question about 24-tET

Well, last night at Johnny Reinhard's AFMM board meeting some
interesting questions came up.

As we have been mentioning on this list, many of the so-
called "spectral" composers such as Gerard Grisey and Tristan Mureil
(soon to be featured on Johnny's series this year) use *quarter
tones* to emulate various acoustic or just intonation-like phenomina.
(for better or *worse*).

Now the question I have concerns properties of 24-tET. Johnny
Reinhard, logically enough, states that whatever properties 12-equal
has, 24 equal must have also, since 12 is an obvious subset.

HOWEVER, on Paul Erlich's chart of the various ETs I note that there
is some discrepency between the properties of 12-tET and the
properties of 24-tET.

Three-limit intervals and five-limit intervals share the
same "accuracy" measure.

HOWEVER, 7-limit and 9-limit intervals are shown as having a about
a .5 "accuracy" for the 12-tET scale and they *aren't even on the
chart* for 24-tET.

Whyzzat? If 24 should have all the properties of 12-tET??

Signed, curious...

Joseph Pehrson

Joe,

This all has to do with consistency, you've got to understand the
implications of that before Paul's charts mean a hill of beans.

I'm of the opinion that consistency, especially if overzealously
applied, is a theoretical bogeyman--it causes more scare than it has
any reason to.

take care,

--Dan Stearns

----- Original Message -----
From: "jpehrson2" <jpehrson@rcn.com>
To: <tuning@yahoogroups.com>
Sent: Monday, February 11, 2002 8:11 AM
Subject: [tuning] question about 24-tET

> Well, last night at Johnny Reinhard's AFMM board meeting some
> interesting questions came up.
>
> As we have been mentioning on this list, many of the so-
> called "spectral" composers such as Gerard Grisey and Tristan Mureil
> (soon to be featured on Johnny's series this year) use *quarter
> tones* to emulate various acoustic or just intonation-like
phenomina.
> (for better or *worse*).
>
> Now the question I have concerns properties of 24-tET. Johnny
> Reinhard, logically enough, states that whatever properties 12-equal
> has, 24 equal must have also, since 12 is an obvious subset.
>
> HOWEVER, on Paul Erlich's chart of the various ETs I note that there
> is some discrepency between the properties of 12-tET and the
> properties of 24-tET.
>
> Three-limit intervals and five-limit intervals share the
> same "accuracy" measure.
>
> HOWEVER, 7-limit and 9-limit intervals are shown as having a about
> a .5 "accuracy" for the 12-tET scale and they *aren't even on the
> chart* for 24-tET.
>
> Whyzzat? If 24 should have all the properties of 12-tET??
>
> Signed, curious...
>
> Joseph Pehrson
>
>
>
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> > From: jpehrson2 <jpehrson@rcn.com>
> > To: <tuning@yahoogroups.com>
> > Sent: Monday, February 11, 2002 8:11 AM
> > Subject: [tuning] question about 24-tET
> >
> >
> > As we have been mentioning on this list, many of the so-
> > called "spectral" composers such as Gerard Grisey and Tristan Mureil
> > (soon to be featured on Johnny's series this year) use *quarter
> > tones* to emulate various acoustic or just intonation-like phenomina.
> > (for better or *worse*).
> >
> > Now the question I have concerns properties of 24-tET. Johnny
> > Reinhard, logically enough, states that whatever properties 12-equal
> > has, 24 equal must have also, since 12 is an obvious subset.
> >
> > HOWEVER, on Paul Erlich's chart of the various ETs I note that there
> > is some discrepency between the properties of 12-tET and the
> > properties of 24-tET.
> >
> > Three-limit intervals and five-limit intervals share the
> > same "accuracy" measure.
> >
> > HOWEVER, 7-limit and 9-limit intervals are shown as having a about
> > a .5 "accuracy" for the 12-tET scale and they *aren't even on the
> > chart* for 24-tET.
> >
> > Whyzzat? If 24 should have all the properties of 12-tET??
>
>
> From: D.Stearns <STEARNS@CAPECOD.NET>
> To: <tuning@yahoogroups.com>
> Sent: Monday, February 11, 2002 11:34 AM
> Subject: Re: [tuning] question about 24-tET
>
>
> Joe,
>
> This all has to do with consistency, you've got to understand the
> implications of that before Paul's charts mean a hill of beans.
>
> I'm of the opinion that consistency, especially if overzealously
> applied, is a theoretical bogeyman--it causes more scare than it has
> any reason to.

Dan's right about it having to do with consistency
in a nutshell: 24edo is different from 12edo in regard to
prime-factor 7 because 24 offers better approximations it
than 12 does, but still not close enough to be consistent.

for example, let's say we want to analyze the composition
of an implied 7:4 as the sum of 5:4 and 7:5. we get:

number of degrees:
12edo 24edo

best 5:4 4 8
best 7:5 6 12
sum 10 20
best 7:4 10 19

24edo offers a better approximation to 7:4 with
2^(19/24) = 950 cents, but the sum of its best
approximations to 5:4 = 2^(8/19) = 400 cents and to
7:5 = 2^(12/24) = 600 cents is 2^(20/24) = 1000 cents.
so it's inconsistent in the 7-limit.

(Paul just explained this on one of the lists very recently,
like in the last week or so.)

but given my liking for 24edo, i also tend to agree with
Dan about the overzealous concern over consistency.
i think that's because both of us compose music in 24edo
without really thinking too hard about the rational
implications ... at least i know that's the case with me.

the same goes for my occasional use of 144edo for notational
purposes <http://www.ixpres.com/interval/dict/144edo.htm>
which Dan suggested to me a couple of years ago, altho here,
since the whole objective is to devise a notation, the
issue of consistency is a lot more relevant.

-monz

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

/tuning/topicId_33969.html#33974

>
> 24edo offers a better approximation to 7:4 with
> 2^(19/24) = 950 cents, but the sum of its best
> approximations to 5:4 = 2^(8/19) = 400 cents and to
> 7:5 = 2^(12/24) = 600 cents is 2^(20/24) = 1000 cents.
> so it's inconsistent in the 7-limit.
>
> (Paul just explained this on one of the lists very recently,
> like in the last week or so.)
>

****Thanks, Monz for the help with this. Yes, the discussion on
consistency was in relationship to the Patrick Ozzard-Low
publication, and it was on this list...

Well, I think I get the overall picture on that, but, on the other
hand, if 24-tET contains all the pitches of 12, like Johnny Reinhard
attests, (I think he's right, too! :) )shouldn't it *at least* have
all the properties of 12, regardless of the "niceties" of the
mathmatics??

JP

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, February 11, 2002 10:56 AM
> Subject: [tuning] Re: question about 24-tET
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_33969.html#33974
>
> >
> > 24edo offers a better approximation to 7:4 with
> > 2^(19/24) = 950 cents, but the sum of its best
> > approximations to 5:4 = 2^(8/19) = 400 cents and to
> > 7:5 = 2^(12/24) = 600 cents is 2^(20/24) = 1000 cents.
> > so it's inconsistent in the 7-limit.
> >
> > (Paul just explained this on one of the lists very recently,
> > like in the last week or so.)
> >
>
> ****Thanks, Monz for the help with this. Yes, the discussion on
> consistency was in relationship to the Patrick Ozzard-Low
> publication, and it was on this list...
>
> Well, I think I get the overall picture on that, but, on the other
> hand, if 24-tET contains all the pitches of 12, like Johnny Reinhard
> attests, (I think he's right, too! :) )shouldn't it *at least* have
> all the properties of 12, regardless of the "niceties" of the
> mathmatics??

well, sure, Joe, 24edo d o e s have all the properties of 12
i f y o u c h o o s e t o u s e * e v e r y o t h e r *
note of the 24edo scale.

the only reason consistency becomes a problem is because 24edo
d o e s offer a better approximation to it than 12. but that
doesn't mean anyone h a s to use that better approximation.

if you continue to use 2^(20/24) as your representation of 7:4,
then there's no problem -- it works just like 12edo.

the problem only occurs if you want to make the seemingly
reasonable choice of using the closer approximation.
but if you're concerned about consistency, you'll soon
find that that better approximation may not be the more
reasonable choice after all.

my own personal approach: i happen to really love the
950-cent interval 24edo provides, and i use it regardless
of the inconsistency. but as i said in my earlier post,
when i compose in 24edo i'm generally going entirely by
the visceral feel of the sound of it, and not thinking too
much about the implied ratios . . . which is an approach
i don't take with most other tunings, and which is one of
the reasons i like composing in 24edo. it gets me away
from so much analysis, and more into "pure feeling".

of course one can use this approach with any tuning, but
i find that certain edos (the usual suspects: 17, 19, 31,
55, 72, etc.) have such good approximations to at least
a few important JI ratios that it's hard for me to get
away from all the *thinking* that automatically accompanies
sonorities with whose mathematics i'm so familiar. 24edo
solves that problem for me by not offering much beyond
3, in terms of approximating prime-factors well. so it
gives me a freedom to simply play with the sound that i
can't capture for the other tunings.

-monz

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> From: monz <joemonz@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, February 11, 2002 11:18 AM
> Subject: Re: [tuning] Re: question about 24-tET
>
>
> . . . but i find that certain edos (the usual suspects: 17,
> 19, 31, 55, 72, etc.) have such good approximations to at
> least a few important JI ratios that it's hard for me to get
> away from all the *thinking* that automatically accompanies
> sonorities with whose mathematics i'm so familiar. 24edo
> solves that problem for me by not offering much beyond
> 3, in terms of approximating prime-factors well. so it
> gives me a freedom to simply play with the sound that i
> can't capture for the other tunings.

72edo is the perfect example of a tuning from whose rational
implications i can't escape. i wrote about this here before,
when we were discussing Maneri's approach to 72edo training.
viewing 72edo simply as a more subtle division of the pitch-
continuum, he deliberately avoids a n y reference to ratios
in his book.

but because my 72edo and HEWM ll-limit JI notations both use
the same accidentals for the same JI ratios which 72edo implies
well, and because the two systems do translate into each other
so well (i.e., because 72edo has good a n d consistent
approximations to 11-limit JI), i found that as i tried to
sight-sing Maneri's musical examples, i couldn't get away
from the understanding i already had about which ratios were
being implied in those examples. so there's no way for me
to use 72edo without consciously thinking about the implied
ratios. this is not a problem in 24edo.

-monz

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

/tuning/topicId_33969.html#33976
>
> well, sure, Joe, 24edo d o e s have all the properties of 12
> i f y o u c h o o s e t o u s e * e v e r y o t h e r *
> note of the 24edo scale.
>
> the only reason consistency becomes a problem is because 24edo
> d o e s offer a better approximation to it than 12. but that
> doesn't mean anyone h a s to use that better approximation.
>
> if you continue to use 2^(20/24) as your representation of 7:4,
> then there's no problem -- it works just like 12edo.
>
> the problem only occurs if you want to make the seemingly
> reasonable choice of using the closer approximation.
> but if you're concerned about consistency, you'll soon
> find that that better approximation may not be the more
> reasonable choice after all.
>

***Well, I guess that makes sense, but *still* it seems rather
peculiar not to list the "goodness" of 24-tET as *at least* as "good"
as 12-tET.

When Paul gets back on, maybe he can explain this to me, but it seems
a little like "the forest for the trees" syndrome at the moment,
since it *would* be possible to use *every other note* in 24-tET and
get *at least* the "goodness" of 12.

That be bad, bro!

JP

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Joe,
>
> This all has to do with consistency, you've got to understand the
> implications of that before Paul's charts mean a hill of beans.

which is why that particular chart is accompanied by a footnote in my
paper explaining the definition of consistency, and that i don't plot
points that suffer from it. they're irrelevant for the purposes of
the paper since, however the intervals are mapped, the corresponding
accuracy values could not possibly come out within the realm of
interest. note that i only went up to 34-equal.

> I'm of the opinion that consistency, especially if overzealously
> applied, is a theoretical bogeyman--it causes more scare than it has
> any reason to.

as a mere footnote in the paper, i don't think it's going to
be 'frightening' a lot of people.

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> Well, I think I get the overall picture on that, but, on the other
> hand, if 24-tET contains all the pitches of 12, like Johnny
Reinhard
> attests, (I think he's right, too! :) )shouldn't it *at least*
have
> all the properties of 12, regardless of the "niceties" of the
> mathmatics??

again, the chart has to be taken in the context of the paper to which
it belongs.

but then again, other people might have different expectations. for
example, johnny's friend marc jones feels that the errors in 24
actually *sound* twice as large as those in 12, because of the
context, even though they're acoustically identical. marc can correct
be if i've phrase this poorly . . .

anyhow, the *right* way to do that chart would be to have *several*
different points for 24-equal 7-limit, *several* different points for
24-equal 9-limit, etc., depending on how the primes are mapped. i'd
be happy to do this if you wish, but as it stands now, the chart
would become horribly cluttered.

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

/tuning/topicId_33969.html#33992

> but then again, other people might have different expectations. for
> example, johnny's friend marc jones feels that the errors in 24
> actually *sound* twice as large as those in 12, because of the
> context, even though they're acoustically identical. marc can
correct be if i've phrase this poorly . . .
>
> anyhow, the *right* way to do that chart would be to have *several*
> different points for 24-equal 7-limit, *several* different points
for 24-equal 9-limit, etc., depending on how the primes are mapped.
i'd be happy to do this if you wish, but as it stands now, the chart
> would become horribly cluttered.

***Thanks, Paul, for the update.

Well, since all these important European "cat" composers are trying
to use 24-tET to map just intonation and acoustical properties in
the "spectral" school, it might be worth while for *me* at least, to
know more about it's properties! So anything you can do in this
regard would be appreciated!

Thanks!

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> Well, since all these important European "cat" composers are trying
> to use 24-tET to map just intonation and acoustical properties in
> the "spectral" school, it might be worth while for *me* at least,
to
> know more about it's properties! So anything you can do in this
> regard would be appreciated!

so you'd like a version of that chart that shows all the
possibilities, then? can we trim down the chart somehow . . . what's
the highest limit you want to look at?

Paul,

As you probably know, most of my objections here are simply
ideological--I appreciate and often enjoy the math. But there's no
doubting that measures like consistency, and nearly all of what's
discussed on these lists (theory wise) for that matter, give tunings
like 13 and 20-tet (et al.) the short end of the stick--if they give
them an end at all.

Whatever, that's the way it is and that's okay. However, this does
lead some, even more than some I'd bet, to prematurely concluded that
these types of tunings are therefore inferior or of little use, and
that's were my objections come from--they're not, they're fine!
Especially if we're talking about music (or even ideology).

BTW, did somebody forget to mail me the new restricted use of capital
letters guidelines!

take care,

--Dan Stearns

----- Original Message -----
From: "paulerlich" <paul@stretch-music.com>
To: <tuning@yahoogroups.com>
Sent: Monday, February 11, 2002 1:48 PM
Subject: [tuning] Re: question about 24-tET

> --- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> > Joe,
> >
> > This all has to do with consistency, you've got to understand the
> > implications of that before Paul's charts mean a hill of beans.
>
> which is why that particular chart is accompanied by a footnote in
my
> paper explaining the definition of consistency, and that i don't
plot
> points that suffer from it. they're irrelevant for the purposes of
> the paper since, however the intervals are mapped, the corresponding
> accuracy values could not possibly come out within the realm of
> interest. note that i only went up to 34-equal.
>
> > I'm of the opinion that consistency, especially if overzealously
> > applied, is a theoretical bogeyman--it causes more scare than it
has
> > any reason to.
>
> as a mere footnote in the paper, i don't think it's going to
> be 'frightening' a lot of people.
>
>
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hey Dan,

> From: D.Stearns <STEARNS@CAPECOD.NET>
> To: <tuning@yahoogroups.com>
> Sent: Monday, February 11, 2002 5:39 PM
> Subject: Re: [tuning] Re: question about 24-tET
>
>
> Paul,
>
> As you probably know, most of my objections here are simply
> ideological--I appreciate and often enjoy the math. But there's no
> doubting that measures like consistency, and nearly all of what's
> discussed on these lists (theory wise) for that matter, give tunings
> like 13 and 20-tet (et al.) the short end of the stick--if they give
> them an end at all.
>
> Whatever, that's the way it is and that's okay. However, this does
> lead some, even more than some I'd bet, to prematurely concluded that
> these types of tunings are therefore inferior or of little use, and
> that's were my objections come from--they're not, they're fine!
> Especially if we're talking about music (or even ideology).

did you happen to catch my responses to this?
(especially the second one)

/tuning/topicId_33969.html#33974
Message 33974, Date: Mon Feb 11, 2002 5:52 pm

/tuning/topicId_33969.html#33976
Message 33976, Date: Mon Feb 11, 2002 7:18 pm

thoughts of you kept popping into my mind as i wrote it.

> BTW, did somebody forget to mail me the new restricted
> use of capital letters guidelines!

other folks have been doing it, and paul and i both
decided together to switch to it one day when we were
having an IM chat.

i have to say that paul went more extreme than i did
... i still retain caps for proper names, he doesn't
use them at all anymore, except for acronyms.

