Orchestration / Microtonality / Adler

I am looking for a good orchestration book that I can use for Composition as
reference.

According to my search.... there is a new book by Samuel Adler called:

Study of Orchestration, Third Edition ($60.35)

Has anybody read it? How is it?

Does anybody know his publication:

The study of Orchestration (which has tapes and seems to be very
constructive/ I don't know about CDs availability?) ($85)

Are these 2 publications complementary and a good set to cover the subject,
or they repeat the same things? If they repeat things ,which one is better?
Do they cover microtonality?

What book is good (&updated) for Ochestration in general?
What book is good for Orchestration and microtonality?

I was adviced an old publication by... Reed Gardener!

Please tell me about your experience!

J.A.M.Salinas

--- In tuning@y..., "antonio" <h-antonio@n...> wrote:

/tuning/topicId_33601.html#33601

> I am looking for a good orchestration book that I can use for
Composition as reference.
>
> According to my search.... there is a new book by Samuel Adler
called:
>
> Study of Orchestration, Third Edition ($60.35)
>
> Has anybody read it? How is it?
>

*****Hello Antonio!

Yes, I have seen this book. It's been out for several years now. I
know Sam Adler well and, in fact, have worked briefly with him. I'm
sure you can't go wrong with this book although, personally, I still
recommend the older standard on the topic: the book _Orchestration_
by Walter Piston.

I believe you are correct when you say that most of these books
basically cover the same material... instrumental ranges and so forth.

> Does anybody know his publication:
>
> The study of Orchestration (which has tapes and seems to be very
> constructive/ I don't know about CDs availability?) ($85)
>
> Are these 2 publications complementary and a good set to cover the
subject, or they repeat the same things? If they repeat
things ,which one is better?

****I don't know this latter "interactive" work. It might be
valuable, but nothing, of course, will substitute for writing pieces
and working *directly* with players. In fact, believe it or not, the
study of *orchestration* is best facilitated *not* by writing
orchestral pieces (where, in *my* experience almost *everything*
sounds glorious, even a major triad or a unison... :) ) but in *solo*
pieces, where the *real* strengths and weaknesses of traditional
instruments are revealed.

There is *also* a book that I own by Cecil Forsyth called, again,
_Orchestration_. Again, it covers just about the same material:
range of instruments, *some* possible effects, generally not many...

This work has an introduction by Bill Bolcom (somebody I *also* have
worked with...) and it's only $13.95 (!) Well, *now* it's probably
$20, but still...

> Do they cover microtonality?
>

****To my knowledge *none* of these books cover microtonality, with
the exception, possibly, of the limits of "glissandi" and so forth on
the trombone, etc.

In order to have a book covering *orchestration* and microtonality,
it would have to include *fingering charts* for alternate tunings.
None of these books have that.

About the only book around that has this is the famous _New Sounds
for Woodwind_ by Bruno Barotolozzi, which is, I believe, no longer in
print, but you can probably find it in the library.

And, there is Johnny Reinhard's _Pitch_ Vol. 1 #4 which has quite a
few fingerings, but presented in a fascinating but "ideosyncratic"
manner by several performers who presented the material to the
magazine.

There is *much* work to be done. I would like, personally, to have
fingering charts for the "Blackjack" scale in 72-tET for *all* the
woodwinds, for example. This material has yet to be assembled and
standardized... (by "standardized" I just mean presented in a readily-
usable form...)

> What book is good (&updated) for Ochestration in general?
> What book is good for Orchestration and microtonality?
>
> I was adviced an old publication by... Reed Gardener!
>

****I've seen this book, but I can't remember much about it. I
sincerely doubt, though, that there is much, if anything, in it about
microtonality. If there is and you see it in the library, please let
me know.

> Please tell me about your experience!
>
> J.A.M.Salinas

****So the Adler will be fine -- but don't expect Adler to be very
sympathetic to microtonality! He's quite a *conservative* composer
and teacher!

I still use the "old" Piston. Walter Piston really came up with a
good book with _Orchestration_. His _Harmony_ book has *much* to be
desired, and his _Counterpoint_ is only "so so..."

And the Forsyth is an inexpensive paperback from Dover that covers,
essentially, the same material.

But the "interactive" one I haven't seen or heard... but, again,
nothing beats *direct* work with players.

Regarding microtonality, though, all of these publications are
concerned entirely with *traditional* instruments and the assumptions
are that people are performing in 12-tET, so you have to find *other*
references like the Bartolozzi or Reinhard if you want to explore the
xenharmonic universe.

Otherwise, such an orchestration book has yet to be written!

Joseph Pehrson

Actually, I used Keenan's "Orchestration" and though it is conservative as
are most, it is clear cut, short, and easy to use. An example of
conservative treatment is when the actual ranges of instruments are shortened
"to be safe." Also, virtuosi can do most of what books say cannot. For
example, the bassoon is described as having no dynamic range in its lowest
tetrachord (not true for me). Also, certain trills in the lowest tetrachord
are described as impossible (but not true for me).

The tuning charts in PITCH I:4 were all that were available at the time they
were published. The Bartolozzi book was dead wrong in its fingerings,
especially for flute (much to the disappointment of Toru Takemitsu when he
printed Bartolozzi fingerings for his flute solo "Voice").

Actually, Bartolozzi was a bassoonist/composer who studied with a bassoonist
named Muchetti who is credited with the first serious Italian exploration of
microtonal bassoon (largely in multiphonics). The other instruments have
similar stories.

About the bassoon, did you know it can do greater continuous glissandi than a
trombone?

best, Johnny Reinhard

hi antonio and joe,

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, February 03, 2002 6:11 AM
> Subject: [tuning] Re: Orchestration / Microtonality / Adler
>
>
> --- In tuning@y..., "antonio" <h-antonio@n...> wrote:
>
> /tuning/topicId_33601.html#33601
>
>
> > I am looking for a good orchestration book that I can use for
> > Composition as reference.
> >

those here who know me well won't be surprised to learn about
my favorite orchestration books:

Koenig, Arthur William, 1971
_The orchestral techniques of the Mahler symphonies
with emphasis on the second and ninth symphonies_

and another one in German that i can't find in the library
catalog right now

> > Do they cover microtonality?
> >
>
> ****To my knowledge *none* of these books cover microtonality, with
> the exception, possibly, of the limits of "glissandi" and so forth on
> the trombone, etc.
>
> In order to have a book covering *orchestration* and microtonality,
> it would have to include *fingering charts* for alternate tunings.
> None of these books have that.
>
> About the only book around that has this is the famous _New Sounds
> for Woodwind_ by Bruno Barotolozzi, which is, I believe, no longer in
> print, but you can probably find it in the library.
>
> And, there is Johnny Reinhard's _Pitch_ Vol. 1 #4 which has quite a
> few fingerings, but presented in a fascinating but "ideosyncratic"
> manner by several performers who presented the material to the
> magazine.

in addition to Joe's two suggestions, i know of only two
other books that deal specifically with microtonality and
orchestration together

one, of course, is Harry Partch's _Genesis of a Music_ ... but
the only instruments given any detailed coverage are his own,
so that will only be of use to you if you wish to replicate
his instruments or design and build your own along similar lines

the other is _21st Century Orchestral Instruments_ by
Patrick Ozzard-Low <http://www.c21-orch-instrs.demon.co.uk/>

this is not really an "orchestration" text, but rather an
exploration into the questions concerning the design of future
microtonal instruments ... but it will probably give you lots
of valuable info, and it's available free on the web

> There is *much* work to be done. I would like, personally, to have
> fingering charts for the "Blackjack" scale in 72-tET for *all* the
> woodwinds, for example. This material has yet to be assembled and
> standardized... (by "standardized" I just mean presented in a readily-
> usable form...)
>
>
> > What book is good (&updated) for Ochestration in general?
> > What book is good for Orchestration and microtonality?
> >
> > I was adviced an old publication by... Reed Gardener!
> >
>
> ****I've seen this book, but I can't remember much about it. I
> sincerely doubt, though, that there is much, if anything, in it about
> microtonality. If there is and you see it in the library, please let
> me know.

Joe, Gardner Read's book is entirely about microtonality!

Author: Read, Gardner, 1913-
Title: _20th-century microtonal notation_
Publisher: New York : Greenwood Press, 1990.
Description: Book, viii + 198 p.
Series: Contributions to the study of music and dance ; no. 18
L.o.C. Call Number: MT35 .R252 1990

-monz

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

Alas, Gardner's book is about microtonal notation. Otherwise, it is not a
book on orchestration. Have y'all seen Rimsky-Korsakoff's "Orchestration"?
Stravinsky's success was ofttimes associated with breaking his teacher's
(Rimsky's) orchestration chestnuts.

Johnny Reinhard

--- In tuning@y..., Afmmjr@a... wrote:

/tuning/topicId_33601.html#33615

> Actually, I used Keenan's "Orchestration" and though it is
conservative as are most, it is clear cut, short, and easy to use.

****Hi Johnny!

I think you mean "Kennan" or something similar. "Keenan" is our cat
on this list...

An example of
> conservative treatment is when the actual ranges of instruments are
shortened "to be safe." Also, virtuosi can do most of what books say
cannot. For example, the bassoon is described as having no dynamic
range in its lowest tetrachord (not true for me). Also, certain
trills in the lowest tetrachord are described as impossible (but not
true for me).

****That makes sense, so we should warn the gentleman who requested
this information on this list that the orchestration books only give
the "safest" "sure-fire" details. The best policy, of course, is to
work *directly* with players during composition...

If not, you'll find out more about this during the *performance*... :)

>
> The tuning charts in PITCH I:4 were all that were available at the
time they were published.

****Absolutely! And a grand accomplishment it is! However, as we
know, at *that* time microtonality was a bit more of a "curiosity."
Now it's headed more for the "mainstream" and, I believe, we'll
eventually need a different treatment for it...

The Bartolozzi book was dead wrong in its fingerings,
> especially for flute (much to the disappointment of Toru Takemitsu
when he printed Bartolozzi fingerings for his flute solo "Voice").
>

*****Thanks for this information. I actually didn't know this.
Well, I guess you *told* it to me once, but I forgot about it as
usual... :)

This book, of course, was *very* early. I think I bought it around
1973 or so. I suppose it's not surprising that it's inaccurate
since, I think, it was one of the first of it's kind *anywhere...*

> Actually, Bartolozzi was a bassoonist/composer who studied with a
bassoonist named Muchetti who is credited with the first serious
Italian exploration of microtonal bassoon (largely in multiphonics).
The other instruments have similar stories.

****Interesting!

>
> About the bassoon, did you know it can do greater continuous
glissandi than a trombone?
>

****Well, in *your* hands, Johnny, I'm sure it can! In fact, I'm
looking forward to the new Blackjack chart of fingerings for bassoon
that I hope we will do soon. Bassoon is the *very first* woodwind
that I'll try!!!

JP

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

/tuning/topicId_33601.html#33617

>
> the other is _21st Century Orchestral Instruments_ by
> Patrick Ozzard-Low <http://www.c21-orch-instrs.demon.co.uk/>
>
> this is not really an "orchestration" text, but rather an
> exploration into the questions concerning the design of future
> microtonal instruments ... but it will probably give you lots
> of valuable info, and it's available free on the web
>

****Thanks, Monz... I've downloaded this. This is the first such
study of xenharmonic *acoustic* instruments that I've seen... Such
studies will be valuable if said instruments are *ever* going to
evolve.

> > ****I've seen this book, but I can't remember much about it. I
> > sincerely doubt, though, that there is much, if anything, in it
about microtonality. If there is and you see it in the library,
please let me know.
>
>
> Joe, Gardner Read's book is entirely about microtonality!
>
>
> Author: Read, Gardner, 1913-
> Title: _20th-century microtonal notation_
> Publisher: New York : Greenwood Press, 1990.
> Description: Book, viii + 198 p.
> Series: Contributions to the study of music and dance ; no. 18
> L.o.C. Call Number: MT35 .R252 1990
>

****Hi Monz...

Yes, I've seen this book, but it wasn't the one I was talking
about... He also has a book on, specifically, *orchestration* called
_Style and Orchestration_ but I don't know if there is anything about
microtonality in it...

JP

Joe!
I have always liked Rimsky's book referring to the works of Stravinsky and Ravel ( ok
sometimes Mahler) for being the best handler of this medium. I will say that John Adams would be a
great example of a composer that have no idea on how to write for orchestra having to resort to
mic mixing to compensate for his lack of being able to produce any balance at all!

jpehrson2 wrote:

> --- In tuning@y..., Afmmjr@a... wrote:
>
> /tuning/topicId_33601.html#33615
>
> > Actually, I used Keenan's "Orchestration" and though it is
> conservative as are most, it is clear cut, short, and easy to use.
>
> ****Hi Johnny!
>
> I think you mean "Kennan" or something similar. "Keenan" is our cat
> on this list...
>
> An example of
> > conservative treatment is when the actual ranges of instruments are
> shortened "to be safe." Also, virtuosi can do most of what books say
> cannot. For example, the bassoon is described as having no dynamic
> range in its lowest tetrachord (not true for me). Also, certain
> trills in the lowest tetrachord are described as impossible (but not
> true for me).
>
>

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

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

> From: jpehrson2 <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, February 03, 2002 3:31 PM
> Subject: [tuning] Re: Orchestration / Microtonality / Adler
>
>
> > the other is _21st Century Orchestral Instruments_ by
> > Patrick Ozzard-Low <http://www.c21-orch-instrs.demon.co.uk/>
> > ...
>
> ****Thanks, Monz... I've downloaded this. This is the first such
> study of xenharmonic *acoustic* instruments that I've seen... Such
> studies will be valuable if said instruments are *ever* going to
> evolve.

It seems this is the first you're finding out about Patrick's
book, Joe. He finished it at the end of 1998; it's been
online ever since.

> > Joe, Gardner Read's book is entirely about microtonality!
>
> Yes, I've seen this book, but it wasn't the one I was talking
> about... He also has a book on, specifically, *orchestration* called
> _Style and Orchestration_ but I don't know if there is anything about
> microtonality in it...

