschismic) linear temperaments. It's a little
less clear how this relates to meantone (5&7), but then only some meantones
are compatible with 225;224 (specifically, the 12&19 subset of meantone).
As long as the ET is consistent with whatever subset of the primes you're
interested in, it uniquely identifies a point in this space, so you should
be able to use three consistent ET's to uniquely identify a plane (as long
as the three ET's aren't on the same line). So you do need to specify which
primes you're interested in; "5&7" is the same as "12&19" on the 5-limit
chart, but they're distinct in the 7-limit. So a more complete identifier
for meantone might be something like "5&7(2,3,5)".

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

--- In tuning@yahoogroups.com, Graham Breed <graham@m...> wrote:
If you want to define a temperament by a pair of numbers, you most
certainly do need to turn them into vals. If you want to make DE
scales out of them its another story.

> When giving only the numbers, you should always try to label
consistent
> ETs with them, so then there won't be any confusion.

Thereby, of course, allowing us to know which val is intended.
> It's likely to be in the higher limits that planar temperaments
come
> into their own, and this is the most efficient way of specifying
one.
> There will also be fewer different ways of specifying it with
consistent
> ETs.

> It is worth giving the 225:224 planar temperament a name, because
it
> covers a lot of linear temperaments (meantone, miracle, schismic,
magic,
> orwell) so we're likely to talk about it a fair bit.

5-limit planar is otherwise known as just intonation, so you at least
must go to the 7-limit. There you will immediately find, if you look
at the approximiate consonances which turn up in, for instance,
12-note JI scales, that 225/224 is all over the place.

And some music
> written in any of these linear temperaments will likely translate
to the
> planar temperament. So Marvel's a good name, and ties in with
the "M"
> theory. But can you still specify it some other way the first time
you
> mention it, for the benefit of those of us who can't remember all
the names?

Do names like 225/224-planar or {225/224, 385/384}-planar work for
you?

> As for other planar temperaments, what do we have to say about
them,
> beyond listing a few numbers?

Marvel and Starling are the only ones I've actually worked with. A
planar should be enough better than associated linear temperaments
obtained by adding another roughly equal sized comma that it is worth
paying attention, I suppose. Even in the case of linear temperaments,
we find ones which are so close to an equal temperament than they
more or less merge with it--Dominant seventh to 12-et, Pajara to 22-
et, etc.

Gene Ward Smith wrote:

> If you want to define a temperament by a pair of numbers, you most > certainly do need to turn them into vals. If you want to make DE > scales out of them its another story.

You can define a linear temperament with a a pair of equal temperaments.

> Do names like 225/224-planar or {225/224, 385/384}-planar work for > you?

"225/224-planar" is fine. Although it could be shortened, and if it's going to be used frequently it should be. "225/224, 385/384 planar" is a real mouthful, but you have to introduce it somehow.

Graham

On Sat, 10 Jan 2004 16:04:23 +0000, Graham Breed <graham@microtonal.co.uk>
wrote:

>Yes. Not only are they inconsistent, and so ambiguous, they don't give
>you much idea of the temperament either. Who would have guessed that
>9-equal tempers out 225:224? Better is 12&19&22, or 29&31&41 if you
>want it to look more accurate.

9-ET is 7-limit consistent according to the list at
http://library.wustl.edu/~manynote/consist.txt -- it doesn't seem like it
should be, but there it is! The deviations from JI are -0.26, +0.10, and
-0.27 of a step (for 3:1, 5:1, and 7:1); none of the differences between
these add up to more than 0.5 (unless you're using some other definition of
consistency).

I can see the problem if you don't always use the lowest numbered
consistent ET's; it wouldn't be obvious whether "12&19&22" or "29&31&41" is
the same as something already on your list. For marvel, 9-ET happens to be
the smallest ET, but I neglected to consider 4-ET for starling (who'd have
thought that 4-ET would be consistent with _anything_?), so starling should
properly be "4&12&15".

It might be better to set an arbitrary lower limit (nothing less than
12-ET?) on the ET's that define the points through which the linear
temperament runs. But then you'd leave out a few odd temperaments like beep
[0 3 -2], which isn't consistent with anything above 9-ET (although from
looking at Paul Erlich's enormously useful horagram charts, it has some
potentially interesting-looking larger scales, as I noted in the "beep-9
pelog" thread).

>It also happens that 31, 41, 58, 72, 89, 113 and 130-equal all temper
>out both 243:242 and 2401:2400. So 41&58&72 defines a 13-limit
>temperament that fits my 7-limit neutral-third lattice! And also
>includes 130-equal. 31&41&58 also tempers out 144:143, taking the
>nearest approximation to 31-equal.

I have a tendency to overlook commas like 243;242, since I tend to find
these unsystematically, usually looking for some lower limit approximation
of 11/8 (so the 11 exponent always ends up as 1 or -1). Is there a list of
"useful" 11-limit commas anywhere?

>It is worth giving the 225:224 planar temperament a name, because it
>covers a lot of linear temperaments (meantone, miracle, schismic, magic,
>orwell) so we're likely to talk about it a fair bit. And some music
>written in any of these linear temperaments will likely translate to the
>planar temperament. So Marvel's a good name, and ties in with the "M"
>theory. But can you still specify it some other way the first time you
>mention it, for the benefit of those of us who can't remember all the names?

Yes, I should have at least given the monzo [-5 2 2 -1]. That still seems
to be the best way to identify 7-limit planar temperaments, as it is with
5-limit linear temperaments.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

>***I may be getting a glimmer of this. So, in other words, these two
>ETs provide a kind of intersection that defines the temperament: as
>in the wonderful new horagrams that Paul Erlich made, where the
>pentatonic and diatonic are, quite obviously, sharing the same
>pitches.

Yup, that's right! Even better, look on the zoomer charts (on
monz's et page) and find two ets (points). Remember from geometry
that two points define a line (temperament).

>Sounds like a much better way of describing these things to *me* than
>inventing new terminology...

There are reasons why the two-ET naming isn't the best idea, if
you've been following Gene & Graham's thread.

-Carl

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> Is there a list of
> "useful" 11-limit commas anywhere?

I have 11-limit comma lists; you can produce something you may think
is "useful" by putting an upper bound on both epimericity and size,
but I don't know what bounds you'd want.

>>If you want precise names that map 1:1 to temperaments, I think wedgies
>>fit the bill, and I don't think anything less fits the bill. Since
>>wedgies generally make terrible names, further mapping them to cute and
>>Intriguing names like "vulture" seems to fit the bill.
>
>Unfortunately, I was away from tuning-math precisely when the wedgie
>discussion was taking place, and I've never had a full understanding of
>much of what's been going on since then. The so-called "definitions" of
>wedge product have been unhelpful, and exactly how they relate to tuning
>is still a mystery to me -- you put some commas into a black box and end
>up with a wedgie, and it's not obvious looking at a wedgie what commas
>might pop out of it. I'm a computer programmer and deal with quaternions
>and matrices on a regular basis, but I just haven't had the time to
>absorb the theoretical algebra background for understanding wedge
>products.

