Hexatonic scale in 11-EDO

Hello, everyone, and special thanks to Graham Breed, Paul Erlich, and
Joseph Pehrson for a thread on "Decimal Counterpoint" which has led me
to one of the most wonderful experiences I have had in the world of
xenharmonics.

Reading that thread inspired me to try what I couldn't resist calling
"Undecimal Counterpoint" using a hexatonic scale found within 22-EDO.
The term "undecimal" refers to the chromatic superset, so to speak,
from which this basic scale is taken: the set of even-numbered degrees
in 22-EDO, or in other words, the complete set of 11-EDO.

Please let me try to resist the temptation to get too absorbed in
technical details: that would neither show due reverence to the beauty
of this scale and tuning system, nor do justice to my experience.

Some of the progressions seem to have the purity of snowflakes: it is
like a dance of snowflakes in some new geometry. The patterns of
counterpoint and harmony are at once familiar, and yet quite
altered. It is a new universe, a xentonal expanse only very partially
to be described in words, musical notations, or tabulations in cents.

Of course, as many of you may suspect, the new universe of concord
which I have experienced depends largely on the critical factor of
timbre, that marvellous dimension of music which Pierce, Darreg,
Chowning, Carlos, Sethares, Ligon, and others have helped to make
accessible to these ongoing explorations.

Finding the "right timbre" for 11-EDO, or more specifically my
approach to it, has been my aspiration since last summer, and only in
the last few days, prodding by that "Decimal Counterpoint" thread,
have I come up with some FM settings that have really drawn me into
that approach -- amplifying and modifying it in the process, of
course.

At the same time as I was getting the timbre settings into place --
not that I claim any definitive solution -- the idea of the hexatonic
scale occurred to me, with lots of inspiration, Paul, from your paper
and some more recent comments.

This scale, easy to find on my 22-EDO keyboard, provides a ready
"compass" to 11-EDO -- indeed the complete 11-EDO set can be mapped as
two hexatonic scales at 1/11 octave apart, with one note shared in
common on both manuals. In 11-EDO degrees and cents, the hexatonic
scale is:

0 2 4 6 8 9 11
0 218.18 436.36 654.55 872.73 981.82 1200
2 2 2 2 1 2
218.18 218.18 218.18 218.18 109.09 218.18
L L L L s L

In my next post, I'll share more on this scale (and some comments
about it returned by the SHOW DATA command in Manuel Op de Coul's
excellent Scala program available free on the Internet), explain my
keyboard layout for 22-EDO and 11-EDO, and give a quick first example
of note-against-note counterpoint in the hexatonic scale.

Also, Paul, I can't resist giving a table of hexatonic names for the
interval categories in 11-EDO; and Graham, I'll give a quick table of
concord/discord categories as I tend to treat them at this early
stage.

However, since short posts are easier to read, I'll conclude these
first impressions by saying that 11-EDO is beautiful, that it has a
special kind of consonance and enchanting patterns of counterpoint and
harmony to offer, and that the wonders of customized timbre do indeed
reveal new musical geometries, new expressions of musical coherence
and meaning.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:

/tuning/topicId_36696.html#36696

> Hello, everyone, and special thanks to Graham Breed, Paul Erlich,
and Joseph Pehrson for a thread on "Decimal Counterpoint" which has
led me to one of the most wonderful experiences I have had in the
world of xenharmonics.
>

***Many thanks to Margo Schulter and Dan Stearns for the interesting
posts concerning 11-tET. I am anxious to hear some of the music that
results from this, although I do believe I have heard some 11-tET
music before (maybe Herman Miller??) and was impressed by the exotic
strangeness of it all.

What impresses me is the fact that on Paul Erlich's famous sonority
chart, 11-tET does quite terribly. There is only a 3-limit ratio
approximated and that rather poorly.

This seems to rather argue against the view that music that slavishly
follows the harmonic series is, unquestionably, superior...

??

Thanks!

J. Pehrson

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:

> ***Many thanks to Margo Schulter and Dan Stearns for the
interesting
> posts concerning 11-tET. I am anxious to hear some of the music
that
> results from this,

me too!

> although I do believe I have heard some 11-tET
> music before (maybe Herman Miller??)

have you heard bill sethares' 11-equal piece, which is entitled (i
believe) "turquoise dabo girl"? it should be on his website. of
course (like margo), bill uses timbres specifically designed for 11-
equal.

> This seems to rather argue against the view that music that
slavishly
> follows the harmonic series is, unquestionably, superior...

i've been trying to convince dave keenan that, if the timbres are
adapted to the tuning (or even just "pastelized"), deviations of 24
cents or more from the harmonic series are no problem. specifically,
i've had a hard time convincing dave that the 678-cent fifths of
our "pelogic" tuning are perfectly wonderful when coupled with any
marimba-like timbre and an appropriate musical style. the coherence
of the 5-tone pelogic MOS makes this one of the most useful 5-limit
temperaments in my book, while dave places it near the bottom. i hope
margo and others will join me in trying to convince him otherwise; a
well crafted example with fifths that are 47 cents (!) off the
harmonic series might just do the trick.

If someone would like to volunteer to do the cassette to mp3 transfer,
then I'd be happy to send them some music in 11-tet to share with
anybody who's interested--sans any specially tailored timbres even!

take care,

--Dan Stearns

----- Original Message -----
From: "emotionaljourney22" <paul@stretch-music.com>
To: <tuning@yahoogroups.com>
Sent: Tuesday, April 30, 2002 12:42 PM
Subject: [tuning] Re: Hexatonic scale in 11-EDO

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > --- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
>
> > ***Many thanks to Margo Schulter and Dan Stearns for the
> interesting
> > posts concerning 11-tET. I am anxious to hear some of the music
> that
> > results from this,
>
> me too!
>
> > although I do believe I have heard some 11-tET
> > music before (maybe Herman Miller??)
>
> have you heard bill sethares' 11-equal piece, which is entitled (i
> believe) "turquoise dabo girl"? it should be on his website. of
> course (like margo), bill uses timbres specifically designed for 11-
> equal.
>
> > This seems to rather argue against the view that music that
> slavishly
> > follows the harmonic series is, unquestionably, superior...
>
> i've been trying to convince dave keenan that, if the timbres are
> adapted to the tuning (or even just "pastelized"), deviations of 24
> cents or more from the harmonic series are no problem. specifically,
> i've had a hard time convincing dave that the 678-cent fifths of
> our "pelogic" tuning are perfectly wonderful when coupled with any
> marimba-like timbre and an appropriate musical style. the coherence
> of the 5-tone pelogic MOS makes this one of the most useful 5-limit
> temperaments in my book, while dave places it near the bottom. i
hope
> margo and others will join me in trying to convince him otherwise; a
> well crafted example with fifths that are 47 cents (!) off the
> harmonic series might just do the trick.
>
>
> ------------------------ Yahoo! Groups
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--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> This seems to rather argue against the view that music that slavishly
> follows the harmonic series is, unquestionably, superior...

The 11-et has the same approximations to 7,9,11,5/3,9/7,11/9 and
11/7 as the 22-et, and does just fine on the subgroup they generate together with 2, or on other subgroups such as {2,5/3,7,9}. One way to evaluate ets is to look at what they do well, in terms of the harmonic series.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

> The 11-et has the same approximations to 7,9,11,5/3,9/7,11/9 and
> 11/7 as the 22-et, and does just fine on the subgroup they generate together with 2, or on other subgroups such as {2,5/3,7,9}. One way to evaluate ets is to look at what they do well, in terms of the harmonic series.

The 23-et is similar; in terms of integer generators it approximates
{2,33,55,77,121}, which is a subgroup of rank two of the 11-limit--half of the 11-limit is attainable. The same is true of 11-et, whose group could also be given as generated by {2,9,15,7,11}.

Other ets which do not lead to such large subgroups are still interesting; for instance:

17: {2, 3, 11/7} (shares with 68)
34: {2, 3, 5, 11/7} (shares with 68)
24: {2, 3, 11, 11/3} (shares with 72)
36: {2, 3, 7, 11/5} (shares with 72--"Wonder Tuning".)

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

13: {2,9,5,7/3,11,13,17} shares with 26; index 2.

25: {2,9,5,7,11/3,13,17} shares with 50; index 2.

These should perhaps have recieved more attention than they seem to have, but Margo has considered this:

29: {2,3,7/5,11/7,13/11,17/13}

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> > This seems to rather argue against the view that music that
> slavishly
> > follows the harmonic series is, unquestionably, superior...
>
> i've been trying to convince dave keenan that, if the timbres are
> adapted to the tuning (or even just "pastelized"), deviations of 24
> cents or more from the harmonic series are no problem. specifically,
> i've had a hard time convincing dave that the 678-cent fifths of
> our "pelogic" tuning are perfectly wonderful when coupled with any
> marimba-like timbre and an appropriate musical style.

I've long been convinced of this, having read Bill Sethares ideas on this
in 1993, and having listened to his 'Xentonality' CD many times.

> the coherence
> of the 5-tone pelogic MOS makes this one of the most useful 5-limit
> temperaments in my book, while dave places it near the bottom.

This is the part I have trouble with.

First let me clarify. Near the bottom of what? Certainly not near the
bottom of a list of all possible 5-limit temperaments. It is number 16 on
my personal list, that starts like this (excluding the degenerate twin and
half meantones which would otherwise go just above neutral thirds).

meantone
schismic
diaschismic
kleismic
augmented
magic
semiminorthirds (porcupine)
wuerschmidt
subminor thirds (orwell)
semisixths (tiny diesic)
quartafifths (minimal diesic)
quintelevenths (AMT)
neutral thirds
tertiathirds (Negri's system)
diminished
pelogic
quintuple thirds (Blackwood's decatonic)

Now any kind of ranking of tunings for some kind of "usefulness" or
"interestingness" is bound to make someone unhappy. It's a crazy thing to
try to do, really. But the purpose was mainly to limit, from the infinity
of possibilities, the number of temperaments to appear in a sort of catalog
of 5-limit temperaments. So Paul should simply be happy that pelogic is in
there.

Please note that, the identification of a 5 note chain in pelogic
temperament, with actual pelog, is still open to debate. But even assuming
this to be valid, placing a low value on pelog _as_a_5-limit_temperament_
is not the same as placing a low value on pelog per se. I know very little
about pelog but I understand that the approximate 5-limit triads of pelogic
temperament do not feature highly (if at all) in traditional pelog music. I
assume there are pelog experts on the list who will correct me if I'm wrong
here.