Oh, ok, sorry ... i didn't know about Read's book on orchestration.
But Antonio seemed to know little about any of Read's work, so
he should profit from my citation anyway.

-monz

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

> From: Kraig Grady <kraiggrady@anaphoria.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, February 03, 2002 5:00 PM
> Subject: Re: [tuning] Re: Orchestration / Microtonality / Adler
>
>
> I have always liked Rimsky's book referring to the
> works of Stravinsky and Ravel ( ok sometimes Mahler) for
> being the best handler of this medium.

"sometimes Mahler" !!!!! :(

watch it, buddy ... there's N O other composer who
handles the orchestra as well as my man Gustav!

-monz

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

I seem to also remember a book called Thesaurus of Orchestral Devices.

monz wrote:

>
> >
> > > the other is _21st Century Orchestral Instruments_ by
> > > Patrick Ozzard-Low <http://www.c21-orch-instrs.demon.co.uk/>
> > > ...
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

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

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

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

/tuning/topicId_33601.html#33636
> >
> > > the other is _21st Century Orchestral Instruments_ by
> > > Patrick Ozzard-Low <http://www.c21-orch-instrs.demon.co.uk/>
> > > ...
>
> It seems this is the first you're finding out about Patrick's
> book, Joe. He finished it at the end of 1998; it's been
> online ever since.
>

***I just wrote a long response to this topic that got lost when I
sat on the keyboard or something, but I will try a shorter version
again:

I basically really enjoyed reading this study, but I think some of it
is a little Sci-Fi! Particularly the sections where he has "logical"
electronic interfaces that then "play" the acoustic instruments
mechanically.

I would like to see one of those work!

I think it would be much easier to effect such xenharmonics in some
kind of "post processing" which he also mentions.

Or perhaps, even more practically, what the fine composer Jonathan
Harvey does... puts all the xenharmonics in the *electronic* part and
uses *conventional* instruments. Ok, so that's not going to be so
much fun for somebody who wants to *play* xenharmonics, but the total
piece is *definitely* xenharmonic, and Harvey gets *lots* of
performances.

So what is my own *personal* conjecture as to what could be done:

1) Develop more and dependable *alternate fingerings.* Sure, they
vary from instrument and player to player, but using an audio CD
there should be some kind of "consistency" there (more on this word
later)

2) Make *some* kind of new "standard" be it 72-tET, or subsets
thereof, Blackjack, whatever. But, there are real limitations in
acoustic instruments... I'll bet Kraig Grady will agree on that...
dunno. But even Harry Partch really standardized everything. He
*had* to in order to get all his instruments in sync.

So, with those two methods possibly, just *possibly* there can be new
development of new acoustic instruments. Otherwise no manufacturers
or individuals are going to spend the time and money to do it.

There also has to be a *demand* for such. Ozzard-Low does mention
this aspect... he touches on just about everything.

One can only have a *demand* if things are limited and not "all over
the place..."

Suddenly it has to be "in vogue" to have a just guitar, or a 19-tone
guitar, whatever.

I still don't quite understand Patrick Ozzard-Low's predilection for
ETs. He mentions the concept of "consistency" that, apparently Paul
Erlich invented or helped to invent.

Are ETs more "consistent" generally than irregular scales. Maybe. ??

Anyway, Ozzare-Low seems to like them better. I was trying to find a
clear reason in his writing, but wasn't coming up with the answer.

It was also fun to see the names of so many of our illustrious list
members, including Paul Erlich and George Secor. Bill Sethares was
mentioned, too, quite a bit, even though he's more over on
MakeMicroMusic of late.

So, that was a fascinating read. I'm not quite sure why he felt he
had to try to encapsulate the entire history of tuning theory in the
paper rather than refer to other things, but maybe he thought that
background was necessary in many people's understanding of the
paper. He must have..

Anyway, it's got to be about the only paper of it's kind on the
topic, and thanks, Monz for pointing this one out to me...

JP

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

/tuning/topicId_33601.html#33637

>
> > From: Kraig Grady <kraiggrady@a...>
> > To: <tuning@y...>
> > Sent: Sunday, February 03, 2002 5:00 PM
> > Subject: Re: [tuning] Re: Orchestration / Microtonality / Adler
> >
> >
> > I have always liked Rimsky's book referring to the
> > works of Stravinsky and Ravel ( ok sometimes Mahler) for
> > being the best handler of this medium.
>

****Well, Kraig is right that that orchestration book is a
great "classic..." I've been meaning to add it to my library. And,
then, of course, there's also Berlioz' work which, I believe,
includes some information on the *guitar* which most of them don't
have...

Not the *electric* guitar, though... :)

JP

In-Reply-To: <a3m77p+dm0s@eGroups.com>
jpehrson2 wrote:

> Not the *electric* guitar, though... :)

I found some details on this in a Deep Purple CD booklet. The biggest
problem seems to be stopping the guitarist turning the amp up too high and
drowning out the rest of the orchestra. There may also be problems with
persuading the guitarist to take part in the first place.

Graham

Of course, Berlioz wrote in 1850 (published in English in 1851) that the bassoons are incapable of playing in tune!

Johnny Reinhard

> From: <Afmmjr@aol.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, February 04, 2002 7:41 AM
> Subject: Re: [tuning] Re: Orchestration / Microtonality / Adler
>
>
> Of course, Berlioz wrote in 1850 (published in English
> in 1851) that the bassoons are incapable of playing in tune!
>
> Johnny Reinhard

but wasn't he right about that? :p

-monz

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

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

/tuning/topicId_33601.html#33656

> In-Reply-To: <a3m77p+dm0s@e...>
> jpehrson2 wrote:
>
> > Not the *electric* guitar, though... :)
>
> I found some details on this in a Deep Purple CD booklet. The
biggest problem seems to be stopping the guitarist turning the amp
up too high and drowning out the rest of the orchestra. There may
also be problems with persuading the guitarist to take part in the
first place.
>
>
> Graham

***Not any longer, Graham!! Not in America anyway. What with "cats"
like Jon Catler and Steve Mackey out there. Not at all. Classic/new
music electric guitar composers are all over the place these days...
They all "started" in rock bands. Others include guys like Randall
Woolf and my friend Gene Pritsker. These are electric guitar
virtuosos that *actually read music!* This is happening all over the
place...

I don't know if it's the same in England, but I imagine it might be...

Back to the U.S.:

Bill Bolcom's great big 3-hour Blake piece also has a prominent
electric guitar part throughout, and many other composers...

I like it, personally.

JP

--- In tuning@y..., Afmmjr@a... wrote:

/tuning/topicId_33601.html#33657

> Of course, Berlioz wrote in 1850 (published in English in 1851)
that the bassoons are incapable of playing in tune!
>
> Johnny Reinhard

***Oh, Johnny, I also wanted to compliment you for the prominent
citations in the Patrick Ozzard-Low which I read for the first time...

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_33601.html#33636
> > >
> > > > the other is _21st Century Orchestral Instruments_ by
> > > > Patrick Ozzard-Low <http://www.c21-orch-instrs.demon.co.uk/>
> > > > ...
> >
>
> I basically really enjoyed reading this study, but I think some of
it
> is a little Sci-Fi! Particularly the sections where he
has "logical"
> electronic interfaces that then "play" the acoustic instruments
> mechanically.
>
> I would like to see one of those work!
>

Joseph,

I have been corresponding with Patrick Ozzard-Low for the past 3
years. He first contacted me (by phone, at what was around 3 a.m. in
the U.K.) because he had read my Xenharmonikon article (c. 1976) on
possibilities for microtonal brass instruments. (This was also the
event which first awakened me out of my microtonal slumber, so if you
happen to read this, thank you Patrick!)

I strongly feel that logical technology would free the woodwind
instruments from the severe limitations imposed by physical linkages
and would simultaneously simplify fingerings and optimize tone
quality. On the clarinet, oboe, and bassoon in particular (which
have relatively small tone holes compared to the size of the
instrument), I could envision being able to change the instrument
from 31-EDO to 41-EDO (for example) with the flick of a switch. It
would also be possible to build an instrument without having to
decide in advance what the fingerings will be -- you could program
these via a computer interface and test them out. In case a
difference of opinion might arise as to the best fingering system,
production instruments could have more than one set of fingerings
built in, selectable by means of a switch. Patrick reports that this
sort of technology has already been tested (to a limit extent), and
it has elicited some very favorable reactions from the players
involved.

> I think it would be much easier to effect such xenharmonics in some
> kind of "post processing" which he also mentions.
>
> Or perhaps, even more practically, what the fine composer Jonathan
> Harvey does... puts all the xenharmonics in the *electronic* part
and
> uses *conventional* instruments. Ok, so that's not going to be so
> much fun for somebody who wants to *play* xenharmonics, but the
total
> piece is *definitely* xenharmonic, and Harvey gets *lots* of
> performances.
>
> So what is my own *personal* conjecture as to what could be done:
>
> 1) Develop more and dependable *alternate fingerings.* Sure, they
> vary from instrument and player to player, but using an audio CD
> there should be some kind of "consistency" there (more on this word
> later)
>
> 2) Make *some* kind of new "standard" be it 72-tET, or subsets
> thereof, Blackjack, whatever. But, there are real limitations in
> acoustic instruments... I'll bet Kraig Grady will agree on that...
> dunno. But even Harry Partch really standardized everything. He
> *had* to in order to get all his instruments in sync.
>
> So, with those two methods possibly, just *possibly* there can be
new
> development of new acoustic instruments. Otherwise no
manufacturers
> or individuals are going to spend the time and money to do it.

I have already mentioned the woodwinds in connection with 31 and 41-
EDO. Why 31 and 41? These are arguably the best negative and
positive EDO's for approximating small-number ratios, and, given that
72 would not be anywhere nearly as practical, together they would
afford a considerable amount of versatility.

Why EDO's? You asked that question below, but I will give an answer
here. The orchestral instruments are, for the most part, flexible-
pitch instruments. If the player can control the intonation, then
why design an instrument based on just or near-just intonation, when
it only presents other problems, such as:

*** What set of tones does one select? How many tones, and how much
modulation will they allow? To what harmonic limit? Why? And if I
don't like your answers, then what?

Since EDO's provide free modulation, they are the most flexible
standard for flexible-pitch instruments.

I also mentioned brass instruments. Within the past couple of years
I completely rethought my original brass proposal and discarded it in
favor of a completely new approach that does the same thing for the
brass instruments that the Bosanquet keyboard could do for
synthesizers (and did for the Scalatron) or that the sagittal symbols
can do for notation: My new approach employs easy-to-learn fingerings
that partially build on existing (12-EDO) patterns and carry over
from one tonal system to another. This can be implemented in multi-
system brass instruments that would allow a player to have 17, 19,
22, 24, 31, 36, and 41-EDO (and perhaps others) all in a single four-
valve instrument. I need to emphasize that these are not
hypothetical instruments; I've done the math on the tube lengths, and
it can all be done with mechanical valves. (Patrick has been
pursuing the use of electrically controlled valves lately, and if
that will offer any significant advantage in cost or reliability,
then that could be a possibility.)

With a multi-system instrument the player would not be locked into a
single tonal system upon making a purchase, would not incur any
adverse financial consequences upon a change of mind about that
system, and would not have to carry more than one instrument to a
performance to play in different systems. Likewise, the manufacturer
would not have to produce separate models for different tonal systems
(as if that would happen anyway!), thus giving the convertible
instruments the widest possible market, i.e., the entire microtonal
community (which is small enough as things go).

Does this sound like the sort of "standard" that might appeal to you
or anybody else out there?

>
> There also has to be a *demand* for such. Ozzard-Low does mention
> this aspect... he touches on just about everything.
>
> One can only have a *demand* if things are limited and not "all
over
> the place..."
>
> Suddenly it has to be "in vogue" to have a just guitar, or a 19-
tone
> guitar, whatever.

Both Patrick and Harry Partch gave the same answer to this question.
The one (and probably only) thing that is going to put microtonality
in demand is to have some significant microtonal music come into
existence. Whether it might be the sort of instant success that
would accomplish what "Switch-on Bach" did for electronic music, or
whether it would more likely be a significant cumulative body of work
of a group of talented people, it's ultimately up to those of us who
consider ourselves microtonal composers to compose something
significant. Short of that, I don't think we have a prayer.

>
> I still don't quite understand Patrick Ozzard-Low's predilection
for
> ETs. He mentions the concept of "consistency" that, apparently
Paul
> Erlich invented or helped to invent.
>
> Are ETs more "consistent" generally than irregular scales.
Maybe. ??
>
> Anyway, Ozzare-Low seems to like them better. I was trying to find
a
> clear reason in his writing, but wasn't coming up with the answer.
>
> It was also fun to see the names of so many of our illustrious list
> members, including Paul Erlich and George Secor. Bill Sethares was
> mentioned, too, quite a bit, even though he's more over on
> MakeMicroMusic of late.
>
> So, that was a fascinating read. I'm not quite sure why he felt he
> had to try to encapsulate the entire history of tuning theory in
the
> paper rather than refer to other things, but maybe he thought that
> background was necessary in many people's understanding of the
> paper. He must have..
>
> Anyway, it's got to be about the only paper of it's kind on the
> topic, and thanks, Monz for pointing this one out to me...
>
> JP

A primary purpose of the paper is to secure funding for what is
admittedly a highly ambitious project, and in endeavoring to convey a
vision of what should be the future of music, I think that Patrick
felt that it was useful to show that musical tuning has a varied and
illustrious past. What we are using today has been in general use
for a relatively short time; and what we will use in the future does
not have to be what we are using today.

I hope this contributes a little more perspective on what we are
attempting to do.

--George

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

> I have already mentioned the woodwinds in connection with 31 and 41-
> EDO. Why 31 and 41? These are arguably the best negative and
> positive EDO's for approximating small-number ratios, and, given
that
> 72 would not be anywhere nearly as practical,

i'm surprised to hear you say that, given the imaginative mechanisms
you've proposed for new wind and brass instruments. it seems that 72
would be far more practical, since one could preserve a musician's
lifetime of training in 12-equal, and then use the electronic keying
technology to provide a way, with just a couple of extra buttons, to
inflect by a twelfth-tone, by a sixth-tone, and by a quarter-tone.
and you're done!