Yes well, you're not alone!

>There's nothing much wrong with "vulture" as a name, but it doesn't help
>you to locate it on Paul Erlich's chart (the one on Joe Monzo's equal
>temperament page).

But there are a lot of things right about it, such as its a unique name
that can easily be searched for or looked up alphabetically in a list.
Also, at least my memory seems to work the same way.

If you want 1:1 mapping to any kind of temperament and you don't want
to use wedgies or lots of numbers, names like this are the only way.
And they sound cool.

-Carl

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > I don't think there's any need for a name other than
> > "miracle-meantone" or "miracle/meantone" at this stage (or maybe
> ever).
>
> Miracle-meantone is a terrible name.

You're right! It's terrible! It isn't cool, sexy, or bizarre, and it
doesn't rock. And what's worse, someone might figure out what you're
talking about, without the secret decoder ring. They might realise
that it must be planar and not linear since it has a double-barelled
name. They might even figure out which two linear temperaments it is
most closely related to.

> Marvel it is.

I'm glad you haven't let the fact that I was the first to describe
this planar temperament influence you in any way.

Paul,

As I said before, I think it would be better if you just go ahead
without me on this stuff. It would be less painful for all concerned.

I can no longer understand the jargon used on tuning-math in any case.
It just looks like gobbledygook to me now, most of the time.

Regards,
-- Dave Keenan

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

/tuning/topicId_51065.html#51489

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> >
> > > I don't think there's any need for a name other than
> > > "miracle-meantone" or "miracle/meantone" at this stage (or
maybe
> > ever).
> >
> > Miracle-meantone is a terrible name.
>
> You're right! It's terrible! It isn't cool, sexy, or bizarre, and it
> doesn't rock. And what's worse, someone might figure out what you're
> talking about, without the secret decoder ring. They might realise
> that it must be planar and not linear since it has a double-barelled
> name. They might even figure out which two linear temperaments it is
> most closely related to.
>
> > Marvel it is.
>
> I'm glad you haven't let the fact that I was the first to describe
> this planar temperament influence you in any way.
>
> Paul,
>
> As I said before, I think it would be better if you just go ahead
> without me on this stuff. It would be less painful for all
concerned.
>
> I can no longer understand the jargon used on tuning-math in any
case.
> It just looks like gobbledygook to me now, most of the time.
>
> Regards,
> -- Dave Keenan

***You know, I think I might be glad there are *two* lists, now... (I
never thought I'd see the day... :)

J. Pehrson

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

> > Miracle-meantone is a terrible name.
>
> You're right! It's terrible! It isn't cool, sexy, or bizarre, and it
> doesn't rock. And what's worse, someone might figure out what you're
> talking about, without the secret decoder ring.

No, it's terrible because it's wrong. If you combine miracle and
meantone, you get 31-et. If the person without the secret decoder
ring manages to decode it, that's what he will get.

> I'm glad you haven't let the fact that I was the first to describe
> this planar temperament influence you in any way.

When was that, and what makes you sure of this?

hi Dave and Joe,

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

> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > I can no longer understand the jargon used on
> > tuning-math in any case.
> > It just looks like gobbledygook to me now, most of the time.
>
>
> ***You know, I think I might be glad there are *two*
> lists, now... (I never thought I'd see the day... :)

i agree with both of you guys, and have for quite a while.

i haven't been able to follow much on the tuning-math list
since Gene started posting about wedgies ... that's almost
two years IIRC.

-monz

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > > Miracle-meantone is a terrible name.
> >
> > You're right! It's terrible! It isn't cool, sexy, or bizarre, and it
> > doesn't rock. And what's worse, someone might figure out what you're
> > talking about, without the secret decoder ring.
>
> No, it's terrible because it's wrong. If you combine miracle and
> meantone, you get 31-et. If the person without the secret decoder
> ring manages to decode it, that's what he will get.

That may be what a pure mathematician would get, but I think a
musician is more likely to try a rectangular grid of notes separated
by meantone generators in one dimension and miracle generators in the
other.

> > I'm glad you haven't let the fact that I was the first to describe
> > this planar temperament influence you in any way.
>
> When was that, and what makes you sure of this?

Late February 1999 on the tuning list I believe. One can never be
totally sure of such things. It's quite possible that Fokker described
it. But as far as we've been able to tell, although he recognised the
importance of 224:225 for defining periodicity blocks, he never
advocated tempering it out.

hi Dave (and Gene),

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

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:

> > > I'm glad you haven't let the fact that I was the
> > > first to describe this planar temperament influence
> > > you in any way.
> >
> > When was that, and what makes you sure of this?
>
> Late February 1999 on the tuning list I believe. One
> can never be totally sure of such things. It's quite
> possible that Fokker described it. But as far as we've
> been able to tell, although he recognised the importance
> of 224:225 for defining periodicity blocks, he never
> advocated tempering it out.

oh yes he most certainly did.

i only have two of Fokker's writings, and both of them
concern just-intonation. but i know for sure that he
was a *very* strong advocate of 31-ET, and 31-ET's
closest approximation to both 4:7 and 128:225 is the
same: 2^(25,31) = ~967.7419355 cents. thus the 224:225
vanishes.

(on the 31-ET meantone chain, 2^(25/31) is both +10
and -21 generator 5ths. if 1/1 is called "C", then
these are A# and Cbbb respectively. but since it *does*
give a good approximation of 4:7 -- only ~1.083970985
cent too small -- 2^(25/31) can also be notated specifically
as an approximation of a 7-limit note, which in this case
i could call Bb< in HEWM notation.)

so, since Fokker advocated 31-ET, i'd say that he *did*
advocate tempering out the 224:225.

anyone who has the relevant Fokker papers should post.
Manuel?

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> oh yes he most certainly did.

Not according to what you say below.

> i only have two of Fokker's writings, and both of them
> concern just-intonation. but i know for sure that he
> was a *very* strong advocate of 31-ET, and 31-ET's
> closest approximation to both 4:7 and 128:225 is the
> same: 2^(25,31) = ~967.7419355 cents. thus the 224:225
> vanishes.

31-et is hardly the same as Marvel, which has far more accurate
tuning.

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
> wrote:
>
> > > > I'm glad you haven't let the fact that I was the
> > > > first to describe this planar temperament influence
> > > > you in any way.
> > >
> > > When was that, and what makes you sure of this?
> >
> > Late February 1999 on the tuning list I believe. One
> > can never be totally sure of such things. It's quite
> > possible that Fokker described it. But as far as we've
> > been able to tell, although he recognised the importance
> > of 224:225 for defining periodicity blocks, he never
> > advocated tempering it out.
>
>
>
> oh yes he most certainly did.
...
> 31-ET
...