The other issue is of course that of "custom timbres". I expect that _any_
temperament on that list whose low position is due to its large deviations
from 5-limit consonances (as opposed to being due to it requiring large
numbers of notes to get a few chords) could be elevated to near the top of
the list by finding or designing a custom timbre for it in the manner of
Sethares. The last three on the list are in this category.

This is not "slavishly following the harmonic series" but it is still
following a (inharmonic) partial series. And the reason why we do this is
simple. I assume we can take it that interesting music, if it uses harmony
at all, must have consonances of some kind. Few people find music
containing only dissonance interesting for very long. Of the two (of course
it is really a continuum) consonance is by far the hardest to find in (or
put into) a scale, because other desirable scale properties tend to be
incompatible with it; a recessive gene as it were. This is because
consonance is experienced only when the partials of the simultaneous notes
coincide or nearly coincide in frequency. This includes the partials
generated by nonlinearities in our ears. Note that the latter are harmonic
even if the original timbre isn't.

If one is to give a single ranking of 5-limit temperaments for general use,
one must of course assume a lot of things, one of which is that the timbre
is harmonic. We do this because the most common timbres _are_ harmonic, or
very nearly so. And surely, the ability to produce consonance with only
one, or a small class of timbres, makes a tuning less generally useful.

Maybe there is some commonality among inharmonic timbres so that someone
could produce another list ranked for consonance with "a typical inharmonic
timbre".

> I hope
> margo and others will join me in trying to convince him otherwise; a
> well crafted example with fifths that are 47 cents (!) off the
> harmonic series might just do the trick.

I would love to hear such music, but in this case I don't think it will
convince me of anything I am not already convinced of.

In regard to 11-EDO, if I remember rightly, Dan Stearns pointed out that it
has reasonably good approximations to 7:9:11, which can function as
consonances even _with_ a harmonic timbre. In that regard, it's still
following the harmonic series (there's nothing slavish about it), but it's
following a part of the series that doesn't fit into the n-limit way of
categorising tunings, which has been dominant for too long.

Regards,
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com

Another way (to evaluate ETs), one that has been notably argued triple
fortissimo by folks like Darreg and McLaren as the only truly useful
way, is to make music in these tunings.

This would be the hands-on approach--the MMM approach.

It would be great if there were many talented and gossipy folks
committed to composing and creating with these tunings for a while,
exchanging notes and ideas... seeing what works and what doesn't WHERE
IT REALLY COUNTS (in actual music). But the truth is, certainly in
this community anyway, that the talented and gossipy folks are
committed to discussing what these tunings do theoretically or
mathematically.

While the tuning-math bandwidth far outweighs those committed to the
hands-on approach, and that's just the way it's all panned out, I
truly believe that it's the hands-on approach that is most valid. It
just doesn't cover its tracks as well when it comes to neat
explanations why... it's messy. But I for one am glad that some things
are still vexing, ornery, messy, and irascible enough to fight back...
like music.

(If I were music, I would chuckle at any attempts to neuter, grasp and
bottle my horizons via the sympathetically vibrating parts of your
ears... harmonic series approximations and the sundry like?
Hahahahaha... oh, bring it on math boys... bring it on!)

take care,

--Dan (if he were music) Stearns

----- Original Message -----
From: "genewardsmith" <genewardsmith@juno.com>
To: <tuning@yahoogroups.com>
Sent: Wednesday, May 01, 2002 1:17 AM
Subject: [tuning] Re: Hexatonic scale in 11-EDO

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > This seems to rather argue against the view that music that
slavishly
> > follows the harmonic series is, unquestionably, superior...
>
> The 11-et has the same approximations to 7,9,11,5/3,9/7,11/9 and
> 11/7 as the 22-et, and does just fine on the subgroup they generate
together with 2, or on other subgroups such as {2,5/3,7,9}. One way to
evaluate ets is to look at what they do well, in terms of the harmonic
series.
>
>
> ------------------------ Yahoo! Groups
Sponsor ---------------------~-->
> Buy Stock for $4
> and no minimums.
> FREE Money 2002.
> http://us.click.yahoo.com/orkH0C/n97DAA/ySSFAA/RrLolB/TM
> --------------------------------------------------------------------
-~->
>
> You do not need web access to participate. You may subscribe
through
> email. Send an empty email to one of these addresses:
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In-Reply-To: <aaofbl+8hqf@eGroups.com>
genewardsmith wrote:

> These should perhaps have recieved more attention than they seem to
> have, but Margo has considered this:
>
> 29: {2,3,7/5,11/7,13/11,17/13}

shares with 58 and 87 (well, except the 17/13) leading to my multiple-29
temperament.

Graham

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_36696.html#36714

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > This seems to rather argue against the view that music that
slavishly
> > follows the harmonic series is, unquestionably, superior...
>
> The 11-et has the same approximations to 7,9,11,5/3,9/7,11/9 and
> 11/7 as the 22-et, and does just fine on the subgroup they generate
together with 2, or on other subgroups such as {2,5/3,7,9}. One way
to evaluate ets is to look at what they do well, in terms of the
harmonic series.

***Hi Gene...

Well, that's nice, but perhaps somebody can explain to me why 11-tET
only shows a poor 3-limit approximation wheras 22-tET shows a good 3,
5, 7, 9 and 11 limit approximation on Paul Erlich's famous ET chart??

J. Pehrson

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

/tuning/topicId_36696.html#36719

> Another way (to evaluate ETs), one that has been notably argued
triple
> fortissimo by folks like Darreg and McLaren as the only truly useful
> way, is to make music in these tunings.
>
> This would be the hands-on approach--the MMM approach.
>
> It would be great if there were many talented and gossipy folks
> committed to composing and creating with these tunings for a while,
> exchanging notes and ideas... seeing what works and what doesn't
WHERE
> IT REALLY COUNTS (in actual music). But the truth is, certainly in
> this community anyway, that the talented and gossipy folks are
> committed to discussing what these tunings do theoretically or
> mathematically.
>

***Is that entirely fair, Dan?? It seems to me that there are
*several* people on this list who are actively either writing music,
producing concerts, or such like...

Maybe it's just that, in conversing about music, it's easier to talk
about the theoretical aspects than the "ineffable" ones. That would
make sense, yes?

Of course we could always have discussions:

Ummm, I like it!

Ummm, I don like it!

Ummm, ummm good!

J. Pehrson

Joe,

Only the 7:9:11 are 11-tet intervals. The 3 and the 5 are 22-tet
intervals (i.e., odd numbers). So the 3 (and the 5) in 11-tet is a
much different interval than the 3 (and the 5) in 22... 6/11 and 13/22
are quite different, and that's why "11-tET only shows a poor 3-limit
approximation" in Paul's chart.

But so what? Either that's important to somebody or it's not. Having
heard a good amount of your music--of which I'm a fan--I'd have to
wonder why it should matter too much to you personally, or perhaps
musically. It's not that you don't write tonal music per se, but in a
lot of your music consistency and nearness to harmonic series timbers
hardly strikes me as big consideration. There area lot of exotic,
xenharmonic resources in ETs that would rank poorly on a chart such as
Paul's, and I bet you'd have a ball with them... just a hunch.

take care,

--Dan Stearns

----- Original Message -----
From: "jpehrson2" <jpehrson@rcn.com>
To: <tuning@yahoogroups.com>
Sent: Wednesday, May 01, 2002 7:35 AM
Subject: [tuning] Re: Hexatonic scale in 11-EDO

> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
>
> /tuning/topicId_36696.html#36714
>
>
> > --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> >
> > > This seems to rather argue against the view that music that
> slavishly
> > > follows the harmonic series is, unquestionably, superior...
> >
> > The 11-et has the same approximations to 7,9,11,5/3,9/7,11/9 and
> > 11/7 as the 22-et, and does just fine on the subgroup they
generate
> together with 2, or on other subgroups such as {2,5/3,7,9}. One way
> to evaluate ets is to look at what they do well, in terms of the
> harmonic series.
>
> ***Hi Gene...
>
> Well, that's nice, but perhaps somebody can explain to me why 11-tET
> only shows a poor 3-limit approximation wheras 22-tET shows a good
3,
> 5, 7, 9 and 11 limit approximation on Paul Erlich's famous ET
chart??
>
> J. Pehrson
>
>
> ------------------------ Yahoo! Groups
Sponsor ---------------------~-->
> Buy Stock for $4
> and no minimums.
> FREE Money 2002.
> http://us.click.yahoo.com/orkH0C/n97DAA/ySSFAA/RrLolB/TM
> --------------------------------------------------------------------
-~->
>
> You do not need web access to participate. You may subscribe
through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
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>
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>
>

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

/tuning/topicId_36696.html#36728

> Joe,
>
> Only the 7:9:11 are 11-tet intervals. The 3 and the 5 are 22-tet
> intervals (i.e., odd numbers). So the 3 (and the 5) in 11-tet is a
> much different interval than the 3 (and the 5) in 22... 6/11 and
13/22
> are quite different, and that's why "11-tET only shows a poor 3-
limit
> approximation" in Paul's chart.
>
> But so what? Either that's important to somebody or it's not. Having
> heard a good amount of your music--of which I'm a fan--I'd have to
> wonder why it should matter too much to you personally, or perhaps
> musically. It's not that you don't write tonal music per se, but in
a
> lot of your music consistency and nearness to harmonic series
timbers
> hardly strikes me as big consideration. There area lot of exotic,
> xenharmonic resources in ETs that would rank poorly on a chart such
as
> Paul's, and I bet you'd have a ball with them... just a hunch.
>
>
> take care,
>
> --Dan Stearns
>

***Thanks, Dan, for explaining that to me. Why, sure! That's why I
mentioned above that you deserve kudos for opening up scales that
don't "slavishly" follow the harmonic series. Some people,
apparently, thought the word "slavish" was a little strong... perhaps
it is, but, absolutely, musical "context" is all that counts.

best,

Joe

Hi Joe,

Fair... no, probably not but maybe so too. I don't know, I guess I'm
too much in the middle of it myself. I do know that the people on this
list "who are actively either writing music, producing concerts, or
such like" are barely a blip on the posting radar screen.