> My new approach employs easy-to-learn fingerings
> that partially build on existing (12-EDO) patterns and carry over
> from one tonal system to another. This can be implemented in multi-
> system brass instruments that would allow a player to have 17, 19,
> 22, 24, 31, 36, and 41-EDO (and perhaps others) all in a single
four-
> valve instrument.

well this sounds fascinating. but you are aware that even the
standard trumpet does not play in anything like 12-equal without a
large amount of training on the part of the performer. i'm wondering
what the result would be for unfamiliar equal temperaments. does your
system overcome these difficulties as well?

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > I have already mentioned the woodwinds in connection with 31 and
41-
> > EDO. Why 31 and 41? These are arguably the best negative and
> > positive EDO's for approximating small-number ratios, and, given
> that
> > 72 would not be anywhere nearly as practical,
>
> i'm surprised to hear you say that, given the imaginative
mechanisms
> you've proposed for new wind and brass instruments. it seems that
72
> would be far more practical, since one could preserve a musician's
> lifetime of training in 12-equal, and then use the electronic
keying
> technology to provide a way, with just a couple of extra buttons,
to
> inflect by a twelfth-tone, by a sixth-tone, and by a quarter-tone.
> and you're done!
>
> > My new approach employs easy-to-learn fingerings
> > that partially build on existing (12-EDO) patterns and carry over
> > from one tonal system to another. This can be implemented in
multi-
> > system brass instruments that would allow a player to have 17,
19,
> > 22, 24, 31, 36, and 41-EDO (and perhaps others) all in a single
> four-
> > valve instrument.
>
> well this sounds fascinating. but you are aware that even the
> standard trumpet does not play in anything like 12-equal without a
> large amount of training on the part of the performer. i'm
wondering
> what the result would be for unfamiliar equal temperaments. does
your
> system overcome these difficulties as well?

Paul,

I played the French horn for 10 years, although I never became highly
proficient at it; just well enough to play in church bands for fun.
I don't any more, since I don't own a horn, but I do have a trumpet,
which I currently play every week in a church ensemble for which I
improvise my own part for what they call a "contemporary" (i.e., pop
style) music service. So I have some idea of just what is involved,
and learning some new fingerings (the new part) is a lot simpler than
developing a good tone, a strong embouchure, and a complete range
(the old part).

By the way, in my valve plan, the first and second valves do exactly
the same thing they do now, which is to lower the pitch by a major
2nd and minor 2nd, respectively, so that the great majority of the
fingerings previously learned carry right over to the microtonal
instrument, which is not bad for carrying over one's existing
training.

The problem with 72-EDO is that it requires another valve -- more
complicated and more expensive to make, although (now that I think
about it) I did come up with another idea recently that would
completely change the picture. Hmmm -- I need to give that some more
thought; it's really different!

What I like about 31 is that it preserves the conventional diatonic
system and is least disruptive to established harmonic norms.
Considering all the fuss lately about "major third 1/12 down" in 72
(will the real major third please stand up), this is easily avoided
in 31. In 72 you have to train to handle more than one kind of major
third, which can get downright confusing, considering current musical
training.

And what I like about 41 is that you have complete consistency in the
15 limit.

My main interest in 72 is as a basis for notation that takes
advantage of the common ground between 31 and 41.

--George

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

> By the way, in my valve plan, the first and second valves do
exactly
> the same thing they do now, which is to lower the pitch by a major
> 2nd and minor 2nd, respectively, so that the great majority of the
> fingerings previously learned carry right over to the microtonal
> instrument, which is not bad for carrying over one's existing
> training.

but what i was referring to, george, is the fact that the interval
that the two valves together lower the pitch by, is not exactly the
sum of the intervals that the two valves separately lower the pitch
by. i was just wondering if you were taking this effect into account,
and how.

> The problem with 72-EDO is that it requires another valve -- more
> complicated and more expensive to make, although (now that I think
> about it) I did come up with another idea recently that would
> completely change the picture. Hmmm -- I need to give that some
more
> thought; it's really different!

ok -- i was thinking more in terms of reed instruments, rather than
brasses.

> What I like about 31 is that it preserves the conventional diatonic
> system and is least disruptive to established harmonic norms.

right.

> Considering all the fuss lately about "major third 1/12 down" in 72
> (will the real major third please stand up), this is easily avoided
> in 31.

until you start playing augmented chords or schubert or "giant steps"
by coltrane.

> In 72 you have to train to handle more than one kind of major
> third, which can get downright confusing, considering current
musical
> training.
>
> And what I like about 41

where you'd also have to train to handle more than one kind of major
third -- farther from 12-tET and farther from just, respectively,
than the two kinds in 72.

> is that you have complete consistency in the
> 15 limit.

glad you're enjoying the consistency concept that i came up with.
looking deeper, though, one finds that each equal temperament has its
own set of "identities" or "equivalencies" or "unison vectors" which
will determine compositional behavior to a large extent -- for
example in determining MOS or omnitetrachordal scales where
Krumhansl's psychological conditions for the encoding of tonal
information may be satisfied. 41 has some very specific things that
it can and can't do, and one can look at 46, for example, a 13-limit
consistent equal temperament, and see a whole host of possibilities
that 41 misses.

also, joseph's question about favoring equal temperaments uber alles
merits a little more attention. 29-equal is also consistent, but not
very accurate, through the 15-limit. but graham breed recently
reminded us that *two* 29-equal chains, a few cents apart, gives you
outstanding accuracy in the 15-limit, not to mention a great wealth
of modulational and transpositional freedom. given the desiderata of
fewer than sixty notes per octave, great 15-limit accuracy, and great
transpositional freedom, it would be hard to do better than this
*non*-equal-temperament.

i wrote:

> given the desiderata of
> fewer than sixty notes per octave, great 15-limit accuracy, and
great
> transpositional freedom, it would be hard to do better than this
> *non*-equal-temperament.

in case you wanted the specifics on this, you'll find it at the top of

http://x31eq.com/limit15.txt (thanks graham)

where you can discover that two 29-equal cycles, tuned 15.563 cents
apart, would give the 15-limit ogdoads with a maximum error in any
interval of 4.695 cents from just.

this compares with maximum 15-limit errors of 14.079 cents for 41-
equal, 8.283 cents for 58-equal, 7.194 cents for 72-equal, 7.259
cents for 80-equal, 6.295 cents for 87-equal, and 5.361 cents for 94-
equal.

Well to be honest, there is more hoopla than need IMO. A clarinet and a
flute and a bassoon and an oboe can all play microtones with conviction, and
do. Below is a small list of wind players:

On flute: Stefani Starin (Newband) plays deliciously in JI. Andrew
Bolotowsky can play any tuning system. I've hired numerous flute players
(over 20) in a lifetime and was never a problem for them to play precise
microtones. Accordingly, play microtonal recorder in any tuning.

On clarinet: Michiyo Suzuki can play, and does play, anything. Anyone could
if they tried.

On bassoon: Yup bassoon out of tune for 1851 Berlioz, but now able to play in
any tuning of any kind using different fingering combinations -- or
"grippings." All bassoonists are using my fingerings. Enough with the old
canard about the fingerings being so different from one player to another.
Usually only one or a few are slightly different.

On oboe: Admiringly, no one has taken the reins more than Heinz Holliger,
himself. There is no doubt that the specificity is there, as soon as an
oboist can imagine the notes in his head correctly. This is a treasure trove
for multiphonic extremes thanks to the ease of changing multiphonics, and the
ease to circular breathe on oboe.

On horn: Greg Evans can play in any tuning with authority and suave
(presently teaching in New Mexico). He has raised the bar.

On trombone: Julie Josephson and Chris Washburne has proved that they hear
everything...and can play it repeatedly.

On tuba: Dave Grego with his quartertone tuba has played everything I can
throw at him (check him in my piece "Atlantis").

Strings: Tom Chiu, Dave Eggar, Matt Fields...these guys eat college
professors for breakfast. There is no comparison between what they are
playing and what people are teaching...light years apart.

Percussion: natural microtonal citizens in their genesis.

Vocals? Now why not try a new vocal instrument for the future?

Best, Johnny Reinhard

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

/tuning/topicId_33601.html#33670

>
>
> I strongly feel that logical technology would free the woodwind
> instruments from the severe limitations imposed by physical
linkages
> and would simultaneously simplify fingerings and optimize tone
> quality. On the clarinet, oboe, and bassoon in particular (which
> have relatively small tone holes compared to the size of the
> instrument), I could envision being able to change the instrument
> from 31-EDO to 41-EDO (for example) with the flick of a switch. It
> would also be possible to build an instrument without having to
> decide in advance what the fingerings will be -- you could program
> these via a computer interface and test them out. In case a
> difference of opinion might arise as to the best fingering system,
> production instruments could have more than one set of fingerings
> built in, selectable by means of a switch. Patrick reports that
this
> sort of technology has already been tested (to a limit extent), and
> it has elicited some very favorable reactions from the players
> involved.

****Hello George!

Well, certainly I'm not trying to "diss" this technology. I was just
thinking it might be easier to use "regular" fingerings with some
kind of MIDI post-processing to obtain xenharmonics rather than a
*physical* electronic interface that one plays and which goes to a
computer and comes back to *physically* play an instrument.

Maybe it can be done! Dunno. I would just like to see one of these
gadgets in action! More power to anybody who can get it to work!

>
> I have already mentioned the woodwinds in connection with 31 and 41-
> EDO. Why 31 and 41? These are arguably the best negative and
> positive EDO's for approximating small-number ratios, and, given
that 72 would not be anywhere nearly as practical, together they
would afford a considerable amount of versatility.
>

****But how about our beloved "Miracle" scales... Blackjack 21 and
Canasta 31! Actually, as you know, *you're* partially the inventor
of all of these:

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

> Why EDO's? You asked that question below, but I will give an
answer here. The orchestral instruments are, for the most part,
flexible-pitch instruments. If the player can control the
intonation, then why design an instrument based on just or near-just
intonation, when it only presents other problems, such as:
>
What set of tones does one select? How many tones, and how much
modulation will they allow? To what harmonic limit? Why? And if I
don't like your answers, then what?
>
> Since EDO's provide free modulation, they are the most flexible
> standard for flexible-pitch instruments.
>

****Thanks, George. I guess that would work, but somehow the
insistence on ETs turns my stomach... :) Too many identical little
steps! :) But your answer is a bit what I imagined... although I
also thought it might have something to do with Paul
Erlich's "consistency" but maybe it doesn't.

Paul? Are ETs, in general, more "consistent?" or does it depend...

> I also mentioned brass instruments. Within the past couple of
years I completely rethought my original brass proposal and discarded
it in favor of a completely new approach that does the same thing for
the brass instruments that the Bosanquet keyboard could do for
> synthesizers (and did for the Scalatron) or that the sagittal
symbols can do for notation: My new approach employs easy-to-learn
fingerings that partially build on existing (12-EDO) patterns and
carry over from one tonal system to another. This can be implemented
in multi-system brass instruments that would allow a player to have
17, 19, 22, 24, 31, 36, and 41-EDO (and perhaps others) all in a
single four-valve instrument. I need to emphasize that these are not
> hypothetical instruments; I've done the math on the tube lengths,
and it can all be done with mechanical valves. (Patrick has been
> pursuing the use of electrically controlled valves lately, and if
> that will offer any significant advantage in cost or reliability,
> then that could be a possibility.)
>

****That sounds, *terrific* George, if you can get it working!

> With a multi-system instrument the player would not be locked into
a single tonal system upon making a purchase, would not incur any
> adverse financial consequences upon a change of mind about that
> system, and would not have to carry more than one instrument to a
> performance to play in different systems. Likewise, the
manufacturer would not have to produce separate models for different
tonal systems (as if that would happen anyway!), thus giving the
convertible instruments the widest possible market, i.e., the entire
microtonal community (which is small enough as things go).
>

****That sounds absolutely great! Perhaps that involves inserting
different "crooks" or such like. (I don't mean Enron...)

If so, it becomes a little like the "olden days" when different
crooks were inserted to obtain different "keys"... maybe.

> Does this sound like the sort of "standard" that might appeal to
you or anybody else out there?
>

****Why, of course, but I should also add that there is much to be
done, particularly in the area of JUST INTONATION (cult caps) with
brass instruments. For example, I wrote a couple of pieces for the
Belgian horn virtuoso Francis Orval where he uses *all* the harmonics
from different positions in the series. Of course, there are
*normally* very few of these used, just the ones that are closest to
12-tET. Orval came up with a marvelous chart of *all* these overtones
which was included in Johnny Reinhard's magnificent _Pitch_ Vol 1 #4
that Patrick Ozzard-Low mentions several times in his study. So,
there's even a *lot* of microtonality to be done with *conventional*
brass instruments!

>
> Both Patrick and Harry Partch gave the same answer to this
question. The one (and probably only) thing that is going to put
microtonality in demand is to have some significant microtonal music
come into existence. Whether it might be the sort of instant success
that would accomplish what "Switch-on Bach" did for electronic music,
or whether it would more likely be a significant cumulative body of
work of a group of talented people, it's ultimately up to those of us
who consider ourselves microtonal composers to compose something
> significant. Short of that, I don't think we have a prayer.
>

****Absolutely!

>
> A primary purpose of the paper is to secure funding for what is
> admittedly a highly ambitious project, and in endeavoring to convey
a vision of what should be the future of music, I think that Patrick
> felt that it was useful to show that musical tuning has a varied
and illustrious past. What we are using today has been in general
use for a relatively short time; and what we will use in the future
does not have to be what we are using today.

*****You know, George, I wasn't thinking about the fact that this
paper was to be sent to *funding sources!* Of course, that explains
the "recap" and also the tone of the paper! Good luck!

>
> I hope this contributes a little more perspective on what we are
> attempting to do.
>

****It absolutely does, and I found the entire thing engrossing. I
read the paper over once, but I'm studying it again in greater detail.

I was just interested in discussing it a bit...

best to you,

Joseph

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

/tuning/topicId_33601.html#33671

> i'm surprised to hear you say that, given the imaginative
mechanisms you've proposed for new wind and brass instruments. it
seems that 72 would be far more practical, since one could preserve a
musician's lifetime of training in 12-equal, and then use the
electronic keying technology to provide a way, with just a couple of
extra buttons, to inflect by a twelfth-tone, by a sixth-tone, and by
a quarter-tone. and you're done!