Monz,

You misunderstood. I'm well aware that Fokker advocated 31-ET and that
224:225 vanishes in it, but we were talking about a _planar_ temperament.

If you have any information about Fokker or anyone else advocating
tempering out _only_ 224:225 from the 7-limit, thereby giving rise to
a planar temperament, I'd be very interested.

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

> That may be what a pure mathematician would get, but I think a
> musician is more likely to try a rectangular grid of notes separated
> by meantone generators in one dimension and miracle generators in
the
> other.

Here is what I got mathematically as a lattice for 7 and 11 limit
Marvel. In the 7-limit, which is what we are talking about, it looks
like it could equally well be described in terms of a 3/2-5/4
rectangualar grid. What's worse, the 3/2s on the grid are being tuned
in a way which isn't even close to meantone. Your name suggests that
it should be.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > That may be what a pure mathematician would get, but I think a
> > musician is more likely to try a rectangular grid of notes
separated
> > by meantone generators in one dimension and miracle generators in
> the
> > other.
>
> Here is what I got mathematically as a lattice for 7 and 11 limit
> Marvel.

Sorry, I forgot to stick in the urls:

/tuning-math/files/planar plots/p225.jpg

/tuning-math/files/planarplots/marvel.jpg

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > oh yes he most certainly did.
>
> Not according to what you say below.
>
> > i only have two of Fokker's writings, and both of them
> > concern just-intonation. but i know for sure that he
> > was a *very* strong advocate of 31-ET, and 31-ET's
> > closest approximation to both 4:7 and 128:225 is the
> > same: 2^(25,31) = ~967.7419355 cents. thus the 224:225
> > vanishes.
>
> 31-et is hardly the same as Marvel, which has far more accurate
> tuning.

but 31-ET *does* temper out 224:25, does it not?
that's the only point to which i was responding.

-monz

hi Dave,

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

> Monz,
>
> You misunderstood. I'm well aware that Fokker advocated
> 31-ET and that 224:225 vanishes in it, but we were talking
> about a _planar_ temperament.

oh, OK, thanks for straightening that out.
i did misunderstand.

> If you have any information about Fokker or anyone
> else advocating tempering out _only_ 224:225 from the
> 7-limit, thereby giving rise to a planar temperament,
> I'd be very interested.

nah, as i said, i only have one paper and one short book
by him, and both concern JI.

-monz

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > That may be what a pure mathematician would get, but I think a
> > musician is more likely to try a rectangular grid of notes separated
> > by meantone generators in one dimension and miracle generators in
> the
> > other.
>
> Here is what I got mathematically as a lattice for 7 and 11 limit
> Marvel. In the 7-limit, which is what we are talking about, it looks
> like it could equally well be described in terms of a 3/2-5/4
> rectangualar grid. What's worse, the 3/2s on the grid are being tuned
> in a way which isn't even close to meantone. Your name suggests that
> it should be.
>
> /tuning-math/files/planar plots/p225.jpg
>
> /tuning-math/files/planarplots/marvel.jpg

The second file doesn't seem to be there.

You're right about the fifths, they would typically be close to 700
cents which isn't exactly meantone. But one of the things I intend to
imply by the name miracle-meantone is that the most interesting finite
and even scales are obtained from approximate rectangles where one
side is parallel to the chains of fifths and the other parallel to the
chains of secors, when these are arranged at right angles to each
other. So maybe it has something to do with the chromatic commas as
well as the vanishing ones. But I suppose that goes beyond the planar
temperament per se and gets into the question of hyper-MOS or hyper-DE.

There may well be better names than miracle-meantone, but I think it's
too early to decide. However I'd prefer the name to be descriptive in
some way.

"Marvel" suggests to me something related to "Miracle" and "Magic".

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > I'm glad you haven't let the fact that I was the first to describe
> > this planar temperament influence you in any way.
>
> When was that, and what makes you sure of this?

See
/tuning/topicId_1012.html#1012

This time it was Carl Lumma who got the credit for asking the right
question. Like Joseph Pehrson with Miracle.

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

> but 31-ET *does* temper out 224:25, does it not?
> that's the only point to which i was responding.

Any equal temperament where 15/14 and 16/15 are the same size does
that, and that includes 12.

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

> > /tuning-math/files/planar
plots/p225.jpg
> >
> > /tuning-
math/files/planarplots/marvel.jpg
>
> The second file doesn't seem to be there.

There needs to be a space between planar and plots, but it's over
there on tuning-math.

> You're right about the fifths, they would typically be close to 700
> cents which isn't exactly meantone. But one of the things I intend
to
> imply by the name miracle-meantone is that the most interesting
finite
> and even scales are obtained from approximate rectangles where one
> side is parallel to the chains of fifths and the other parallel to
the
> chains of secors, when these are arranged at right angles to each
> other.

There are LOTS of 5-limit scales where 225/224 tempers in 7-limit
harmony. Lots and lots and lots, and when I finish by Fokker block
classification, we can see how many distict ones we have after Marvel
tempering.

> "Marvel" suggests to me something related to "Miracle" and "Magic".

It *is* related to Miracle and Magic. You are thinking of Marvel as a
sort of 31-equal temperament, but it can just as well be associated
to 41-equal. This demonstrates another reason why this is simply a
bad way to name planar temperaments.

>> > Miracle-meantone is a terrible name.
>>
>> You're right! It's terrible! It isn't cool, sexy, or bizarre, and it
>> doesn't rock. And what's worse, someone might figure out what you're
>> talking about, without the secret decoder ring.
>
>No, it's terrible because it's wrong. If you combine miracle and
>meantone, you get 31-et. If the person without the secret decoder
>ring manages to decode it, that's what he will get.

It's also a non-improvement, because "miracle" is every bit as bizarre
as "marvel".

-Carl

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

> I've had that trouble too, but that's ok because I'm essentially
> peaking

Easy on the drugs, OK? :)
(cheap shot at your spelling, sorry Carl . . .)

>> I've had that trouble too, but that's ok because I'm essentially
>> peaking
>
>Easy on the drugs, OK? :)
>(cheap shot at your spelling, sorry Carl . . .)

:)

Though sometimes I think the list is a bit like a drug. :(

-Carl

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> >
> > > I don't know how to. And I think the onus is on you to provide
> > > examples of linear tunings which do _not_ sound like 5-limit
> > > temperaments to you when treated in the same was as
the "father"
> > >examples.
> >
> > The treatment was a mapping from 5-limit JI to the temperament;
how
> > are you supposed to do this if the tuning you want to use is not
a
> > temperament?
>
> Good question? Does this mean your claim is untestable and therefore
> vacuous?

Yes
:)

This is all so sad; the xeno-temperaments or exo-temperaments or
whatever you want to call them are so small in number, don't they
deserve to stand up and be counted, if only for the first few to be
mocked and ridiculed, and then for the last few to be argued about by
those with different ears, timbres, etc. . . .?

I know your answer -- no. So father and beep are out. Swallowed and
accepted.