-monz

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On 2/11/02 4:53 PM, "paulerlich" <paul@stretch-music.com> wrote:

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
>> Well, I think I get the overall picture on that, but, on the other hand, if
>> 24-tET contains all the pitches of 12, like Johnny Reinhard attests, (I think
>> he's right, too! :) )shouldn't it *at least* have all the properties of 12,
>> regardless of the "niceties" of the mathmatics??
>>
> again, the chart has to be taken in the context of the paper to which it
> belongs.
>
> but then again, other people might have different expectations. for example,
> johnny's friend marc jones feels that the errors in 24 actually *sound* twice
> as large as those in 12, because of the context, even though they're
> acoustically identical. marc can correct be if i've phrase this poorly . . .
>
> anyhow, the *right* way to do that chart would be to have *several* different
> points for 24-equal 7-limit, *several* different points for 24-equal 9-limit,
> etc., depending on how the primes are mapped. i'd be happy to do this if you
> wish, but as it stands now, the chart would become horribly cluttered.
>

Hi Paul.

I see this new mail rule works, copying any "marc" in an email text to my
"YOU RANG?" folder.

As far as something incidental, I had this idea, as an extreme example:

* If you look at a mixer, when there's a consistent signal that drops to
silence, it takes a small amount of time for the meter to return to zero
volume because to display decibels, it has to calculate the average power of
the signal over that amount of time.

* If you also consider the volume-vs-frequency results of applying an
equalizer to a certain frequency, a sort of bell curve rises and falls
around that frequency, affecting every frequency around it, but less and
less, the farther away it is.

-- Similarly, say you have a 12 tone piece with one quartertone in it. If
you could map temperament vs time, the list might go something like this:

"12 12 12 12 24 12 12 12 12 ..."

At the point the quartertone is hit, there it is, it's in 24. At any other
point, you could say it's in 12.

If you had a little more leading up to and away from it, somehow, it would
feel something like this:

"Normal, normal, normal, hey that weird note is coming, BWONK, wasn't that
strange, back to normal, normal, normal..."

If you could imagine why I was thinking of the afterglow effect, unless you
really psyche yourself into this being a "quartertone piece", per se, the
context is going to shift in and out of that one moment, if you have a solid
sense of what 12 sounds like.

Personally, I think it's much more likely to be this than "normal normal
normal normal QUARTERTONE aaaa what was that oh no nothing will ever be the
same, quartertone,
quartertone,
Quartertone...

In a sense, this just pierced the center of all my work. The idea that one
note could cause that much of a change in your sense of context is really
the bottom line in terms of whether something is traumatic or not. In the
first case, if you can get back to normal, it wasn't. In the second case,
it comes back to affect you, so it is traumatic.

Anyway.

Before looking at this in terms of 12 vs 24, you can do the same thing
within 12 by itself. Consider playing a major scale oriented piece for
awhile and throw in a minor chord. It's going to sound strange at first.

That¹s just it. If it's just a matter of 12 is in 24, for that matter, 24
is in 48, 120, 24000 etc. What it really comes down to in non prime
temperaments, if their factors are at all relevant, is at what point are you
interpolating with the multiple, and how much, and how severe. The bottom
line is EXACTLY WHAT NOTES are you using.

"Acoustically":

All of the above only really applies to the case of the non-guitar. Any
acoustic instrument that doesn't have a temperament-specific resonance is
what I was talking about. Basically any instrument, piano, winds, brass,
strings, anything you tune a note to, within the context of every other note
you hear from it, forms a sort of overall image of what's going on, and all
of your temperament and harmonic issues can work themselves out.

Actually I'd have to cut that back a little because this is 100 percent true
in electronic timbre that doesn't have any acoustic stake once it's out of
the machine. That on second thought, the acoustic instruments that resonate
*a little*, MIGHT actually have a low volume kickback that might have some
interesting subtle effects on the next note. But in general, you hear what
you play and that's it.

The placement of frets on a guitar drastically affects the timbre. I was
always completely amazed that all of my interchangeable boards sound
completely different on the SAME GUITAR. This mystified me for years.
After about the last 10 years of trying to figure out the whole
microacoustic deal behind that, a couple months ago I started getting the
idea a little.

You might think "maybe it's just the wood". I did. For that matter, I have
to mention this. One of my first METAL fretted guitars was a 34. Not 34
like it's 32 and someone said it was 34. COUGH COUGH. It was a 34 :) I
had it for quite a few months. I'd also wanted to try 17 so I figured I
could do enough with 17 on the 34, since I only really had room for *one*
more guitar at the time. I was a bit disappointed in that suite though. It
didn't seem like 17 had as much power in its sharp fifths as I'd imagined.

But why.

Here's an even thicker plot. At one point I decided since it was such a
cheap guitar, I'd just pluck out every other fret and make the 34 a 17. I
thought one of the pickups was shot. It DIDN'T SOUND ANYTHING LIKE the 34.
A much deeper tone. None of the really high harmonics I'd heard before.
But you know what. All of the diversity of the whole "stretched"
Pythagorean or whatever you call it, believe me, it was there in full force.

Now for the life of me, for like 10 years, I could NOT understand how this
same guitar, fretted in 34, could have such a beautiful tone and have such
horrible sounding fifths. And on the other hand, how could it have such a
bludgeoning tone in 17 but have fifths you could sink your teeth into just a
bit more than 12, enough to make it worthwhile?

I couldn't even imagine the physics to it, but I was sure it had something
to do with THE FRETS, and their placement, and after very little thought, of
course, it has something to do with the vibration of the string echoing down
into the cavities between and back up into the string. I often asked people
to imagine a bare wall with sound reflecting off it, then imagine the wall
with a BIRCH TREE every two feet. You think it would change the sound JUST
a little??

There's just something about a guitar ;)

So one day my friend Ken, the only person who's really been able to keep up
with playing "my guitars" (the one who stood me up for the guitar quartet
performance...) was working with my interchangeable. I was sitting typing
at the computer. He hits this note... Waaaaaaaa... I said oh you wanted to
check out the 46 huh I figured as much. He was silent for a few minutes. I
kept typing oblivious. I looked over and he had this look. He said how did
you KNOW it was 46? I said because it sounded like it. He said but... I
only played one note. Talk about "WATSON COME HERE I NEED YOU"... It's the
stupidest thing, really, but it led to one of the most broad philosophical
discussions about temperament and guitar. We went into experiment mode and
by the end of the day, much like the psychic playing card test, we were able
to guess what temperament the other was playing by hearing one note. We
worked with, I think, 41, 43, 46 and 50.

You know what it is? I have to say. I HAVE TO give credit to the guy that
came up with the show "CSI: Crime Scene Investigation"... If you've ever
seen them trying to solve a crime, as far as bullets hitting bones, they do
this almost telepathic movie type footage and zooms all the way into the
persons body and shows with computer graphics in slow motion the bullet
breaking the bone. Then whoosh, back out into the crime lab. It's almost
like you're getting a quick trip through hyperspace into the actual mental
space where they're imagining what's happened, trying to reconstruct a
crime. With my stake in physics, I've since started imagining quantum
motion in time and space with that kind of CSI footage once in awhile.

If you'd please forgive the size and structure of this huge analogy I'm
trying to lay out for you...

... I really put myself on the guitar string and moved as it would, and I
FINALLY started understanding the root of ALL of this. It's easy enough to
imagine a sound wave as a sort of EKG of, say, one particle's testimony of
having traveled up and down the string, and what intensities of energies it
had found along the way. I was SO CLOSE by thinking that the different size
CAVITIES in fretboards of different temperaments would SUPRESS certain
harmonics!!! And this, to myself, is how I sulk thinking I ALWAYS MISS THE
UTTERLY OBVIOUS. The fact that the cavities muffle certain frequencies is
only a distant symptom of the idea that the FRETS *REINFORCE* certain
frequencies!!! I mean DUH.

On a side note, if you think about what "pinching" a harmonic does, it's not
so distantly related.

So think about starting at the bridge, and traveling to the nut, making the
top half of a sort of sine wave. Every time you hit a fret, you would get a
sort of volume spike. But this is the trick. The distance between bridge
and note describes the frequency in the first place. So when you hit that
volume spike, you're making a sort of goosebump which strongly suggests the
note by fretting directly under it. It teases, and passes, on to the next
spike. The trick is, that the distance in time from the beginning of the
wave to every volume spike hints at EVERY NOTE IN THE TEMPERAMENT from the
topmost fret down to the one you're playing!

In other words? In simpler terms?

When you play one note in a fully fretted temperament, you hear traces of
every other note in the temperament up an octave or so. Alongside of those
frequencies, you also have traces of the frequencies produced at the OTHER
END of the string, which pigtail along as a temperament's own unique array
of something along the lines of formants.

Simpler...

If you play one note on a microtonal guitar, you hear every note in the
temperament. You also hear its own "vocal pattern".

Which is why I had problems between 34 and 17 on the same guitar despite
each other.

I've heard a few people say that playing a temperament within its double
makes it counter-intuitive.

Long long ago, I played a 24. I don't remember whose it was, or whether I'd
made it or not. Playing 12 in fully fretted 24, sounded like whole tone
scales. It actually felt like playing 6 in 12, sort of floating along with
no resolution. That was long ago though.

But still, to answer your question:

1. If you're playing an acoustic or electronic instrument, the sensitivity
to a multiple temperament has more to do with how much of it you use versus
its factor.

2. If you're playing a GUITAR, the temperament lingers. Heh heh.

Here's an idea Paul. My next guitar quartet is going to be in 49. There's
a certain amount of it that's going to be in the 22 + 27 scale. I would bet
that if you (you, personally) played along with the retuned midi foundation,
you'd feel it was in 22. And that if you played along with the final mix in
49, that you would feel something along the lines of your hands being pulled
away from the guitar in three different directions; sort of like you're
almost playing the right guitar but there's something really wrong with the
air today.

Actually I couldn't say what the effect of 22 under 49 would be. Playing 31
guitar under a 43 or 50 usually sounds like breaking glass, although in midi
it makes it all the more rich. Sort of the difference between mixing paint
to black and mixing light to white. Anyway I'll get you a copy of one of
the 22 segments maybe in March or so.

Well anyway :)

I hope this gave you a little insight. Actually Johnny Reinhard's
sensitivity to increment of cents values and my sensitivity to increment of
temperament density all but negate each other. One desensitizes you to the
other, almost like reciprocals.

Thanks for thinking of me.

Marc

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

/tuning/topicId_33969.html#33976

>
> of course one can use this approach with any tuning, but
> i find that certain edos (the usual suspects: 17, 19, 31,
> 55, 72, etc.) have such good approximations to at least
> a few important JI ratios that it's hard for me to get
> away from all the *thinking* that automatically accompanies
> sonorities with whose mathematics i'm so familiar. 24edo
> solves that problem for me by not offering much beyond
> 3, in terms of approximating prime-factors well. so it
> gives me a freedom to simply play with the sound that i
> can't capture for the other tunings.
>

****This is a *fascinating* post, Monz! Maybe, in a way, you think
of it as something "familiar" as an "extension" of 12-equal??

Anyway, I think I'm going to have to give 24-tET more respect...

Joe

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> ****This is a *fascinating* post, Monz! Maybe, in a way, you think
> of it as something "familiar" as an "extension" of 12-equal??
>
> Anyway, I think I'm going to have to give 24-tET more respect...

well, sorry i misled you . . . i thought it would have been obvious
that 24-equal could do anything 12-equal could do . . . but as far as
the 7-limit, it doesn't give you the improvement you might expect,
and funny things can happen if you try to approximate 7-limit
intervals in 24-equal . . . i think robert walker composed a piece of
music illustrating some of these 'funny things' . . .

Hey Marc,

Good to see big old high strangeness Orphon Soul post again! You've
got a wonderfully, easy flowing touch that's as refreshing as it is
imaginative--like some sudden and alarmingly colorful blossom in the
middle of a perennially arid environment.

thanks,

--Dan Stearns

----- Original Message -----
From: "Orphon Soul, Inc." <tuning@orphonsoul.com>
To: "Tuning List" <tuning@yahoogroups.com>
Sent: Monday, February 11, 2002 5:33 PM
Subject: Re: [tuning] Re: question about 24-tET

On 2/11/02 4:53 PM, "paulerlich" <paul@stretch-music.com> wrote:

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
>> Well, I think I get the overall picture on that, but, on the other
hand, if
>> 24-tET contains all the pitches of 12, like Johnny Reinhard
attests, (I think
>> he's right, too! :) )shouldn't it *at least* have all the
properties of 12,
>> regardless of the "niceties" of the mathmatics??
>>
> again, the chart has to be taken in the context of the paper to
which it
> belongs.
>
> but then again, other people might have different expectations. for
example,
> johnny's friend marc jones feels that the errors in 24 actually
*sound* twice
> as large as those in 12, because of the context, even though they're
> acoustically identical. marc can correct be if i've phrase this
poorly . . .
>
> anyhow, the *right* way to do that chart would be to have *several*
different
> points for 24-equal 7-limit, *several* different points for 24-equal
9-limit,
> etc., depending on how the primes are mapped. i'd be happy to do
this if you
> wish, but as it stands now, the chart would become horribly
cluttered.
>

Hi Paul.

I see this new mail rule works, copying any "marc" in an email text to
my
"YOU RANG?" folder.

As far as something incidental, I had this idea, as an extreme
example:

* If you look at a mixer, when there's a consistent signal that drops
to
silence, it takes a small amount of time for the meter to return to
zero
volume because to display decibels, it has to calculate the average
power of
the signal over that amount of time.

* If you also consider the volume-vs-frequency results of applying an
equalizer to a certain frequency, a sort of bell curve rises and falls
around that frequency, affecting every frequency around it, but less
and
less, the farther away it is.

-- Similarly, say you have a 12 tone piece with one quartertone in it.
If
you could map temperament vs time, the list might go something like
this:

"12 12 12 12 24 12 12 12 12 ..."

At the point the quartertone is hit, there it is, it's in 24. At any
other
point, you could say it's in 12.

If you had a little more leading up to and away from it, somehow, it
would
feel something like this:

"Normal, normal, normal, hey that weird note is coming, BWONK, wasn't
that
strange, back to normal, normal, normal..."

If you could imagine why I was thinking of the afterglow effect,
unless you
really psyche yourself into this being a "quartertone piece", per se,
the
context is going to shift in and out of that one moment, if you have a
solid
sense of what 12 sounds like.

Personally, I think it's much more likely to be this than "normal
normal
normal normal QUARTERTONE aaaa what was that oh no nothing will ever
be the
same, quartertone,
quartertone,
Quartertone...

In a sense, this just pierced the center of all my work. The idea
that one
note could cause that much of a change in your sense of context is
really
the bottom line in terms of whether something is traumatic or not. In
the
first case, if you can get back to normal, it wasn't. In the second
case,
it comes back to affect you, so it is traumatic.

Anyway.

Before looking at this in terms of 12 vs 24, you can do the same thing
within 12 by itself. Consider playing a major scale oriented piece
for
awhile and throw in a minor chord. It's going to sound strange at
first.

That�s just it. If it's just a matter of 12 is in 24, for that
matter, 24
is in 48, 120, 24000 etc. What it really comes down to in non prime
temperaments, if their factors are at all relevant, is at what point
are you
interpolating with the multiple, and how much, and how severe. The
bottom
line is EXACTLY WHAT NOTES are you using.

"Acoustically":

All of the above only really applies to the case of the non-guitar.
Any
acoustic instrument that doesn't have a temperament-specific resonance
is
what I was talking about. Basically any instrument, piano, winds,
brass,
strings, anything you tune a note to, within the context of every
other note
you hear from it, forms a sort of overall image of what's going on,
and all
of your temperament and harmonic issues can work themselves out.

Actually I'd have to cut that back a little because this is 100
percent true
in electronic timbre that doesn't have any acoustic stake once it's
out of
the machine. That on second thought, the acoustic instruments that
resonate
*a little*, MIGHT actually have a low volume kickback that might have
some
interesting subtle effects on the next note. But in general, you hear
what
you play and that's it.

The placement of frets on a guitar drastically affects the timbre. I
was
always completely amazed that all of my interchangeable boards sound
completely different on the SAME GUITAR. This mystified me for years.
After about the last 10 years of trying to figure out the whole
microacoustic deal behind that, a couple months ago I started getting
the
idea a little.

You might think "maybe it's just the wood". I did. For that matter,
I have
to mention this. One of my first METAL fretted guitars was a 34. Not
34
like it's 32 and someone said it was 34. COUGH COUGH. It was a 34 :)
I
had it for quite a few months. I'd also wanted to try 17 so I figured
I
could do enough with 17 on the 34, since I only really had room for
*one*
more guitar at the time. I was a bit disappointed in that suite
though. It
didn't seem like 17 had as much power in its sharp fifths as I'd
imagined.