We can argue the reasons for this long the proverbial night but I
don't think it's going to matter much... it is as it is and it's been
this way for a long, long time. Your point about the comparatively
limited range of things that can be discussed about a given piece of
music is spot on. But I don't think that's the primary reason why this
list engenders the type of controversies that it does, though I'm sure
some people do feel squeezed or drowned out or more than a few are
subtly manipulated to do as the Romans do... but that's okay, that's
just the way it's all worked out. Though it is strange, or at least it
still seems strange to me (even after 3 years of it).

take care,

--Dan Stearns

----- Original Message -----
From: "jpehrson2" <jpehrson@rcn.com>
To: <tuning@yahoogroups.com>
Sent: Wednesday, May 01, 2002 10:39 AM
Subject: [tuning] the inaffable ineffable

> --- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
>
> /tuning/topicId_36696.html#36719
>
> > Another way (to evaluate ETs), one that has been notably argued
> triple
> > fortissimo by folks like Darreg and McLaren as the only truly
useful
> > way, is to make music in these tunings.
> >
> > This would be the hands-on approach--the MMM approach.
> >
> > It would be great if there were many talented and gossipy folks
> > committed to composing and creating with these tunings for a
while,
> > exchanging notes and ideas... seeing what works and what doesn't
> WHERE
> > IT REALLY COUNTS (in actual music). But the truth is, certainly in
> > this community anyway, that the talented and gossipy folks are
> > committed to discussing what these tunings do theoretically or
> > mathematically.
> >
>
> ***Is that entirely fair, Dan?? It seems to me that there are
> *several* people on this list who are actively either writing music,
> producing concerts, or such like...
>
> Maybe it's just that, in conversing about music, it's easier to talk
> about the theoretical aspects than the "ineffable" ones. That would
> make sense, yes?
>
> Of course we could always have discussions:
>
> Ummm, I like it!
>
> Ummm, I don like it!
>
> Ummm, ummm good!
>
> J. Pehrson
>
>
>
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--- In tuning@y..., David C Keenan <d.keenan@u...> wrote:

> I know very little
> about pelog but I understand that the approximate 5-limit triads of
pelogic
> temperament do not feature highly (if at all) in traditional pelog
music.

not if you're expecting western-style block chords or functional
harmonic progressions, no. but the music is highly polyphonic, and
the presense of these intervals in the resulting "crystal" is
unmistakable.

> The other issue is of course that of "custom timbres". I expect
that _any_
> temperament on that list whose low position is due to its large
deviations
> from 5-limit consonances (as opposed to being due to it requiring
large
> numbers of notes to get a few chords) could be elevated to near the
top of
> the list by finding or designing a custom timbre for it in the
manner of
> Sethares.

ah -- but this is quite different from what i (and to some extent
margo and dan) am suggesting. one can get away with a "pastelized"
timbre -- a wide variety of inharmonic timbres are possible for this -
- and 'pelogic' will work just fine -- no need to tune timbre to
tuning a la sethares. i've related this to my harmonic entropy
theory -- the greater the inharmonicity, the more uncertain the
virtual fundamental of each tone, and therefore the larger the s
value in the appropriate harmonic entropy calculation for dyadic or
chordal consonance, and therefore the larger the mistuning allowable
for simple intervals. the details of the inharmonic timbre are
relatively unimportant!

> > I hope
> > margo and others will join me in trying to convince him
otherwise; a
> > well crafted example with fifths that are 47 cents (!) off the
> > harmonic series might just do the trick.
>
> I would love to hear such music, but in this case I don't think it
will
> convince me of anything I am not already convinced of.
>
> In regard to 11-EDO, if I remember rightly, Dan Stearns pointed out
that it
> has reasonably good approximations to 7:9:11, which can function as
> consonances even _with_ a harmonic timbre. In that regard, it's
still
> following the harmonic series (there's nothing slavish about it),
but it's
> following a part of the series that doesn't fit into the n-limit
way of
> categorising tunings, which has been dominant for too long.

you're missing the point above. read margo's post again. it's the
*fifths* and *fourths*, standing in for 3:2 and 4:3, that margo seems
to be happy with in her 'Chowningized' 11-equal example. this has
nothing to do with 7:9:11. we're talking 3-limit!

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

> (If I were music, I would chuckle at any attempts to neuter, grasp
and
> bottle my horizons via the sympathetically vibrating parts of your
> ears... harmonic series approximations and the sundry like?
> Hahahahaha... oh, bring it on math boys... bring it on!)

me too!

dan, let's admit that both you and i have a music-making facet to our
personalities, and an arcane-math-music-theory side as well, and that
the two sides may have less to say to one another than one might
naively hope. each side obeys a different 'lord' as it were. perhaps
the latter endeavor is nothing more that a blood-sucking leech on the
arm of the former endeavor. but we both engage in it, because our
rational minds want to make some sense of it all -- that's a (perhaps
unfortunate) part of being an intelligent human being.

best,
paul

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

> ***Hi Gene...
>
> Well, that's nice, but perhaps somebody can explain to me why 11-
tET
> only shows a poor 3-limit approximation wheras 22-tET shows a good
3,
> 5, 7, 9 and 11 limit approximation on Paul Erlich's famous ET
chart??
>
> J. Pehrson

you must be misunderstanding the definition of 'limit'. you might
want to break out your partch _genesis_ again. the 9-limit, for
example, means *all* the ratios of odd numbers _up to 9_ -- that
includes 1, 3, 5, 7, and 9. 11-equal completely fails to approximate
7:3, 9:5, 11:3, or 11:5 -- thus it's rated as very poor in the 7-
limit, 9-limit, and 11-limit.

p.s. that chart isn't famous, and shouldn't be taken out of the
context of the paper in which it was included.

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

> Not surprising to find out that Margo, Dan, Paul and Gene enjoy 11.
> It's one of my faves too!
>
> Here's some spectral tuned 11 EDO examples to check out:
>
> http://www.microtonal.org/mp3/11EDO-5ths.mp3

i have to admit, i'm rather disappointed -- but i hope to hear
margo's spectral tuned 11-equal fifths as well, maybe they'll sound
more like fifths . . . (?)

> http://www.microtonal.org/mp3/11EDO-Min_Triads.mp3
>
> http://www.microtonal.org/mp3/11EDO-Maj_Triads.mp3
>
> http://www.microtonal.org/mp3/11EDO_Gamelan.mp3
>
> (Right Click and chose "Save Target As" to save these to your drive)
>
> The timbre used here actually began as an electric piano-like
timbre,
> but after being altered to match 11 EDO it takes on a very bell-
like
> quality. The "5ths" of 11 EDO @ 654.545 cents become quite smooth,
> although still pretty alien sounding when the 3rd harmonic of the
> timbre has a frequency ratio of 2.918960211 rather than 3. Makes a
> great case for how our perception of consonance/smoothness/justness
> is many times directly tied to matching the *tuning and the timbre*
> at once.

makes that case -- how exactly? the timbre sounds 'disconnected' to
me -- not like a well-defined pitch at all (nothing wrong with that
in itself). so the triad examples fail to demonstrate the "sethares
effect" to my ears -- i hear a large number of disconnected partials,
not triads (let alone 'consonant' triads). your piece (the final
example) makes wonderful use of the 'disconnected' effect of the
timbres -- very beautiful, thanks to your musicality -- but i'd wager
you could do just as well if you did not match the tuning to the
timbre in this way. you might notice that one or two of the chords
might have an additional layer of beating that they did not have when
you matched the tuning to the timbre, but it would not be a huge
musical effect (you'd simply shape your composition appropriately),
and certainly would not spell the difference between consonance and
dissonance. (this has been your friendly neighborhood devil's
advocacy speaking . . .)

[i hope you'll stick around to discuss this, or at least not respond
in your usual manner, which is to completely misinterpret my
statements, make a post misrepresenting me, and then delete that post
and ignore any responses to it that i may have. of course, none of
that will have any bearing on the fact that we both value music-
making more highly than theory, and seem to have high regard for one
another's music. so i'll feel a brotherly love toward you regardless.]

--- In tuning@y..., "jacky_ligon" <jacky_ligon@y...> wrote:
> --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> >
> > i have to admit, i'm rather disappointed -- but i hope to hear
> > margo's spectral tuned 11-equal fifths as well, maybe they'll
sound
> > more like fifths . . . (?)
>
> Thanks for your honesty.
>
> The "5ths" of 11 are really at the border of what one might
consider
> either a fifth or a tritone.

right, but i was hoping, based on margo's remarks, that the act of
altering the timbre to fit the tuning, might somehow 'fool' the ear
into thinking that these are 'natural' or 'consonant' fifths. my
impression is that that doesn't happen at all, at least not in this
particular example.

> I'm not sure I understand the word 'disconnected'.

i mean 'multiple-pitched', not 'integrated' like a harmonic timbre
with its clear, single pitch.

> Perhaps you could suggest partials that would sound more pleasing
to
> you for this tuning?

read what i wrote again. i suspect a wide array of inharmonic timbres
would work great for you, though you might be guided down slightly
different compositional directions with them. try a few and let me
know if you disagree.

> Not to worry. I know this work here is kind of off the beaten path,
> so I don't expect folks to be too overjoyed about it.

well, i'm thrilled (if not overjoyed) at your ability to let your
compositional imagination be guided by the ethos of unusual
tuning/timbre combinations. so please keep it up!!

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

> Paul,
>
> Try these fifths here with odd partials from 11:
>
> http://www.microtonal.org/mp3/11EDO-5ths-w-odd-partials.mp3

hey, thanks!

> Four questions:
>
> 1. Do they sound more "fifth-like" to you?

no.

> 2. Do you detect beating?

no.

> 3. Would you describe them as "smooth"?

yes, but (in case anyone cares) "smoothness" (lack of so-
called 'sensory dissonance') is only a component of musical
consonance, and i agree with terhardt that it's not even the most
important one.

> 4. Would you go so far as to describe them as "just" because they
do
> not display beating? (A favorite pitch Koan of mine)

i'm a consciencious objector to the "definition of just" debate. i
won't get involved in that.

> If it pleases you and others, I'd be happy to re-record the piece
> again with this timbre here. It is strikingly different sounding. I
> like them both though personally. Could be interesting to hear both
> timbres together in an arrangement. Could be complimentary
together,
> I would imagine.

yes, please keep on experimenting and composing!

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

/tuning/topicId_36696.html#36730

> Hi Joe,
>
> Fair... no, probably not but maybe so too. I don't know, I guess I'm
> too much in the middle of it myself. I do know that the people on
this
> list "who are actively either writing music, producing concerts, or
> such like" are barely a blip on the posting radar screen.
>
> We can argue the reasons for this long the proverbial night but I
> don't think it's going to matter much... it is as it is and it's
been
> this way for a long, long time. Your point about the comparatively
> limited range of things that can be discussed about a given piece of
> music is spot on. But I don't think that's the primary reason why
this
> list engenders the type of controversies that it does,

***That bad, huh, Dan?? Are you sure it isn't possibly the medium
and not just this list??

My catch-all solution is to write a lot of "smilies..."