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > What about planar temperaments?
>
> I'd probably name these after the two best linear temps that produce
> it. I also suggested calling the most important one (miracle-
meantone)
> "byzantine". But lets not get ahead of ourselves.
>
> > And how do you distinguish between
> > different maps with the same size generator?
>
> I explained that here.
> /tuning/topicId_51065.html#51338
>
> The one with the lowest badness gets the unqualified name and the
> others get "complex" or "simple" prepended depending on their
> complexity relative to the lowest badness one, and if more such
> qualifiers are needed, then supercomplex, hypercomplex, ultracomplex
> and supersimple, hypersimple, ultrasimple. Any reasonable badness
> measure will work for this since they usually differ widely.
>
> > >But once again I'd prefer to name it after what just interval the
> > >generator approximates _according_to_the_mapping_.
> >
> > You mean what diatonic interval?
>
> No, I name after the just interval, or at least the diamond
interval,
> that is approximated by the fewest generators. I prefer to use the
> extended-diatonic names for these intervals, after Fokker, because
it
> is basically the only game in town. Possibly further extending these
> using the miracle/72-ET-based scheme outlined here.
>
http://dkeenan.com/Music/Miracle/MiracleIntervalNami
ng.txt

If this is the only game in town, I'm packing up and moving my
things. When the difference between a major second and a major sixth
is not a perfect fifth, I'm running away to HEWM-land.
>
> I know you (and Paul?) want to redefine these terms (e.g. third,
> fourth, fifth, octave) in other linear temperaments so that they
>refer
> to the number-of-steps-plus-one in the 5-to-10-note MOS >
(or "natural"
> nominals) of that temperament, but I think this is doomed to
>failure.

That's another way.

> I just can't see people calling an approximate 1:2 a fifth in some
> cases and a tenth in others, and everything in between.

Oddly enough, though, the referees for our paper may prefer this, as
they're used to this sort of thing from "generalized diatonicity"
papers.

> I think an approximate 1:2 will always be an octave. I think we're
> just going to have to come up with some other way of referring to
the
> number of steps in the "natural MOS" of a non-diatonic temperament,
> and while we're at it we might fix the off-by-one problem so the
> arithmetic works properly.

So you *can* see people caling a fifth a fourth, a seventh a sixth, a
second a first, and a unison a "zeroth"?

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> > > --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > > > What about planar temperaments?
> > >
> > > I'd probably name these after the two best linear temps that
produce
> > > it.
> >
> > Two linear temperaments don't necessarily produce a planar
> > temperament. Three linearly independent vals will do so.
> >
> > I also suggested calling the most important one (miracle-meantone)
> > > "byzantine". But lets not get ahead of ourselves.
> >
> > And people objected. I've proposed "marvel" as a name. What do
you
> > think?
>
> I don't think there's any need for a name other than
> "miracle-meantone" or "miracle/meantone" at this stage (or maybe
>ever).

I find that absurd. Miracle involves tempering out a comma
(1029:1024, 2401:2400), or that is outside the complexity range
where "marvel" becomes "marvelous". You really just want the other
comma, 225:224, so why get these, not to mention 81:80, tangled up in
all this? And if you want to pick two systems where 225:224 vanishes,
why isn't pajara (that is, the 'decatonic' system of my papers) one
of them? Miracle-meantone or miracle/meantone is 31-equal, of course.

Herman Miller wrote:

> 9-ET is 7-limit consistent according to the list at
> http://library.wustl.edu/~manynote/consist.txt -- it doesn't seem like it
> should be, but there it is! The deviations from JI are -0.26, +0.10, and
> -0.27 of a step (for 3:1, 5:1, and 7:1); none of the differences between
> these add up to more than 0.5 (unless you're using some other definition of
> consistency).

It isn't 9-limit consistent, and 225:224 is valid in the 9-limit as well.

> I can see the problem if you don't always use the lowest numbered
> consistent ET's; it wouldn't be obvious whether "12&19&22" or "29&31&41" is
> the same as something already on your list. For marvel, 9-ET happens to be
> the smallest ET, but I neglected to consider 4-ET for starling (who'd have
> thought that 4-ET would be consistent with _anything_?), so starling should
> properly be "4&12&15".
> > It might be better to set an arbitrary lower limit (nothing less than
> 12-ET?) on the ET's that define the points through which the linear
> temperament runs. But then you'd leave out a few odd temperaments like beep
> [0 3 -2], which isn't consistent with anything above 9-ET (although from
> looking at Paul Erlich's enormously useful horagram charts, it has some
> potentially interesting-looking larger scales, as I noted in the "beep-9
> pelog" thread).

7-limit planar and 5-limit linear temperaments can happily be defined using their commas. The ET definitions only become simpler in higher limits, where fortunately there are fewer consistent ETs to choose from. Generally, you should choose ETs that the reader is likely to be familiar with in the relevant limit.

> I have a tendency to overlook commas like 243;242, since I tend to find
> these unsystematically, usually looking for some lower limit approximation
> of 11/8 (so the 11 exponent always ends up as 1 or -1). Is there a list of
> "useful" 11-limit commas anywhere?

I remember 243:242 as being the "neutral third comma". It guarantees that two intervals of 11:9 add up to the same as 3:2. It's a useful comma to have around because, even if you don't want the 11-limit harmony, it's a simple way of ensuring 3:2 can be equally divided without spoiling the 5-limit harmony. I can't remember the numbers, except that it's superparticular, so I do the sum -- 11/9*11/9*2/3.

You can find other good commas by setting a pair of adjacent ratios in the string 7:8:9:10:11:12:13:14:15:16 to be equal.

> Yes, I should have at least given the monzo [-5 2 2 -1]. That still seems
> to be the best way to identify 7-limit planar temperaments, as it is with
> 5-limit linear temperaments.

There's also the octave-equivalent mapping for linear temperaments, but it's related to the monzo.

Graham

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> > > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
> wrote:
> > >
> > > > I don't know how to. And I think the onus is on you to provide
> > > > examples of linear tunings which do _not_ sound like 5-limit
> > > > temperaments to you when treated in the same was as
> the "father"
> > > >examples.
> > >
> > > The treatment was a mapping from 5-limit JI to the temperament;
> how
> > > are you supposed to do this if the tuning you want to use is not
> a
> > > temperament?
> >
> > Good question? Does this mean your claim is untestable and therefore
> > vacuous?
>
> Yes
> :)

Why a smiley here but sad below?

> This is all so sad; the xeno-temperaments or exo-temperaments or
> whatever you want to call them

Do you mean the linear tunings that are not approximations of JI?

> are so small in number, don't they
> deserve to stand up and be counted,

Absolutely!

> if only for the first few to be
> mocked and ridiculed,

The only thing I remember coming close to being mocked or riduled
about these was the idea that, in order to be accepted, they had to be
shown to be an approximation of JI.

> and then for the last few to be argued about by
> those with different ears, timbres, etc. . . .?
>
> I know your answer -- no. So father and beep are out. Swallowed and
> accepted.