But why.

Here's an even thicker plot. At one point I decided since it was such
a
cheap guitar, I'd just pluck out every other fret and make the 34 a
17. I
thought one of the pickups was shot. It DIDN'T SOUND ANYTHING LIKE
the 34.
A much deeper tone. None of the really high harmonics I'd heard
before.
But you know what. All of the diversity of the whole "stretched"
Pythagorean or whatever you call it, believe me, it was there in full
force.

Now for the life of me, for like 10 years, I could NOT understand how
this
same guitar, fretted in 34, could have such a beautiful tone and have
such
horrible sounding fifths. And on the other hand, how could it have
such a
bludgeoning tone in 17 but have fifths you could sink your teeth into
just a
bit more than 12, enough to make it worthwhile?

I couldn't even imagine the physics to it, but I was sure it had
something
to do with THE FRETS, and their placement, and after very little
thought, of
course, it has something to do with the vibration of the string
echoing down
into the cavities between and back up into the string. I often asked
people
to imagine a bare wall with sound reflecting off it, then imagine the
wall
with a BIRCH TREE every two feet. You think it would change the sound
JUST
a little??

There's just something about a guitar ;)

So one day my friend Ken, the only person who's really been able to
keep up
with playing "my guitars" (the one who stood me up for the guitar
quartet
performance...) was working with my interchangeable. I was sitting
typing
at the computer. He hits this note... Waaaaaaaa... I said oh you
wanted to
check out the 46 huh I figured as much. He was silent for a few
minutes. I
kept typing oblivious. I looked over and he had this look. He said
how did
you KNOW it was 46? I said because it sounded like it. He said
but... I
only played one note. Talk about "WATSON COME HERE I NEED YOU"...
It's the
stupidest thing, really, but it led to one of the most broad
philosophical
discussions about temperament and guitar. We went into experiment
mode and
by the end of the day, much like the psychic playing card test, we
were able
to guess what temperament the other was playing by hearing one note.
We
worked with, I think, 41, 43, 46 and 50.

You know what it is? I have to say. I HAVE TO give credit to the guy
that
came up with the show "CSI: Crime Scene Investigation"... If you've
ever
seen them trying to solve a crime, as far as bullets hitting bones,
they do
this almost telepathic movie type footage and zooms all the way into
the
persons body and shows with computer graphics in slow motion the
bullet
breaking the bone. Then whoosh, back out into the crime lab. It's
almost
like you're getting a quick trip through hyperspace into the actual
mental
space where they're imagining what's happened, trying to reconstruct a
crime. With my stake in physics, I've since started imagining quantum
motion in time and space with that kind of CSI footage once in awhile.

If you'd please forgive the size and structure of this huge analogy
I'm
trying to lay out for you...

... I really put myself on the guitar string and moved as it would,
and I
FINALLY started understanding the root of ALL of this. It's easy
enough to
imagine a sound wave as a sort of EKG of, say, one particle's
testimony of
having traveled up and down the string, and what intensities of
energies it
had found along the way. I was SO CLOSE by thinking that the
different size
CAVITIES in fretboards of different temperaments would SUPRESS certain
harmonics!!! And this, to myself, is how I sulk thinking I ALWAYS
MISS THE
UTTERLY OBVIOUS. The fact that the cavities muffle certain
frequencies is
only a distant symptom of the idea that the FRETS *REINFORCE* certain
frequencies!!! I mean DUH.

On a side note, if you think about what "pinching" a harmonic does,
it's not
so distantly related.

So think about starting at the bridge, and traveling to the nut,
making the
top half of a sort of sine wave. Every time you hit a fret, you would
get a
sort of volume spike. But this is the trick. The distance between
bridge
and note describes the frequency in the first place. So when you hit
that
volume spike, you're making a sort of goosebump which strongly
suggests the
note by fretting directly under it. It teases, and passes, on to the
next
spike. The trick is, that the distance in time from the beginning of
the
wave to every volume spike hints at EVERY NOTE IN THE TEMPERAMENT from
the
topmost fret down to the one you're playing!

In other words? In simpler terms?

When you play one note in a fully fretted temperament, you hear traces
of
every other note in the temperament up an octave or so. Alongside of
those
frequencies, you also have traces of the frequencies produced at the
OTHER
END of the string, which pigtail along as a temperament's own unique
array
of something along the lines of formants.

Simpler...

If you play one note on a microtonal guitar, you hear every note in
the
temperament. You also hear its own "vocal pattern".

Which is why I had problems between 34 and 17 on the same guitar
despite
each other.

I've heard a few people say that playing a temperament within its
double
makes it counter-intuitive.

Long long ago, I played a 24. I don't remember whose it was, or
whether I'd
made it or not. Playing 12 in fully fretted 24, sounded like whole
tone
scales. It actually felt like playing 6 in 12, sort of floating along
with
no resolution. That was long ago though.

But still, to answer your question:

1. If you're playing an acoustic or electronic instrument, the
sensitivity
to a multiple temperament has more to do with how much of it you use
versus
its factor.

2. If you're playing a GUITAR, the temperament lingers. Heh heh.

Here's an idea Paul. My next guitar quartet is going to be in 49.
There's
a certain amount of it that's going to be in the 22 + 27 scale. I
would bet
that if you (you, personally) played along with the retuned midi
foundation,
you'd feel it was in 22. And that if you played along with the final
mix in
49, that you would feel something along the lines of your hands being
pulled
away from the guitar in three different directions; sort of like
you're
almost playing the right guitar but there's something really wrong
with the
air today.

Actually I couldn't say what the effect of 22 under 49 would be.
Playing 31
guitar under a 43 or 50 usually sounds like breaking glass, although
in midi
it makes it all the more rich. Sort of the difference between mixing
paint
to black and mixing light to white. Anyway I'll get you a copy of one
of
the 22 segments maybe in March or so.

Well anyway :)

I hope this gave you a little insight. Actually Johnny Reinhard's
sensitivity to increment of cents values and my sensitivity to
increment of
temperament density all but negate each other. One desensitizes you
to the
other, almost like reciprocals.

Thanks for thinking of me.

Marc

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

/tuning/topicId_33969.html#33977

> but because my 72edo and HEWM ll-limit JI notations both use
> the same accidentals for the same JI ratios which 72edo implies
> well, and because the two systems do translate into each other
> so well (i.e., because 72edo has good a n d consistent
> approximations to 11-limit JI), i found that as i tried to
> sight-sing Maneri's musical examples, i couldn't get away
> from the understanding i already had about which ratios were
> being implied in those examples. so there's no way for me
> to use 72edo without consciously thinking about the implied
> ratios. this is not a problem in 24edo.
>

***But, Monz, that's a *feature* not a *bug* no?? :)

So you just move the 3 cents and you are singing in Just Intonation
in a very easily notable system!

Joe

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

/tuning/topicId_33969.html#33997

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > Well, since all these important European "cat" composers are
trying
> > to use 24-tET to map just intonation and acoustical properties in
> > the "spectral" school, it might be worth while for *me* at least,
> to
> > know more about it's properties! So anything you can do in this
> > regard would be appreciated!
>
> so you'd like a version of that chart that shows all the
> possibilities, then? can we trim down the chart somehow . . .
what's the highest limit you want to look at?

****Well, that would be cool...is there any point in going much
beyond 11?? If you did, I'm not sure it would mean too much to
me... ??

JP

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

/tuning/topicId_33969.html#34003
>
> Whatever, that's the way it is and that's okay. However, this does
> lead some, even more than some I'd bet, to prematurely concluded
that
> these types of tunings are therefore inferior or of little use, and
> that's were my objections come from--they're not, they're fine!
> Especially if we're talking about music (or even ideology).
>

***Well, Dan! That's one of the reasons it's so important that *you*
participate vigorously on this list!

> BTW, did somebody forget to mail me the new restricted use of
capital letters guidelines!
>

****Didn't you know?? A couple of our correspondents are typing in e-
mail remotely, beaming up "in transit" on little hand-held pagers!

JP

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

/tuning/topicId_33969.html#34042

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > ****This is a *fascinating* post, Monz! Maybe, in a way, you
think
> > of it as something "familiar" as an "extension" of 12-equal??
> >
> > Anyway, I think I'm going to have to give 24-tET more respect...
>
> well, sorry i misled you . . . i thought it would have been obvious
> that 24-equal could do anything 12-equal could do . . . but as far
as
> the 7-limit, it doesn't give you the improvement you might expect,
> and funny things can happen if you try to approximate 7-limit
> intervals in 24-equal . . . i think robert walker composed a piece
of
> music illustrating some of these 'funny things' . . .

****Hi Paul..

I just wasn't clear why the 7 and 9 limits were indicated on
your "famous" chart as being .5 "good" in 12-tET and didn't show up
on 24-tET. Monz did a pretty good job of explaining why this
happens... it makes sense now.

Joseph

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, February 11, 2002 6:22 PM
> Subject: [tuning] Re: question about 24-tET
>
>
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_33969.html#33976
>
> >
> > of course one can use this approach with any tuning, but
> > i find that certain edos (the usual suspects: 17, 19, 31,
> > 55, 72, etc.) have such good approximations to at least
> > a few important JI ratios that it's hard for me to get
> > away from all the *thinking* that automatically accompanies
> > sonorities with whose mathematics i'm so familiar. 24edo
> > solves that problem for me by not offering much beyond
> > 3, in terms of approximating prime-factors well.

oops ... i should have included 11. 24edo is great at
implying 3 and even better at 11.

> > so it gives me a freedom to simply play with the sound
> > that i can't capture for the other tunings.
>
> ****This is a *fascinating* post, Monz!

thanks, Joe. i felt as if i had tapped into something
special when i wrote that, so i think you confirm that.
:)

> Maybe, in a way, you think of it as something
> "familiar" as an "extension" of 12-equal??

yep, i do think of it that way a lot. my _24-eq tune_
http://www.ixpres.com/interval/monzo/24-eq/24-eq.htm

has a repeating 5-measure phrase, in which i deliberately
made use of 1/4-tones in the first 4 measures in all 4
voices, then in the final (5th) measure none of them use
1/4-tones, so that it is very much along the lines of what
Marc described in his long post: it has a "24edo feel"
for 4 measures and then a "12edo feel" for the last, and
this acts (to my ears, anyway) as a kind of "resolution".

i think of it as a microtonal analogue of something
that's familiar from diatonic harmony (a "final cadence":
tension-->resolution), but i'm doing it in a totally
different way, by contrasting tunings. the "neutral"
intervals possible with (and typical of) 24edo, which
imply 11 a lot to my ears, resolve into the
"pseudo-3-and5-limit" ones of 12edo.

ok, so there you go . . . maybe i did have this a little
bit in mind as i composed this piece, and so therefore
it w a s n ' t done totally "viscerally" as i had
claimed . . . oh well, at least, i t r i e d to write
it without thinking too hard. and i felt that i had
succeeded, that it mostly just flowed out of me in an
inspiration. guess i can't get away from using the old
noodle when i compose . . . :(

> Anyway, I think I'm going to have to give 24-tET more respect...

sounds good to me. :)

-monz

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

On 2/12/02 12:44 AM, "D.Stearns" <STEARNS@CAPECOD.NET> wrote:

> Hey Marc,
>
> Good to see big old high strangeness Orphon Soul post again!
>
High strangeness, that which prompts one to say "hi, stranger"? Which would
be said to one who hasn't been around in awhile. Which We have not. We
would settle for being different from the norm, in a pure form. That was
not a rap.

Always shooting for Definition Two, however, from physics, Our unfortunate
forte, strangeness is the possible transformations of an elementary particle
upon strong interaction with another elementary particle. That might seem
more appropriate for those who know Us.

> You've got a wonderfully, easy flowing touch that's as refreshing as it is
> imaginative--like some sudden and alarmingly colorful blossom in the middle of
> a perennially arid environment.
>
To be one who flows, a "flower"? (flow - er) We must subliminally inspire
visual puns. This is a most rewarding interpretation of an otherwise not so
much cry for attention but a desperate attempt to remain interesting.

The last post was just one thing after another, before another, logic here
and there as it seemed necessary. Didn't read it once it was done.

Was it any good?

> thanks,
>
> --Dan Stearns
>

You're welcome,
Strangeflower.

Hi Joseph et. al.

Sorry for taking *2 years* to get back to you on this! The below was
message #33992, but of course you can just click on "Up Thread"
repeatedly to remind you of what was said here.

Anyway, we have a new paradigm for temperament called TOP, in which
octave-equivalence is not assumed, odd-limit is out the window, and
therefore, so is consistency! (NB Dan Stearns)

The details have been discussed here and especially on tuning-math,
but the main point for you is that I can now show you the 7-limit
(this time it's a prime-, not odd- limit) graph with several
instances of 24-equal on it, all of which map prime 2 to 24 steps,
but which use different mappings of the other primes. As a result,
they each have slightly different "stretch" applied to them in the
TOP paradigm. The horizontal axis shows the number of notes per 1200
cents, so the three "24"s on this graph are almost, but not exactly,
on a vertical line. The vertical axis is the error measure. So unlike
the graph you were referring to below, the accurate temperaments show
up along the bottom, not the top, of the graph:

/tuning/files/et7.gif

Here's are the graphs for some other prime limits:

/tuning/files/et3.gif
/tuning/files/et5.gif
/tuning/files/et11.gif

Now Johnny and others may have a different objection which was not a
problem in the original graph -- why doesn't 24-equal show up with
basically the same error as 12-equal in the 5-limit graph? The reason
is that I'm taking "equal temperament" literally, and *not* using
the "equal division of the octave" definition. That is, each note of
the tuning *must* come from (an infinite number of places in) the
just intonation lattice. To get 12-equal to arise from 5-prime-limit
JI, a relatively small amount of tempering is applied. To get 24-
equal to arise from the 5-prime-limit lattice, a *whole* lot more
tempering needs to be applied -- otherwise those "quartertones" will
never arise in the first place.

If anyone wishes, I could redo the graphs to show all "equal
divisions of the octave" and not merely "equal temperaments".
However, this will make the graphs *a lot* more cluttered, since
every ET point will now have "shadows" at 2x, 3x, 4x . . . the
distance along the horizontal axis.

Sorry to break the silence here -- almost like stepping in virgin
snow . . .

-Paul

--- In tuning@yahoogroups.com, "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > Well, I think I get the overall picture on that, but, on the
other
> > hand, if 24-tET contains all the pitches of 12, like Johnny
> Reinhard
> > attests, (I think he's right, too! :) )shouldn't it *at least*
> have
> > all the properties of 12, regardless of the "niceties" of the
> > mathmatics??
>
> again, the chart has to be taken in the context of the paper to
which
> it belongs.
>
> but then again, other people might have different expectations. for
> example, johnny's friend marc jones feels that the errors in 24
> actually *sound* twice as large as those in 12, because of the
> context, even though they're acoustically identical. marc can
correct
> be if i've phrase this poorly . . .
>
> anyhow, the *right* way to do that chart would be to have *several*
> different points for 24-equal 7-limit, *several* different points
for
> 24-equal 9-limit, etc., depending on how the primes are mapped. i'd
> be happy to do this if you wish, but as it stands now, the chart
> would become horribly cluttered.

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

/tuning/topicId_33969.html#52272

> Hi Joseph et. al.
>
> Sorry for taking *2 years* to get back to you on this! The below
was
> message #33992, but of course you can just click on "Up Thread"
> repeatedly to remind you of what was said here.
>

***I knew you were a little behind in reading the list, Paul, but I
didn't realize it was *two years!* :)

> Anyway, we have a new paradigm for temperament called TOP, in which
> octave-equivalence is not assumed, odd-limit is out the window, and
> therefore, so is consistency! (NB Dan Stearns)
>
> The details have been discussed here and especially on tuning-math,
> but the main point for you is that I can now show you the 7-limit
> (this time it's a prime-, not odd- limit) graph with several
> instances of 24-equal on it, all of which map prime 2 to 24 steps,
> but which use different mappings of the other primes. As a result,
> they each have slightly different "stretch" applied to them in the
> TOP paradigm. The horizontal axis shows the number of notes per
1200
> cents, so the three "24"s on this graph are almost, but not
exactly,
> on a vertical line. The vertical axis is the error measure. So
unlike
> the graph you were referring to below, the accurate temperaments
show
> up along the bottom, not the top, of the graph:
>
> /tuning/files/et7.gif
>
> Here's are the graphs for some other prime limits:
>
> /tuning/files/et3.gif
> /tuning/files/et5.gif
> /tuning/files/et11.gif
>
> Now Johnny and others may have a different objection which was not
a
> problem in the original graph -- why doesn't 24-equal show up with
> basically the same error as 12-equal in the 5-limit graph? The
reason
> is that I'm taking "equal temperament" literally, and *not* using
> the "equal division of the octave" definition.