*YES!* Or even, possibly, with *conventional* fingerings and a *FOOT
PEDAL* or some such to affect the three "inflections!"

>
> > My new approach employs easy-to-learn fingerings
> > that partially build on existing (12-EDO) patterns and carry over
> > from one tonal system to another. This can be implemented in
multi-system brass instruments that would allow a player to have 17,
19, 22, 24, 31, 36, and 41-EDO (and perhaps others) all in a single
> four-valve instrument.
>
> well this sounds fascinating. but you are aware that even the
> standard trumpet does not play in anything like 12-equal without a
> large amount of training on the part of the performer. i'm
wondering what the result would be for unfamiliar equal temperaments.
does your system overcome these difficulties as well?

****I was thinking about that, too, while reading the entire Ozzard-
Low study. There's *lots* of training involved in *any* new system
with acoustic instruments!

JP

In-Reply-To: <a3n58p+mcnp@eGroups.com>
paulerlich wrote:

> in case you wanted the specifics on this, you'll find it at the top of
>
> http://x31eq.com/limit15.txt (thanks graham)
>
> where you can discover that two 29-equal cycles, tuned 15.563 cents
> apart, would give the 15-limit ogdoads with a maximum error in any
> interval of 4.695 cents from just.

29-equal is already 15-limit consistent, so you could get these results by
bending the 15.6 cents on an instrument designed for 29-equal. Or even if
you could add an extra valve or hole to move the 15.6 cents from the
default tuning. 29-equal is close to Pythagorean, so this might be
practical on a brass instrument.

You could also fret a qui tar to 29-equal, and tune the strings in neutral
thirds. With equal thirds that'd give 58-equal in a fairly convenient
way. Make them unequal and you lose half the chords, but gain in
accuracy.

But generally, how easy is it to add an arbitrary "comma shift" key to a
woodwind instrument? I was also wondering if you could build a woodwind
around an unequal decimal scale, and add some kind of switch for getting
the quommas for Blackjack-1. Would it have to be a particular shift of
frequency or wavelength rather than pitch? It may even be that you could
pitch-bend for the quommas with a consistent timbre.

Graham

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > By the way, in my valve plan, the first and second valves do
> exactly
> > the same thing they do now, which is to lower the pitch by a
major
> > 2nd and minor 2nd, respectively, so that the great majority of
the
> > fingerings previously learned carry right over to the microtonal
> > instrument, which is not bad for carrying over one's existing
> > training.
>
> but what i was referring to, george, is the fact that the interval
> that the two valves together lower the pitch by, is not exactly the
> sum of the intervals that the two valves separately lower the pitch
> by. i was just wondering if you were taking this effect into
account,
> and how.

The shortfall in tube length caused by the addition of the first and
second valves is not enough to cause a serious problem (maximum
departure of 5.0 cents in 31-EDO once the valve slides are adjusted
properly), considering that corrections of this small magnitude can
be easily compensated for by an adjustment in the player's
embouchure. A compensating mechanism is used for the third valve
(which in my plan alters the pitch by 4:5 instead of a minor third;
there are a couple of very good reasons for doing this), which brings
alternate lengths of tubing into play for the other valves and keeps
the maximum departure to 5.0 cents. In 22-EDO the maximum departure
goes up to 6.9 cents, whereas in 41-EDO it drops to 4.4 cents; in 19-
EDO it is 5.4 cents. (These are for the best fingerings; the lower-
numbered systems have some alternate fingerings, some of which have a
greater departure from the theoretically correct length for the EDO.)

Notice that I used the term "departure" to indicate a difference (in
the equivalent number of cents) of the actual tube length from that
which would be theoretically exact for a given EDO. I believe that
this term (which originated with Bosanquet) is preferable to "error"
or "deviation" for this purpose (which terms are generally used to
describe the difference in cents of an interval from its just or
rational value). Perhaps "departure" would be a good term to add to
Monz's tuning dictionary. (If so, let me know, Joe, and I will give
you the reference, if you don't already have it.)

I have all of these figures on a spreadsheet, but some explanation
would be required. Perhaps it would be good to present this soon,
once we have gotten the notation discussion finished.

By the way, I should add one disclaimer: 41-EDO has too many tones to
permit it to follow conventional usage of the first and second
valves; but everything else, from 36-EDO down, does, with the first
and second valves together producing (where possible) a close
approximation of a 5:6 alteration in pitch (the one notable
exception: 17-EDO).

>
> > The problem with 72-EDO is that it requires another valve -- more
> > complicated and more expensive to make, although (now that I
think
> > about it) I did come up with another idea recently that would
> > completely change the picture. Hmmm -- I need to give that some
> more
> > thought; it's really different!
>
> ok -- i was thinking more in terms of reed instruments, rather than
> brasses.

Woodwind instruments with discrete keying for 72-EDO would be a lot
more complicated, involving a lot of tone holes, not to mention the
problem of coming up with fingerings for all of those notes; it's not
impossible, but I have the impression that, in order to maintain both
a sufficient amount of logical order and fingering facility, it would
have to be very different from what woodwind players are currently
accustomed to. (By the way, I have some woodwind background too. I
played the clarinet and bass clarinet in high school, and I once took
a college course in which I spent 9 weeks apiece learning to play the
oboe and bassoon.)
>
> > What I like about 31 is that it preserves the conventional
diatonic
> > system and is least disruptive to established harmonic norms.
>
> right.
>
> > Considering all the fuss lately about "major third 1/12 down" in
72
> > (will the real major third please stand up), this is easily
avoided
> > in 31.
>
> until you start playing augmented chords or schubert or "giant
steps"
> by coltrane.

Any system has its trade-offs, its own unique combination of
capabilities and limitations, and anybody who wants to get into
microtonality is just going to have to face the fact that there is
going to be some sort of readjustment in one's way of thinking. I
just happen to believe that 31-EDO is least disorienting, while
offering some new harmonic materials that are reasonably well in
tune. If I can come up with a just (or near-just) tonal system that
suits my purposes and will map consistently into 31 (which I have), I
would then have the option to build instruments of fixed pitch tuned
to this and use them in combination with orchestral instruments (of
flexible pitch) in 31. (If you don't care for 31, the same could be
done with 41 or perhaps something else.) This is how I envision
the "big picture."
>
> > In 72 you have to train to handle more than one kind of major
> > third, which can get downright confusing, considering current
> musical
> > training.
> >
> > And what I like about 41
>
> where you'd also have to train to handle more than one kind of
major
> third -- farther from 12-tET and farther from just, respectively,
> than the two kinds in 72.

That's just one of those trade-offs; it all depends on what you want
to do.

> > is that you have complete consistency in the
> > 15 limit.
>
> glad you're enjoying the consistency concept that i came up with.
> looking deeper, though, one finds that each equal temperament has
its
> own set of "identities" or "equivalencies" or "unison vectors"
which
> will determine compositional behavior to a large extent -- for
> example in determining MOS or omnitetrachordal scales where
> Krumhansl's psychological conditions for the encoding of tonal
> information may be satisfied. 41 has some very specific things that
> it can and can't do, and one can look at 46, for example, a 13-
limit
> consistent equal temperament, and see a whole host of possibilities
> that 41 misses.

I have always believed in a multi-system approach, so I think you've
made a couple of points here for a position which I already hold, one
which leaves the door open to pursue one's preference(s). I just
want to make sure that we don't give those who wish to pursue some of
these other systems the impression that we are excluding them in our
rush to embrace 72-EDO as some sort of "standard."

And what about some of those other systems?

But for a small fraction of a cent 46-EDO misses 17-limit consistency
for a single pair of intervals (15/13 & 26/15)! I don't think this
precludes using it for 17-limit harmony (no EDO of lower number can
compete with it), and I know from experience that 15-limit harmonies
can be successfully employed in 31-EDO without any disorientation
whatsoever (with 13 being implied, much more successfully, in my
opinion, than 7 is in 12-EDO), even if you have a couple of pairs of
intervals that go over the boundary of consistency by a couple of
cents or so. (The same can be said for 19/13 and 26/19 in 72-EDO.)
I would compare this to briefly driving a car very slightly onto the
shoulder, but not far enough off the road to lose control. (However,
if you are really a nut for consistency, try 311-EDO -- to the 41
limit!)

I have been familiar with the concept of consistency for almost as
long as I have been exploring microtonality (which has spanned some
38 years), and I even used the term "inconsistent" in my own notes to
indicate the lack thereof in certain tonal systems, most notably 24-
EDO, so it is quite natural for me to refer to it, not only for the
way in which just intervals are represented in various EDO's, but
also for the suitability of mapping just intervals onto various
divisions of the octave (VDO's? or various DO's?), for which latter
case 31-DO is suitable for some rational-interval or near-just
tunings at least up to the 25 limit.

This said, I am also aware that you have formally developed the
concept of consistency quite a bit beyond the simple way in which I
have employed it, for which accomplishment you richly deserve credit
and recognition.

> also, joseph's question about favoring equal temperaments uber
alles
> merits a little more attention. 29-equal is also consistent, but
not
> very accurate, through the 15-limit. but graham breed recently
> reminded us that *two* 29-equal chains, a few cents apart, gives
you
> outstanding accuracy in the 15-limit, not to mention a great wealth
> of modulational and transpositional freedom. given the desiderata
of
> fewer than sixty notes per octave, great 15-limit accuracy, and
great
> transpositional freedom, it would be hard to do better than this
> *non*-equal-temperament.

I have prized the 29-DO for the opportunity it provided me in mapping
a certain 15-limit near-just system that is one of my favorite
tunings. This kind of approach, more than just intonation, EDO's,
regular-interval temperaments (RT's?), or even well-temperaments, is
for me the most satisfying implementation of the new harmonic
materials that I have been exploring these many years.

--George

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

> Paul? Are ETs, in general, more "consistent?" or does it depend...

joseph, consistency is only *defined* for equal temperaments. in
addition, i cautioned patrick against applying it to equal
temperaments higher than 34, because at 35 already you have two
viable candidates for the 2:3 and one need not necessarily restrict
oneself to the 'best approximation'. i particularly like 76-equal and
its doubling, 152-equal, because many coherent tonal systems can be
formed within them by exploiting the _different_ approximations one
has for consonant intervals. consistency ceases to be meaningful in
such contexts, let alone for systems like linear temperaments and
other non-equal temperaments.

as to your question to george about blackjack and canasta, no doubt
he will reply that both of these are adequately represented in both
31- and 41-equal . . .

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

> Woodwind instruments with discrete keying for 72-EDO would be a lot
> more complicated, involving a lot of tone holes, not to mention the
> problem of coming up with fingerings for all of those notes;

i thought the point of the electromechanical bit was to take care of
all these automatically. why couldn't one just add a very small
number of 'alteration' keys to the standard 12-equal fingerings, and
have the electromechanical mechanism translate this into the
appropriate coverings of the tone holes for 72-equal??

> Any system has its trade-offs, its own unique combination of
> capabilities and limitations, and anybody who wants to get into
> microtonality is just going to have to face the fact that there is
> going to be some sort of readjustment in one's way of thinking.

well, it's a different order of readjustement if standard 12-equal
pitches and notation are preserved intact.

> I
> just happen to believe that 31-EDO is least disorienting, while
> offering some new harmonic materials that are reasonably well in
> tune.

and i agreed with you fully on that.

> If I can come up with a just (or near-just) tonal system that
> suits my purposes and will map consistently into 31 (which I have),
I
> would then have the option to build instruments of fixed pitch
tuned
> to this and use them in combination with orchestral instruments (of
> flexible pitch) in 31.

interesting. i, for one, have used, and plan to use, 31 in ways that
no just system could adequately represent.

> I have always believed in a multi-system approach, so I think
you've
> made a couple of points here for a position which I already hold,
one
> which leaves the door open to pursue one's preference(s). I just
> want to make sure that we don't give those who wish to pursue some
of
> these other systems the impression that we are excluding them in
our
> rush to embrace 72-EDO as some sort of "standard."

well, if so, then i must be suffering from quite a split personality
disorder! you see, all my microtonal instruments so far, and those
that are currently being built, are in 22-equal or 31-equal. i'm
considering adding 46-equal at some point in the distant future. my
music is based on fixed chord progressions and themes but is often
improvised beyond that. and yet i'm arguing for 72-equal as a way of
introducing microtonality, and consonant harmonies beyond the triad,
to a different sphere -- the sphere of classically trained, literate
musicians who already intonate 12-equal quite accurately and read it
fluently. we have a unique opportunity to build upon this training
and history, to take advantage of all the possibilities it offers us
as composers, by introducing only three new degrees of pitch
alteration, and not dismantling *any* of the structure that has been
built up already. i see this as a vastly more realistic approach,
*for now*, toward acheiving a goal that many composers seek.

> And what about some of those other systems?
>
> But for a small fraction of a cent 46-EDO misses 17-limit
consistency
> for a single pair of intervals (15/13 & 26/15)! I don't think this
> precludes using it for 17-limit harmony

absolutely! see my post today about consistency and 35-equal . . .

> (no EDO of lower number can
> compete with it), and I know from experience that 15-limit
harmonies
> can be successfully employed in 31-EDO without any disorientation
> whatsoever (with 13 being implied, much more successfully, in my
> opinion, than 7 is in 12-EDO),

hmm . . . i suppose this depends on what kind of 15-limit
harmonies . . . certainly i don't feel that about the utonal ones.

> (However,
> if you are really a nut for consistency, try 311-EDO -- to the 41
> limit!)

this comes up here and on tuning-math from time to time.

> I have been familiar with the concept of consistency for almost as
> long as I have been exploring microtonality (which has spanned some
> 38 years), and I even used the term "inconsistent" in my own notes
to
> indicate the lack thereof in certain tonal systems, most notably 24-
> EDO,

well, i'm glad to hear that i wasn't the first person to come up with
this concept, though it seems to have eluded researchers such as
carlos and yunik & swift.