You assume too much.

They may be out, _as_5-limit_temperaments_, and they may be out under
those names, but surely we can acknowledge that our theories are
incomplete.

The closing of one door, may make it possible to open another. Surely
we can have a category of mysterious and marvelous linear
NON-temperaments. But of course the borderline is fuzzy and it is not
clear where pelogic should go, or even neutral thirds.

Since we can mathematically define what it means to be as far as
possible from any simple ratio (i.e. the noble numbers), we might even
be able to institute a computer search for the best ANTI-temperaments.
This may relate to the metastability idea in Margo's and my 'Noble
Mediants' paper.

Perhaps the linear temperaments paper should be written first.
Although it should definitely include a disclaimer to the effect that
approximating JI isn't everything, and should briefly describe some of
the historical linear non-temperaments and borderline cases.

-- Dave Keenan

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > > >But once again I'd prefer to name it after what just interval the
> > > >generator approximates _according_to_the_mapping_.
> > >
> > > You mean what diatonic interval?
> >
> > No, I name after the just interval, or at least the diamond
> interval,
> > that is approximated by the fewest generators. I prefer to use the
> > extended-diatonic names for these intervals, after Fokker, because
> it
> > is basically the only game in town. Possibly further extending these
> > using the miracle/72-ET-based scheme outlined here.
> >
> http://dkeenan.com/Music/Miracle/MiracleIntervalNami
> ng.txt
>
> If this is the only game in town, I'm packing up and moving my
> things. When the difference between a major second and a major sixth
> is not a perfect fifth, I'm running away to HEWM-land.

Paul, I feel you're misrepresenting me here. The desription "only game
in town" above is clearly referring to the Fokker names where the
difference between a major second and a major sixth _is_indeed_ a
perfect fifth.

For the Miracle/72-ET-based system of further qualifying these with
"wide" and "narrow", I only said "possibly". And even in this system
you only need to add "wide" before "major sixth" or "narrow" before
"major second" (but not both) to make their difference a perfect fifth.

I'm well aware that you favour an extended diatonic interval name
system based on 12-ET, where I prefer it based on JI. (e.g. your
central "major third" is 300 c while mine is 316 c). But in the
context of Carl's question, I believe this minor difference is irrelevant.

This choice of fine detail in the interval naming system also has
nothing to do with the choice of HEWM as a pitch notation system. Both
can equally be used with HEWM, as I've explained before.

> > I know you (and Paul?) want to redefine these terms (e.g. third,
> > fourth, fifth, octave) in other linear temperaments so that they
> >refer
> > to the number-of-steps-plus-one in the 5-to-10-note MOS >
> (or "natural"
> > nominals) of that temperament, but I think this is doomed to
> >failure.
>
> That's another way.

I understood it was what Carl was alluding to.

> > I just can't see people calling an approximate 1:2 a fifth in some
> > cases and a tenth in others, and everything in between.
>
> Oddly enough, though, the referees for our paper may prefer this, as
> they're used to this sort of thing from "generalized diatonicity"
> papers.

Well that's a significant consideration. Thanks for pointing that out.

> > I think an approximate 1:2 will always be an octave. I think we're
> > just going to have to come up with some other way of referring to
> the
> > number of steps in the "natural MOS" of a non-diatonic temperament,
> > and while we're at it we might fix the off-by-one problem so the
> > arithmetic works properly.
>
> So you *can* see people caling a fifth a fourth, a seventh a sixth, a
> second a first, and a unison a "zeroth"?

Absolutely not. The potential for confusion between the two systems
would then be almost total. Only zeroths could not be mistaken.

No. I had in mind other words that mean numbers, e.g. Greek, Latin,
Old Icelandic. Or even different or modified English words for
numbers. Someone suggested adding a "meta" prefix. Anything except the
current English ordinal words.

-- Dave Keenan

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> > I don't think there's any need for a name other than
> > "miracle-meantone" or "miracle/meantone" at this stage (or maybe
> >ever).
>
> I find that absurd. Miracle involves tempering out a comma
> (1029:1024, 2401:2400), or that is outside the complexity range
> where "marvel" becomes "marvelous". You really just want the other
> comma, 225:224, so why get these, not to mention 81:80, tangled up in
> all this? And if you want to pick two systems where 225:224 vanishes,
> why isn't pajara (that is, the 'decatonic' system of my papers) one
> of them? Miracle-meantone or miracle/meantone is 31-equal, of course.

I've already conceded that miracle-meantone is not a good name for the
planar temperament. But when I look at Rami Vitale's Byzantine
superset scale with the 224:225 tempered out (19 notes), and see that
it is very well described as several parallel chains of secors spaced
apart by slightly narrowed fifths. This seems (to me) like a good
description of it.

Can you explain then why, if "miracle-meantone" is not a good name,
why "marvel" (which strongly suggests "miracle-magic") is?

"224:225 planar temperament" or "septimal-kleismic" seem to me like
good names for the temperament.

-- Dave Keenan

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
>
> /tuning/topicId_51065.html#51403
>
> > Another way to identify linear temperaments is as a combination
of
> two
> > ET's; meantone could be the "5&7" temperament (as on Graham
Breed's
> page
> > http://x31eq.com/temper/method.html).
>
>
> ***I may be getting a glimmer of this. So, in other words, these
two
> ETs provide a kind of intersection that defines the temperament:
as
> in the wonderful new horagrams that Paul Erlich made, where the
> pentatonic and diatonic are, quite obviously, sharing the same
> pitches.

This description applies to both the meantone and schismic horagrams.
To be sure, you need to go further out to more complex rings, where
you'll see them diverge when meantone goes to 19 and schismic goes to
17 . . .

On Sun, 11 Jan 2004 23:42:44 -0000, "Dave Keenan" <d.keenan@bigpond.net.au>
wrote:

>The closing of one door, may make it possible to open another. Surely
>we can have a category of mysterious and marvelous linear
>NON-temperaments. But of course the borderline is fuzzy and it is not
>clear where pelogic should go, or even neutral thirds.

So if we're not going to call a tuning that distributes a comma a
"temperament", what should we call it? I can see that it makes sense to
limit "temperament" to tunings that are reasonably close approximations to
JI (as long as the definition is broad enough to include meantone, 12-ET,
and 12-note circulating temperaments), but whatever we call these other
things needs to start with "t" so that I can keep referring to ET's as
"ET's". :-)

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> Others, like "misty", are less obvious (an
> acronym?).

I had several things in mind when I made up this name (and all of
these names, as I think I warned in my original posting mentioning
them, were not meant to be taken seriously). One of which was that
one earlier list had 'missed' it; another was that, since it vanishes
in 12-equal, one could conceivably do a sophisticated jazz
reharmonization of the tune _Misty_ which exploited the vanishing of
the relevant comma. Which, by the way, just came up on tuning-math.