***This is really *very* interesting. In other words these are a
kind of "stretchy" equal temperaments... (??)

That is, each note of
> the tuning *must* come from (an infinite number of places in) the
> just intonation lattice. To get 12-equal to arise from 5-prime-
limit
> JI, a relatively small amount of tempering is applied. To get 24-
> equal to arise from the 5-prime-limit lattice, a *whole* lot more
> tempering needs to be applied -- otherwise those "quartertones"
will
> never arise in the first place.
>

***Is that because it takes more "work" to get the quartertones
anywhere near just??

> If anyone wishes, I could redo the graphs to show all "equal
> divisions of the octave" and not merely "equal temperaments".
> However, this will make the graphs *a lot* more cluttered, since
> every ET point will now have "shadows" at 2x, 3x, 4x . . . the
> distance along the horizontal axis.
>
> Sorry to break the silence here -- almost like stepping in virgin
> snow . . .
>

***Anyway, thanks for the beginning summary of the research. It's
exciting stuff... and I thank you for the time spent with
the "layman's view..."

Joseph

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

> Anyway, we have a new paradigm for temperament called TOP, in which
> octave-equivalence is not assumed, odd-limit is out the window, and
> therefore, so is consistency! (NB Dan Stearns)

Consistency may be out the window but wouldn't you still have better
approximations for some intervals than what the mapping might give?

> Now Johnny and others may have a different objection which was not
a
> problem in the original graph -- why doesn't 24-equal show up with
> basically the same error as 12-equal in the 5-limit graph? The
reason
> is that I'm taking "equal temperament" literally, and *not* using
> the "equal division of the octave" definition. That is, each note
of
> the tuning *must* come from (an infinite number of places in) the
> just intonation lattice. To get 12-equal to arise from 5-prime-
limit
> JI, a relatively small amount of tempering is applied. To get 24-
> equal to arise from the 5-prime-limit lattice, a *whole* lot more
> tempering needs to be applied -- otherwise those "quartertones"
will
> never arise in the first place.

I'm not getting this. How are you calculating the errors?

Kalle

> Anyway, we have a new paradigm for temperament called TOP, in which
> octave-equivalence is not assumed, odd-limit is out the window, and
> therefore, so is consistency! (NB Dan Stearns)

Oh yeah. Say Paul, what does dropping octave-equivalence have to do
with consistency? We're still enforcing consistency, in the definition
of regular temperament, or in the map, or wherever, we just no longer
exclude "inconsistent" ETs, but this happened a long time before TOP,
did it not?

-Carl

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

> > Now Johnny and others may have a different objection which was
not
> a
> > problem in the original graph -- why doesn't 24-equal show up
with
> > basically the same error as 12-equal in the 5-limit graph? The
> reason
> > is that I'm taking "equal temperament" literally, and *not* using
> > the "equal division of the octave" definition.
>
> ***This is really *very* interesting. In other words these are a
> kind of "stretchy" equal temperaments... (??)

Yes, but what I was referring to above has nothing to do with
the "stretch". In addition to the equal temperaments, I could very
well have included the other "equal divisions" in there, and they
would have been "stretched" too, but I didn't.

> > That is, each note of
> > the tuning *must* come from (an infinite number of places in) the
> > just intonation lattice. To get 12-equal to arise from 5-prime-
> limit
> > JI, a relatively small amount of tempering is applied. To get 24-
> > equal to arise from the 5-prime-limit lattice, a *whole* lot more
> > tempering needs to be applied -- otherwise those "quartertones"
> will
> > never arise in the first place.
> >
>
> ***Is that because it takes more "work" to get the quartertones
> anywhere near just??

It takes more "work" to regularly temper 5-limit JI and end up with
quartertones. Not sure if that's what you meant or not . . .

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > Anyway, we have a new paradigm for temperament called TOP, in
which
> > octave-equivalence is not assumed, odd-limit is out the window,
and
> > therefore, so is consistency! (NB Dan Stearns)
>
> Consistency may be out the window but wouldn't you still have
better
> approximations for some intervals than what the mapping might give?

Yup! In fact, this becomes unavoidable now that you're looking at
prime-limit instead of odd-limit.

> > Now Johnny and others may have a different objection which was
not
> a
> > problem in the original graph -- why doesn't 24-equal show up
with
> > basically the same error as 12-equal in the 5-limit graph? The
> reason
> > is that I'm taking "equal temperament" literally, and *not* using
> > the "equal division of the octave" definition. That is, each note
> of
> > the tuning *must* come from (an infinite number of places in) the
> > just intonation lattice. To get 12-equal to arise from 5-prime-
> limit
> > JI, a relatively small amount of tempering is applied. To get 24-
> > equal to arise from the 5-prime-limit lattice, a *whole* lot more
> > tempering needs to be applied -- otherwise those "quartertones"
> will
> > never arise in the first place.
>
> I'm not getting this.

In order to get 24-equal as a *temperament* rather than an *equal
division*, you have to start with the just lattice, define unison
vectors, and end up with a 24-tone periodicity block with no torsion.
If you start with the 5-limit lattice, there's essentially no good
way to do this (you'd have to take on some very large errors, for
example tempering both the major and minor thirds to 350 cents). But
of course you're free to obtain 24-ED by a simple bisection of 12-ET,
it's just no longer a "temperament", strictly speaking . . .

> How are you calculating the errors?

It's 1200 times the maximum "Tenney-weighted error" we've discussed
here and on tuning-math, for these TOP ETs.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > Anyway, we have a new paradigm for temperament called TOP, in
which
> > octave-equivalence is not assumed, odd-limit is out the window,
and
> > therefore, so is consistency! (NB Dan Stearns)
>
> Oh yeah. Say Paul, what does dropping octave-equivalence have to do
> with consistency?

Essentially, *all* ETs become inconsistent!

> We're still enforcing consistency, in the definition
> of regular temperament, or in the map, or wherever, we just no
longer
> exclude "inconsistent" ETs, but this happened a long time before
TOP,
> did it not?

Sure. You would have to read the 2-year old thread I was replying to
to see why I brought it up. I noticed Dan's sort-of-back so I thought
I'd "fill him in".

>> Consistency may be out the window but wouldn't you still have
>> better approximations for some intervals than what the mapping
>> might give?
>
>Yup! In fact, this becomes unavoidable now that you're looking at
>prime-limit instead of odd-limit.

Could you sketch the reasoning here? I can't imagine where you're
coming from.

-C.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Consistency may be out the window but wouldn't you still have
> >> better approximations for some intervals than what the mapping
> >> might give?
> >
> >Yup! In fact, this becomes unavoidable now that you're looking at
> >prime-limit instead of odd-limit.
>
> Could you sketch the reasoning here? I can't imagine where you're
> coming from.

Each prime-limit contains an infinite number of ratios, so as long as
the primes are not tuned justly, *some* ratio out there is going to
come closer to the "wrong" number of scale degrees than to what you
would expect by compounding approximations of consonances that would
lead to that ratio in JI.

Basically, since we're talking about prime-limit and not odd-limit,
Paul Hahn's "consistency level" would have to be infinite to
guarantee no inconsistencies. And of course, that never happens.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> >
> > > Anyway, we have a new paradigm for temperament called TOP, in
> which
> > > octave-equivalence is not assumed, odd-limit is out the window,
> and
> > > therefore, so is consistency! (NB Dan Stearns)
> >
> > Consistency may be out the window but wouldn't you still have
> better
> > approximations for some intervals than what the mapping might
give?
>
> Yup! In fact, this becomes unavoidable now that you're looking at
> prime-limit instead of odd-limit.

What about integer-limit consistency?

> > > Now Johnny and others may have a different objection which was
> not
> > a
> > > problem in the original graph -- why doesn't 24-equal show up
> with
> > > basically the same error as 12-equal in the 5-limit graph? The
> > reason
> > > is that I'm taking "equal temperament" literally, and *not*
using
> > > the "equal division of the octave" definition. That is, each
note
> > of
> > > the tuning *must* come from (an infinite number of places in)
the
> > > just intonation lattice. To get 12-equal to arise from 5-prime-
> > limit
> > > JI, a relatively small amount of tempering is applied. To get
24-
> > > equal to arise from the 5-prime-limit lattice, a *whole* lot
more
> > > tempering needs to be applied -- otherwise those "quartertones"
> > will
> > > never arise in the first place.
> >
> > I'm not getting this.
>
> In order to get 24-equal as a *temperament* rather than an *equal
> division*, you have to start with the just lattice, define unison
> vectors, and end up with a 24-tone periodicity block with no
torsion.
> If you start with the 5-limit lattice, there's essentially no good
> way to do this (you'd have to take on some very large errors, for
> example tempering both the major and minor thirds to 350 cents).
But
> of course you're free to obtain 24-ED by a simple bisection of 12-
ET,
> it's just no longer a "temperament", strictly speaking . . .

So I can't call an arbitrary mapping of primes to equal scale steps a
temperament? What about some kind of "standard" mapping?

> > How are you calculating the errors?
>
> It's 1200 times the maximum "Tenney-weighted error" we've discussed
> here and on tuning-math, for these TOP ETs.

I'm not sure if you're interested in this kind of thing but in ET
comparisons one could also multiply the error by the number of scale
steps in an octave (for example). This way one can measure
the "practical utility" of an ET. If one compares 5-limit meantone
equal temperaments, unweighted 5-odd limit minimax gives 19-equal as
the best one. If one uses Tenney-weighted error the winner is
actually 12-equal!

Kalle

>> >> Consistency may be out the window but wouldn't you still have
>> >> better approximations for some intervals than what the mapping
>> >> might give?
>> >
>> >Yup! In fact, this becomes unavoidable now that you're looking at
>> >prime-limit instead of odd-limit.
>>
>> Could you sketch the reasoning here? I can't imagine where you're
>> coming from.
>
>Each prime-limit contains an infinite number of ratios, so as long as
>the primes are not tuned justly, *some* ratio out there is going to
>come closer to the "wrong" number of scale degrees than to what you
>would expect by compounding approximations of consonances that would
>lead to that ratio in JI.

Ah, yes.

I wonder if something like Herman's "consistency range" could be
cultured?

-Carl

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:
> > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> > wrote:
> > >
> > > > Anyway, we have a new paradigm for temperament called TOP, in
> > which
> > > > octave-equivalence is not assumed, odd-limit is out the
window,
> > and
> > > > therefore, so is consistency! (NB Dan Stearns)
> > >
> > > Consistency may be out the window but wouldn't you still have
> > better
> > > approximations for some intervals than what the mapping might
> give?
> >
> > Yup! In fact, this becomes unavoidable now that you're looking at
> > prime-limit instead of odd-limit.
>
> What about integer-limit consistency?

One could worry about that, but the point of 'odd-limit' and 'integer-
limit' consistency in the past were to establish a finite set of
consonances, upon which the evaluation of the tuning's error and
complexity would be based. In TOP, at least when you're only
tempering out one comma as in 5-limit meantone or 3-limit 12-tET, it
gets you a tuning where a whole lot of the ratios have a 'Tenney-
weighted error' log(n/d)/log(n*d) equal to that of the comma itself,
while the rest of the ratios have lower 'Tenney-weighted error'. (I
think we're supposed to be multiplying by 1200 now, says schoolmaster
K. . . . :) ) But we're looking at *all* the ratios in the lattice,
not just a finite set of consonances . . . so it doesn't have the
quality of being 'limited' which generates concerns about consistency
vs. inconsistency . . .

> > > > Now Johnny and others may have a different objection which
was
> > not
> > > a
> > > > problem in the original graph -- why doesn't 24-equal show up
> > with
> > > > basically the same error as 12-equal in the 5-limit graph?
The
> > > reason
> > > > is that I'm taking "equal temperament" literally, and *not*
> using
> > > > the "equal division of the octave" definition. That is, each
> note
> > > of
> > > > the tuning *must* come from (an infinite number of places in)
> the
> > > > just intonation lattice. To get 12-equal to arise from 5-
prime-
> > > limit
> > > > JI, a relatively small amount of tempering is applied. To get
> 24-
> > > > equal to arise from the 5-prime-limit lattice, a *whole* lot
> more
> > > > tempering needs to be applied -- otherwise
those "quartertones"
> > > will
> > > > never arise in the first place.
> > >
> > > I'm not getting this.
> >
> > In order to get 24-equal as a *temperament* rather than an *equal
> > division*, you have to start with the just lattice, define unison
> > vectors, and end up with a 24-tone periodicity block with no
> torsion.
> > If you start with the 5-limit lattice, there's essentially no
good
> > way to do this (you'd have to take on some very large errors, for
> > example tempering both the major and minor thirds to 350 cents).
> But
> > of course you're free to obtain 24-ED by a simple bisection of 12-
> ET,
> > it's just no longer a "temperament", strictly speaking . . .
>
> So I can't call an arbitrary mapping of primes to equal scale steps
a
> temperament?

In strict tuning-math terms, that will only be a different
temperament if its GCD is 1. Otherwise it'll be identical to a
simpler temperament obtained by putting the mapping in lowest terms.
Similarly, if we consider tempering out commas, that comma shouldn't
be the square or cube or higher power of some smaller comma, because
it yields exactly the same temperament the smaller comma does.

> What about some kind of "standard" mapping?

Well, I can say there are various different definitions of standard
mapping at this point . . . what was your question?

> > > How are you calculating the errors?
> >
> > It's 1200 times the maximum "Tenney-weighted error" we've
discussed
> > here and on tuning-math, for these TOP ETs.
>
> I'm not sure if you're interested in this kind of thing but in ET
> comparisons one could also multiply the error by the number of
scale
> steps in an octave (for example). This way one can measure
> the "practical utility" of an ET.

Yup, this is what we've been calling 'badness' on tuning-math.
Indeed, we've looked at a lot of different functions of error and
complexity, not only error times complexity. It seems to Dave and me
that tunings like 4296-tET, no matter how high their 'practical
utility' by this particular measure and even things like error times
complexity squared, are not likely to be of widespread interest, so
we've been looking at things more like a*error + b*complexity . . .

> If one compares 5-limit meantone
> equal temperaments, unweighted 5-odd limit minimax gives 19-equal
as
> the best one. If one uses Tenney-weighted error the winner is
> actually 12-equal!

It must be a virtual tie . . . And it's a slightly 'compressed' 12-
equal you're talking about, to be exact, correct?

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >> Consistency may be out the window but wouldn't you still have
> >> >> better approximations for some intervals than what the mapping
> >> >> might give?
> >> >
> >> >Yup! In fact, this becomes unavoidable now that you're looking
at
> >> >prime-limit instead of odd-limit.
> >>
> >> Could you sketch the reasoning here? I can't imagine where
you're
> >> coming from.
> >
> >Each prime-limit contains an infinite number of ratios, so as long
as
> >the primes are not tuned justly, *some* ratio out there is going
to
> >come closer to the "wrong" number of scale degrees than to what
you
> >would expect by compounding approximations of consonances that
would
> >lead to that ratio in JI.
>
> Ah, yes.
>
> I wonder if something like Herman's "consistency range" could be
> cultured?
>
> -Carl

Natural measures would seem to be include lowest Tenney complexity
limit needed to violate consistency and so on . . . in any case no
simple on/off for a given prime limit . . . . .

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

/tuning/topicId_33969.html#52284

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > > Now Johnny and others may have a different objection which was
> not
> > a
> > > problem in the original graph -- why doesn't 24-equal show up
> with
> > > basically the same error as 12-equal in the 5-limit graph? The
> > reason
> > > is that I'm taking "equal temperament" literally, and *not*
using
> > > the "equal division of the octave" definition.
> >
> > ***This is really *very* interesting. In other words these are a
> > kind of "stretchy" equal temperaments... (??)
>
> Yes, but what I was referring to above has nothing to do with
> the "stretch". In addition to the equal temperaments, I could very
> well have included the other "equal divisions" in there, and they
> would have been "stretched" too, but I didn't.
>
> > > That is, each note of
> > > the tuning *must* come from (an infinite number of places in)
the
> > > just intonation lattice. To get 12-equal to arise from 5-prime-
> > limit
> > > JI, a relatively small amount of tempering is applied. To get
24-
> > > equal to arise from the 5-prime-limit lattice, a *whole* lot
more
> > > tempering needs to be applied -- otherwise those "quartertones"
> > will
> > > never arise in the first place.
> > >
> >
> > ***Is that because it takes more "work" to get the quartertones
> > anywhere near just??
>
> It takes more "work" to regularly temper 5-limit JI and end up with
> quartertones. Not sure if that's what you meant or not . . .