It's easy: :) :) :) :) :) :) :) :) :)

Happy times!

:)

J. Pehrson

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_36696.html#36732

>>
> ah -- but this is quite different from what i (and to some extent
> margo and dan) am suggesting. one can get away with a "pastelized"
> timbre -- a wide variety of inharmonic timbres are possible for
this -
> - and 'pelogic' will work just fine -- no need to tune timbre to
> tuning a la sethares. i've related this to my harmonic entropy
> theory -- the greater the inharmonicity, the more uncertain the
> virtual fundamental of each tone, and therefore the larger the s
> value in the appropriate harmonic entropy calculation for dyadic or
> chordal consonance, and therefore the larger the mistuning
allowable
> for simple intervals. the details of the inharmonic timbre are
> relatively unimportant!
>

***You know, Paul, I understand the paragraph above [insert applause
here :)] and find it absolutely fascinating. I'm serious...

Joseph

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_36696.html#36733

> --- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
>
> > (If I were music, I would chuckle at any attempts to neuter,
grasp
> and
> > bottle my horizons via the sympathetically vibrating parts of your
> > ears... harmonic series approximations and the sundry like?
> > Hahahahaha... oh, bring it on math boys... bring it on!)
>
> me too!
>
> dan, let's admit that both you and i have a music-making facet to
our
> personalities, and an arcane-math-music-theory side as well, and
that
> the two sides may have less to say to one another than one might
> naively hope. each side obeys a different 'lord' as it were.
perhaps
> the latter endeavor is nothing more that a blood-sucking leech on
the
> arm of the former endeavor. but we both engage in it, because our
> rational minds want to make some sense of it all -- that's a
(perhaps
> unfortunate) part of being an intelligent human being.
>
> best,
> paul

***What's with you 'cats' anyway?? I smell a rat in the cat-house...

jp

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_36696.html#36734

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > ***Hi Gene...
> >
> > Well, that's nice, but perhaps somebody can explain to me why 11-
> tET
> > only shows a poor 3-limit approximation wheras 22-tET shows a
good
> 3,
> > 5, 7, 9 and 11 limit approximation on Paul Erlich's famous ET
> chart??
> >
> > J. Pehrson
>
> you must be misunderstanding the definition of 'limit'. you might
> want to break out your partch _genesis_ again. the 9-limit, for
> example, means *all* the ratios of odd numbers _up to 9_ -- that
> includes 1, 3, 5, 7, and 9. 11-equal completely fails to
approximate
> 7:3, 9:5, 11:3, or 11:5 -- thus it's rated as very poor in the 7-
> limit, 9-limit, and 11-limit.
>
> p.s. that chart isn't famous, and shouldn't be taken out of the
> context of the paper in which it was included.

***Hi Paul!

Oh... so it's that old "prime" vs. "odd" quandary again!

So, I think I'm getting that, but could you please translate from
mathematize what Gene was getting at in saying 11-tET and 22-tET are
really so similar??

P.S. I only extract the chart since it's the part of the paper
that's *easiest* to read... :) (just joking, Paul...)

Joseph

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_36696.html#36735

> --- In tuning@y..., "jacky_ligon" <jacky_ligon@y...> wrote:
>
> > Not surprising to find out that Margo, Dan, Paul and Gene enjoy
11.
> > It's one of my faves too!
> >
> > Here's some spectral tuned 11 EDO examples to check out:
> >
> > http://www.microtonal.org/mp3/11EDO-5ths.mp3
>
> i have to admit, i'm rather disappointed -- but i hope to hear
> margo's spectral tuned 11-equal fifths as well, maybe they'll sound
> more like fifths . . . (?)
>

***Paul, these are indeed fascinating examples that Jacky has "cooked
up..." Are you saying that the high pitch that kind of "glistens"
along with this doesn't "deceive" your ear enough for you to think a
perfect fifth is happening! It does seem like a rather
high "glitter" on it.... More like a "deception" than a
pastelization??

Is *that* what you're hearing??

>
> [i hope you'll stick around to discuss this, or at least not
respond in your usual manner, which is to completely misinterpret my
> statements, make a post misrepresenting me, and then delete that
post and ignore any responses to it that i may have.

***Paul! Are you getting a bit paranoid? You're not doing
anything "nasty" on that end, are you? (Even though Mayor Bloomberg
endorses it...)

Joseph

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

/tuning/topicId_unknown.html#36737

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> > i have to admit, i'm rather disappointed -- but i hope to hear
> > margo's spectral tuned 11-equal fifths as well, maybe they'll
sound
> > more like fifths . . . (?)
>
>
> Paul,
>
> Try these fifths here with odd partials from 11:
>
> http://www.microtonal.org/mp3/11EDO-5ths-w-odd-partials.mp3
>
>
> Four questions:
>
> 1. Do they sound more "fifth-like" to you?
>
> 2. Do you detect beating?
>
> 3. Would you describe them as "smooth"?
>
> 4. Would you go so far as to describe them as "just" because they
do
> not display beating? (A favorite pitch Koan of mine)
>
>
> If it pleases you and others, I'd be happy to re-record the piece
> again with this timbre here. It is strikingly different sounding. I
> like them both though personally. Could be interesting to hear both
> timbres together in an arrangement. Could be complimentary
together,
> I would imagine.
>
> J:L

***Hi Jacky!

Well, I didn't read Paul's response yet, so I don't know what to
think... :)

But, I mean, to *me* it sound like a more convincing exercise as to
what you want to do here. The sounds appear much more integrated.

And, yes, I *would* like to hear the piece with the revisions.

Thanks for "perking up" this list. It's been a little "sick" here of
late and now it's fascinating again, due to your superb insights and
musicianship!

Joseph

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> --- In tuning@y..., David C Keenan <d.keenan@u...> wrote:
>
> > I know very little
> > about pelog but I understand that the approximate 5-limit triads
of
> pelogic
> > temperament do not feature highly (if at all) in traditional pelog
> music.
>
> not if you're expecting western-style block chords or functional
> harmonic progressions, no. but the music is highly polyphonic, and
> the presense of these intervals in the resulting "crystal" is
> unmistakable.

To more people than just you?

> > The other issue is of course that of "custom timbres". I expect
> that _any_
> > temperament on that list whose low position is due to its large
> deviations
> > from 5-limit consonances (as opposed to being due to it requiring
> large
> > numbers of notes to get a few chords) could be elevated to near
the
> top of
> > the list by finding or designing a custom timbre for it in the
> manner of
> > Sethares.
>
> ah -- but this is quite different from what i (and to some extent
> margo and dan) am suggesting. one can get away with a "pastelized"
> timbre -- a wide variety of inharmonic timbres are possible for this
-
> - and 'pelogic' will work just fine -- no need to tune timbre to
> tuning a la sethares. i've related this to my harmonic entropy
> theory -- the greater the inharmonicity, the more uncertain the
> virtual fundamental of each tone, and therefore the larger the s
> value in the appropriate harmonic entropy calculation for dyadic or
> chordal consonance, and therefore the larger the mistuning allowable
> for simple intervals. the details of the inharmonic timbre are
> relatively unimportant!

OK. This is a new idea for me. That some tunings may work well with
_any_ harmonic timbre. I'd like to hear some evidence for that. Such
as the same pelogic piece done with two timbres having 6 partials,
with the same amplitude and envelopes for the corresponding partials,
but one of them having the partials designed to match the scale and
the other one having them moved by the same number of cents on the
_other_ side of harmonic. This could simply be all partials compressed
by 23 cents versus stretched by 23 cents.

> > > I hope
> > > margo and others will join me in trying to convince him
> otherwise; a
> > > well crafted example with fifths that are 47 cents (!) off the
> > > harmonic series might just do the trick.
> >
> > I would love to hear such music, but in this case I don't think it
> will
> > convince me of anything I am not already convinced of.
> >
> > In regard to 11-EDO, if I remember rightly, Dan Stearns pointed
out
> that it
> > has reasonably good approximations to 7:9:11, which can function
as
> > consonances even _with_ a harmonic timbre. In that regard, it's
> still
> > following the harmonic series (there's nothing slavish about it),
> but it's
> > following a part of the series that doesn't fit into the n-limit
> way of
> > categorising tunings, which has been dominant for too long.
>
> you're missing the point above. read margo's post again. it's the
> *fifths* and *fourths*, standing in for 3:2 and 4:3, that margo
seems
> to be happy with in her 'Chowningized' 11-equal example. this has
> nothing to do with 7:9:11. we're talking 3-limit!

I apparently haven't read the post you are referring to at all. The
one that started this thread
/tuning/topicId_36696.html#36696
makes no mention of fourths or fifths or Chowningising (whatever that
is).

But I didn't miss the point. I wasn't assuming Margo's stuff depended
on 7:9:11, since it clearly _depended_ on an inharmonic timbre. I was
merely making an additional point about 11-EDO.

Incidentally, the best 11-EDO-related linear temperament for 7:9:11s
looks to have a semi-neutralsixth generator, which corresponds to 4
steps of 11-EDO (about a 426 cent optimum generator, so 5 steps of
14-EDO is better) and does not have a hexatonic MOS, but has
pentatonic (improper) and octatonic (improper in anything but 11-EDO).

Of course Margo's hexatonic MOS has a 2/11 oct generator.

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

/tuning/topicId_36696.html#36739

> --- In tuning@y..., "jacky_ligon" <jacky_ligon@y...> wrote:
>
> > Paul,
> >
> > Try these fifths here with odd partials from 11:
> >
> > http://www.microtonal.org/mp3/11EDO-5ths-w-odd-partials.mp3
>
> hey, thanks!
>
> > Four questions:
> >
> > 1. Do they sound more "fifth-like" to you?
>
> no.
>
> > 2. Do you detect beating?
>
> no.
>
> > 3. Would you describe them as "smooth"?
>
> yes, but (in case anyone cares) "smoothness" (lack of so-
> called 'sensory dissonance') is only a component of musical
> consonance, and i agree with terhardt that it's not even the most
> important one.
>
> > 4. Would you go so far as to describe them as "just" because
they
> do
> > not display beating? (A favorite pitch Koan of mine)
>
> i'm a consciencious objector to the "definition of just" debate. i
> won't get involved in that.
>
> > If it pleases you and others, I'd be happy to re-record the piece
> > again with this timbre here. It is strikingly different sounding.
I
> > like them both though personally. Could be interesting to hear
both
> > timbres together in an arrangement. Could be complimentary
> together,
> > I would imagine.
>
> yes, please keep on experimenting and composing!