> When it comes to planar temperaments, it would be hard to visualize
without
> a stereogram of a chart like this, but you could still get an idea
of what
> it could be useful for; "9&10&12" could be seen as a combination of
the
> "9&10" (Negri) and "10&12" (diaschismic) linear temperaments.

My objection to negri/diaschismic for this planar temperament would
be similar to my objection to meantone/miracle for the one others
call 'marvel' . . .

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> So if we're not going to call a tuning that distributes a comma a
> "temperament", what should we call it?

If its musical usefulness derives from distributing particular commas,
then it's a temperament. If not, then it's not a temperament and the
fact that it happens to distribute those (huge) commas would seem
irrelevant, possibly only the generator size is of interest in that
case. Admittedly the boundary is fuzzy.

> I can see that it makes sense to
> limit "temperament" to tunings that are reasonably close
approximations to
> JI (as long as the definition is broad enough to include meantone,
12-ET,
> and 12-note circulating temperaments),

No problem with that. It can certainly allow errors of 20 cents,
possibly 35 cents (at least for 5-limit).

> but whatever we call these other
> things needs to start with "t" so that I can keep referring to ET's as
> "ET's". :-)

"Tunings"? Equal tunings, linear tunings, etc.

on 1/11/04 5:17 PM, Dave Keenan <d.keenan@bigpond.net.au> wrote:

> --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
>> So if we're not going to call a tuning that distributes a comma a
>> "temperament", what should we call it?
>
> If its musical usefulness derives from distributing particular commas,
> then it's a temperament. If not, then it's not a temperament and the
> fact that it happens to distribute those (huge) commas would seem
> irrelevant, possibly only the generator size is of interest in that
> case. Admittedly the boundary is fuzzy.

So I think you are saying that "tempering" involves finding a balance, and
creating something that is whacky-out-of-balance is thus not tempering and
so the result is thus not a temperament. The only problem I see there is
that it makes the word temperament depend too much on opinion. Better
instead to admit whacky things.

Or may I should just admit that many definitions are fussy, and fully of
opinion. After all, we can individually choose not to use the word
temperament for certain things, and that is not problematic as long as we
can still understand other people when they talk.

>> I can see that it makes sense to
>> limit "temperament" to tunings that are reasonably close
> approximations to
>> JI (as long as the definition is broad enough to include meantone,
> 12-ET,
>> and 12-note circulating temperaments),
>
> No problem with that. It can certainly allow errors of 20 cents,
> possibly 35 cents (at least for 5-limit).
>
>> but whatever we call these other
>> things needs to start with "t" so that I can keep referring to ET's as
>> "ET's". :-)
>
> "Tunings"? Equal tunings, linear tunings, etc.

Well I think ET is well-established to mean equal temperament. Changing
history is awkward, leaves a confusing trail, and does not help mainstream
adoption. Mind you I am not advocating tuning evangelism. Let things take
their time. In the meantime, we are a fringe community and so maybe it
would be good to temper our tendencies to redefine terms that *have* made it
into the mainstream.

-Kurt

In a message dated 2004:01:11 10:38:37 PM, lumma1 writes:

>Though sometimes I think the list is a bit like a drug. :(

At first meeting of the TLA (Tuning List Anon):

Hi my name is ____ and I am a microtonal list addict. So baaadly to the
point I forgot the music...

---|-----|--------|-------------|---------------------|
Hanuman Zhang, musical mad scientist

"One taps into the core when one can leave the ego at the door..." - Jacky
Ligon

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> >
> > > I don't think there's any need for a name other than
> > > "miracle-meantone" or "miracle/meantone" at this stage (or
maybe
> > ever).
> >
> > Miracle-meantone is a terrible name.
>
> You're right! It's terrible! It isn't cool, sexy, or bizarre, and it
> doesn't rock.

That's not why it's a terrible name, as I explained. Did you read my
explanation?

> > Marvel it is.
>
> I'm glad you haven't let the fact that I was the first to describe
> this planar temperament influence you in any way.

OK, forget "Marvel" then.

> Paul,
>
> As I said before, I think it would be better if you just go ahead
> without me on this stuff. It would be less painful for all
>concerned.

It would be far more painful for me.

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

> That's not why it's a terrible name, as I explained. Did you read
my
> explanation?

I know he read my explanation, which was the same.

> > > Marvel it is.
> >
> > I'm glad you haven't let the fact that I was the first to describe
> > this planar temperament influence you in any way.
>
> OK, forget "Marvel" then.

I don't think so. Why should Dave be a naming dog in the manger?

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

> But one of the things I intend to
> imply by the name miracle-meantone is that the most interesting
finite
> and even scales are obtained from approximate rectangles where one
> side is parallel to the chains of fifths and the other parallel to
the
> chains of secors, when these are arranged at right angles to each
> other.

Absolutely 'the most interesting'? And by no other pair of "axes"? If
it's true, then I'd be most interested to learn more and follow this
naming idea . . . but otherwise, I maintain my objection to the
miracle-meantone name, and for the reasons I gave, not the reasons
Dave falsely ascribed to me.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> > Here is what I got mathematically as a lattice for 7 and 11 limit
> > Marvel.
>
> Sorry, I forgot to stick in the urls:
>
> /tuning-math/files/planar
plots/p225.jpg

That's not a valid URL -- please advise.

> /tuning-
math/files/planarplots/marvel.jpg

"The requested file or directory is not found on the server."

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

> > Sorry, I forgot to stick in the urls:
> >
/tuning-math/files/planar plots/p225.jpg

/tuning-math/files/planar
plots/marvel.jpg

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

> > This is all so sad; the xeno-temperaments or exo-temperaments or
> > whatever you want to call them
>
> Do you mean the linear tunings that are not approximations of JI?

Yes.

> > and then for the last few to be argued about by
> > those with different ears, timbres, etc. . . .?
> >
> > I know your answer -- no. So father and beep are out. Swallowed
and
> > accepted.
>
> You assume too much.
>
> They may be out, _as_5-limit_temperaments_, and they may be out
under
> those names, but surely we can acknowledge that our theories are
> incomplete.
>
> The closing of one door, may make it possible to open another.
Surely
> we can have a category of mysterious and marvelous linear
> NON-temperaments. But of course the borderline is fuzzy and it is
not
> clear where pelogic should go, or even neutral thirds.
>
> Since we can mathematically define what it means to be as far as
> possible from any simple ratio (i.e. the noble numbers),

That doesn't work, as I've tried to point out repeatedly. Those (the
noble numbers) are as far as possible from *any* ratio, not just
simple ones, but it's only the simple ones that should concern us.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > That's not why it's a terrible name, as I explained. Did you read
> my
> > explanation?
>
> I know he read my explanation, which was the same.
>
> > > > Marvel it is.
> > >
> > > I'm glad you haven't let the fact that I was the first to
describe
> > > this planar temperament influence you in any way.
> >
> > OK, forget "Marvel" then.
>
> I don't think so. Why should Dave be a naming dog in the manger?