***Pretty much... but I'm still rather gliding on the surface of
this...

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> /tuning/topicId_33969.html#52284
>
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> >
> > > > Now Johnny and others may have a different objection which
was
> > not
> > > a
> > > > problem in the original graph -- why doesn't 24-equal show up
> > with
> > > > basically the same error as 12-equal in the 5-limit graph?
The
> > > reason
> > > > is that I'm taking "equal temperament" literally, and *not*
> using
> > > > the "equal division of the octave" definition.
> > >
> > > ***This is really *very* interesting. In other words these are
a
> > > kind of "stretchy" equal temperaments... (??)
> >
> > Yes, but what I was referring to above has nothing to do with
> > the "stretch". In addition to the equal temperaments, I could
very
> > well have included the other "equal divisions" in there, and they
> > would have been "stretched" too, but I didn't.
> >
> > > > That is, each note of
> > > > the tuning *must* come from (an infinite number of places in)
> the
> > > > just intonation lattice. To get 12-equal to arise from 5-
prime-
> > > limit
> > > > JI, a relatively small amount of tempering is applied. To get
> 24-
> > > > equal to arise from the 5-prime-limit lattice, a *whole* lot
> more
> > > > tempering needs to be applied -- otherwise
those "quartertones"
> > > will
> > > > never arise in the first place.
> > > >
> > >
> > > ***Is that because it takes more "work" to get the quartertones
> > > anywhere near just??
> >
> > It takes more "work" to regularly temper 5-limit JI and end up
with
> > quartertones. Not sure if that's what you meant or not . . .
>
>
> ***Pretty much... but I'm still rather gliding on the surface of
> this...

OK, which part would you like me to clarify?

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

/tuning/topicId_33969.html#52297
> >
> > ***Pretty much... but I'm still rather gliding on the surface of
> > this...
>
> OK, which part would you like me to clarify?

***Well, to take it from the TOP... :) what does "TOP" actually
stand for, and what could be the utility of these new scales that
would be different from what we have heard before??

Tx,

JP

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:

> What about integer-limit consistency?

Actually, I was thinking about this earlier, and if you'll excuse the
mathematical language . . .

Tenney complexity (or 'limit') is associated with an L_1 or sum or
cityblock norm on the Tenney lattice. If we use an L_inf or max norm
instead, we do not get quite an integer-limit, but a strange beast
that does this (the logs of these are the actual complexities):

2/1 --> 2
3/2 --> 3
4/3 --> 4
5/3 --> 5
5/4 --> 5
6/5 --> 5
7/6 --> 7
8/7 --> 7
15/8 --> 8
21/8 --> 8
35/8 --> 8
9/8 --> 9
10/9 --> 9
35/9 --> 9
35/18 --> 9
36/35 --> 9
11/8 --> 11
13/8 --> 13
25/8 --> 25

Is that right? Doesn't seem to agree with my experience . . .

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> /tuning/topicId_33969.html#52297
> > >
> > > ***Pretty much... but I'm still rather gliding on the surface
of
> > > this...
> >
> > OK, which part would you like me to clarify?
>
>
> ***Well, to take it from the TOP... :)

Oh, you really want to get into that? I was just hoping my new graphs
were making sense to you . . .

> what does "TOP" actually
> stand for,

"Tempered Octaves, Please" or "Tenney-Optimal" . . .

> and what could be the utility of these new scales that
> would be different from what we have heard before??

Do you mean the new tunings of the same old scales? It could, in
theory, decrease the "worst error" in terms of damage to consonance
that we can find in the temperament. There may be more than one
theoretical way to arrive at these tunings, just as there is more
than one theoretical way to arrive at 1/4-comma meantone. But one
observation about them is that they minimize the maximum *weighted*
error of any ratio n:d, where weighted error is cents error divided
by log(n*d). This appears to put more importance on the precise
tuning of the *simple* ratios, the perfect consonances and 5:1, 5:2,
7:1, 9:1, 11:1, and less importance on the precise tuning of "exotic"
consonances like 7:6, 8:7, 9:5, 11:4, 13:4, 11:5, 27:2, and even less
on still more complex ratios. But apperances can be deceiving . . .

>Tenney complexity (or 'limit') is associated with an L_1 or sum or
>cityblock norm on the Tenney lattice. If we use an L_inf or max norm
>instead, we do not get quite an integer-limit, but a strange beast
>that does this (the logs of these are the actual complexities):
>
>2/1 --> 2
>3/2 --> 3
>4/3 --> 4
>5/3 --> 5
>5/4 --> 5
>6/5 --> 5
>7/6 --> 7
>8/7 --> 7
>15/8 --> 8
>21/8 --> 8
>35/8 --> 8
>9/8 --> 9
>10/9 --> 9
>35/9 --> 9
>35/18 --> 9
>36/35 --> 9
>11/8 --> 11
>13/8 --> 13
>25/8 --> 25
>
>Is that right? Doesn't seem to agree with my experience . . .

Off the top of my head, I'd call 5/3 more consonant than 5/4,
7/6 more consonant than 8/7, 15/8 more consonant than 21/8, and
9/8 more consonant than 10/9.

I strongly believe Tenney 'limit' is the best thing out there.
My main interest at this point is in the rms version of TOP.
I forget if Gene has that working for all intervals, or just
integer limit....

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Tenney complexity (or 'limit') is associated with an L_1 or sum or
> >cityblock norm on the Tenney lattice. If we use an L_inf or max
norm
> >instead, we do not get quite an integer-limit, but a strange beast
> >that does this (the logs of these are the actual complexities):
> >
> >2/1 --> 2
> >3/2 --> 3
> >4/3 --> 4
> >5/3 --> 5
> >5/4 --> 5
> >6/5 --> 5
> >7/6 --> 7
> >8/7 --> 7
> >15/8 --> 8
> >21/8 --> 8
> >35/8 --> 8
> >9/8 --> 9
> >10/9 --> 9
> >35/9 --> 9
> >35/18 --> 9
> >36/35 --> 9
> >11/8 --> 11
> >13/8 --> 13
> >25/8 --> 25
> >
> >Is that right? Doesn't seem to agree with my experience . . .
>
> Off the top of my head, I'd call 5/3 more consonant than 5/4,
> 7/6 more consonant than 8/7, 15/8 more consonant than 21/8, and
> 9/8 more consonant than 10/9.

But isn't 36/35 vs. 9/8 much more egregious?

>> >Tenney complexity (or 'limit') is associated with an L_1 or sum or
>> >cityblock norm on the Tenney lattice. If we use an L_inf or max
>> >norm instead, we do not get quite an integer-limit, but a strange
>> >beast that does this (the logs of these are the actual complexities):
>> >
>> >2/1 --> 2
>> >3/2 --> 3
>> >4/3 --> 4
>> >5/3 --> 5
>> >5/4 --> 5
>> >6/5 --> 5
>> >7/6 --> 7
>> >8/7 --> 7
>> >15/8 --> 8
>> >21/8 --> 8
>> >35/8 --> 8
>> >9/8 --> 9
>> >10/9 --> 9
>> >35/9 --> 9
>> >35/18 --> 9
>> >36/35 --> 9
>> >11/8 --> 11
>> >13/8 --> 13
>> >25/8 --> 25
>> >
>> >Is that right? Doesn't seem to agree with my experience . . .
>>
>> Off the top of my head, I'd call 5/3 more consonant than 5/4,
>> 7/6 more consonant than 8/7, 15/8 more consonant than 21/8, and
>> 9/8 more consonant than 10/9.
>
>But isn't 36/35 vs. 9/8 much more egregious?

Probably; I wasn't expecting it to take tolerance into account.
But 36/35 is more egregious anyway, and it seems Tenney does
not run afoul of tolerance so...

I just continued a thread on tuning-math in which Gene apparently
demonstrated odd-limit TOP...

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >Tenney complexity (or 'limit') is associated with an L_1 or sum
or
> >> >cityblock norm on the Tenney lattice. If we use an L_inf or max
> >> >norm instead, we do not get quite an integer-limit, but a
strange
> >> >beast that does this (the logs of these are the actual
complexities):
> >> >
> >> >2/1 --> 2
> >> >3/2 --> 3
> >> >4/3 --> 4
> >> >5/3 --> 5
> >> >5/4 --> 5
> >> >6/5 --> 5
> >> >7/6 --> 7
> >> >8/7 --> 7
> >> >15/8 --> 8
> >> >21/8 --> 8
> >> >35/8 --> 8
> >> >9/8 --> 9
> >> >10/9 --> 9
> >> >35/9 --> 9
> >> >35/18 --> 9
> >> >36/35 --> 9
> >> >11/8 --> 11
> >> >13/8 --> 13
> >> >25/8 --> 25
> >> >
> >> >Is that right? Doesn't seem to agree with my experience . . .
> >>
> >> Off the top of my head, I'd call 5/3 more consonant than 5/4,
> >> 7/6 more consonant than 8/7, 15/8 more consonant than 21/8, and
> >> 9/8 more consonant than 10/9.
> >
> >But isn't 36/35 vs. 9/8 much more egregious?
>
> Probably; I wasn't expecting it to take tolerance into account.

How is tolerance relevant here?

> But 36/35 is more egregious anyway, and it seems Tenney does
> not run afoul of tolerance so...

Ditto . . .

>> >> >Is that right? Doesn't seem to agree with my experience . . .
>> >>
>> >> Off the top of my head, I'd call 5/3 more consonant than 5/4,
>> >> 7/6 more consonant than 8/7, 15/8 more consonant than 21/8, and
>> >> 9/8 more consonant than 10/9.
>> >
>> >But isn't 36/35 vs. 9/8 much more egregious?
>>
>> Probably; I wasn't expecting it to take tolerance into account.
>
>How is tolerance relevant here?

It's part of why 36/35 is so dissonant. Maybe I should have said
TOLERANCE. Does that help?

-Carl

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:

> I'm not sure if you're interested in this kind of thing but in ET
> comparisons one could also multiply the error by the number of scale
> steps in an octave (for example).

That's the way it's always been done for ET complexity measures.

This way one can measure
> the "practical utility" of an ET. If one compares 5-limit meantone
> equal temperaments, unweighted 5-odd limit minimax gives 19-equal as
> the best one. If one uses Tenney-weighted error the winner is
> actually 12-equal!

I don't know how you computed "badness", but clearly it's not "log flat".

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >> >Is that right? Doesn't seem to agree with my experience . . .
> >> >>
> >> >> Off the top of my head, I'd call 5/3 more consonant than 5/4,
> >> >> 7/6 more consonant than 8/7, 15/8 more consonant than 21/8,
and
> >> >> 9/8 more consonant than 10/9.
> >> >
> >> >But isn't 36/35 vs. 9/8 much more egregious?
> >>
> >> Probably; I wasn't expecting it to take tolerance into account.
> >
> >How is tolerance relevant here?
>
> It's part of why 36/35 is so dissonant.

Tenney doesn't take tolerance into account either but has no trouble
predicting that. And how about these comparisons:

45/28 --> 9
9/8 --> 9

Tolerance seems to work the other way here, doesn't it? And how about

33/28 --> 11
11/1 --> 11

?

> Maybe I should have said
> TOLERANCE. Does that help?

Yes, I'm going blind.

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

> I just continued a thread on tuning-math in which Gene apparently
> demonstrated odd-limit TOP...

Nothing particularly odd-limit about it. You just need a set of
consonances, with weights (or multiplicities) if you choose.

>Do you mean the new tunings of the same old scales? It could, in
>theory, decrease the "worst error" in terms of damage to consonance
>that we can find in the temperament. There may be more than one
>theoretical way to arrive at these tunings, just as there is more
>than one theoretical way to arrive at 1/4-comma meantone. But one
>observation about them is that they minimize the maximum *weighted*
>error of any ratio n:d, where weighted error is cents error divided
>by log(n*d). This appears to put more importance on the precise
>tuning of the *simple* ratios, the perfect consonances and 5:1, 5:2,
>7:1, 9:1, 11:1, and less importance on the precise tuning of "exotic"
>consonances like 7:6, 8:7, 9:5, 11:4, 13:4, 11:5, 27:2, and even less
>on still more complex ratios. But apperances can be deceiving . . .

. . .they can?

-C.

Kalle wrote:

> > What about integer-limit consistency?

Paul wrote:

> One could worry about that, but the point of 'odd-limit'
and 'integer-
> limit' consistency in the past were to establish a finite set of
> consonances, upon which the evaluation of the tuning's error and
> complexity would be based. In TOP, at least when you're only
> tempering out one comma as in 5-limit meantone or 3-limit 12-tET,
it
> gets you a tuning where a whole lot of the ratios have a 'Tenney-
> weighted error' log(n/d)/log(n*d) equal to that of the comma
itself,
> while the rest of the ratios have lower 'Tenney-weighted error'. (I
> think we're supposed to be multiplying by 1200 now, says
schoolmaster
> K. . . . :) ) But we're looking at *all* the ratios in the
lattice,
> not just a finite set of consonances . . . so it doesn't have the
> quality of being 'limited' which generates concerns about
consistency
> vs. inconsistency . . .

But why would we be interested about *all* of them? Why not look at a
set of n-odd limit consonances plus their octave extensions?
I guess at some point there will always be inconsistency there too.

> > So I can't call an arbitrary mapping of primes to equal scale
steps
> a
> > temperament?

> In strict tuning-math terms, that will only be a different
> temperament if its GCD is 1. Otherwise it'll be identical to a
> simpler temperament obtained by putting the mapping in lowest
terms.

Now I understand!

> Similarly, if we consider tempering out commas, that comma
shouldn't
> be the square or cube or higher power of some smaller comma,
because
> it yields exactly the same temperament the smaller comma does.

With torsion?

> > What about some kind of "standard" mapping?
>
> Well, I can say there are various different definitions of standard
> mapping at this point . . . what was your question?

Nevermind. The above clarified it all to me.

> > I'm not sure if you're interested in this kind of thing but in ET
> > comparisons one could also multiply the error by the number of
> scale
> > steps in an octave (for example). This way one can measure
> > the "practical utility" of an ET.
>
> Yup, this is what we've been calling 'badness' on tuning-math.
> Indeed, we've looked at a lot of different functions of error and
> complexity, not only error times complexity. It seems to Dave and
me
> that tunings like 4296-tET, no matter how high their 'practical
> utility' by this particular measure and even things like error
times
> complexity squared, are not likely to be of widespread interest, so
> we've been looking at things more like a*error + b*complexity . . .

That's why I used this (error times complexity) just to compare
different *meantone* equal temperaments. I think it's a good way to
compare ETs that contain the same scale for example. But you can
always invent a different measure if you don't like the results. :)

> > If one compares 5-limit meantone
> > equal temperaments, unweighted 5-odd limit minimax gives 19-equal
> as
> > the best one. If one uses Tenney-weighted error the winner is
> > actually 12-equal!
>
> It must be a virtual tie . . . And it's a slightly 'compressed' 12-
> equal you're talking about, to be exact, correct?

Yes.

>> >> >But isn't 36/35 vs. 9/8 much more egregious?
>> >>
>> >> Probably; I wasn't expecting it to take tolerance into account.
>> >
>> >How is tolerance relevant here?
>>
>> It's part of why 36/35 is so dissonant.
>
>Tenney doesn't take tolerance into account either but has no trouble
>predicting that.

Which is why I said: "But 36/35 is more egregious anyway, and it seems
Tenney does not run afoul of tolerance so..."

>And how about these comparisons:
>
>45/28 --> 9
>9/8 --> 9
>
>Tolerance seems to work the other way here, doesn't it?

Oops, I didna mean tolerance at all, but rather SPAN. I'm loosing
it... (I am a deathly head-colded at the moment).

>And how about
>
>33/28 --> 11
>11/1 --> 11
>
>?

Is this more of the L_inf nonsense? Throw it out, I say!

>> Maybe I should have said
>> TOLERANCE. Does that help?
>
>Yes, I'm going blind.

Dave writes it that way, to distinguish it from 'a person's limit
of accepting something'.

-Carl

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:
>
> > I'm not sure if you're interested in this kind of thing but in ET
> > comparisons one could also multiply the error by the number of
scale
> > steps in an octave (for example).

> That's the way it's always been done for ET complexity measures.

Aha.

> This way one can measure
> > the "practical utility" of an ET. If one compares 5-limit
meantone
> > equal temperaments, unweighted 5-odd limit minimax gives 19-equal
as
> > the best one. If one uses Tenney-weighted error the winner is
> > actually 12-equal!
>
> I don't know how you computed "badness", but clearly it's not "log
flat".

I simply computed max error times the complexity (number of ET steps
in an octave).

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:
> Kalle wrote:
>
> > > What about integer-limit consistency?
>
> Paul wrote:
>
> > One could worry about that, but the point of 'odd-limit'
> and 'integer-
> > limit' consistency in the past were to establish a finite set of
> > consonances, upon which the evaluation of the tuning's error and
> > complexity would be based. In TOP, at least when you're only
> > tempering out one comma as in 5-limit meantone or 3-limit 12-tET,
> it
> > gets you a tuning where a whole lot of the ratios have a 'Tenney-
> > weighted error' log(n/d)/log(n*d) equal to that of the comma
> itself,
> > while the rest of the ratios have lower 'Tenney-weighted error'.
(I
> > think we're supposed to be multiplying by 1200 now, says
> schoolmaster
> > K. . . . :) ) But we're looking at *all* the ratios in the
> lattice,
> > not just a finite set of consonances . . . so it doesn't have the
> > quality of being 'limited' which generates concerns about
> consistency
> > vs. inconsistency . . .
>
> But why would we be interested about *all* of them? Why not look at
a
> set of n-odd limit consonances plus their octave extensions?