> so it is quite natural for me to refer to it, not only for the
> way in which just intervals are represented in various EDO's, but
> also for the suitability of mapping just intervals onto various
> divisions of the octave (VDO's? or various DO's?), for which latter
> case 31-DO is suitable for some rational-interval or near-just
> tunings at least up to the 25 limit.

i'd love to learn more about this, as would others here, i'm sure.

> This said, I am also aware that you have formally developed the
> concept of consistency quite a bit beyond the simple way in which I
> have employed it,

really? then perhaps i'm misunderstanding something.

> for which accomplishment you richly deserve credit
> and recognition.

i appreciate the sentiment, but actually, i relegated the concept of
consistency to a footnote in my last xenharmonikon paper, and manuel
op de coul performed extensive calculations of it, and paul hahn
extended it with the 'level' concept. i, for one, have never looked
at it as more than a warning against the erroneous evaluation of low-
number equal temperaments (below 35) based on isolated dyads, for
example in the studies by carlos and yunik & swift.

> > also, joseph's question about favoring equal temperaments uber
> alles
> > merits a little more attention. 29-equal is also consistent, but
> not
> > very accurate, through the 15-limit. but graham breed recently
> > reminded us that *two* 29-equal chains, a few cents apart, gives
> you
> > outstanding accuracy in the 15-limit, not to mention a great
wealth
> > of modulational and transpositional freedom. given the desiderata
> of
> > fewer than sixty notes per octave, great 15-limit accuracy, and
> great
> > transpositional freedom, it would be hard to do better than this
> > *non*-equal-temperament.
>
> I have prized the 29-DO for the opportunity it provided me in
mapping
> a certain 15-limit near-just system that is one of my favorite
> tunings. This kind of approach, more than just intonation, EDO's,
> regular-interval temperaments (RT's?), or even well-temperaments,
is
> for me the most satisfying implementation of the new harmonic
> materials that I have been exploring these many years.

are any of these published or recorded in any form?

--- In tuning@y..., Afmmjr@a... wrote:
> Well to be honest, there is more hoopla than need IMO. A clarinet
and a
> flute and a bassoon and an oboe can all play microtones with
conviction, and
> do. Below is a small list of wind players:
>
> On flute: Stefani Starin (Newband) plays deliciously in JI. Andrew
> Bolotowsky can play any tuning system. I've hired numerous flute
players
> (over 20) in a lifetime and was never a problem for them to play
precise
> microtones. Accordingly, play microtonal recorder in any tuning.
>
> On clarinet: Michiyo Suzuki can play, and does play, anything.
Anyone could
> if they tried.
>
> On bassoon: Yup bassoon out of tune for 1851 Berlioz, but now able
to play in
> any tuning of any kind using different fingering combinations -- or
> "grippings." All bassoonists are using my fingerings. Enough with
the old
> canard about the fingerings being so different from one player to
another.
> Usually only one or a few are slightly different.
>
> On oboe: Admiringly, no one has taken the reins more than Heinz
Holliger,
> himself. There is no doubt that the specificity is there, as soon
as an
> oboist can imagine the notes in his head correctly. This is a
treasure trove
> for multiphonic extremes thanks to the ease of changing
multiphonics, and the
> ease to circular breathe on oboe.
>
> On horn: Greg Evans can play in any tuning with authority and
suave
> (presently teaching in New Mexico). He has raised the bar.
>
> On trombone: Julie Josephson and Chris Washburne has proved that
they hear
> everything...and can play it repeatedly.
>
> On tuba: Dave Grego with his quartertone tuba has played everything
I can
> throw at him (check him in my piece "Atlantis").
>
> Strings: Tom Chiu, Dave Eggar, Matt Fields...these guys eat
college
> professors for breakfast. There is no comparison between what they
are
> playing and what people are teaching...light years apart.
>
> Percussion: natural microtonal citizens in their genesis.
>
> Vocals? Now why not try a new vocal instrument for the future?
>
> Best, Johnny Reinhard

It is all very wonderful that virtuosi such as these can do such
amazing things with instruments that, in the majority of cases, were
never intended or expected to be used for this purpose (the strings
and trombone being the most notable exceptions) -- especially if they
can do it with any decent sort of tone at a quick tempo.

But what about the great majority of us, who are something less than
technical superheroes, who find it enough of a challenge to play
these instruments in the ways that they were *intended* to be
played? If microtonality is going to be so difficult to achieve that
it is going to be beyond the reach of all but an elite group, then
there is no chance of its becoming a part of the musical mainstream,
achievable by unexceptional amateur musicians, and it will be doomed
to remain a very small niche in the world of music.

This, I submit, is the compelling reason for the creation of
microtonal instruments.

--George

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > If I can come up with a just (or near-just) tonal system that
> > suits my purposes and will map consistently into 31 (which I
have),
> I
> > would then have the option to build instruments of fixed pitch
> tuned
> > to this and use them in combination with orchestral instruments
(of
> > flexible pitch) in 31.
>
> interesting. i, for one, have used, and plan to use, 31 in ways
that
> no just system could adequately represent.

All that I'm trying to do here is to make the point that, inasmuch as
I have stated that I believe that it would be best to construct
microtonal instruments of flexible pitch (i.e., most orchestral
instruments) in whatever we might consider to be the "best" or most
useful EDO's, that would in no way mandate that instruments of fixed
pitch that might be used in conjunction with them be limited to
EDO's. Conversely, constructing fixed-pitch instruments in just or
near-just tunings would in no way exclude flexible-pitch instruments
from being used in conjunction with those fixed-pitch instruments.
Of course, it is the responsibility of the composer to ensure that
the just or near-just tuning will be compatible with the choice of
EDO, but that's something that must be accepted if you want the
freedom to design your own tuning system.

By the way, the "(which I have)" system that I referred to above is
the one that I intend to start composing in. It's a near-just 15-
limit system of only 17 tones/octave, and it maps consistently
(meaning: like intervals span the same number of degrees within the
system) onto 17, 31, and 41. Mapped onto 31 or 41 there will, of
course, be a lot of vacant positions in the mapping; but instruments
of flexible pitch in either of those EDO's could be used to play
parts written in my 17-tone near-just system.

> > (no EDO of lower number can
> > compete with it), and I know from experience that 15-limit
> harmonies
> > can be successfully employed in 31-EDO without any disorientation
> > whatsoever (with 13 being implied, much more successfully, in my
> > opinion, than 7 is in 12-EDO),
>
> hmm . . . i suppose this depends on what kind of 15-limit
> harmonies . . . certainly i don't feel that about the utonal ones.

Good point! I had only otonal ones in mind.

> > I have been familiar with the concept of consistency for almost
as
> > long as I have been exploring microtonality (which has spanned
some
> > 38 years), and I even used the term "inconsistent" in my own
notes
> to
> > indicate the lack thereof in certain tonal systems, most notably
24-
> > EDO,
>
> well, i'm glad to hear that i wasn't the first person to come up
with
> this concept, though it seems to have eluded researchers such as
> carlos and yunik & swift.

I think that, considering some of our early correspondence, that both
Erv Wilson and I thought that the concept was so obvious that we took
it for granted.

> > so it is quite natural for me to refer to it, not only for the
> > way in which just intervals are represented in various EDO's, but
> > also for the suitability of mapping just intervals onto various
> > divisions of the octave (VDO's? or various DO's?), for which
latter
> > case 31-DO is suitable for some rational-interval or near-just
> > tunings at least up to the 25 limit.
>
> i'd love to learn more about this, as would others here, i'm sure.
>
> > This said, I am also aware that you have formally developed the
> > concept of consistency quite a bit beyond the simple way in which
I
> > have employed it,
>
> really? then perhaps i'm misunderstanding something.

I had the idea of "levels" in mind, but I guess it was I who
misunderstood, inasmuch as you also mentioned that Paul Hahn extended
consistency to levels. Anyway, you were the one who was perceptive
enough to consider that consistency might not be so obvious to a lot
of people. So you get credit for raising and answering an important
consideration, which then prompted others to develop this idea.

> > I have prized the 29-DO for the opportunity it provided me in
> mapping
> > a certain 15-limit near-just system that is one of my favorite
> > tunings. This kind of approach, more than just intonation,
EDO's,
> > regular-interval temperaments (RT's?), or even well-temperaments,
> is
> > for me the most satisfying implementation of the new harmonic
> > materials that I have been exploring these many years.
>
> are any of these published or recorded in any form?

Yes, if you're willing to dig through some back issues of
Xenharmonikon (somewhere in III to V for the 29-tone tuning, which
also maps consistently onto 41) or Interval (in one of the early
issues for the 17-tone tuning), but what was written there is at best
sketchy and sometimes misleading. It would be best if I rewrote some
of this as *Buried Treasure* articles.

--George

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

> All that I'm trying to do here is to make the point that, inasmuch
as
> I have stated that I believe that it would be best to construct
> microtonal instruments of flexible pitch (i.e., most orchestral
> instruments) in whatever we might consider to be the "best" or most
> useful EDO's, that would in no way mandate that instruments of
fixed
> pitch that might be used in conjunction with them be limited to
> EDO's.

ah . . . ok, so this was in reply to joseph. it's often hard to keep
all the threads straight!

> By the way, the "(which I have)" system that I referred to above is
> the one that I intend to start composing in. It's a near-just 15-
> limit system of only 17 tones/octave, and it maps consistently
> (meaning: like intervals span the same number of degrees within the
> system)

this alternate meaning of consistency is one that is often found as
well, especially in graham breed's writings (monz take note).

> onto 17, 31, and 41. Mapped onto 31 or 41 there will, of
> course, be a lot of vacant positions in the mapping; but
instruments
> of flexible pitch in either of those EDO's could be used to play
> parts written in my 17-tone near-just system.

may i ask you to reveal the system in its true tuning?

> > > (no EDO of lower number can
> > > compete with it), and I know from experience that 15-limit
> > harmonies
> > > can be successfully employed in 31-EDO without any
disorientation
> > > whatsoever (with 13 being implied, much more successfully, in
my
> > > opinion, than 7 is in 12-EDO),
> >
> > hmm . . . i suppose this depends on what kind of 15-limit
> > harmonies . . . certainly i don't feel that about the utonal ones.
>
> Good point! I had only otonal ones in mind.

with four or five notes or more, i presume?

> > > I have been familiar with the concept of consistency for almost
> as
> > > long as I have been exploring microtonality (which has spanned
> some
> > > 38 years), and I even used the term "inconsistent" in my own
> notes
> > to
> > > indicate the lack thereof in certain tonal systems, most
notably
> 24-
> > > EDO,
> >
> > well, i'm glad to hear that i wasn't the first person to come up
> with
> > this concept, though it seems to have eluded researchers such as
> > carlos and yunik & swift.
>
> I think that, considering some of our early correspondence, that
both
> Erv Wilson and I thought that the concept was so obvious that we
took
> it for granted.

well, it's not a difficult concept, but clearly there were those,
even among musical geniuses, to whom it was not obvious.

> I had the idea of "levels" in mind, but I guess it was I who
> misunderstood, inasmuch as you also mentioned that Paul Hahn
extended
> consistency to levels.

and i personally disagree with paul hahn about the utility of
these "levels", as multiple-number ratios of a particular limit, for
me, only succeed insofar as they arise from combinations of the level-
1 ('consonant') intervals, and if constituent ratios *within* the
limit are approximated well enough, then any combination of them will
succeed (in my experience), regardless of the deviation from
the "true" "just" realizations of these multiple-number ratios. note
that for the purposed of this argument, ratios of 9 are not
considered multiple-number ratios if the limit is 9 or higher . . .

> Anyway, you were the one who was perceptive
> enough to consider that consistency might not be so obvious to a
lot
> of people. So you get credit for raising and answering an
important
> consideration, which then prompted others to develop this idea.

thank you! i wonder how many other ideas you and erv wilson may have
come up with, that similarly need to be disseminated more widely . . .

> > > I have prized the 29-DO for the opportunity it provided me in
> > mapping
> > > a certain 15-limit near-just system that is one of my favorite
> > > tunings. This kind of approach, more than just intonation,
> EDO's,
> > > regular-interval temperaments (RT's?), or even well-
temperaments,
> > is
> > > for me the most satisfying implementation of the new harmonic
> > > materials that I have been exploring these many years.
> >
> > are any of these published or recorded in any form?
>
> Yes, if you're willing to dig through some back issues of
> Xenharmonikon (somewhere in III to V for the 29-tone tuning, which
> also maps consistently onto 41) or Interval (in one of the early
> issues for the 17-tone tuning), but what was written there is at
best
> sketchy and sometimes misleading. It would be best if I rewrote
some
> of this as *Buried Treasure* articles.

this would be much appreciated, as i'd like to absorb and respond to
your ideas in their latest form . . .

BTW, where do you live (you can reply off-list if you like)?

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

/tuning/topicId_33601.html#33708

> > By the way, the "(which I have)" system that I referred to above
is
> > the one that I intend to start composing in. It's a near-just 15-
> > limit system of only 17 tones/octave, and it maps consistently
> > (meaning: like intervals span the same number of degrees within
the
> > system)
>
> this alternate meaning of consistency is one that is often found as
> well, especially in graham breed's writings (monz take note).
>

****This isn't so great, is it? These *two* ideas of "consistency"
are *totally* different, if I'm understanding them correctly.
Shouldn't there be another term for *one* of them??

?

JP

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

> > By the way, the "(which I have)" system that I referred to above is
> > the one that I intend to start composing in. It's a near-just 15-
> > limit system of only 17 tones/octave, and it maps consistently
> > (meaning: like intervals span the same number of degrees within the
> > system)

> this alternate meaning of consistency is one that is often found as
> well, especially in graham breed's writings (monz take note).

That seems to be related to the epimorphic property; it would be nice to agree on some "consistent" definitions and sort all this out.

> well, it's not a difficult concept, but clearly there were those,
> even among musical geniuses, to whom it was not obvious.