I don't know what that means. In any case, this discussion needs to
move, either to tuning-math, or to a private discussion between the
authors of the prospective paper. Let's try to "moderate" the amount
of pain we inflict on readers attempting to keep up with this list,
shall we?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > > Sorry, I forgot to stick in the urls:
> > >
> /tuning-math/files/planar
plots/p225.jpg
>
> /tuning-math/files/planar
> plots/marvel.jpg

This isn't helping . . . anyway, I'll look directly in the folders
when I check tuning-math, and perhaps post comments there.

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

> This isn't helping . . . anyway, I'll look directly in the folders
> when I check tuning-math, and perhaps post comments there.

I changed the name of the folder. Let's see if that does it.

/tuning-math/files/planarplots/p225.jpg

/tuning-math/files/planarplots/marvel.jpg

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
>
> > That's not why it's a terrible name, as I explained. Did you read
> my
> > explanation?
>
> I know he read my explanation, which was the same.
>
> > > > Marvel it is.
> > >
> > > I'm glad you haven't let the fact that I was the first to describe
> > > this planar temperament influence you in any way.
> >
> > OK, forget "Marvel" then.
>
> I don't think so. Why should Dave be a naming dog in the manger?

I don't know what this means, but I was not claiming naming rights,
merely pointing out that they do not belong exclusively to you.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > But one of the things I intend to
> > imply by the name miracle-meantone is that the most interesting
> finite
> > and even scales are obtained from approximate rectangles where one
> > side is parallel to the chains of fifths and the other parallel to
> the
> > chains of secors, when these are arranged at right angles to each
> > other.
>
> Absolutely 'the most interesting'? And by no other pair of "axes"?

I admit I don't really know. But the only ones that have come to my
attention are.

> If
> it's true, then I'd be most interested to learn more and follow this
> naming idea . . . but otherwise, I maintain my objection to the
> miracle-meantone name, and for the reasons I gave, not the reasons
> Dave falsely ascribed to me.

Paul, check the date on that post. It was _before_ your post on the
subject. I was not falsely ascribing them to you, but to Gene. And you
can forget miracle-meantone.

>/tuning-math/files/planar plots/p225.jpg
>
>/tuning-math/files/planar plots/marvel.jpg

Gene, it's best to use %20 if you have a space in a URL.
It's best not to have a space, though, and instead...

() Use an underscore _ or a dash - .

() Use Microsoft-style capitalization; GetAddInfo.

...

/tuning-math/files/planar%20plots/p225.jpg
/tuning-math/files/planar%20plots/marvel.jpg

-Carl

hi paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> >
> > > > Sorry, I forgot to stick in the urls:
> > > >
> > /tuning-math/files/planar
> plots/p225.jpg
> >
> > /tuning-math/files/planar
> > plots/marvel.jpg
>
> This isn't helping . . . anyway, I'll look directly in the folders
> when I check tuning-math, and perhaps post comments there.

all you had to do was eliminate the line-break.

anyway, it would be nice if Gene would get in the habit
of using TinyURL for long links:

http://tinyurl.com/yumtm

http://tinyurl.com/2yb8z

-monz

>I don't know what this means, but I was not claiming naming rights,
>merely pointing out that they do not belong exclusively to you.

You guys... this is so petty...

-Carl

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi paul,
>
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> > wrote:
> > >
> > > > > Sorry, I forgot to stick in the urls:
> > > > >
> > > /tuning-math/files/planar
> > plots/p225.jpg
> > >
> > > /tuning-math/files/planar
> > > plots/marvel.jpg
> >
> > This isn't helping . . . anyway, I'll look directly in the
folders
> > when I check tuning-math, and perhaps post comments there.
>
>
>
> all you had to do was eliminate the line-break.

That only works now. He implemented that fix later, by changing the
name of the subdirectory. At the time, that did not work, since the
subdirectory name had a space in it, so I would have had to insert "%
20" into the URL, as Carl pointed out.

hi paul,

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

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > all you had to do was eliminate the line-break.
>
> That only works now. He implemented that fix later,
> by changing the name of the subdirectory. At the time,
> that did not work, since the subdirectory name had a
> space in it, so I would have had to insert "%20"
> into the URL, as Carl pointed out.

yup, sorry. you're right. in fact, now i remember
that i clicked on those links when Gene first posted
them and they didn't work for me either. i couldn't
even access them by going directly to the tuning-math
files folder. anyway, everything's fine now. :)

-monz

Gene -- I've already created horagrams for most of the
(mathematically speaking, at least) temperaments based on tempering
out a comma with log(n-d)/log(n*d)<1/4 from the 5-limit lattice. The
ones I'm missing would lead to temperaments only mathematically
speaking, but given Dave's "opening a new door", I'd still like to
see them -- for one thing, they may suggest useful 'transposable'
scales for custom-made inharmonic timbres that are still structured
somewhat like the harmonic series. So could you provide the period
and generator for each of the following 'commas':

6/5
32/27
4/3
9/8
10/9
5/4
3/2

I presume 2/1 is an impossibility (since we are assuming octave-
repeating scales)? And of course 1/1 is not a temperament at all . . .

>Gene -- I've already created horagrams for most of the
>(mathematically speaking, at least) temperaments based on tempering
>out a comma with log(n-d)/log(n*d)<1/4 from the 5-limit lattice. The
>ones I'm missing would lead to temperaments only mathematically
>speaking, but given Dave's "opening a new door", I'd still like to
>see them -- for one thing, they may suggest useful 'transposable'
>scales for custom-made inharmonic timbres that are still structured
>somewhat like the harmonic series. So could you provide the period
>and generator for each of the following 'commas':
>
> 6/5
> 32/27
> 4/3
> 9/8
> 10/9
> 5/4
> 3/2
>
>I presume 2/1 is an impossibility (since we are assuming octave-
>repeating scales)? And of course 1/1 is not a temperament at all . . .

1, doesn't this belong on tuning-math?

2, Why not use TOP?

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Gene -- I've already created horagrams for most of the
> >(mathematically speaking, at least) temperaments based on
tempering
> >out a comma with log(n-d)/log(n*d)<1/4 from the 5-limit lattice.
The
> >ones I'm missing would lead to temperaments only mathematically
> >speaking, but given Dave's "opening a new door", I'd still like to
> >see them -- for one thing, they may suggest useful 'transposable'
> >scales for custom-made inharmonic timbres that are still
structured
> >somewhat like the harmonic series. So could you provide the period
> >and generator for each of the following 'commas':
> >
> > 6/5
> > 32/27
> > 4/3
> > 9/8
> > 10/9
> > 5/4
> > 3/2
> >
> >I presume 2/1 is an impossibility (since we are assuming octave-
> >repeating scales)? And of course 1/1 is not a temperament at
all . . .
>
> 1, doesn't this belong on tuning-math?

Since people seem to 'grok' horagrams, I figured it would be nice to
have them here . . .