I believe that may actually give the same result in many cases
(particularly when only one comma is being tempered out), if the same
weighting is used! But some people might not buy into octave-
equivalence, in which case odd limits are not the way to get your
consonances. For example, some people might want to use 9:2 and 15:1
as consonances, but not 9:8 or 15:8. Perhaps more significantly,
different people may disagree on which intervals they want to use as
consonances within a given prime limit -- for example, within a prime
limit of 5, some people may wish to use all the 9-odd-limit intervals
as consonances, while others may stick to 5-odd-limit. Since the TOP
solution, especially when fewer commas are tempered out, gives a
large proportion of the intervals the maximum weighted error, any set
of 'consonances' that includes enough of these will, when optimized
in the TOP way, yield that same solution. In other words, it's
robust, and requires fewer arbitrary assumptions that other
methods . . .

> I guess at some point there will always be inconsistency there too.

Don't know what you mean . . . odd-limit already includes all
inversions and octave extensions of its constituent intervals, so
simply considering those as well won't introduce inconsistency if it
wasn't there before . . .

> > > So I can't call an arbitrary mapping of primes to equal scale
> steps
> > a
> > > temperament?
>
> > In strict tuning-math terms, that will only be a different
> > temperament if its GCD is 1. Otherwise it'll be identical to a
> > simpler temperament obtained by putting the mapping in lowest
> terms.
>
> Now I understand!
>
> > Similarly, if we consider tempering out commas, that comma
> shouldn't
> > be the square or cube or higher power of some smaller comma,
> because
> > it yields exactly the same temperament the smaller comma does.
>
> With torsion?

Yes, that's right. Similarly, we've referred to the mapping case you
now understand, above, as "contorsion".

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >> >But isn't 36/35 vs. 9/8 much more egregious?
> >> >>
> >> >> Probably; I wasn't expecting it to take tolerance into
account.
> >> >
> >> >How is tolerance relevant here?
> >>
> >> It's part of why 36/35 is so dissonant.
> >
> >Tenney doesn't take tolerance into account either but has no
trouble
> >predicting that.
>
> Which is why I said: "But 36/35 is more egregious anyway, and it
seems
> Tenney does not run afoul of tolerance so..."
>
> >And how about these comparisons:
> >
> >45/28 --> 9
> >9/8 --> 9
> >
> >Tolerance seems to work the other way here, doesn't it?
>
> Oops, I didna mean tolerance at all, but rather SPAN. I'm loosing
> it... (I am a deathly head-colded at the moment).

OK, I hope you are getting some rest and relaxation, and recovering.
But if you're reading, can you explain what SPAN has to say in 36/35
vs. 9/8 comparison?

>>>Tenney doesn't take tolerance into account either but has no
>>>trouble predicting that.
>>
>> Which is why I said: "But 36/35 is more egregious anyway, and
>> it seems Tenney does not run afoul of tolerance so..."
>>
>> >And how about these comparisons:
>> >
>> >45/28 --> 9
>> >9/8 --> 9
>> >
>> >Tolerance seems to work the other way here, doesn't it?
>>
>> Oops, I didna mean tolerance at all, but rather SPAN. I'm loosing
>> it... (I am a deathly head-colded at the moment).
>
>OK, I hope you are getting some rest and relaxation, and recovering.

How's your hand?

Maybe we should start a tuning-infirmary list, where members could
keep one another updated on their various illnesses. :)

>But if you're reading, can you explain what SPAN has to say in 36/35
>vs. 9/8 comparison?

SPAN includes critical band effects, and the general weakening
of 'cordance' for very large intervals (as on your recent "heinz"
graph). Therefore it says 9/8, which borders the critical band,
should be more concordant than 36/35, which is clearly within it.

-Carl

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

> > But why would we be interested about *all* of them? Why not look
at
> a
> > set of n-odd limit consonances plus their octave extensions?

> I believe that may actually give the same result in many cases
> (particularly when only one comma is being tempered out), if the
same
> weighting is used!

What same result? Are you talking about consistency now?

> But some people might not buy into octave-
> equivalence, in which case odd limits are not the way to get your
> consonances.

I wouldn't use odd-limits to define what I hear as consonances but I
might use it to define what I want to use as consonances. That would
be determined by the scale and harmony I want to use. Isn't this
still a legitimate use of odd-limit?

> For example, some people might want to use 9:2 and 15:1
> as consonances, but not 9:8 or 15:8.
> Perhaps more significantly,
> different people may disagree on which intervals they want to use
as
> consonances within a given prime limit -- for example, within a
prime
> limit of 5, some people may wish to use all the 9-odd-limit
intervals
> as consonances, while others may stick to 5-odd-limit.

Do you mean 9-odd-limit intervals without factors of 7 in them?

> Since the TOP
> solution, especially when fewer commas are tempered out, gives a
> large proportion of the intervals the maximum weighted error, any
set
> of 'consonances' that includes enough of these will, when optimized
> in the TOP way, yield that same solution. In other words, it's
> robust, and requires fewer arbitrary assumptions that other
> methods . . .

I understand this but how does this relate to consistency?

> > I guess at some point there will always be inconsistency there
too.

> Don't know what you mean . . . odd-limit already includes all
> inversions and octave extensions of its constituent intervals, so
> simply considering those as well won't introduce inconsistency if
it
> wasn't there before . . .

But what if the octaves are tempered?

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >>>Tenney doesn't take tolerance into account either but has no
> >>>trouble predicting that.
> >>
> >> Which is why I said: "But 36/35 is more egregious anyway, and
> >> it seems Tenney does not run afoul of tolerance so..."
> >>
> >> >And how about these comparisons:
> >> >
> >> >45/28 --> 9
> >> >9/8 --> 9
> >> >
> >> >Tolerance seems to work the other way here, doesn't it?
> >>
> >> Oops, I didna mean tolerance at all, but rather SPAN. I'm
loosing
> >> it... (I am a deathly head-colded at the moment).
> >
> >OK, I hope you are getting some rest and relaxation, and
recovering.
>
> How's your hand?

Terrible -- but the prognosis looks reasonably good, thanks.

> Maybe we should start a tuning-infirmary list, where members could
> keep one another updated on their various illnesses. :)
>
> >But if you're reading, can you explain what SPAN has to say in
36/35
> >vs. 9/8 comparison?
>
> SPAN includes critical band effects,

Hmm . . . that doesn't quite seem right to me. According to
Plomp/Levelt/Sethares, *all* discordance is due to critical band
effects . . . I thought SPAN was supposed to be some very slowly-
changing monotonic function as one moved from the unison to several
octaves.

> and the general weakening
> of 'cordance' for very large intervals (as on your recent "heinz"
> graph).

This makes more sense.

> Therefore it says 9/8, which borders the critical band,
> should be more concordant than 36/35, which is clearly within it.

Can't buy that. Also, harmonic entropy and Tenney complexity don't
incorporate the 'critical band' consideration in any way, and yet
they have no trouble making this prediction . . .

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

> SPAN includes critical band effects, and the general weakening
> of 'cordance' for very large intervals (as on your recent "heinz"
> graph). Therefore it says 9/8, which borders the critical band,
> should be more concordant than 36/35, which is clearly within it.

The critical band peaks at about a quartetone, so 36/35 isn't just in
it, it's soaking in it--about as dissonant as an interval can be.

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:
>
> > > But why would we be interested about *all* of them? Why not
look
> at
> > a
> > > set of n-odd limit consonances plus their octave extensions?
>
> > I believe that may actually give the same result in many cases
> > (particularly when only one comma is being tempered out), if the
> same
> > weighting is used!
>
> What same result? Are you talking about consistency now?

No, I meant the same tuning as TOP.

> > But some people might not buy into octave-
> > equivalence, in which case odd limits are not the way to get your
> > consonances.
>
> I wouldn't use odd-limits to define what I hear as consonances but
I
> might use it to define what I want to use as consonances. That
would
> be determined by the scale and harmony I want to use. Isn't this
> still a legitimate use of odd-limit?

Yes!

> > For example, some people might want to use 9:2 and 15:1
> > as consonances, but not 9:8 or 15:8.
> > Perhaps more significantly,
> > different people may disagree on which intervals they want to use
> as
> > consonances within a given prime limit -- for example, within a
> prime
> > limit of 5, some people may wish to use all the 9-odd-limit
> intervals
> > as consonances, while others may stick to 5-odd-limit.
>
> Do you mean 9-odd-limit intervals without factors of 7 in them?

Yes.

> > Since the TOP
> > solution, especially when fewer commas are tempered out, gives a
> > large proportion of the intervals the maximum weighted error, any
> set
> > of 'consonances' that includes enough of these will, when
optimized
> > in the TOP way, yield that same solution. In other words, it's
> > robust, and requires fewer arbitrary assumptions that other
> > methods . . .
>
> I understand this but how does this relate to consistency?

Since no tuning is consistent with respect to a prime-limit,
consistency basically disappears as a consideration in the TOP
paradigm.

> > > I guess at some point there will always be inconsistency there
> too.
>
> > Don't know what you mean . . . odd-limit already includes all
> > inversions and octave extensions of its constituent intervals, so
> > simply considering those as well won't introduce inconsistency if
> it
> > wasn't there before . . .
>
> But what if the octaves are tempered?

They won't be if your tuning was optimized by treating each odd-limit
consonance as equally sensitive to mistuning regardless of octave
inversion or extension. Otherwise, the octaves will usually be
tempered, and then yes I suppose you will see inconsistency when you
look at some intervals extended by enough octaves -- but these may be
inaudible in practice . . .

>> >But if you're reading, can you explain what SPAN has to say in
>> 36/35 vs. 9/8 comparison?
>>
>> SPAN includes critical band effects,
>
>Hmm . . . that doesn't quite seem right to me. According to
>Plomp/Levelt/Sethares, *all* discordance is due to critical band
>effects . . .

Yes well, they're very wrong about that. But did they ever say
that?

>I thought SPAN was supposed to be some very slowly-
>changing monotonic function as one moved from the unison to several
>octaves.

Dave is keeper of the SPAN definition. When he and I hashed out
TOLERANCE and SPAN in 1999, what I remember is they together account
for any failings of n*d, with TOLERANCE being failings of n*d
being too high (n/d is approximating a strong concordance) and
SPAN being any failing to do with the size of n/d, from critical
band effects (too small) to weak-'cordance' effects (too big).

>> Therefore it says 9/8, which borders the critical band,
>> should be more concordant than 36/35, which is clearly within it.
>
>Can't buy that.

?

>Also, harmonic entropy and Tenney complexity don't
>incorporate the 'critical band' consideration in any way, and yet
>they have no trouble making this prediction . . .

Is 36/35 any more discordant than 25/24?

-Carl

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@m...> wrote:

> I simply computed max error times the complexity (number of ET steps
> in an octave).

This gives something proportional to max error in "relative cents";
you get "log-flat" for the 5-limit by multiplying by the square root
of n. Now the first thing to beat 19 is not 34, but 53. Both lists
have an infinite number of ets which can beat 19, but the first list
has a constant proportion of all ets, while the second list falls off
in density while still managing to beat 19.

19 and 31 are nearly the same in relative cents error, which is
additive, so 50 about splits the difference; consequently it is near
to Zarlino's 2/7-comma and Woolhouse's rms optimum. A meantone of
around 50 is also excellent in the 7-limit, and makes those -8
generator step thirds and even the -11 generator step wolf fifths
sound better than than they might. It also gives you scales where the
intervals in cents come out exactly and don't need rounding off. For
these reasons, I think 50 is an excellent candidate for the One True
Meantone System which everyone must and shall use.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >But if you're reading, can you explain what SPAN has to say in
> >> 36/35 vs. 9/8 comparison?
> >>
> >> SPAN includes critical band effects,
> >
> >Hmm . . . that doesn't quite seem right to me. According to
> >Plomp/Levelt/Sethares, *all* discordance is due to critical band
> >effects . . .
>
> Yes well, they're very wrong about that. But did they ever say
> that?

Yes. They predict that for sine waves, the only local minimum of
discordance is at 1:1. They claim that harmonic-timbre dyads have
local minima at other simple ratios only because of the critical
bands between pairs of nearly coinciding harmonics.

> >Also, harmonic entropy and Tenney complexity don't
> >incorporate the 'critical band' consideration in any way, and yet
> >they have no trouble making this prediction . . .
>
> Is 36/35 any more discordant than 25/24?

In many cases it isn't, and the reason is TOLERANCE -- the big local
minimum around 1:1 is wide enough that even 36:35 may be brought down
(in discordance) by it.

>> >Also, harmonic entropy and Tenney complexity don't
>> >incorporate the 'critical band' consideration in any way, and yet
>> >they have no trouble making this prediction . . .
>>
>> Is 36/35 any more discordant than 25/24?
>
>In many cases it isn't, and the reason is TOLERANCE -- the big local
>minimum around 1:1 is wide enough that even 36:35 may be brought down
>(in discordance) by it.

Critical band effects are clearly overwhelming anything like this
here.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >Also, harmonic entropy and Tenney complexity don't
> >> >incorporate the 'critical band' consideration in any way, and
yet
> >> >they have no trouble making this prediction . . .
> >>
> >> Is 36/35 any more discordant than 25/24?
> >
> >In many cases it isn't, and the reason is TOLERANCE -- the big
local
> >minimum around 1:1 is wide enough that even 36:35 may be brought
down
> >(in discordance) by it.
>
> Critical band effects are clearly overwhelming anything like this
> here.

Anything like what?

>> >> >Also, harmonic entropy and Tenney complexity don't
>> >> >incorporate the 'critical band' consideration in any way, and
>> >> >yet they have no trouble making this prediction . . .
>> >>
>> >> Is 36/35 any more discordant than 25/24?
>> >
>> >In many cases it isn't, and the reason is TOLERANCE -- the big
>> >local minimum around 1:1 is wide enough that even 36:35 may be
>> >brought down (in discordance) by it.
>>
>> Critical band effects are clearly overwhelming anything like this
>> here.
>
>Anything like what?

Anyhting like the 'magnetism' of "1:1" adding to the concordance of
36:35.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >> >Also, harmonic entropy and Tenney complexity don't
> >> >> >incorporate the 'critical band' consideration in any way, and
> >> >> >yet they have no trouble making this prediction . . .
> >> >>
> >> >> Is 36/35 any more discordant than 25/24?
> >> >
> >> >In many cases it isn't, and the reason is TOLERANCE -- the big
> >> >local minimum around 1:1 is wide enough that even 36:35 may be
> >> >brought down (in discordance) by it.
> >>
> >> Critical band effects are clearly overwhelming anything like this
> >> here.
> >
> >Anything like what?
>
> Anyhting like the 'magnetism' of "1:1" adding to the concordance of
> 36:35.

And what is that 'magnetism' caused by?

>> >> >> >Also, harmonic entropy and Tenney complexity don't
>> >> >> >incorporate the 'critical band' consideration in any way, and
>> >> >> >yet they have no trouble making this prediction . . .
>> >> >>
>> >> >> Is 36/35 any more discordant than 25/24?
>> >> >
>> >> >In many cases it isn't, and the reason is TOLERANCE -- the big
>> >> >local minimum around 1:1 is wide enough that even 36:35 may be
>> >> >brought down (in discordance) by it.
>> >>
>> >> Critical band effects are clearly overwhelming anything like this
>> >> here.
>> >
>> >Anything like what?
>>
>> Anyhting like the 'magnetism' of "1:1" adding to the concordance of
>> 36:35.
>
>And what is that 'magnetism' caused by?

I thought you just said, harmonic entropy.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >> >> >Also, harmonic entropy and Tenney complexity don't
> >> >> >> >incorporate the 'critical band' consideration in any way,
and
> >> >> >> >yet they have no trouble making this prediction . . .
> >> >> >>
> >> >> >> Is 36/35 any more discordant than 25/24?
> >> >> >
> >> >> >In many cases it isn't, and the reason is TOLERANCE -- the
big
> >> >> >local minimum around 1:1 is wide enough that even 36:35 may
be
> >> >> >brought down (in discordance) by it.
> >> >>
> >> >> Critical band effects are clearly overwhelming anything like
this
> >> >> here.
> >> >
> >> >Anything like what?
> >>
> >> Anyhting like the 'magnetism' of "1:1" adding to the concordance
of
> >> 36:35.
> >
> >And what is that 'magnetism' caused by?
>
> I thought you just said, harmonic entropy.

Not necessarily. Some or all of it is due to critical band effects.

You're either talking psychoacoustics or numerical theories, both of
which should, ideally, give the same predictions. It doesn't make
sense for one to overwhelm the other.