***Gee. I ended up disagreeing with Paul. That can be dangerous! :)

To me, the fifths sounded better, more "integrated..."

??

Joseph

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

/tuning/topicId_unknown.html#36740

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> > --- In tuning@y..., "jacky_ligon" <jacky_ligon@y...> wrote:
> >
> > > Paul,
> > >
> > > Try these fifths here with odd partials from 11:
> > >
> > > http://www.microtonal.org/mp3/11EDO-5ths-w-odd-partials.mp3
> >
> > hey, thanks!
> >
> > > Four questions:
> > >
> > > 1. Do they sound more "fifth-like" to you?
> >
> > no.
>
> {: (
>
>
> >
> > > 2. Do you detect beating?
> >
> > no.
> >
> > > 3. Would you describe them as "smooth"?
> >
> > yes, but (in case anyone cares) "smoothness" (lack of so-
> > called 'sensory dissonance') is only a component of musical
> > consonance, and i agree with terhardt that it's not even the most
> > important one.
>
>
> Paul,
>
> To replies 2 and 3, I say that it might not sound exactly like
> the "Sethares-Effect", but it is precisely the goal of the examples
> and music to make that interval (whatever we wish to call it) @
> 654.545 cents, sound smooth and beatless. Glad you agree that it
does
> what I set out to accomplish!
>
> ; )
>
>
> >
> > > 4. Would you go so far as to describe them as "just" because
> they
> > do
> > > not display beating? (A favorite pitch Koan of mine)
> >
> > i'm a consciencious objector to the "definition of just" debate.
i
> > won't get involved in that.
>
> Yep. Avoid "the slings and arrows or outrageous ratios" I always
say.
> Even though I've been known to tune'em up on occasion.
>
> How about you Dave? What do you think? Haven't forgot about your
old
> numerologist buddy Jacky have you? Seriously, your thoughts and
input
> would be of great value.
>
>
> >
> > > If it pleases you and others, I'd be happy to re-record the
piece
> > > again with this timbre here. It is strikingly different
sounding.
> I
> > > like them both though personally. Could be interesting to hear
> both
> > > timbres together in an arrangement. Could be complimentary
> > together,
> > > I would imagine.
> >
> > yes, please keep on experimenting and composing!
>
> Ok - here's the very same tune, but with the odd partial timbre:
>
> http://www.microtonal.org/mp3/11EDO_Gamelan_odd-partials.mp3
>
> Upon doing a little a&b'ing between these, I seem to prefer the one
> above a little more somehow. Let me know what you think.
>
> Best,
>
> J:L

***This tuning "revision" seems to be *much* more resonant for me
than the other one, and has a far greater impact... for what it's
worth...

Joseph

I wrote:

> OK. This is a new idea for me. That some tunings may work well with
> _any_ harmonic timbre.

That should of course have been "_any_ inharmonic timbre".

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

> So, I think I'm getting that, but could you please translate from
> mathematize what Gene was getting at in saying 11-tET and 22-tET are
> really so similar??

that would be very valuable (as all gene's work is very valuable) -- i'll get to it tomorrow -- send me an e-mail to remind me to do this.

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

> ***Paul, these are indeed fascinating examples that Jacky has "cooked
> up..." Are you saying that the high pitch that kind of "glistens"
> along with this doesn't "deceive" your ear enough for you to think a
> perfect fifth is happening!

i'm not really referring to any high pitch.

> It does seem like a rather
> high "glitter" on it.... More like a "deception" than a
> pastelization??
>
> Is *that* what you're hearing??

no, it's more like this:

when bill sethares created a piece for 19-equal guitar sound with partials remapped to 19-equal, what was going on harmonically sounded like *just intonation*. in that the vertical fifths sounded like vertical fifths, intervals with an unambiguous root, and everything else you expect from 'just fifths'.

here, with this different timbre (so we're comparing apples and oranges) and with 11-equal the tuning/timbre source, i don't get that impression at all. i hear an interval, the sound of which is sensuously smooth, but it doesn't imply a fifth to my ears -- the harmony is unsettled, probably because my ear doesn't recognize a periodicity or a pattern that implies a clear root.

if this effect is what you're looking for as a composer, then by all means one should go for it. i just think it's misleading to speak of this situation as 'complete consonance having been acheived'.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> > --- In tuning@y..., David C Keenan <d.keenan@u...> wrote:
> >
> > > I know very little
> > > about pelog but I understand that the approximate 5-limit triads
> of
> > pelogic
> > > temperament do not feature highly (if at all) in traditional pelog
> > music.
> >
> > not if you're expecting western-style block chords or functional
> > harmonic progressions, no. but the music is highly polyphonic, and
> > the presense of these intervals in the resulting "crystal" is
> > unmistakable.
>
> To more people than just you?

how about erv wilson or lou harrison?

> OK. This is a new idea for me. That some tunings may work well with
> _any_ harmonic timbre. I'd like to hear some evidence for that. Such
> as the same pelogic piece done with two timbres having 6 partials,
> with the same amplitude and envelopes for the corresponding partials,
> but one of them having the partials designed to match the scale and
> the other one having them moved by the same number of cents on the
> _other_ side of harmonic. This could simply be all partials compressed
> by 23 cents versus stretched by 23 cents.

this is a great idea. perhaps jacky could oblige us. i'd start with a wide-open timbre, something like that electric piano sound would be great.

just a comment: authentic gamelan music doesn't use tunings that eliminate beating at all. they *relish* beating. does that mean they're maximizing dissonance? no way.

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

> It would be great if there were many talented and gossipy folks
> committed to composing and creating with these tunings for a while,
> exchanging notes and ideas... seeing what works and what doesn't WHERE
> IT REALLY COUNTS (in actual music). But the truth is, certainly in
> this community anyway, that the talented and gossipy folks are
> committed to discussing what these tunings do theoretically or
> mathematically.

The truth is, I do both, as do a number of other people--or had you noticed? If you want more music written, I suggest writing some.

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

> Well, that's nice, but perhaps somebody can explain to me why 11-tET
> only shows a poor 3-limit approximation wheras 22-tET shows a good 3,
> 5, 7, 9 and 11 limit approximation on Paul Erlich's famous ET chart??

To get a good 3-limit you need a good 3; 11 has an acceptable 9 (the same 9 as 22-et) but not a 3 I would want to use. It has better minor thirds/major sixths than 12-et does (the same ones 22 uses), but no real major thirds; it has instead the same excellent supermajor (9/7) thirds as the 22-et. In other words, it doesn't really have the complete limits, hence the subgroup analysis.

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

> Not surprising to find out that Margo, Dan, Paul and Gene enjoy 11.
> It's one of my faves too!

My point of view is different, but of course I don't have the software to do spectral tuning. Instead of adapting 654.545 cents to serve as a fifth, I would propose treating it as a 16/11 and taking the 11-et to be 11-overtone-capable.

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

> dan, let's admit that both you and i have a music-making facet to our
> personalities, and an arcane-math-music-theory side as well, and that
> the two sides may have less to say to one another than one might
> naively hope.

Mine are in constant communication, it's what drives me when I write.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> The truth is, I do both, as do a number of other people--or had you noticed?

What I've noticed, over the years (and not specifically to you, Gene) are many little piece-lets, music that has (apparantly) taken a very far back seat to the hours and hours of theoretical workings-out (working-outs?). What I think can be extrapolated from Dan's sentiments is that not only has the ratio of verbiage-to-music been skewed to the left side of the equation *as a community*, but I tend to see it in individuals as well. This has all been noted before.

>If you want more music written, I suggest writing some.

As you said, Gene, "or had you noticed?" Dan has posted more music than most of the people on any of these tuning lists, and continues to work. And asking others to write is not addressing the issue he raised, though I'm sure (as he hinted, and as I have noted as well) that particular scenario is not likely to change. It appears to simply be the make-up of the online tuning community.

Cheers,
Jon

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

/tuning/topicId_36696.html#36757

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > Well, that's nice, but perhaps somebody can explain to me why 11-
tET
> > only shows a poor 3-limit approximation wheras 22-tET shows a
good 3,
> > 5, 7, 9 and 11 limit approximation on Paul Erlich's famous ET
chart??
>
> To get a good 3-limit you need a good 3; 11 has an acceptable 9
(the same 9 as 22-et) but not a 3 I would want to use. It has better
minor thirds/major sixths than 12-et does (the same ones 22 uses),
but no real major thirds; it has instead the same excellent
supermajor (9/7) thirds as the 22-et. In other words, it doesn't
really have the complete limits, hence the subgroup analysis.

***Hi Gene!

Well, finally I *think* I'm getting a "glimmer" of this. So, by
implication, does this mean that 11-tET can "substitute" acceptable,
or at least "workable" emulations of 3-limit chords and such like??

That seems to be the implication, but maybe I'm reading too much into
it...??

Joseph

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
>
> /tuning/topicId_36696.html#36757
>
>
> > --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> >
> > > Well, that's nice, but perhaps somebody can explain to me why
11-
> tET
> > > only shows a poor 3-limit approximation wheras 22-tET shows a
> good 3,
> > > 5, 7, 9 and 11 limit approximation on Paul Erlich's famous ET
> chart??
> >
> > To get a good 3-limit you need a good 3; 11 has an acceptable 9
> (the same 9 as 22-et) but not a 3 I would want to use. It has
better
> minor thirds/major sixths than 12-et does (the same ones 22 uses),
> but no real major thirds; it has instead the same excellent
> supermajor (9/7) thirds as the 22-et. In other words, it doesn't
> really have the complete limits, hence the subgroup analysis.
>
> ***Hi Gene!
>
> Well, finally I *think* I'm getting a "glimmer" of this. So, by
> implication, does this mean that 11-tET can "substitute"
acceptable,
> or at least "workable" emulations of 3-limit chords and such like??

it means it *can't*. rather, you can get some nice incomplete chords
in 11-equal, such as 4:7:9:11, and 3:5 -- these are just as good as
they are in 22-equal.

--- In tuning@y..., "jacky_ligon" <jacky_ligon@y...> wrote:
> --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

> > if this effect is what you're looking for as a composer, then by
> > all means one should go for it. i just think it's misleading to
speak
> > of this situation as 'complete consonance having been acheived'.
>
> Never said that it was.

never said you said it was. :)

> Besides, is there any tuning that does this 100%?

well, sure, adaptive ji for harmonic timbres, for example.

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

> As you said, Gene, "or had you noticed?" Dan has posted more music
than most of the people on any of these tuning lists, and continues
to work.