> 2, Why not use TOP?

Did I say not to? But if he doesn't, I'll of course make the
necessary adjustments.

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

> 6/5

[1200 544] [<1 1 2| <0 1 1|]
TOP [1135 1800 2936]

> 32/27

[400 35] [<3 5 7| <0 0 1|]
TOP [1170 1950 2716]
> 4/3

[1200 565] [<1 2 3| <0 0 -1|]
TOP [1061 2122 2464]

> 9/8

[600 264.66] [<2 3 5| <0 0 -1|]
TOP [1233.05 1849.57 2863.05]

> 10/9

[1200 406.84] [<1 2 3| <0 -1 -2|]
TOP [1171.90 1946.49 2721.07]

> 5/4

[1200 508.8] [<1 1 2| <0 1 0|]
TOP [1289 2044 2579]

> 3/2

[1200 35] [<1 1 2| <0 0 1|]
TOP [1472 1472 3417]

> I presume 2/1 is an impossibility (since we are assuming octave-
> repeating scales)? And of course 1/1 is not a temperament at all . .

TOP(2) = [0 3804 0]

TOP(1) = undefined

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > 6/5
>
> [1200 544] [<1 1 2| <0 1 1|]
> TOP [1135 1800 2936]
>
> > 32/27
>
> [400 35] [<3 5 7| <0 0 1|]
> TOP [1170 1950 2716]
> > 4/3
>
> [1200 565] [<1 2 3| <0 0 -1|]
> TOP [1061 2122 2464]
>
> > 9/8
>
> [600 264.66] [<2 3 5| <0 0 -1|]
> TOP [1233.05 1849.57 2863.05]
>
> > 10/9
>
> [1200 406.84] [<1 2 3| <0 -1 -2|]
> TOP [1171.90 1946.49 2721.07]
>
> > 5/4
>
> [1200 508.8] [<1 1 2| <0 1 0|]
> TOP [1289 2044 2579]
>
> > 3/2
>
> [1200 35] [<1 1 2| <0 0 1|]
> TOP [1472 1472 3417]

Thanks (though I wonder why you're not expressing the period and
generator in the same tuning as the primes), I'll be making a new set
of horagrams with these shortly. I've made improvements to the
horagram-generating program; among other things, it shows the size of
each step in each scale, rounded to the nearest cent, in the 'box'
corresponding to that step . . .

> > I presume 2/1 is an impossibility (since we are assuming octave-
> > repeating scales)? And of course 1/1 is not a temperament at
all . .
>
> TOP(2) = [0 3804 0]

What's that vector? It's not the primes, since TOP tempering 2:1 out
should leave 3 and 5 unchanged . . .

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

> Thanks (though I wonder why you're not expressing the period and
> generator in the same tuning as the primes), I'll be making a new
set
> of horagrams with these shortly.

I need to redo all the ones which have less than three primes in
their factorization because of the two-prime bug you caught.

--- In tuning@yahoogroups.com, czhang23@a... wrote:

/tuning/topicId_51065.html#51623

>
> In a message dated 2004:01:11 10:38:37 PM, lumma1 writes:
>
> >Though sometimes I think the list is a bit like a drug. :(
>
> At first meeting of the TLA (Tuning List Anon):
>
> Hi my name is ____ and I am a microtonal list addict. So
baaadly to the
> point I forgot the music...
>

***Heh, heh... that's been a consistent accusation... :)

JP

In a message dated 2004:01:13 04:22:37 AM:

>> >Though sometimes I think the list is a bit like a drug. :(
>
>> At first meeting of the TLA (Tuning List Anon):
>>
>> Hi my name is ____ and I am a microtonal list addict. So
>>baaadly to the point I forgot the music...
>
>***Heh, heh... that's been a consistent accusation... :)

:) we are all guilty of some bit o' obsession - esp'ly any musical mad
scientist worth his salt...
I once got arrested for it, too...Imagine now what could and can happen
to a crazy Asian male "armed" with drumsticks and mallets on a Houston, Texas
street near a luxury hotel and rich fair-skinned folks behind their private
security armies and gated estates at 3am in the early rabid Reaganite Era.....
"Misdemeanor Disturbing the Peace", "Vandalism," "Criminal Mischief,"
"Possession of a Concealed Weapon," & "Resisting Arrest" ...

---///// __/_//_/ __/_//
Nom de Guerre: Hanuman "Stitch/626" Zhang

"Music is real only when it is carried by the flesh and blood of
performance. Ideas stay pale when they lie flat on the printed page." - Peter Brook

on 1/13/04 5:29 AM, czhang23@aol.com <czhang23@aol.com> wrote:

>
> In a message dated 2004:01:13 04:22:37 AM:
>
>>>> Though sometimes I think the list is a bit like a drug. :(
>>
>>> At first meeting of the TLA (Tuning List Anon):
>>>
>>> Hi my name is ____ and I am a microtonal list addict. So
>>> baaadly to the point I forgot the music...
>>
>> ***Heh, heh... that's been a consistent accusation... :)
>
> :) we are all guilty of some bit o' obsession - esp'ly any musical mad
> scientist worth his salt...
> I once got arrested for it, too...Imagine now what could and can happen
> to a crazy Asian male "armed" with drumsticks and mallets on a Houston, Texas
> street near a luxury hotel and rich fair-skinned folks behind their private
> security armies and gated estates at 3am in the early rabid Reaganite Era.....
> "Misdemeanor Disturbing the Peace", "Vandalism," "Criminal Mischief,"
> "Possession of a Concealed Weapon," & "Resisting Arrest" ...

Straight out of Vineland. No exhaggeration on your part?

-Kurt

In a message dated 2004:01:14 10:58:19 AM, kkb@breathsense.com writes:

>> :) we are all guilty of some bit o' obsession - esp'ly any musical mad
>> scientist worth his salt...
>> I once got arrested for it, too...Imagine now what could and can happen
>> to a crazy Asian male "armed" with drumsticks and mallets on a Houston,
>Texas
>> street near a luxury hotel and rich fair-skinned folks behind their private
>> security armies and gated estates at 3am in the early rabid Reaganite
>Era....."Misdemeanor Disturbing the Peace", "Vandalism," "Criminal Mischief,"
>> "Possession of a Concealed Weapon," & "Resisting Arrest" ...
>
>Straight out of Vineland. No exhaggeration on your part?

::chagrinnie:: nope. I'm glad I am not doin impulsive acts like these in
these peculiar times... & luckily I only got psych monitoring/probation for 5 yrs
(5 yrs max w/o parole in the Huntsville Hole otherwise... skipped outta TX 2-3
days before it was up... lawyer said TX doesn't care just as long as I don't
return w/o permission/forewarning... end of story. back to music.)

Z.

"Taoism in a nutshell: Shit Happens. Roll with the Punches. Hang 10 - Go
with the Flow!" - anon. California surferBeatnik, c.1950's/1960's