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

/tuning/topicId_33969.html#52301

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> >
> > /tuning/topicId_33969.html#52297
> > > >
> > > > ***Pretty much... but I'm still rather gliding on the surface
> of
> > > > this...
> > >
> > > OK, which part would you like me to clarify?
> >
> >
> > ***Well, to take it from the TOP... :)
>
> Oh, you really want to get into that? I was just hoping my new
graphs
> were making sense to you . . .
>
> > what does "TOP" actually
> > stand for,
>
> "Tempered Octaves, Please" or "Tenney-Optimal" . . .
>
> > and what could be the utility of these new scales that
> > would be different from what we have heard before??
>
> Do you mean the new tunings of the same old scales? It could, in
> theory, decrease the "worst error" in terms of damage to consonance
> that we can find in the temperament. There may be more than one
> theoretical way to arrive at these tunings, just as there is more
> than one theoretical way to arrive at 1/4-comma meantone. But one
> observation about them is that they minimize the maximum *weighted*
> error of any ratio n:d, where weighted error is cents error divided
> by log(n*d). This appears to put more importance on the precise
> tuning of the *simple* ratios, the perfect consonances and 5:1,
5:2,
> 7:1, 9:1, 11:1, and less importance on the precise tuning
of "exotic"
> consonances like 7:6, 8:7, 9:5, 11:4, 13:4, 11:5, 27:2, and even
less
> on still more complex ratios. But apperances can be deceiving . . .

***But what is the verdict of people who have been *listening* to
these new versions of the old scales? Is there something
particularly exciting about them?? (Still don't have an .ogg
player... busy enough with mp3s... :)

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> /tuning/topicId_33969.html#52301
>
> > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
> wrote:
> > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> > wrote:
> > >
> > > /tuning/topicId_33969.html#52297
> > > > >
> > > > > ***Pretty much... but I'm still rather gliding on the
surface
> > of
> > > > > this...
> > > >
> > > > OK, which part would you like me to clarify?
> > >
> > >
> > > ***Well, to take it from the TOP... :)
> >
> > Oh, you really want to get into that? I was just hoping my new
> graphs
> > were making sense to you . . .
> >
> > > what does "TOP" actually
> > > stand for,
> >
> > "Tempered Octaves, Please" or "Tenney-Optimal" . . .
> >
> > > and what could be the utility of these new scales that
> > > would be different from what we have heard before??
> >
> > Do you mean the new tunings of the same old scales? It could, in
> > theory, decrease the "worst error" in terms of damage to
consonance
> > that we can find in the temperament. There may be more than one
> > theoretical way to arrive at these tunings, just as there is more
> > than one theoretical way to arrive at 1/4-comma meantone. But one
> > observation about them is that they minimize the maximum
*weighted*
> > error of any ratio n:d, where weighted error is cents error
divided
> > by log(n*d). This appears to put more importance on the precise
> > tuning of the *simple* ratios, the perfect consonances and 5:1,
> 5:2,
> > 7:1, 9:1, 11:1, and less importance on the precise tuning
> of "exotic"
> > consonances like 7:6, 8:7, 9:5, 11:4, 13:4, 11:5, 27:2, and even
> less
> > on still more complex ratios. But apperances can be
deceiving . . .
>
>
> ***But what is the verdict of people who have been *listening* to
> these new versions of the old scales? Is there something
> particularly exciting about them?? (Still don't have an .ogg
> player... busy enough with mp3s... :)
>
> JP

They seem marginally more consonant, since the octaves are allowed to
be slightly detuned and this can often improve the majority of the
other important intervals. For scales that already approximate JI
chords rather well, the difference won't be material.

TOP is mainly interesting conceptually/mathematically. At least for
temperaments involving only one comma, the method is easy to explain
and justify in terms of the Tenney lattice -- and the resulting error
easy to calculate. You also don't have to get your hands dirty with
all kinds of possible "limits" besides the prime limit (or whatever
list of mutually prime basis intervals you want) of the lattice.

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

/tuning/topicId_33969.html#52395

> TOP is mainly interesting conceptually/mathematically.

***Oh... well, thanks, Paul. I guess that's fun, too, but not
generally an area I'm too involved in...

best,

JP

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

> They seem marginally more consonant, since the octaves are allowed to
> be slightly detuned and this can often improve the majority of the
> other important intervals. For scales that already approximate JI
> chords rather well, the difference won't be material.

Conversely, if the temperament in question is high-error, the
difference can be striking.

One very minor talent of ennealimmal is that the TOP generators round
off very nicely in terms of mus, giving generators of 273075/2048
cents and 6275/128 cents. This gives an octave 75/2048 cents sharp,
which seems pretty immaterial to me, but opinions on that may differ.
Miracle in the 5, 7 or 11 limit (they have identical tunings) has a
TOP octave 0.631 cents sharp, and how immaterial that is is obviously
far more debateable. Meantone has an octave 1.699 cents sharp in the
5, 7, and one version of the 11-limit, which I am proposing we just
call "meantone" (Could the other be "huygens"?) This octave has been
the subject of heated debate and I'm not inclined to call it
immaterial. Conversely, however, I think this also means that we are
talking about a serious difference in tuning in practical terms, and
therefore TOP miracle or meantone are by no means interesting only as
theoretical exericises.

> TOP is mainly interesting conceptually/mathematically. At least for
> temperaments involving only one comma, the method is easy to explain
> and justify in terms of the Tenney lattice -- and the resulting error
> easy to calculate.

It's equally easy to justify for any number of commas, explaining it
is another matter, I suppose.

You also don't have to get your hands dirty with
> all kinds of possible "limits" besides the prime limit (or whatever
> list of mutually prime basis intervals you want) of the lattice.

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
>
> /tuning/topicId_33969.html#52395
>
>
> > TOP is mainly interesting conceptually/mathematically.
>
>
> ***Oh... well, thanks, Paul. I guess that's fun, too, but not
> generally an area I'm too involved in...

My opinion is that TOP tuning Blackjack could very well be something
you might consider if you are not using live performers, or if someone
was going to create a fixed tuning instrument set for Blackjack.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > They seem marginally more consonant, since the octaves are
allowed to
> > be slightly detuned and this can often improve the majority of
the
> > other important intervals. For scales that already approximate JI
> > chords rather well, the difference won't be material.
>
> Conversely, if the temperament in question is high-error, the
> difference can be striking.

Indeed -- for example, the harmonies in this:

http://www.io.com/~hmiller/midi/canon-top-pelogic.mid

actually sound quite nice -- if the melodies (with their reversal of
large and small intervals in the scale and all) don't disturb you too
much to cloud the issue. Herman did a nice job with this one and to
anyone who hasn't listened to any of these warped canons for a while,
it should be enjoyable.

> and I'm not inclined to call it
> immaterial. Conversely, however, I think this also means that we are
> talking about a serious difference in tuning in practical terms, and
> therefore TOP miracle or meantone are by no means interesting only
as
> theoretical exericises.

That's true.

> > TOP is mainly interesting conceptually/mathematically. At least
for
> > temperaments involving only one comma, the method is easy to
explain
> > and justify in terms of the Tenney lattice -- and the resulting
error
> > easy to calculate.
>
> It's equally easy to justify for any number of commas,

Doesn't seem that way to me, unfortunately. Maybe some of my pending
questions on tuning-math will get addressed . . .

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> >
> > /tuning/topicId_33969.html#52395
> >
> >
> > > TOP is mainly interesting conceptually/mathematically.
> >
> >
> > ***Oh... well, thanks, Paul. I guess that's fun, too, but not
> > generally an area I'm too involved in...
>
> My opinion is that TOP tuning Blackjack could very well be something
> you might consider if you are not using live performers, or if
someone
> was going to create a fixed tuning instrument set for Blackjack.

The octave is 1200.63 cents in TOP Miracle. It's questionable whether
it even passes the Johnny (1-cent) test of being significantly
different from 72-equal.

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

> One very minor talent of ennealimmal is that the TOP generators round
> off very nicely in terms of mus, giving generators of 273075/2048
> cents and 6275/128 cents. This gives an octave 75/2048 cents sharp,
> which seems pretty immaterial to me, but opinions on that may differ.

I forgot to add that this is 6 mus, so it makes a difference in MTS
and even pitch-bending, where you would alternate dodekamus or cawapus
or whatever your preferred term is for the pitch-bend unit in the
pattern 1,2,1,2 etc. When we get down to stuff like this, I am willing
to consider it reasonably immaterial.

> Miracle in the 5, 7 or 11 limit (they have identical tunings) has a
> TOP octave 0.631 cents sharp, and how immaterial that is is obviously
> far more debateable. Meantone has an octave 1.699 cents sharp

That's 103 mus for miracle, 278 mus for meantone, and this has now
become significant by my standards.

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

> Doesn't seem that way to me, unfortunately. Maybe some of my pending
> questions on tuning-math will get addressed . . .

It's all explained on xenharmony.org; I'd suggest anyone having
questions ask about what this says on tuning-math.

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

> The octave is 1200.63 cents in TOP Miracle. It's questionable whether
> it even passes the Johnny (1-cent) test of being significantly
> different from 72-equal.

It's not a difference I'd like to try to enforce on live performers
but it should be noticable. I could render two versions of the same
Blackjack piece if I can find my old scores, and test it that way.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > Doesn't seem that way to me, unfortunately. Maybe some of my
pending
> > questions on tuning-math will get addressed . . .
>
> It's all explained on xenharmony.org;

Maybe to your mind, but to mine, my tuning-math questions remain
unanswered.

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

> Maybe to your mind, but to mine, my tuning-math questions remain
> unanswered.

Why don't we try to answer each other's pending questions? Can you
give yours on tuning-math?

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

/tuning/topicId_33969.html#52412

> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > The octave is 1200.63 cents in TOP Miracle. It's questionable
whether
> > it even passes the Johnny (1-cent) test of being significantly
> > different from 72-equal.
>
> It's not a difference I'd like to try to enforce on live performers
> but it should be noticable. I could render two versions of the same
> Blackjack piece if I can find my old scores, and test it that way.

***Well, that would be good Gene, but could somebody please
post .mp3s... I'm still rather stubborn about ogling .oggs at the
moment... :)

JP

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

> ***Well, that would be good Gene, but could somebody please
> post .mp3s... I'm still rather stubborn about ogling .oggs at the
> moment... :)

Why? Here's ashampoo media player, which is apparently better than
what you are using, so why not use it instead?

http://www.ashampoo.com/frontend/products/php/product.php?
idstring=0014&session_langid=2

If it works...

Scads of audio and audio-visual formats, plus its skinnable in case
you care.

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

/tuning/topicId_33969.html#52416

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > ***Well, that would be good Gene, but could somebody please
> > post .mp3s... I'm still rather stubborn about ogling .oggs at the
> > moment... :)
>
> Why? Here's ashampoo media player, which is apparently better than
> what you are using, so why not use it instead?
>
> http://www.ashampoo.com/frontend/products/php/product.php?
> idstring=0014&session_langid=2
>
> If it works...
>
> Scads of audio and audio-visual formats, plus its skinnable in case
> you care.

***Hi Gene,

Well, I installed this on my system, but every time I try to play
an .ogg, I get a "fatal error" message...

Maybe it's missing some component??

Thanks!

Joe

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >But if you're reading, can you explain what SPAN has to say in
> >> 36/35 vs. 9/8 comparison?
> >>
> >> SPAN includes critical band effects,
> >
> >Hmm . . . that doesn't quite seem right to me. According to
> >Plomp/Levelt/Sethares, *all* discordance is due to critical band
> >effects . . .
>
> Yes well, they're very wrong about that. But did they ever say
> that?
>
> >I thought SPAN was supposed to be some very slowly-
> >changing monotonic function as one moved from the unison to several
> >octaves.
>
> Dave is keeper of the SPAN definition. When he and I hashed out
> TOLERANCE and SPAN in 1999, what I remember is they together account
> for any failings of n*d, with TOLERANCE being failings of n*d
> being too high (n/d is approximating a strong concordance) and
> SPAN being any failing to do with the size of n/d, from critical
> band effects (too small) to weak-'cordance' effects (too big).
>
> >> Therefore it says 9/8, which borders the critical band,
> >> should be more concordant than 36/35, which is clearly within it.
> >
> >Can't buy that.

Sorry to take so long to respond to this.

I don't think we ever nailed SPAN down that closely. But I do seem to
remember that it was primarily a term for the fact that very wide
intervals (typically greater than an octave) are not very dissonant no
matter what their complexity. Of course they are not particularly
consonant either. It seems like the brain just "doesn't care" about
trying to fit them to a harmonic series.

I don't think the term was ever meant to have any particular relevance
below the critical band.

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

> Well, I installed this on my system, but every time I try to play
> an .ogg, I get a "fatal error" message...
>
> Maybe it's missing some component??

I doubt that. What is your system?

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

/tuning/topicId_33969.html#52421

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > Well, I installed this on my system, but every time I try to play
> > an .ogg, I get a "fatal error" message...
> >
> > Maybe it's missing some component??
>
> I doubt that. What is your system?

***Well, it's still Windows 98 (until my new computer coming soon...)

Ashampoo isn't even playing .mp3s without the "fatal error..."
message.

Here is the "error text...":

playing 'file://C:\WINDOWS\Temporary Internet Files\Content.IE5
\S1QNWLIV\mozvict[1].ogg'

Fatal Exception at 0x00507580 (AMPPLUS.EXE, base address: 0x00400000):

The thread tried to execute an invalid instruction.

The exception is continuable.

Context:

Debug Registers:
Dr0: 0x00000000
Dr1: 0x00000000
Dr2: 0x00000000
Dr3: 0x00000000
Dr6: 0x00000000
Dr7: 0x00000000

Floating Point State:
Control: 0xffff027f
Status: 0xffff0020
Tag: 0xffffffff
ErrorOffset: 0x00505615
DataOffset: 0x00bd4108
DataSelector: 0xffff0267
Registers:
0: 0.000000e+000
1: 0.000000e+000
2: 0.000000e+000
3: 0.000000e+000
4: 0.000000e+000
5: 0.000000e+000
6: 0.000000e+000
7: -1.405554e+049
Cr0NpxState: 0x0000000a

Segment registers:
GS: 0x00000000
FS: 0x00007157
ES: 0x00000267
DS: 0x00000267

Integer registers:
EAX: 0x00000006
EBX: 0x00bd4100
ECX: 0x00000002
EDX: 0x00bd3b20
EDI: 0x00000002
ESI: 0x0406fe1c

Control registers:
EBP: 0x0406fd4c
EIP: 0x00507580
ESP: 0x0406fd1c
SegCS: 0x0000025f
SegSS: 0x00000267
EFlags: 0x00010213

Extended registers:
1cfe0604 02000000 003bbd00 0c70bb85
02000000 c2585000 0041bd00 203bbd00
06000000 a0fd0604 65b95000 a4000000
52b95000 a4000000 00000000 87565000
a0fd0604 9f7e5000 0041bd00 203bbd00
06000000 ee13f7bf 5f020000 e3a2f7bf
203bbd00 00000000 06000000 08000000
04000000 0041bd00 2c000000 57c05000
a0d05800 c8fd0604 efb95000 09000000
dcb95000 e0fd0604 71615000 02000000
1cfe0604 02000000 80ca9701 80ca9701
02000000 01000000 ffffffff 28fe0604
65b95000 2c000000 52b95000 2c000000
80ca9701 28fe0604 f25a5000 02000000
1cfe0604 02000000 80ca9701 a047bd00
0841bd00 1841bd00 a047bd00 00000000
f040bd00 09000000 dcb95000 1cff0604
203bbd00 c040bd00 ffffffff 00000000
60565000 01000000 0041bd00 02000000
80ca9701 b841bd00 a047bd00 18d65700
00000000 bb535000 00000000 9047bd00
00000000 00000000 3047bd00 dd474b00
00000000 10b10200 3047bd00 02000000
a047bd00 0a000000 02000000 44ac0000
0000803f 00000000 112b0000 e1314b00
00000000 3047bd00 02000000 00000000
04000000 01000200 44ac0000 10b10200
04001000 0000fcbf 14000000 80800100
20620500 00000000 b0fe0604 bcb64800
00000000 20620500 44ac0000 10000000
3447bd00 0d000000 10125703 a8395803
88395803 98ff0604 d0395803 00000000

***I don't have the vaguest idea what this means, and I don't know
whether "the exception is continuable" is a hopeful or damning
statement... :)

JP

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

> Fatal Exception at 0x00507580 (AMPPLUS.EXE, base address:
0x00400000):

AMPplus.exe is the player. It seems either the version you have won't
work on your system for reasons unknown, or you had a bad download.
If you downloaded the beta version maybe you should have tried 1.85
instead.

It's sad to see this happening after I pestered you into downloading
this. You can either try another download, or download another
program. I just downloaded Mp3coolplayX, and while it won't play
movie clips or midi files like ashampoo, it seems to work fine for
ogg, mp3, wma and wav. It has no drivers you need to download and is
freeware, plus it is a smaller download than ashampoo.