Dan has posted more theory *and* written more than most,
which means he should know better than to adopt this "theory
kills practice" line. It's a crock, and counter-productive.
In the first place it's not true, in the second place why can't
someone just do one or the other without carping comments, and
in the third place theory is good for practice.

Gene,

The point I hoped to reinforce, a la Ivor Darreg et al, is that a
tuning like 11-tet is going to tend to be analyzed and theorized
certain way, and these tunings have traditionally gotten the short end
of the stick because of it--their (bad) reputation precedes them.

To my mind this is the crock. The music I make in tunings like 11 and
13 equal is no atonal, ravenous pack of werewolves. It is, somewhat
incongruously if you read what the theorists tend to have to say about
these tunings, nice and normal (if your ears have been half the places
mine have) and exotically pleasant.

As far as the community as a whole... how many pieces of music have I
heard from the big happy family in 11-tet compared to how many posts
have I've read about what it does or does not approximate well? 100 to
1, 1,000 to 1?

Darreg was wise enough to know that you've got to get in there to find
out what's what. He didn't throw theory out the window, or give it the
finger and damn it to hell a la McLaren, but he was smart enough to
know where it wasn't very well suited to go... when tunings are just a
component of a music (rather than a theory or a general line of
reasoning), surprising things can happen that you can't always
predict.

I think tuning theory holds up very nicely for listening tests and
little examples, but then music comes along and screws the whole thing
up with alarming ease... at least that has been my experience. Also I
should probably point out that I like tuning theory as a creative
pursuit rather than a pursuit of truth (so to speak), and maybe that
explains some of my views too.

take care,

--Dan Stearns

----- Original Message -----
From: "genewardsmith" <genewardsmith@juno.com>
To: <tuning@yahoogroups.com>
Sent: Thursday, May 02, 2002 1:32 PM
Subject: [tuning] Re: Hexatonic scale in 11-EDO

> --- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:
>
> > As you said, Gene, "or had you noticed?" Dan has posted more music
> than most of the people on any of these tuning lists, and continues
> to work.
>
> Dan has posted more theory *and* written more than most,
> which means he should know better than to adopt this "theory
> kills practice" line. It's a crock, and counter-productive.
> In the first place it's not true, in the second place why can't
> someone just do one or the other without carping comments, and
> in the third place theory is good for practice.
>
>
>
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--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Gene,
>
> The point I hoped to reinforce, a la Ivor Darreg et al, is that a
> tuning like 11-tet is going to tend to be analyzed and theorized
> certain way, and these tunings have traditionally gotten the short
end
> of the stick because of it--their (bad) reputation precedes them.

I just had such a comment made about 36-et over on MMM, but
in fact the basis of the music was theory of the same kind
which suggests to me at least what could be done with
11 or 13-et. I suggest better theory is the answer, not no
theory.

--- In tuning@y..., "jacky_ligon" <jacky_ligon@y...> wrote:
> --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:

> > > Besides, is there any tuning that does this 100%?
> >
> > well, sure, adaptive ji for harmonic timbres, for example.
>
>
> I beg to differ. At least I have heard no adaptive JI that
completely
> removed dissonance. Allot of it sounded good to me, but still had
> dissonance. (Loved John's B. Herrmann renditions - btw.)

john delaubenfels does adaptive tuning, not adaptive JI.

> Completely
> consonant music would be a bore anyhow.

i agree!

so by your question you meant a tuning that removes all the
dissonance, even in the chords that are *supposed* to be dissonant?
that's not what i thought you were asking . . .

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

> To my mind this is the crock. The music I make in tunings like 11
and
> 13 equal is no atonal, ravenous pack of werewolves.

actually, this term reminds me of some 31-equal music i've
heard . . . yes, that's 31.

> It is, somewhat
> incongruously if you read what the theorists tend to have to say
about
> these tunings, nice and normal (if your ears have been half the
places
> mine have) and exotically pleasant.

hoping to have another listen, i came across this post:

/tuning/topicId_10004.html#10004

where dan makes some comments everyone should read.

but the link to the actual sound file doesn't seem to work
anymore . . . nor do any of the other mp3.com links to dan's music i
found. dan, are we out of luck?

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> Dan has posted more theory *and* written more than most,
> which means he should know better than to adopt this "theory
> kills practice" line.

IYHO.

> It's a crock, and counter-productive.

IYHO, again.

> In the first place it's not true

Ditto.

> in the second place why can't someone just do one or the other
> without carping comments

Because the pedantic and 'authoritative' answers dealing with musical matters appear, at times, to come from sources that don't have anything at all to do with making music, and only from running calculations?

I have gone, at great lengths (as you well know, in private emails) to come to a greater understanding of what motivates the mathematical and scientific investigators - both in this community and in the mathematical world as well - so that I could feel more comfortable with the "one or the other". I *do* feel better about it, and I've always been happy to live and let live. But what I notice is that no one ever tries to understand why practicing musicians would find this so frustratingly masturbatory! I have a pretty good handle on the fascination in finding the things 'behind the scenes' that are making all these tunings, consonances, beats, etc., tick; it seems that few, if any, of the research-oriented members are curious as to what makes a musician tick, and why they would throw their hands up in dispair at the lists of numbers and equations.

Or, as one tuning-math correspondent referred to it "their constant whining". There's a paen to understanding if ever I saw one...

> in the third place theory is good for practice.

Tell that to all the people throughout history that have advance cultures, created magic, and moved other humans *without* the benefit of your theories.

Cheers,
Jon

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

>But what I notice is that no one ever tries to understand why
>practicing musicians would find this so frustratingly masturbatory!

I know many people don't have a scientific mindset, and that this
cast of mind bothers them. I don't see why I should concern myself
with that beyond considerations of self-protection or education;
otherwise, it's not *my* problem, any more than a hatred of music is
your problem. I doubt that practicing musicians, as a class, are
mostly science-adverse, but am open to correction.

In any case, the name of this group is "tuning"; an obvious solution
if discussions of tuning bother you is not to read them.

>I have a pretty good handle on the fascination in finding the
>things 'behind the scenes' that are making all these tunings,
>consonances, beats, etc., tick; it seems that few, if any, of the
>research-oriented members are curious as to what makes a musician
>tick, and why they would throw their hands up in dispair at the
>lists of numbers and equations.

That sounds as if you think people on this list might be under an
obligation to conduct psychological experiments of some kind. Of
course, they could do something like you did, and research the great
musicians of the past--alas, this won't help them, as I don't think
you see the prejudice in question in operation there. Music has long
been married to technique.

> Tell that to all the people throughout history that have advance
cultures, created magic, and moved other humans *without* the benefit
of your theories.

My theories are good for me, and do you no harm. Why carp about it?

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> I know many people don't have a scientific mindset, and that this
> cast of mind bothers them.

It only bothers me when it fosters attitudes about what is good or
bad about musical materials, which should concern itself with
a "musical mindset" as well. Unless you specifically want to divorce
tuning from music.

> I don't see why I should concern myself with that beyond
> considerations of self-protection or education;

How very community-minded, Gene. I guess understanding is a one-way
street for you, yes?

> otherwise, it's not *my* problem, any more than a hatred of music
> is your problem.

Say WHAT?

> I doubt that practicing musicians, as a class, are mostly science-
> adverse, but am open to correction.

Not my assumption, either. When I decided to get a degree (and a
career, for a while) in software engineering, I read a book
entitled "Programmers at Work" which chronicled some of the early
generation pioneers of the computer and PC revolution. It was
astonishing (or not!) how many had musical backgrounds. And, not
surprisingly, convinced me I'd enjoy it.

And I did (do).

> In any case, the name of this group is "tuning"; an obvious
> solution if discussions of tuning bother you is not to read them.

Hmm. Nice of you to miss my point entirely, which was about trying to
wed tuning to music. Or to, maybe, not divorce it entirely. But I
realize some like it that way.

> That sounds as if you think people on this list might be under an
> obligation to conduct psychological experiments of some kind.

No, I don't. Members of any community can behave however they want,
and I'm just observing. Of course, I may choose to see it as a way to
grow personally and understand other people in the community better;
others prefer to stay less-informed.

> Of course, they could do something like you did, and research the
> great musicians of the past--alas, this won't help them, as I don't
> think you see the prejudice in question in operation there.

Right. Sure. It's not prejudice, Gene, it is lack of insight. Unless
you divorce tuning from music.

> Music has long been married to technique.

For technocrats, sure. Not a very global outlook you have.

> My theories are good for me, and do you no harm. Why carp about it?

"This kind of sloppiness annoys me; to other people it is nit-
picking." - Gene Ward Smith

We all have things that we carp about. This is a community I've long
been a member of, I find much to interest me here, and I'm only
stating views that more than a few echo: how is it that there can be
so many words, so many postings, so many experiments, so many scales,
so many temperments, so many intonations ...

... and so little (comparatively) music?

Not having broached this subject for (I'm pretty sure) over a year,
one little posting or two, amid the maelstrom of vectors and
matrices, can hardly be abusive.

Be sure to see the question I had for you over at MMM about your sax
piece, which I enjoyed...

Cheers,
Jon

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

> > Music has long been married to technique.
>
> For technocrats, sure. Not a very global outlook you have.

Bach, Mozart and Beethoven were all German-speaking Europeans--does that mean they were all techocrats, or that we should dismiss their enormous accopmplishments becasue they are insufficiently global?

> We all have things that we carp about. This is a community I've long
> been a member of, I find much to interest me here, and I'm only
> stating views that more than a few echo: how is it that there can be
> so many words, so many postings, so many experiments, so many scales,
> so many temperments, so many intonations ...
>
> ... and so little (comparatively) music?

Your group is the music group, this is the tuning group.

> Not having broached this subject for (I'm pretty sure) over a year,
> one little posting or two, amid the maelstrom of vectors and
> matrices, can hardly be abusive.

It seems to me that it carried an implication that if you know about vectors and matrices you can't know much about music, which you know better than to suppose. You can't simply assume that Borodin was too good a chemist to be much of a composer, after all.

> Be sure to see the question I had for you over at MMM about your sax
> piece, which I enjoyed...

Thanks--I'll go check.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> Bach, Mozart and Beethoven were all German-speaking Europeans--does
that mean they were all techocrats, or that we should dismiss their
enormous accopmplishments becasue they are insufficiently global?

Not in the least. My point is that when you say "Music has long been
married to technique" you are pointedly ignoring the vast amount of
music that is *not* dependent on technique. And is it technique of
composition, of execution, of...?