Then there are others to whom it is sometimes a sort of fetish. :)

a musical demonstration:

http://artists.mp3s.com/artist_song/369/369685.html

i can no longer listen to this via internet explorer but perhaps
you'll have better luck

please listen a few times and try not too laugh too hard at the
technical incompetency -- mapping the fifth to a minor tenth on the
keyboard makes for a tough reach for these small hands

listen to the piece a few times. then, if you have much experience
with ji or similar systems, you should be able to hear where the
chord change implies a movement of 256:243. it sounds like a
perfectly convincing 256:243 movement, functioning exactly as
strongly as it would in ji. yet the paul hahn consistency levels (or
any associated 'level'-based accuracy measure) for 22-equal in the 3-
, 5-, and 7-limits are 3, 2, and 1. in all cases the implication is
that 22-equal is somehow limited in its ability to evoke the 256:243
function.

the alternative implication is that the ratio involved must be evoked
vertically, not horizontally. but this would imply a 243-limit or
higher! clearly this is beyond our human capabilities -- even partch
admitted that comparing a ratio of 25 with intervals near to it, one
cannot detect any decrease in consonance, only a slight slowing-down
or speeding-up of the beating.

so i can't see what musical meaning a 'level'-based accuracy measure,
or its associated consistency concept, could have.

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

> so i can't see what musical meaning a 'level'-based accuracy measure,
> or its associated consistency concept, could have.

My take on it remains that normally we are using a single particular temperament, and that 22-et is not really a temperament until we specify a mapping to primes.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> > so i can't see what musical meaning a 'level'-based accuracy
measure,
> > or its associated consistency concept, could have.
>
> My take on it remains that normally we are using a single
>particular temperament, and that 22-et is not really a temperament
>until we specify a mapping to primes.

i think the mapping to primes 3, 5, and 7 is very clear in this case.
but what does this have to do with paul hahn's levels?

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

> > My take on it remains that normally we are using a single
> >particular temperament, and that 22-et is not really a temperament
> >until we specify a mapping to primes.

> i think the mapping to primes 3, 5, and 7 is very clear in this case.
> but what does this have to do with paul hahn's levels?

My point is that if you work with a mapping to primes already given, both simple consistency and consistency with levels become a way of measuring relative accuracy of intonation. Do you see an additional meaning to it beyond that?

<<paul hahn consistency levels (or
any associated 'level'-based accuracy measure) for 22-equal in the 3-
, 5-, and 7-limits are 3, 2, and 1. in all cases the implication is
that 22-equal is somehow limited in its ability to evoke the 256:243
function.
>>

Hi Paul, I was introduced to the ideas about consistency, completeness and
diameter through Patrick's work. Does your example really have much to do
with the consistency concept? The whole concept as I understand it involves
the compounding of errors, which is really only at issue with sequences of
intervals analyzed (heard) simultaneously. Errors accrue more quickly in
systems which are less consistent. If we want an ET system that suppies one
acceptable 256:243 approximation, we can take our pick, but if we want an ET
system which allows us to map consecutive intervals without landing on the
"wrong" scale step, then we choose one with a high level of consistency. We
can always choose the "wrong" step to map the compounded interval. The point
is that if we break it up into its constituent parts as a sequence of
intervals, it doesn't work. So it all depends how we want to write music.
Errors can be hidden all over the place. If we want the most freedom in
terms of harmonic combinatoriality of intervals, we should choose a managable
ET with a high degree of consistency. Don't you agree?

thanks,
Aaron

--- In tuning@y..., Pitchcolor@a... wrote:

Errors accrue more quickly in
> systems which are less consistent.

Errors compound to larger errors if they are larger to start with, and to relatively larger errors if they are relatively larger to start with.

If we want an ET system that suppies one
> acceptable 256:243 approximation, we can take our pick, but if we want an ET
> system which allows us to map consecutive intervals without landing on the
> "wrong" scale step, then we choose one with a high level of consistency.

You need to define what you mean by "wrong" in this particular instance, and then see if the system in question is or is not doing what you want it to do. It can easily be the case that to land on the "right" interval, you *need* a certain approximation, so I don't think consistency is relevant to this sort of problem.

Paul,

Here's something I missed earlier:

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > Woodwind instruments with discrete keying for 72-EDO would be a
lot
> > more complicated, involving a lot of tone holes, not to mention
the
> > problem of coming up with fingerings for all of those notes;
>
> i thought the point of the electromechanical bit was to take care
of
> all these automatically. why couldn't one just add a very small
> number of 'alteration' keys to the standard 12-equal fingerings,
and
> have the electromechanical mechanism translate this into the
> appropriate coverings of the tone holes for 72-equal??

And if most or all of one's available fingers are already busy
performing the standard 12-equal fingerings, then where are you going
to come up with fingers to operate these keys?

--George

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> ... instruments
> > of flexible pitch in either of those EDO's could be used to play
> > parts written in my 17-tone near-just system.
>
> may i ask you to reveal the system in its true tuning?

Yes. You are asking this before you got to the end of my message,
where I mentioned that I would have to write this up as a separate
article. As with a number of other things that I have come up with,
there is a story behind it.

>
> > > > ... I know from experience that 15-limit harmonies
> > > > can be successfully employed in 31-EDO without any
> disorientation
> > > > whatsoever (with 13 being implied, much more successfully, in
> my
> > > > opinion, than 7 is in 12-EDO),
> > >
> > > hmm . . . i suppose this depends on what kind of 15-limit
> > > harmonies . . . certainly i don't feel that about the utonal
ones.
> >
> > Good point! I had only otonal ones in mind.
>
> with four or five notes or more, i presume?

Yes, in most cases, although I think you can successfully imply, for
example, 8:10:13 or 10:13:16, if the chords preceding or following
provide the proper harmonic context.

[Re: consistency]
> well, it's not a difficult concept, but clearly there were those,
> even among musical geniuses, to whom it was not obvious.
>
> > I had the idea of "levels" in mind, but I guess it was I who
> > misunderstood, inasmuch as you also mentioned that Paul Hahn
> extended
> > consistency to levels.
>
> and i personally disagree with paul hahn about the utility of
> these "levels", as multiple-number ratios of a particular limit,
for
> me, only succeed insofar as they arise from combinations of the
level-
> 1 ('consonant') intervals, and if constituent ratios *within* the
> limit are approximated well enough, then any combination of them
will
> succeed (in my experience), regardless of the deviation from
> the "true" "just" realizations of these multiple-number ratios.
note
> that for the purposed of this argument, ratios of 9 are not
> considered multiple-number ratios if the limit is 9 or higher . . .

I remembered "levels" from reading Patrick Ozzard-Low's paper, but I
didn't pay much attention to that, because it didn't impress me as
being very useful. It's nice to see that we agree on that.

>
> > Anyway, you were the one who was perceptive
> > enough to consider that consistency might not be so obvious to a
> lot
> > of people. So you get credit for raising and answering an
> important
> > consideration, which then prompted others to develop this idea.
>
> thank you! i wonder how many other ideas you and erv wilson may
have
> come up with, that similarly need to be disseminated more
widely . . .

Probably not much more than that. Erv came up with quite a few
things, and, if any of those duplicated my work up to the time we
first made contact (~December 1974), it was almost a sure bet that he
did it first. Almost.

--George

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > --- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
>
> > > My take on it remains that normally we are using a single
> > >particular temperament, and that 22-et is not really a
temperament
> > >until we specify a mapping to primes.
>
> > i think the mapping to primes 3, 5, and 7 is very clear in this
case.
> > but what does this have to do with paul hahn's levels?
>
> My point is that if you work with a mapping to primes already
>given, both simple consistency and consistency with levels become a
>way of measuring relative accuracy of intonation. Do you see an
>additional meaning to it beyond that?

no -- thus the subject line. it seems we are in agreement.

--- In tuning@y..., graham@m... wrote:
> In-Reply-To: <a3n58p+mcnp@e...>
> paulerlich wrote:
>
> > in case you wanted the specifics on this, you'll find it at the
top of
> >
> > http://x31eq.com/limit15.txt (thanks graham)
> >
> > where you can discover that two 29-equal cycles, tuned 15.563
cents
> > apart, would give the 15-limit ogdoads with a maximum error in
any
> > interval of 4.695 cents from just.
>
> 29-equal is already 15-limit consistent, so you could get these
results by
> bending the 15.6 cents on an instrument designed for 29-equal. Or
even if
> you could add an extra valve or hole to move the 15.6 cents from
the
> default tuning. 29-equal is close to Pythagorean, so this might be
> practical on a brass instrument.

If we're talking about instruments of flexible pitch, I think we're
better off just using instruments in 41-EDO. Adjustment of
intonation by the small amounts (<8.5 cents) required in that system
is easily achievable by anyone who has learned how to play in tune.

For instruments of fixed pitch, this starts to come close to my 29-
tone 15-limit near-just system, which has a maximum error of <3.25
cents for the 15-limit consonances and is compatible with flexible-
pitch instruments in 41-EDO. (Golly, I'm just going to have write
this one up really soon, because I'll be keeping everyone in
suspenders again until I do!)

> You could also fret a qui tar to 29-equal, and tune the strings in
neutral
> thirds. With equal thirds that'd give 58-equal in a fairly
convenient
> way. Make them unequal and you lose half the chords, but gain in
> accuracy.

I don't do guitar, so no comment.

> But generally, how easy is it to add an arbitrary "comma shift" key
to a
> woodwind instrument? I was also wondering if you could build a
woodwind
> around an unequal decimal scale, and add some kind of switch for
getting
> the quommas for Blackjack-1. Would it have to be a particular
shift of
> frequency or wavelength rather than pitch? It may even be that you
could
> pitch-bend for the quommas with a consistent timbre.

Again, as Paul Erlich predicted, I would say for Blackjack and
Canasta, 41-EDO instruments are my quick reply to this one (in answer
to your question, Joseph). It's possible that a 72-EDO subset that
took in all the required pitches could be worked out with my
convertible-brass-instrument design (conversion being done by
adjusting valve slides, where possible, or otherwise swapping out
crooks of tubing -- in answer to your question, Paul). But a
microtonal approach to woodwinds is something that I have only
recently begun to think about, so I haven't yet given this enough
thought to come to any conclusions about whether certain things might
or might not be practical for these instruments. Thinking these
things through takes time, and sometimes I have to leave them off for
a while and work on something else, and then come back and take a
fresh look at whatever problem I was trying to solve.

--George

--- In tuning@y..., Pitchcolor@a... wrote:
> <<paul hahn consistency levels (or
> any associated 'level'-based accuracy measure) for 22-equal in the
3-
> , 5-, and 7-limits are 3, 2, and 1. in all cases the implication is
> that 22-equal is somehow limited in its ability to evoke the
256:243
> function.
> >>
>
> Hi Paul, I was introduced to the ideas about consistency,
completeness and
> diameter through Patrick's work.

excellent.

> Does your example really have much to do
> with the consistency concept?

with paul hahn's consistency levels, yes.

> The whole concept as I understand it involves
> the compounding of errors, which is really only at issue with
sequences of
> intervals analyzed (heard) simultaneously.

do you really mean sequences (as in music), or do you really mean
simultaneously?

> Errors accrue more quickly in
> systems which are less consistent. If we want an ET system that
suppies one
> acceptable 256:243 approximation, we can take our pick, but if we
want an ET
> system which allows us to map consecutive intervals without landing
on the
> "wrong" scale step, then we choose one with a high level of
consistency.

this sounds like an argument for the original secor/wilson/erlich
definition of consistency, without paul hahn's 'levels'. are you sure
you understand paul hahn's 'levels'?

> We
> can always choose the "wrong" step to map the compounded interval.
The point
> is that if we break it up into its constituent parts as a sequence
of
> intervals, it doesn't work. So it all depends how we want to write
music.

i guess i agree with gene on this.

> Errors can be hidden all over the place. If we want the most
freedom in
> terms of harmonic combinatoriality of intervals, we should choose a
managable
> ET with a high degree of consistency. Don't you agree?

a high degree of consistency, yes. a high level of consistency, no.
to me, 256:243 is the interval produced by stacking five fourths --
not an interval that one can understand as an isolated simultaneous
dyad. when harmonic progressions are proceeding by a lot of fourths,
256:243 represents a certain distance along this chain of
progressions. the progressions, and the ability to understand where
you are within them, depend not a whit on the accuracy of
the 'tempered 256:243' vs. the 'just 256:243' -- unless you're so
used to listening to ji that anything else confuses you. as long as
the fourths themselves are recognizable by the auditory system as 4:3
ratios, everything else follows.

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

> You need to define what you mean by "wrong" in this particular
>instance, and then see if the system in question is or is not doing
>what you want it to do. It can easily be the case that to land on
>the "right" interval, you *need* a certain approximation,

this is a very good point -- western common practice diatonic music
provides an excellent example of this. too high a hahn level of
consistency would be troublesome for this style; similarly for my
pajara music as well as anything in MIRACLE.

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> Paul,
>
> Here's something I missed earlier:
>
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> >
> > > Woodwind instruments with discrete keying for 72-EDO would be a
> lot
> > > more complicated, involving a lot of tone holes, not to mention
> the
> > > problem of coming up with fingerings for all of those notes;
> >
> > i thought the point of the electromechanical bit was to take care
> of
> > all these automatically. why couldn't one just add a very small
> > number of 'alteration' keys to the standard 12-equal fingerings,
> and
> > have the electromechanical mechanism translate this into the
> > appropriate coverings of the tone holes for 72-equal??
>
> And if most or all of one's available fingers are already busy
> performing the standard 12-equal fingerings, then where are you going
> to come up with fingers to operate these keys?

when i played clarinet i don't think i ever used all my fingers. but giving you the benefit of the doubt, how about a simple footpedal?

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

> Yes, in most cases, although I think you can successfully imply, for
> example, 8:10:13 or 10:13:16, if the chords preceding or following
> provide the proper harmonic context.

well, this seems to me to be a bit of a borderline case, highly dependent on timbre and register. but ok, 31 is pretty close to the 35 where i conveniently like to put the threshold of 'consistency mattering'.

glad we agree about paul hahn's consistency levels not mattering.