You can try here:

http://www.phsoft.nl/?id=mp3coolplayx

Or if that doesn't work, here:

http://www.snapfiles.com/download/dlmp3coolplayx.html

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

/tuning/topicId_33969.html#52427

wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > Fatal Exception at 0x00507580 (AMPPLUS.EXE, base address:
> 0x00400000):
>
> AMPplus.exe is the player. It seems either the version you have
won't
> work on your system for reasons unknown, or you had a bad
download.
> If you downloaded the beta version maybe you should have tried
1.85
> instead.
>
> It's sad to see this happening after I pestered you into
downloading
> this. You can either try another download,

***Actually, I downloaded it and installed it *twice...* (even
uninstalling it...) So, it must be something with the system...

or download another
> program. I just downloaded Mp3coolplayX, and while it won't play
> movie clips or midi files like ashampoo, it seems to work fine for
> ogg, mp3, wma and wav. It has no drivers you need to download and
is
> freeware,

***I'll try it this evening...

JP

Joe (and Gene),

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
>> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
>> or download another program.

> ***I'll try it this evening...

I don't know about all these relatively unknown players, but I've stuck with WinAmp, the de facto mp3 player for Windows, and I've never had a problem playing any of the formats. I have version 2.91, and it plays .ogg files flawlessly. While it is possible I had to install a plug-in to decode the .ogg (can't remember), this all came about when Carl initially brought up the .ogg format, and it has never given me a problem.

Not to mention the "SlowDown" plug-in, which allows you to speed up or slow down a file being played without changing pitch, making transcription or study of a passage very easy...

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> Joe (and Gene),
>
> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> >> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> >> or download another program.
>
> > ***I'll try it this evening...
>
> I don't know about all these relatively unknown players, but I've
stuck with WinAmp, the de facto mp3 player for Windows, and I've
never had a problem playing any of the formats. I have version 2.91,
and it plays .ogg files flawlessly. While it is possible I had to
install a plug-in to decode the .ogg (can't remember), this all came
about when Carl initially brought up the .ogg format, and it has
never given me a problem.

WinAmp does require a plug-in. I was only interested in freeware
which required no plugins, drivers or already installed programs. A
program which can't manage this much strikes me as lame.

As for the de facto mp3 player for Windows, there is no such animal,
though no doubt Bill Gates would say it is Windows Media Player, not
WinAmp.

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

> I don't know about all these relatively unknown players, but I've
stuck with WinAmp, the de facto mp3 player for Windows, and I've
never had a problem playing any of the formats. I have version 2.91,
and it plays .ogg files flawlessly. While it is possible I had to
install a plug-in to decode the .ogg (can't remember), this all came
about when Carl initially brought up the .ogg format, and it has
never given me a problem.

I checked the documentation for WinAmp 5, and it only mentions ogg
under "Configuring WinAmp as the default player", but no mention is
made of a plug-in. I'd guess WinAmp 5 no longer needs one, so it's
probably now an everything-goes media player.

The download page is

http://www.winamp.com/player/free.php

and I think I'll try it.

Gene and Joe,

Why don't you just use Winamp?

By the way, Joe, it looks like you need to upgrade your OS.
Many vendors do not even test their stuff on Win98 any more.

-Carl

>WinAmp does require a plug-in.

No, it doesn't.

>I was only interested in freeware

Winamp is free, though not GPL.

>As for the de facto mp3 player for Windows, there is no such animal,
>though no doubt Bill Gates would say it is Windows Media Player, not
>WinAmp.

AOL bought the Winamp franchise for $100 million. It's got to be
worth something.

-Carl

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

> >WinAmp does require a plug-in.
>
> No, it doesn't.

It used to.

> AOL bought the Winamp franchise for $100 million. It's got to be
> worth something.

I is. If they would quit treating its features as an embarassing
secret, I would have noticed that sooner. I did download WinAmp5, and
it has some minor bad points and a very, very nice good point.

Bad points:

(1) When you install it, you need to stop it from doing annoying
things like continually asking for your email address.

(2) It takes a long time to launch compared to similar programs.

(3) When you go to the options menu and change the default skin to
the other skin, you get a skin with no options menu, making it hard
to change back again.

Very very nice good point:

It sounds damned good. It has the best sound quality of any of the
players I've listened to.

This, it seems to me, clearly outweighs the rest.

>> >WinAmp does require a plug-in.
>>
>> No, it doesn't.
>
>It used to.

Yes.

>(2) It takes a long time to launch compared to similar programs.

It shouldn't.

>(3) When you go to the options menu and change the default skin to
>the other skin, you get a skin with no options menu, making it hard
>to change back again.

That shouldn't be. All options are available from the application
menu (upper left corner of all windows in Windows, or right-click
the taskbar).

>Very very nice good point:
>
>It sounds damned good. It has the best sound quality of any of the
>players I've listened to.

Yes, I remember when I first ABed it against MediaPlayer 2.
Shocking! I think MediaPlayer 9 has caught up in sound quality
(and gone downhill in every other area!).

>This, it seems to me, clearly outweighs the rest.

It's completely configurable. It has a built in wav writer, a MIDI
lyrics player, a visualizations API you can use to write your own
visualizations... I could go on and on, but the bottom line is that
Winamp 2.91 is probably on my all-time top 5 list of software.

Other notables are Foobar2000...

http://www.foobar2000.org

...and Quintessential Player...

http://www.quinnware.com/

-Carl

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

/tuning/topicId_33969.html#52433

> Gene and Joe,
>
> Why don't you just use Winamp?
>
> By the way, Joe, it looks like you need to upgrade your OS.
> Many vendors do not even test their stuff on Win98 any more.
>
> -Carl

***I'm going to try Winamp this evening. Do you think I should make
it the *default* for *everything??* Is it that good??

Sure, about the OS, but rather silly to upgrade when I expect a new
fast computer in a couple of months or so...

JP

>/tuning/topicId_33969.html#52433
>
>> Gene and Joe,
>>
>> Why don't you just use Winamp?
>>
>> By the way, Joe, it looks like you need to upgrade your OS.
>> Many vendors do not even test their stuff on Win98 any more.
>
>***I'm going to try Winamp this evening. Do you think I should make
>it the *default* for *everything??*

I do.

>Sure, about the OS, but rather silly to upgrade when I expect a new
>fast computer in a couple of months or so...

Ah, well if you're planning to upgrade hardware soon it indeed
doesn't make sense to mess with your OS now.

-Carl

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

/tuning/topicId_33969.html#52438

> >/tuning/topicId_33969.html#52433
> >
> >> Gene and Joe,
> >>
> >> Why don't you just use Winamp?
> >>
> >> By the way, Joe, it looks like you need to upgrade your OS.
> >> Many vendors do not even test their stuff on Win98 any more.
> >
> >***I'm going to try Winamp this evening. Do you think I should
make
> >it the *default* for *everything??*
>
> I do.
>
> >Sure, about the OS, but rather silly to upgrade when I expect a
new
> >fast computer in a couple of months or so...
>
> Ah, well if you're planning to upgrade hardware soon it indeed
> doesn't make sense to mess with your OS now.
>
> -Carl

***Yes, my new computer will have XP on it. My "computer guru"
friend who is arranging this says that he has some problems with XP
though (difficult to set some things up, etc., etc...)

I'll try Winamp tonight and set it to do all the file formats as the
default... I'm presuming it works with Windows 98...

JP

>***Yes, my new computer will have XP on it. My "computer guru"
>friend who is arranging this says that he has some problems with
>XP though (difficult to set some things up, etc., etc...)

Yes, XP went downhill in many respects from Windows 2000. But
sadly there's no escaping the, uh, Winds of Change.

>I'll try Winamp tonight and set it to do all the file formats as
>the default... I'm presuming it works with Windows 98...

Both version 5 and 2.91 should, but try to get 2.91 if you can.

-Carl

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

> Both version 5 and 2.91 should, but try to get 2.91 if you can.

Version 5 works fine with W98.

>I don't know about all these relatively unknown players, but I've
>stuck with WinAmp, the de facto mp3 player for Windows, and I've
>never had a problem playing any of the formats. I have version 2.91,
>and it plays .ogg files flawlessly. While it is possible I had to
>install a plug-in to decode the .ogg (can't remember),

Nope, you didn't!

>Not to mention the "SlowDown" plug-in, which allows you to speed up
>or slow down a file being played without changing pitch, making
>transcription or study of a passage very easy...

Winamp has many features that make it simply the best player out
there. I've recently upgraded to Winamp5, and skinned it to look
like Winamp 2.91. If you can still download 2.91, it's probably
better for most folks here.

-Carl

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

/tuning/topicId_33969.html#52451

> >I don't know about all these relatively unknown players, but I've
> >stuck with WinAmp, the de facto mp3 player for Windows, and I've
> >never had a problem playing any of the formats. I have version
2.91,
> >and it plays .ogg files flawlessly. While it is possible I had to
> >install a plug-in to decode the .ogg (can't remember),
>
> Nope, you didn't!
>
> >Not to mention the "SlowDown" plug-in, which allows you to speed
up
> >or slow down a file being played without changing pitch, making
> >transcription or study of a passage very easy...
>
> Winamp has many features that make it simply the best player out
> there. I've recently upgraded to Winamp5, and skinned it to look
> like Winamp 2.91. If you can still download 2.91, it's probably
> better for most folks here.
>
> -Carl

***Something kinda weird happened. I installed Winamp and it became
the *default* for all my music files, mp3s and .oggs, of course.

On my webpage, it was defaulting to "Winamp," which is what I
wanted. Then *suddenly* it started to default back to "MusicMatch"
which is what I was using before. It stayed with MusicMatch for a
while.

I should also mention that I rebooted, during all of this, and it
came up defaulting to *MusicMatch...*

Then I played .oggs on Gene's site, which used Winamp.

When I went back to my webpage to play .mp3s is was then defaulting
to *Winamp*

I guess I really don't care which player comes up, as long as
*something* does... but anybody have a clue why this "flakey
defaulting" is going on?

Thanks!

JP

Joseph Pehrson wrote:

>***Something kinda weird happened. I installed Winamp and it became >the *default* for all my music files, mp3s and .oggs, of course.
>
>On my webpage, it was defaulting to "Winamp," which is what I >wanted. Then *suddenly* it started to default back to "MusicMatch" >which is what I was using before. It stayed with MusicMatch for a >while.
>
>I should also mention that I rebooted, during all of this, and it >came up defaulting to *MusicMatch...*
>
>Then I played .oggs on Gene's site, which used Winamp.
>
>When I went back to my webpage to play .mp3s is was then defaulting >to *Winamp*
>
>I guess I really don't care which player comes up, as long as >*something* does... but anybody have a clue why this "flakey >defaulting" is going on?
>

Windows?

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

>***Something kinda weird happened. I installed Winamp and it became
>the *default* for all my music files, mp3s and .oggs, of course.
>
>On my webpage, it was defaulting to "Winamp," which is what I
>wanted. Then *suddenly* it started to default back to "MusicMatch"
>which is what I was using before. It stayed with MusicMatch for a
>while.
>
>I should also mention that I rebooted, during all of this, and it
>came up defaulting to *MusicMatch...*
>
>Then I played .oggs on Gene's site, which used Winamp.

MusicMatch is obviously steeling the associations it can handle
when you reboot; a common strategy. You see, the good people of
MusicMatch base the value of their company on nothing more than
how many people use their software, so it's imperative that you
use it whether you want to or not!

Uninstall MM, reboot, and then play an ogg file. This should
reset everything to Winamp for good!

>When I went back to my webpage to play .mp3s is was then
>defaulting to *Winamp*

You see, the good folks at Winamp realize that all the other
software out there steels your associations at reboot. They don't
want to do that, but they realize that you probably want to use
Winamp, so they have an option (enabled by default) to steel them
back whenever you run Winamp.

-Carl

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

/tuning/topicId_33969.html#52454

> >***Something kinda weird happened. I installed Winamp and it
became
> >the *default* for all my music files, mp3s and .oggs, of course.
> >
> >On my webpage, it was defaulting to "Winamp," which is what I
> >wanted. Then *suddenly* it started to default back
to "MusicMatch"
> >which is what I was using before. It stayed with MusicMatch for
a
> >while.
> >
> >I should also mention that I rebooted, during all of this, and it
> >came up defaulting to *MusicMatch...*
> >
> >Then I played .oggs on Gene's site, which used Winamp.
>
> MusicMatch is obviously steeling the associations it can handle
> when you reboot; a common strategy. You see, the good people of
> MusicMatch base the value of their company on nothing more than
> how many people use their software, so it's imperative that you
> use it whether you want to or not!
>
> Uninstall MM, reboot, and then play an ogg file. This should
> reset everything to Winamp for good!
>

***Hi Carl,

Actually, this was something I was thinking of trying... I guess
Winamp is considerably better than MusicMatch, yes? so it would be a
good idea to do this?

Thanks,

JP

>***Hi Carl,
>
>Actually, this was something I was thinking of trying... I guess
>Winamp is considerably better than MusicMatch, yes? so it would be a
>good idea to do this?
>
>Thanks,
>
>JP

It's your preference, dude! Pls. just write me offlist with anymore
support questions.

-Carl

on 2/10/04 7:06 AM, David Beardsley <db@biink.com> wrote:

> Joseph Pehrson wrote:
>
>> ***Something kinda weird happened. I installed Winamp and it became
>> the *default* for all my music files, mp3s and .oggs, of course.
>>
>> On my webpage, it was defaulting to "Winamp," which is what I
>> wanted. Then *suddenly* it started to default back to "MusicMatch"
>> which is what I was using before. It stayed with MusicMatch for a
>> while.
>>
>> I should also mention that I rebooted, during all of this, and it
>> came up defaulting to *MusicMatch...*
>>
>> Then I played .oggs on Gene's site, which used Winamp.
>>
>> When I went back to my webpage to play .mp3s is was then defaulting
>> to *Winamp*
>>
>> I guess I really don't care which player comes up, as long as
>> *something* does... but anybody have a clue why this "flakey
>> defaulting" is going on?
>>
>
> Windows?

The same crap happens on the Mac. Once I installed Real Player and was not
able to use QuickTime again for a long time, until some coincidental event
did the right thing. I vowed to never install Real Player again.

-Kurt

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

> Uninstall MM, reboot, and then play an ogg file. This should
> reset everything to Winamp for good!

You can configure Winamp to prevent MM from doing this, which is a
lot less drastic.

>> Uninstall MM, reboot, and then play an ogg file. This should
>> reset everything to Winamp for good!
>
>You can configure Winamp to prevent MM from doing this, which is a
>lot less drastic.

No, you can't -- the two will continue to duke it out, causing
the oscillations Joseph experienced. There are of course ways
around the problem but since there's no reason anyone should
keep MusicMatch around, I recommend uninstalling.

Joseph, if for some reason you don't want to uninstall, write me
offlist for instructions. I want to get this thread off tuning!

-Carl

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

/tuning/topicId_33969.html#52460

> >> Uninstall MM, reboot, and then play an ogg file. This should
> >> reset everything to Winamp for good!
> >
> >You can configure Winamp to prevent MM from doing this, which is
a
> >lot less drastic.
>
> No, you can't -- the two will continue to duke it out, causing
> the oscillations Joseph experienced. There are of course ways
> around the problem but since there's no reason anyone should
> keep MusicMatch around, I recommend uninstalling.
>
> Joseph, if for some reason you don't want to uninstall, write me
> offlist for instructions. I want to get this thread off tuning!
>
> -Carl

***I blew MusicMatch away... all on this subject.

But where is Gene's .ogg file that was a string quartet with one of
the violinists fired??

JP

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

> But where is Gene's .ogg file that was a string quartet with one of
> the violinists fired??

It's the first movement here:

http://66.98.148.43/~xenharmo/meantop.htm

Another must-listen is Night on Porcupine Mountain, which along with
other weirdness can be found here:

http://66.98.148.43/~xenharmo/mad.html

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

/tuning/topicId_33969.html#52465

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > But where is Gene's .ogg file that was a string quartet with one
of
> > the violinists fired??
>
> It's the first movement here:
>
> http://66.98.148.43/~xenharmo/meantop.htm
>

***Well, this is interesting. Actually, tuning-wise, I think it
sounds pretty good...

But, with the MIDI sounds here, I'm just as glad we have one less
string player... I'll vote for oboe... :)

> Another must-listen is Night on Porcupine Mountain, which along
with
> other weirdness can be found here:
>
> http://66.98.148.43/~xenharmo/mad.html

***This is interesting, but odd. I guess the pitches are "quantized"
to the nearest 22-equal notes?? I'll have to "think on" this a
bit... :) Certainly an interesting alternate tuning exercise...

J. Pehrson

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

> > Another must-listen is Night on Porcupine Mountain, which along
> with
> > other weirdness can be found here:
> >
> > http://66.98.148.43/~xenharmo/mad.html
>
> ***This is interesting, but odd. I guess the pitches are "quantized"
> to the nearest 22-equal notes?? I'll have to "think on" this a
> bit... :) Certainly an interesting alternate tuning exercise...

Nope, it's a lot more sophisicated than that. The Symphony Fantastique
in Pajara[12] is more along that line.