If what you do, and what you investigate, finds it's sole exemplars
in these and similar bodies of work (i.e. Euro-centric classicists),
then you are working with a stunningly small subset of what can
charitably be called music. Perfectly fine by me if you want to be
limited as such; I prefer to have wider latitude.

> Your group is the music group, this is the tuning group.

No, this is *your* take on it. This group existed a long time before
you came aboard, and there was a time when tuning worked hand in hand
with music - actual music. If not in the ratio that I (and/or others)
preferred, at least not to the point where music is actively shunned
by members.

It has been to the detriment of this group that the path has been
skewed so far that one would even make such a statement as the above,
and is also clear evidence of why other groups have *had* to be
formed. Narrow niche interests, steamrollered into vogue, has taken
its toll.

> It seems to me that it carried an implication that if you know
about vectors and matrices you can't know much about music

Not my implication at all, though there is a fair amount of
historical evidence on the list to support such a claim. What I would
say is that much of the work in the tuning area has removed itself so
far from production of music, to the point of being 'pure' tuning (as
in 'pure' science) that it views itself as independent of musical
activity.

I think that there are anywhere from amateur to middlingly good
musicians involved in the research labs of tuning progress. What I
find odd is that music would be, at best, such an afterthough - if
thought of at all.

> You can't simply assume that Borodin was too good a chemist to be
much of a composer, after all.

I don't assume that. My understanding is that Borodin was quite a
good chemist; my opinion is that Borodin was, at best, a mediocre
composer.

Cheers,
Jon

--- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

> > Your group is the music group, this is the tuning group.

> No, this is *your* take on it. This group existed a long time before
> you came aboard, and there was a time when tuning worked hand in hand
> with music - actual music.

I don't think music is actively shunned on this group--certainly not to the extent that math is actively shunned and reviled, so I don't think this works for you. In any case, the name of the group is "tuning", and its description says "This mailing list is intended for exchanging ideas relevant to alternate tunings".

> It has been to the detriment of this group that the path has been
> skewed so far that one would even make such a statement as the above,
> and is also clear evidence of why other groups have *had* to be
> formed. Narrow niche interests, steamrollered into vogue, has taken
> its toll.

Your math-phobia is about as narrow as it gets, chum.

> > It seems to me that it carried an implication that if you know
> about vectors and matrices you can't know much about music
>
> Not my implication at all, though there is a fair amount of
> historical evidence on the list to support such a claim.

What complete rubbish.

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

> > It seems to me that it carried an implication that if you know
> about vectors and matrices you can't know much about music

> Not my implication at all, though there is a fair amount of
> historical evidence on the list to support such a claim.

By the way, I finished another piece today. Given your lack of knowledge of vectors and matricies, why can't you match my pace?

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> I don't think music is actively shunned on this group

I didn't assume you did. But an awful lot of the people who actually take time to compose/play/perform, and used to take more active part on this list, feel this way. You can ignore it, or you can deny it, but is exists and wasn't always so.

> certainly not to the extent that math is actively shunned and
> reviled

I disagree.

> In any case, the name of the group is "tuning", and its description says "This mailing list is intended for exchanging ideas relevant to alternate tunings".

I would say that music is relevant to alternate tunings. That said, you've completely ignored my statements regarding the initial few years of this group, and you should note that the description came long after the group, at Mills, was in existence.

> Your math-phobia is about as narrow as it gets, chum.

Funny, that: I'm the only one that has professed a desire, and actions upon that desire, to both overcome my inadequacies and insecurities with math, as well as to come to a better understanding of pursuits like pure mathematics, and the pleasure found in forays into the mathematics and other underpinnings of the world around us.

I would hardly say that I'm math-phobic, but even if I was inflicted with such a syndrome, your decision to both ridicule it as well as ignore my attempts to both come to grips with it and overcome it are now duly noted. Chum.

> What complete rubbish.

There's a fine retort. I expected better of you, Gene.

Jon

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> By the way, I finished another piece today. Given your lack of knowledge of vectors and matricies, why can't you match my pace?

Because I've performed in five concerts this week, with 7 rehearsals, and one more concert tomorrow? I'm a *musician*, Gene, a working, breathing, living, *performing* musician. Sometimes I squeek in some time for composition and improvisation as well, but not this week.

And I note you've missed my posting about producing a full-evening concert, including the designing and building of new instruments.

Sorry to be such a slacker these days...

Jon

In a message dated 5/5/02 4:22:11 AM Eastern Daylight Time, JSZANTO@ADNC.COM
writes:

> I didn't assume you did. But an awful lot of the people who actually take
> time to compose/play/perform, and used to take more active part on this
> list, feel this way. You can ignore it, or you can deny it, but is exists
> and wasn't always so.
>

This is unnecessary, Jon. I don't mean to be rude, but as a composer and
performer on this big list that does not belong to the splinter lists, I
think you are spinning a bit. To me there is more electronic music interest
on the MMM list, while numbers do run supreme on the Math list. I have
always been against the splintering of the lists, feeling that microtonal
music is fractured enough already.

I don't expect the Mom of another list to agree with me. But I do hope,
Steve, you remain connected to the Big Tent List.

One cannot MAKE someone a composer. The people twisting in the wind about it
need not give others a neurosis about it.

As far as performance is concerned, there is practically nil on any of the
lists. Only one more reason for having a central list.

Best, Johnny Reinhard

--- In tuning@y..., Afmmjr@a... wrote:
> This is unnecessary, Jon.

Simply an opinion, or collection of them.

> I don't mean to be rude, but as a composer and performer on this
> big list that does not belong to the splinter lists, I
> think you are spinning a bit.

Well, that is why I said a lot have gone elsewhere, instead of *all*
of them. I know you've not been in favor of alternate lists, but
their continued existence and activity speaks to this topic.

> To me there is more electronic music interest on the MMM list

Interesting insight, since you aren't a regular member; maybe when
you've perused the list it has seemed that way, but the
acoustic/electronic mix seems about in line with what I've always
observed. We still live in days where the tools for making microtonal
music are skewed towards electronic, certainly for first time users.
Joe Pehrson would be an example, where the electronics served as a
springboard to eventually end up with acoustic instruments.

While I'm the one posting the words, these are sentiments that have
been discussed both publically and privately by a number of people,
so just be aware that I'm not the only one that feels at least some
alienation with my original tuning home on the web...

Cheers,
Jon

> observed. We still live in days where the tools for making microtonal
> music are skewed towards electronic, certainly for first time users.
> Joe Pehrson would be an example, where the electronics served as a
> springboard to eventually end up with acoustic instruments.
>

Hello all, I'm glad this line came up...
Just to introduce myself, my name's Luke and I'm an undergrad, just joined
the list last week. Now to the question; As everyone knows, there are
certain imperfections in the design of most brass instruments that affect
the tuning when multiple valves are involved. I was wondering if you knew
of some quality resources where one might research this phenomenon.. this
may be slightly off the topic of the list, but it is in pursuit of more
perfect (less accidental??) tuning, so hey, thought I'd give it a shot.
Thanks in advance!!

Luke Harrison
vir sapit qui pauca loquitur

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

> > What complete rubbish.
>
> There's a fine retort. I expected better of you, Gene.

After suggesting that everything I do is crap, what exactly did you expect?

--- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

> Because I've performed in five concerts this week, with 7 rehearsals, and one more concert tomorrow? I'm a *musician*, Gene, a working, breathing, living, *performing* musician. Sometimes I squeek in some time for composition and improvisation as well, but not this week.

I've got a day job too. I don't use it as a reason to sneer at people's efforts at composition while doing nothing along those lines myself.

Hey Luke!

--- In tuning@y..., Luke <lbharr01@l...> wrote:
> Hello all, I'm glad this line came up...
> Now to the question; As everyone knows, there are
> certain imperfections in the design of most brass instruments that
> affect the tuning when multiple valves are involved.

Someone else can point it out, maybe Joe Pehrson, but there is a
project in the UK building some new brass instruments using solenoid
valve switches (or something along those lines) to create a
microtonal brass ensemble (a quartet or quintet to start, maybe?).
The project has, IIRC, some connection with maybe the Royal College
of Music.

In any event, it has certainly been discussed in the last six months.
Give a try to searching the archives, and I hope someone who was more
intimately involved in the thread will pipe in. Me, I'm a
percussionist...

Cheers,
Jon

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> After suggesting that everything I do is crap, what exactly did you
expect?

I suggested nothing of the sort, and complimented you on the recent
36tet saxophone piece, along with some interested questions. I'm not
sure why that chip is on your shoulder...

Jon

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> I've got a day job too. I don't use it as a reason to sneer at
people's efforts at composition while doing nothing along those lines
myself.

Where on Earth do you come up with this stuff? I am not sneering at
anyone's efforts at composition, and was mostly wishing for more of
that kind if activity. If I don't happen to like all of the output,
that would simply be expected, because I have yet to meet anyone who
likes literally everything they hear.

And you don't have any idea whether I've been composing or not, do
you? I thought not...

Jon

--- In tuning@y..., "jonszanto" <JSZANTO@A...> wrote:
> --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

> > After suggesting that everything I do is crap, what exactly did
you
> expect?

> I suggested nothing of the sort, and complimented you on the recent
> 36tet saxophone piece, along with some interested questions. I'm
not
> sure why that chip is on your shoulder...

I see you said you enjoyed it, so my apologies and belated thanks. I
presumed, given your claim that judging by the evidence of this list,
it would be reasonable to maintain that anyone who knew about
mathematics was a duffer so far as music want meant that you thought
I was a musical idiot, that Paul can neither write nor play, and so
forth. What else would I think? If you don't mean such things it's
best not to say them--in fact, it saves trouble all around not to say
things of the nature "people belonging to group X have incapacity Y"
even if you do believe it.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> I see you said you enjoyed it, so my apologies and belated thanks.

Well, good. At least *something* positive has come of this!

> I presumed...

That's one of the problems: you presume. And what you've presumed is
a long stretch from what I am saying.

> given your claim that judging by the evidence of this list,
> it would be reasonable to maintain that anyone who knew about
> mathematics was a duffer so far as music

That is *not* what I am/was saying. It is that the musical end of
tuning, the use of tuning(s) for creating/performing/listening (to)
music is given short shrift, if any shrift at all. And it is the
musicians who are looked down upon as unintelligent boobs.

Which has caused a number of musicians (and good ones) to say "I'm
outta here!" to this list, and I find that _not_good_. And *that* is
why I feel it is worth mentioning, censorious efforts notwithstanding.

> you thought I was a musical idiot

Nope. Opinionated and pretty conservative, but very far from an idiot!