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> --- In tuning@y..., graham@m... wrote:
> > In-Reply-To: <a3n58p+mcnp@e...>
> > paulerlich wrote:
> >
> > > in case you wanted the specifics on this, you'll find it at the
> top of
> > >
> > > http://x31eq.com/limit15.txt (thanks graham)
> > >
> > > where you can discover that two 29-equal cycles, tuned 15.563
> cents
> > > apart, would give the 15-limit ogdoads with a maximum error in
> any
> > > interval of 4.695 cents from just.
> >
> > 29-equal is already 15-limit consistent, so you could get these
> results by
> > bending the 15.6 cents on an instrument designed for 29-equal. Or
> even if
> > you could add an extra valve or hole to move the 15.6 cents from
> the
> > default tuning. 29-equal is close to Pythagorean, so this might be
> > practical on a brass instrument.
>
> If we're talking about instruments of flexible pitch, I think we're
> better off just using instruments in 41-EDO. Adjustment of
> intonation by the small amounts (<8.5 cents) required in that system
> is easily achievable by anyone who has learned how to play in tune.

hmm . . . i don't think you can make such a sweeping statement about "better off". it really depends on what equivalencies the composer wishes to exploit. an adaptive 41-tone system and an adaptive 29-tone system may both be great for vertical 15-limit harmonies, but as you seem to have agreed in a different context, there's far more to a tuning system than the quality of its vertical harmonies. for example, adaptive 19-tone and adaptive 22-tone are both wonderful for 5-limit, yet a work of common-practice Western music would come out far better in the former than in the latter.

> For instruments of fixed pitch, this starts to come close to my 29-
> tone 15-limit near-just system, which has a maximum error of <3.25
> cents for the 15-limit consonances and is compatible with flexible-
> pitch instruments in 41-EDO. (Golly, I'm just going to have write
> this one up really soon, because I'll be keeping everyone in
> suspenders again until I do!)

yup . . .

In a message dated 2/5/02 4:49:29 PM Eastern Standard Time, gdsecor@yahoo.com
writes:

> It is all very wonderful that virtuosi such as these can do such
> amazing things with instruments that, in the majority of cases, were
> never intended or expected to be used for this purpose (the strings
> and trombone being the most notable exceptions) -- especially if they
> can do it with any decent sort of tone at a quick tempo.
>
> But what about the great majority of us, who are something less than
> technical superheroes, who find it enough of a challenge to play
> these instruments in the ways that they were *intended* to be
> played?

Hello George. I do appreciate your work as I do Patrick's work. But I think
there may be a few misunderstandings around. I do not think a flute is
intended to play in a tuning so much as it can play most any tuning required.

Similarly, the bassoon is not intended to play in equal temperament as much
as it is intended to play in tune.

If microtonality is going to be so difficult to achieve that
> it is going to be beyond the reach of all but an elite group, then
> there is no chance of its becoming a part of the musical mainstream,
> achievable by unexceptional amateur musicians, and it will be doomed
> to remain a very small niche in the world of music.
>
This is not really true. Foremost, great recordings and performances will do
more than amateur futzing. More importantly, playing a microtonal fingering
is no more difficult than playing a conventional fingering. Now, if
conventional fingerings are too difficult, then we are not talking about
professional musicians of any caliber.

My list of virtuosi are to signal that the terrain has already been mapped
out. Now, less gifted players can simply following the necessary fingering.
Now, if you want to do away with be able to hear a pitch in the head all
together, I'm not sure what you are really driving at, other than a
microtonal sort of Nintendo. Frankly, having the exact fingerings for a
tuning should be gravy for a composer/player.

And fingerings are FREE! No added expenses beyond a traditional
instrument...other than training.

> This, I submit, is the compelling reason for the creation of
> microtonal instruments.
>
> --George
>
>
>

All support to you and your endeavors. I felt it important to report from
the other side of the issue.

Best, Johnny Reinhard

--- In tuning@y..., Afmmjr@a... wrote:

> Now, if you want to do away with be able to hear a pitch in the head all
> together, I'm not sure what you are really driving at, other than a
> microtonal sort of Nintendo.

let's be fair . . . george's detailed suggestion was quite the opposite of this.
>
> All support to you and your endeavors. I felt it important to report from
> the other side of the issue.
>
> Best, Johnny Reinhard

such is the wonder of a diverse and multifarious list!

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

/tuning/topicId_33601.html#33716

> a musical demonstration:
>
> http://artists.mp3s.com/artist_song/369/369685.html
>
> i can no longer listen to this via internet explorer but perhaps
> you'll have better luck
>
> please listen a few times and try not too laugh too hard at the
> technical incompetency -- mapping the fifth to a minor tenth on the
> keyboard makes for a tough reach for these small hands
>
> listen to the piece a few times. then, if you have much experience
> with ji or similar systems, you should be able to hear where the
> chord change implies a movement of 256:243. it sounds like a
> perfectly convincing 256:243 movement, functioning exactly as
> strongly as it would in ji. yet the paul hahn consistency levels
(or any associated 'level'-based accuracy measure) for 22-equal in
the 3-, 5-, and 7-limits are 3, 2, and 1. in all cases the
implication is that 22-equal is somehow limited in its ability to
evoke the 256:243 function.

****Well, I've heard this piece for a while, and I must confess I'm
still unclear where the 256:243 is... However, I did notice something
that I hadn't noticed before in less "critical" listenings and that
is that the top line seems to descend chromatically through the
entire 22-tET scale. Is that what's going on. Sure sounds like it...

Joseph

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

/tuning/topicId_33601.html#33728

> > i thought the point of the electromechanical bit was to take care
> of all these automatically. why couldn't one just add a very small
> > number of 'alteration' keys to the standard 12-equal fingerings,
> and have the electromechanical mechanism translate this into the
> > appropriate coverings of the tone holes for 72-equal??
>
> And if most or all of one's available fingers are already busy
> performing the standard 12-equal fingerings, then where are you
going to come up with fingers to operate these keys?
>
> --George

Alright... I was going to wait until I had *completely* studied the
Ozzard-Low the *second* time, but I've *almost* done that, so it's
time to comment! :)

Over the holidays, I visited a friend in Michigan who sells pianos.
He's *always* handled *acoustic* pianos, mostly uprights, but tried a
beautiful store with magnificent concert grands. That enterprise
failed miserably...

In any case, he was asking me about MIDI keyboards and so forth a few
years ago. Apparently he didn't know much about them.

However, *this* year I asked him about his business and I asked him
what percentage of *electronic* pianos he was selling *this* year.

His answer? That's all I'm selling now...

There has been a seismic shift toward electronic instruments in the
last few years and, of course, this trend has been coupled with the
microprocessing of computers. This is one reason, I believe, that
microtonality is going more and more into the mainstream. *More*
people own equipment that can play microtonality... mostly MIDI
keyboards, than ever before.

There have also been other important aesthetic changes. A few years
ago electronic composers weren't taken seriously unless they worked
in music schools that had a *lot* of equipment. I *know* because I
was trying to do "independent" work in those days and was
solidly "dissed..."

However, this aesthetic has changed. I've seen "calls for scores"
for electronic instruments of late where the only criterion is that
the sound source is something that one "plugs in!"

And, many groups, such as _Bang on a Can_ in New York, and
other "prestigious" groups have a *wide* variety of electrically-
produced pieces.

So my point? Simply that our current "modern" sound is more
electronic than ever before.

(Ok... I'm waiting for a barrage of disagreement from our "acoustic
set" here... probably Kraig Grady and several others, but I didn't
say *everybody* should do this, only that it's an overall trend...)

If this is true, and of course these are sentiments expressed by Ivor
Darreg before just about anybody, then it means that, quite possibly,
the sound of acoustic instruments is *antiquated.*

Now don't get me wrong. I'm not totally dissing "antiquated..." I'm
just saying that it may turn out that our present orchestral
instruments will be considered species of an "early music"
only "early music" will *eventually* mean the music of the 19th
Century and, possibly, the 20th.

If this is true, (My acoustic "enemies" are now waiting for me in a
dark alley by this time in this short post) then it means the
addition of an electronic component to "traditional" instruments is
not only inevitable, but it will "redefine" the sounds of so-
called "art music."

In other words, we won't *expect* the acoustic sound so much any
more... particularly since sampling is getting so good and an
instrument like, for example, the electronic piano, is sounding "good
enough" to satisfy many people. Sure, the enharmonicity is missing,
and the instrument might not do so well in playing Beethoven or
Chopin, but the point is, nobody is going to *use* that instrument
for "authentic" performances of Beethoven or Chopin.

Beethoven and Chopin will be "early music..." and these pieces will
be performed on "period" instruments, i.e. *ACOUSTIC* pianos, and
hopefully, as Ed Foote does and others, in the *correct* tunings of
the day as well...

So what does this mean for our discussion?

Well, it means that the addition of an *electronic* component to
instruments, such as woodwinds, is not such a "big deal." Quite
possibly we will "get used" to the electronically-modified sounds and
the "real" sounds of acoustic instruments will sound and
seem "antiquated" or "period" pieces.

If that be the case, which is the *premise* of this post (please save
the eggs and tomatoes until *after* the post has concluded) then it
means that having some kind of "translation" of the *performed* pitch
of a woodwind, let's say, is "no big deal"...

The performer will just play *normally* and with a *foot pedal* or
some such, could play the *alterations* for 72-tET, for instance...
with only *three* necessary, of course, the 1/12 of a whole tone, the
1/6th of a whole tone and the quarter tone.

That would all be done by *alteration* of the existing tone by some
kind of adaptive mechanism, more akin to the present "MIDI
controllers" for woodwinds today. Of course, those are not really
*excellent* instruments yet. *That* development will have to take
place... but I mean a *fine* instrument that has the capability to
electronically alter the sound as post-processing.

It seems this is a *much* more logical and inevitable development
than the so-called "logical" instruments which demand electronic
alteration of the *acoustic* mechanical mechanisms of traditional
instruments. Not only is it *much* more difficult to make such
instruments but the point is, *nobody will appreciate them* since
the "contemporary" sound that people will expect will be an
*electronic* one.

Ok.. now is the time for the tomatoes... :)

And, by the way, if anyone wants to place a *bet* about all this, I
know I will collect, and will expect to in 100 years! :)

Joseph Pehrson

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

> that
> is that the top line seems to descend chromatically through the
> entire 22-tET scale. Is that what's going on. Sure sounds like
it...

i think i skip two of the 22, but yeah, it's just a harmonized
segment of the chromatic scale (as derived in my paper), then
modulated up a fifth, and then a 'bridge'. excuse the cheesy common
practice devices that are imported for 'illustrational' purposes.

if you think of the piece as having primarily 'pythagorean' chord
roots, the progression is what diatonically you would call

bVII -> vi

and in pythagorean the interval between bVII and the VI is 256:243
(downwards).

when people like mathieu and monz and others say you're hearing an
interval 'as' 256:243, this is essentially what they mean

the fact that you've gone from two fifths _below_ the tonic, to three
fifths _above_ the tonic, sets up a certain expectation in the
listener's mind -- and putting the progression in bars 6 to 7
strongly suggests a resolution through II in bar 8 to 'V' at the
start of the next eight-bar cycle. it's quite cliche.

once the 'flow' of a particular tuning system is understood (and in
the West we all have this understanding already for at least the 12-
equal variety of meantone) there's absolutely no difference in the
clarity or meaning of '256:243', whatever interval it happens to come
out as in a particular tuning system -- provided that tuning system
has good enough fifths to construct 'pythagorean' progressions. the
emotional effect of the interval will be very different depending on
whether it is very small (55¢ in 22-tET) or very large (126¢ in 19-
teT) -- but nothing 'special' happens at a just 256:243 -- the ratio
is too complex to have any acoustical or psychoacoustical meaning as
a 'special' vertical, let alone horizontal, interval.

now mathieu and monz and others may disagree because strict, extended-
lattice ji to them is 'natural', it is perhaps 'inborn'
or 'spiritually experienced'. but these are very often the same
people who have *trained themselves* in ji, so they *expect* the
intervals to come out the same way. such a viewpoint is no more open
to the possibilities of the full universe of tuning systems than the
locked-in-12 viewpoint we're all too familiar with . . . and if you
don't like the temperament of the chords in my piece, use adaptive-22
the john delaubenfels way (pending).

Paul wrote...

>I, for one, have never looked at it as more than a warning against
>the erroneous evaluation of low-number equal temperaments (below
>35) based on isolated dyads, for example in the studies by carlos
>and yunik & swift.

In your paper, don't you mention that consistency makes it easier
for musicians to think about tunings, and that this was important
enough that you excluded inconsistent ets from consideration?

-Carl

--- In tuning@y..., "clumma" <carl@l...> wrote:
> Paul wrote...
>
> >I, for one, have never looked at it as more than a warning against
> >the erroneous evaluation of low-number equal temperaments (below
> >35) based on isolated dyads, for example in the studies by carlos
> >and yunik & swift.
>
> In your paper, don't you mention that consistency makes it easier
> for musicians to think about tunings, and that this was important
> enough that you excluded inconsistent ets from consideration?

i don't mention that, but note that i only went up to 34!

>>Hi Paul, I was introduced to the ideas about consistency,
>>completeness and diameter through Patrick's work.
>
>excellent.

I don't know if it's in the current version of his paper,
but Patrick also made his own suggestion of fractional
consistency... just a reminder in case it was getting mixed
up with Paul Hahn's levels (and because I thought it was
a nice concept).

-Carl

As far as the subject line goes -- multi-level consistency
has three nice features:

() is a superset of consistency, so even if you don't take
it too seriously, it's just like a, special happy bonus

() serves as a good practical "badness" measure -- an
in-tuneness-per-notes measure -- for ets.

() is a good practical measure of how much comma drift
you'll experience relative to JI when modulating by
common tones in the lattice -- the higher the level of
consistency, the less the drift.

-Carl

--- In tuning@y..., "clumma" <carl@l...> wrote:

> () is a good practical measure of how much comma drift
> you'll experience relative to JI when modulating by
> common tones in the lattice -- the higher the level of
> consistency, the less the drift.

not seeing it. examples?