> that Paul can neither write nor play

Hey, I transcribed about 3-4 hours of Paul's music to wave/mp3 files,
so I have a good idea of his playing chops. Paul readily admits to
not composing much music (being more of a player/improviser), and I
don't expect him to. Though when he touts (sp?) particular tunings I
would sure love to *hear* why he thinks they are so cool :) (Paul?)...

> What else would I think? If you don't mean such things it's
> best not to say them

Oh, Gene... You, of all people, who've actively posted about not
wanting to be censored, and your abhorance of PC-ness. Really.
Besides, I've been here long enough to care about some of these
issues, and if you'd take the time to read them with careful eyes and
a curious and/or caring heart, you'd see that I'd simply like things
to be better.

Of course, better is pretty subjective, right?

Jon

jonszanto wrote:

> Someone else can point it out, maybe Joe Pehrson, but there is a
> project in the UK building some new brass instruments using solenoid
> valve switches (or something along those lines) to create a
> microtonal brass ensemble (a quartet or quintet to start, maybe?).
> The project has, IIRC, some connection with maybe the Royal College
> of Music.

You mean the Centre for New Musical Instruments at London Guildhall
University? I don't know how relevant that is to the original question,
because they're modifying existing instruments rather than building them
from scratch. The URL I have is <http://www.lgu.ac.uk/mit/cnmi>.

Oh, Patrick and Lewis were on Radio 3 Sunday night. There were examples
of a 19-equal recorder and some quarter-tone trumpet playing, but I think
that was with a normal trumpet.

Graham

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

/tuning/topicId_36696.html#36838

> Hey Luke!
>
> --- In tuning@y..., Luke <lbharr01@l...> wrote:
> > Hello all, I'm glad this line came up...
> > Now to the question; As everyone knows, there are
> > certain imperfections in the design of most brass instruments
that
> > affect the tuning when multiple valves are involved.
>
> Someone else can point it out, maybe Joe Pehrson, but there is a
> project in the UK building some new brass instruments using
solenoid
> valve switches (or something along those lines) to create a
> microtonal brass ensemble (a quartet or quintet to start, maybe?).
> The project has, IIRC, some connection with maybe the Royal College
> of Music.
>
> In any event, it has certainly been discussed in the last six
months.
> Give a try to searching the archives, and I hope someone who was
more
> intimately involved in the thread will pipe in. Me, I'm a
> percussionist...
>
> Cheers,
> Jon

***Hi Luke and Jon (Matthew and Marc as well...)

I actually tried to post this yesterday as a 5 minute break from
composing, but Yahoo "crapped out" as they say in computer circles,
and the post didn't go through. I didn't have time at that moment to
post it again.

My suggestion was both George Secor, who is on this list and on the
*math* list, who knows quite a bit about alternately tuned horn, and
the site by Patrick Ozzard Low, who is developing alternately tuned
acoustic instruments.

It sounds, Luke, as though you are looking for greater perfection in
12-tET and *this* site is more for *other* tunings than that, but you
might be able to find all your answers about "fine tunings" of brass
instruments from Patrick Ozzard Low, who undoubtedly knows them:

http://www.c21-orch-instrs.demon.co.uk/

good luck!

Joe Pehrson

--- In tuning@y..., graham@m... wrote:
> You mean the Centre for New Musical Instruments at London Guildhall
> University?

Yes, Graham, that's it! Thanks - I, too, don't know if it is exactly relevant, but certainly moreso than *no* information...

Cheers,
Jon

Hello, there, everyone, and having had a bit more opportunity both to
experiment with and to reflect upon xenofifths and xenofourths in
11-EDO, I would like especially to thank two of the many people who
have contributed to this thread.

Last week, Jacky Ligon kindly shared with my by telephone the 11-EDO
examples posted and discussed here -- and also some examples we tried
in Jacky's timbre based on a series of odd partials adjusted to match
the intervals of this tuning.

Around the same time, Dave Keenan shared his ideas about a sonority,
0-4-7 steps or about 0-436.36-763.64 cents as an approximation of
7:9:11, which I tried in my own timbres and found indeed quite
concordant, leading to some very creative stylistic ideas and even a
texture I have playfully named "Australian discant" in Dave's honor.

What this shows me is that practice and theory can creatively nurture
each other, and that both Jacky and Dave have much enriched my
appreciation of 11-EDO as I strive to compose my first multi-voice
piece and also come up with some better organ-like timbres.

-----------------------------
1. Xenofifths and xenofourths
-----------------------------

When presented in timbres where they are optimized for stability and
consonance, the 11-EDO intervals of 6/11 octave (~654.545 cents) and
5/11 octave (~545.454 cents) can have an amazingly "convincing"
fifthlike or fourthlike quality, and yet, as Jacky has said, also one
quite "alien."

To communicate both sides of this reality, which I have experienced
with my own timbres as well as Jacky's, I would like to propose the
terms "xenofifths" and "xenofourths" to describe these timbrally
consonant intervals about a diesis from 3:2 (~701.955 cents) and 4:3
(~498.045 cents).

In 11-EDO, these intervals belong to what I would term the subcategory
of infrafifths and ultrafourths, that is, small xenofifths and large
xenofourths. In tuning systems such as 13-EDO, we have ultrafifths and
infrafourths -- again about a diesis from 3:2 and 4:3, but in the
opposite directions.

So far, I have found it easiest to get reasonably predictable results
with 11-EDO infrafifths and ultrafourths using a celeste-like timbre:
that is, to get these intervals to sound comparably consonant at
different locations in the tuning.

With organlike timbres, I encounter a curious situation where F3-B3-F4
can sound like very convincing "musical equivalent" of a 2:3:4 trine
(or xenotrine), but G3-C#4 might sound quite tense and "dissonant,"
like a usual tritone. My immediate response is more trial and error;
someone like Bill Sethares, or Jacky Ligon for that matter, might be
able to approach the problem in a more directed way.

Anyway, having read the dialogue between Jacky and Paul Erlich and Joe
Pehrson, I would say that all have presented different sides of the
picture.

While I'm ready to accept both Jacky's 11-EDO infrafifths and mine
(with the celeste-like timbre, and sometimes the organ-like timbres)
as "musically interchangeable" with 3:2, this doesn't mean that a
listener like Paul might not be able very quickly to identify the cues
that this is indeed musical metaphor rather than an equation.

At the moment when I hear an 11-EDO xenotrine that succeeds, my
impression is one of delightful concord and aptness, maybe like a
system of artificial gravity. However, Paul could be tuned into the
signs that this is, to follow the analogy, indeed a rotating
spaceship, not a planet exerting the substantial gravitational field
associated with familiar 1G conditions.

As Joe has said, the music produces the impression of a fifth or
fourth, at least for some of us -- and the term _xenofifth_ or
_xenofourth_ focuses on both the similarities and differences.

--------------------------------------
2. Jacky's experiments -- by telephone
--------------------------------------

How exciting it was to hear Jacky's examples by telephone, and to
learn more about the artistic purpose and context.

Listening to the first examples posted here, I indeed heard "fifths"
of a special kind, and at the same time the unusual character of the
timbre itself struck me. As Jacky explained, the intention here was
not simply to maximize the consonance of these xenofifths, but also
deliberately to produce a timbre with overlapping sonorities, in
contrast to more of a usual organ effect making these sonorities
discrete.

Then Jacky tried a timbre with odd partials based on the ratios of
11-EDO, and adjusted the parameters to get more discrete sonorities.
I found the xenofifths clearer, and was impressed by the total
impression of consonance -- present in the first examples also, but
better defined with an increase in clarity of pitches and successive
sonorities.

At this point, we tried a four-voice cadence in Jacky's odd partials
timbre which sounded quite convincing to me, and for which I will
provide a link along with the following discussion.

--------------------------------------
3. An 11-EDO cadence in Jacky's timbre
--------------------------------------

While people may debate how "consonance" or "dissonant" 11-EDO should
be considered in different timbral conditions, one reputation that
this tuning has is that it isn't very cadentially oriented. This could
be deemed an advantage either for styles seeking "random dissonance,"
or for those relishing "random acts of consonance."

Indeed I would agree that treating a 655-cent xenofifth as a stable
"resolution" is a musical metaphor, by force of taste and sheer
historical association, rather than a reflection of the special
simplicity of this interval -- in contrast to a usual 3:2.

However, under the right circumstances, cadentiality can happen, and
here's my favorite four-voice progression as shown in 22-EDO notation
based on a Pythagorean-like chain of 22-EDO fifths (13/22 octave),
with the 11-EDO xenofifth spelled as a tritone, and a + sign showing
a note raised by 1/11 octave:

E4 F4
C#4 B3
A3 B3
G3 F3

Here's Jacky's rendition in the odd-partials timbre:

http://www.microtonal.org/mp3/Schulter-11EDO-Cadence.mp3

The "unstable" sonority at a rounded 0-218-655-873 cents expands to a
xenotrine at 0-655-1200 cents, with a guiding outer progression of
an 8-step inteval expanding to an 11-step octave. This is the
equivalent of a usual medieval resolution from major sixth to octave,
which for me has strong cadential implications.

-----------------------
4. Consonance in 11-EDO
-----------------------

My experiments suggest that while a xenotrine can indeed provide a
convincing resolution, the tuning seems to have many notably restful
or "concordant" sonorities -- for example, Dave Keenan's 0-4-7 steps,
and also, interestingly, 0-4-9 steps. The latter could be taken as an
approximate 1:1-9:7-7:4, with the tempering placing the upper voices
at a 545-cent xenofourth.

This would lead to the conclusion that 11-EDO, like Paul's beloved
22-EDO tetrad of 0-7-13-18 steps (~4:5:6:7), has a potentially stable
and concordant sonority -- at least in some timbres I tried --
combining forms of what would conventionally be termed a "major third"
and "minor seventh." In the 11-EDO sonority, both intervals
approximate septimal forms.

These are notes in the middle of experimentation, and I would also
warmly like to thank Gene Ward Smith and the others who have shared in
this discussion, with special greetings to Stephen Golovnin, and hopes
the excitement about 11-EDO may lead to much beautiful music in this
and other tunings.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> Around the same time, Dave Keenan shared his ideas about a sonority,
> 0-4-7 steps or about 0-436.36-763.64 cents as an approximation of
> 7:9:11, which I tried in my own timbres and found indeed quite
> concordant, leading to some very creative stylistic ideas and even a
> texture I have playfully named "Australian discant" in Dave's honor.

That's very kind of you, but the honour must go to Dan Stearns from
whom I learnt about the approximate 7:9:11s in 11-EDO.