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> > Paul,
> >
> > Here's something I missed earlier:
> >
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > > --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> > >
> > > > Woodwind instruments with discrete keying for 72-EDO would be
a
> > lot
> > > > more complicated, involving a lot of tone holes, not to
mention
> > the
> > > > problem of coming up with fingerings for all of those notes;
> > >
> > > i thought the point of the electromechanical bit was to take
care
> > of
> > > all these automatically. why couldn't one just add a very small
> > > number of 'alteration' keys to the standard 12-equal
fingerings,
> > and
> > > have the electromechanical mechanism translate this into the
> > > appropriate coverings of the tone holes for 72-equal??
> >
> > And if most or all of one's available fingers are already busy
> > performing the standard 12-equal fingerings, then where are you
going
> > to come up with fingers to operate these keys?
>
> when i played clarinet i don't think i ever used all my fingers.
but giving you the benefit of the doubt, how about a simple footpedal?

So you never played B on the third line of the staff or low E?

Anyway, it sounds as if you'll need several pedals to do this. Do
you think clarinet players will be willing to dance in order to play
microtones? (Sorry. I couldn't resist the joke.)

All kidding aside now, I thought about this a little bit, and maybe
this one isn't as difficult as it sounds. Using the logical woodwind
technology, I would start by retaining the existing diatonic
fingering patterns on the instrument and using the 4th (little)
fingers of both hands to operate several different keys, separately
or in combination, to effect uniform pitch alterations to the
diatonic tones.

On the clarinet the player already uses the 4th fingers to operate 7
different keys (3 for the left hand and 4 for the right hand), so the
technique of moving these fingers to operate multiple keys is a
familiar one. Suppose that we use these keys for the microtonal
adjustments to pitch. Assuming that we wouldn't require any finger
to press more than one key at a time, we would have 19 possible
alterations (combinations of one or two 4th-finger keys at a time) of
those diatonic tones available to us. Hmmm, you know, this is more
than enough for 72-EDO, considering that it only takes 11 different
alterations to fill in all of the 1/12ths of a tone over the range of
a whole tone. Those remaining combinations could be used for
alternate fingerings, so this just might work!

There's still the matter of finding another way to get the tones at
both ends of the register, since the 4th fingers are now doing
microtones, but, just as you put fingers down in order to go down the
scale, once you reach the bottom you could them lift them up in order
from the top end to continue downward (for both clarinet *and*
bassoon) until you have only the 3rd finger of the right hand down.

For the bassoon, this idea would also eliminate the need for the
player to be an acrobat with the thumbs in the lowest half-octave of
the range, since the new fingerings would now get you all the way
down to the low B-flat without using any of those extra thumb keys.
(And if you wanted, you could use those thumbs for some of the
microtones instead of or in addition to the 4th fingers.)

For the clarinet, I would make the thumb and three fingers down be a
C, but instead of sounding B-flat, it would sound C -- same fingering
for the written note, but sounding as written. So now we no longer
have the burden of a tranposing instrument! (Isn't that nifty? Who
wanted to contend with a microtonal transposing instrument anyway?)
And here's something else that puts the frosting on the cake: the
extra low-range fingerings would enable you to have an instrument
with an extended low range (down to concert B-flat, a major third
lower than at present; no, even lower: that was without counting what
the microtone keys would do!).

Design microtonal woodwinds on one's lunch hour? I didn't think it
would be this easy! I can't wait to tell Patrick about this!

Stay tuned!

--George

>> () is a good practical measure of how much comma drift
>> you'll experience relative to JI when modulating by
>> common tones in the lattice -- the higher the level of
>> consistency, the less the drift.
>
> not seeing it. examples?

This comes out of the definition of the measure, no?
Paul Hahn's example of 81:80 and 50:49 in 22-tET comes to
mind. 22 is level-1 consistent at the 9-limit, and
represents these intervals as 1 and 0 steps, respectively.
Their best approximations in the tuning are 0 and 1 steps,
respectively.

-Carl

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> > --- In tuning@y..., graham@m... wrote:
> > > In-Reply-To: <a3n58p+mcnp@e...>
> > > paulerlich wrote:
> > >
> > > > in case you wanted the specifics on this, you'll find it at
the
> > top of
> > > >
> > > > http://x31eq.com/limit15.txt (thanks graham)
> > > >
> > > > where you can discover that two 29-equal cycles, tuned 15.563
> > cents
> > > > apart, would give the 15-limit ogdoads with a maximum error
in
> > any
> > > > interval of 4.695 cents from just.
> > >
> > > 29-equal is already 15-limit consistent, so you could get these
> > results by
> > > bending the 15.6 cents on an instrument designed for 29-equal.
Or
> > even if
> > > you could add an extra valve or hole to move the 15.6 cents
from
> > the
> > > default tuning. 29-equal is close to Pythagorean, so this
might be
> > > practical on a brass instrument.
> >
> > If we're talking about instruments of flexible pitch, I think
we're
> > better off just using instruments in 41-EDO. Adjustment of
> > intonation by the small amounts (<8.5 cents) required in that
system
> > is easily achievable by anyone who has learned how to play in
tune.
>
> hmm . . . i don't think you can make such a sweeping statement
about "better off". it really depends on what equivalencies the
composer wishes to exploit. an adaptive 41-tone system and an
adaptive 29-tone system may both be great for vertical 15-limit
harmonies, but as you seem to have agreed in a different context,
there's far more to a tuning system than the quality of its vertical
harmonies. for example, adaptive 19-tone and adaptive 22-tone are
both wonderful for 5-limit, yet a work of common-practice Western
music would come out far better in the former than in the latter.
>

By "better off", I meant that in this particular instance I think
that we would be better off with 41-EDO than with two circles of 29-
EDO 15.6 cents apart.

Yes, I can well appreciate your point about 19 vs. 22 for the
preponderance of Western diatonic music.

But to throw you a curve, there is at least one instance in pop music
where 22 does much better than 19: the blues (such as "Night Train"),
which uses 9-limit chords only on the tonic (9th), subdominant (9th),
and dominant (7th). Conflating Archytas' comma (64:63) has its
advantages here. One can only wonder where some of the more creative
jazz musicians might have taken this, had they been given instruments
in 22-EDO.

--George

--- In tuning@y..., Afmmjr@a... wrote:
> In a message dated 2/5/02 4:49:29 PM Eastern Standard Time,
gdsecor@y...
> writes:
>
> > It is all very wonderful that virtuosi such as these can do such
> > amazing things with instruments that, in the majority of cases,
were
> > never intended or expected to be used for this purpose (the
strings
> > and trombone being the most notable exceptions) -- especially if
they
> > can do it with any decent sort of tone at a quick tempo.
> >
> > But what about the great majority of us, who are something less
than
> > technical superheroes, who find it enough of a challenge to play
> > these instruments in the ways that they were *intended* to be
> > played?
>
> Hello George. I do appreciate your work as I do Patrick's work.
But I think
> there may be a few misunderstandings around. I do not think a
flute is
> intended to play in a tuning so much as it can play most any tuning
required.

Within limits. Without a player, the flute can't play a thing, and
then it is limited by two things, the ability of the player, and the
5-limit, for which it was designed.
>
> Similarly, the bassoon is not intended to play in equal temperament
as much
> as it is intended to play in tune.

Again, in the 5 limit.

> If microtonality is going to be so difficult to achieve that
> > it is going to be beyond the reach of all but an elite group,
then
> > there is no chance of its becoming a part of the musical
mainstream,
> > achievable by unexceptional amateur musicians, and it will be
doomed
> > to remain a very small niche in the world of music.
> >
> This is not really true. Foremost, great recordings and
performances will do
> more than amateur futzing. More importantly, playing a microtonal
fingering
> is no more difficult than playing a conventional fingering. Now,
if
> conventional fingerings are too difficult, then we are not talking
about
> professional musicians of any caliber.
>
> My list of virtuosi are to signal that the terrain has already been
mapped
> out. Now, less gifted players can simply following the necessary
fingering.
> Now, if you want to do away with be able to hear a pitch in the
head all
> together, I'm not sure what you are really driving at, other than a
> microtonal sort of Nintendo. Frankly, having the exact fingerings
for a
> tuning should be gravy for a composer/player.
>
> And fingerings are FREE! No added expenses beyond a traditional
> instrument...other than training.

You'd better underline "training" at least a couple of times. I can
guarantee you that there's more involved in a lot of this than just
learning some new fingerings, and for some of these instruments I
would not even recommend that anyone try these techniques unless they
are already highly proficient players. I, for one, am certain that I
would have a very frustrating time if I tried to do microtonality on
a conventional trumpet; but give me one made for the purpose (now
there's my problem), and you would have a hard time getting me to put
it away.

> All support to you and your endeavors. I felt it important to
report from
> the other side of the issue.
>
> Best, Johnny Reinhard

And my very best to you, also. We each have to take the path that we
believe will be most likely to produce successful results, and we
also need to keep in mind that it is in our best interest for each of
us to hope that the other will succeed.

--George

--- In tuning@y..., "clumma" <carl@l...> wrote:
> >> () is a good practical measure of how much comma drift
> >> you'll experience relative to JI when modulating by
> >> common tones in the lattice -- the higher the level of
> >> consistency, the less the drift.
> >
> > not seeing it. examples?
>
> This comes out of the definition of the measure, no?
> Paul Hahn's example of 81:80 and 50:49 in 22-tET comes to
> mind. 22 is level-1 consistent at the 9-limit, and
> represents these intervals as 1 and 0 steps, respectively.
> Their best approximations in the tuning are 0 and 1 steps,
> respectively.

but where's the drift relative to JI???

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> > > --- In tuning@y..., graham@m... wrote:
> > > > In-Reply-To: <a3n58p+mcnp@e...>
> > > > paulerlich wrote:
> > > >
> > > > > in case you wanted the specifics on this, you'll find it at
> the
> > > top of
> > > > >
> > > > > http://x31eq.com/limit15.txt (thanks graham)
> > > > >
> > > > > where you can discover that two 29-equal cycles, tuned 15.563
> > > cents
> > > > > apart, would give the 15-limit ogdoads with a maximum error
> in
> > > any
> > > > > interval of 4.695 cents from just.
> > > >
> > > > 29-equal is already 15-limit consistent, so you could get these
> > > results by
> > > > bending the 15.6 cents on an instrument designed for 29-equal.
> Or
> > > even if
> > > > you could add an extra valve or hole to move the 15.6 cents
> from
> > > the
> > > > default tuning. 29-equal is close to Pythagorean, so this
> might be
> > > > practical on a brass instrument.
> > >
> > > If we're talking about instruments of flexible pitch, I think
> we're
> > > better off just using instruments in 41-EDO. Adjustment of
> > > intonation by the small amounts (<8.5 cents) required in that
> system
> > > is easily achievable by anyone who has learned how to play in
> tune.
> >
> > hmm . . . i don't think you can make such a sweeping statement
> about "better off". it really depends on what equivalencies the
> composer wishes to exploit. an adaptive 41-tone system and an
> adaptive 29-tone system may both be great for vertical 15-limit
> harmonies, but as you seem to have agreed in a different context,
> there's far more to a tuning system than the quality of its vertical
> harmonies. for example, adaptive 19-tone and adaptive 22-tone are
> both wonderful for 5-limit, yet a work of common-practice Western
> music would come out far better in the former than in the latter.
> >
>
> By "better off", I meant that in this particular instance I think
> that we would be better off with 41-EDO than with two circles of 29-
> EDO 15.6 cents apart.

what particular instance?

> Yes, I can well appreciate your point about 19 vs. 22 for the
> preponderance of Western diatonic music.
>
> But to throw you a curve, there is at least one instance in pop music
> where 22 does much better than 19: the blues (such as "Night Train"),
> which uses 9-limit chords only on the tonic (9th), subdominant (9th),
> and dominant (7th).

sure, there might be short examples, in stravinsky and wagner for
example, which would work better in 22 than in 19. still, i'm
wondering what "particular instance" you were referring to above,
since i don't think you specified any in this particular thread.

> Conflating Archytas' comma (64:63) has its
> advantages here. One can only wonder where some of the more creative
> jazz musicians might have taken this, had they been given instruments
> in 22-EDO.

hopefully i'll contribute to this in my lifetime, as i'm playing
jazz/funk these days (about the sixth style i've delved into) and also
have a 22-tone guitar. hopefully you'll read my paper someday.

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

> and the
> 5-limit, for which [the flute] was designed.
> >
> > Similarly, the bassoon is not intended to play in equal temperament
> as much
> > as it is intended to play in tune.
>
> Again, in the 5 limit.

george, this is news to me. i thought these instruments were designed
to play in 12-equal. what exactly do you mean by saying they were
designed to play in 5-limit? is it just that the register key (or
whatever) can give you the fifth overtone? is that all you're
referring to??

In a message dated 2/7/02 9:14:22 PM Eastern Standard Time,
paul@stretch-music.com writes:

> george, this is news to me. i thought these instruments were designed
> to play in 12-equal. what exactly do you mean by saying they were
> designed to play in 5-limit? is it just that the register key (or
> whatever) can give you the fifth overtone? is that all you're
> referring to??
>
>
>
>

Actually, the keys are added to the instruments to better play in 12-tone
equal temperament. Tone holes were enlarged as well. Perhaps without keys
the woodwind instruments are more 5-limit. But as they stand now,
quartertones are quite easy to accomplish if you have your decent 12. They
are no harder to play than "norms" and they are often easy. One would have
to try this to realize it, or compare fingerings on charts to see what
physical change was required to make a pitch difference, etc.

Best, Johnny Reinhard

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

> sure, there might be short examples, in stravinsky and wagner for
> example, which would work better in 22 than in 19. still, i'm
> wondering what "particular instance" you were referring to above,
> since i don't think you specified any in this particular thread.

When I did my adaptive tempering experiment, 22 turned out to be extremely useful; no surprise considering the commas it shares with 12.

>>>>() is a good practical measure of how much comma drift
>>>>you'll experience relative to JI when modulating by
>>>>common tones in the lattice -- the higher the level of
>>>>consistency, the less the drift.
>>>
>>>not seeing it. examples?
>>
>>This comes out of the definition of the measure, no?
>>Paul Hahn's example of 81:80 and 50:49 in 22-tET comes to
>>mind. 22 is level-1 consistent at the 9-limit, and
>>represents these intervals as 1 and 0 steps, respectively.
>>Their best approximations in the tuning are 0 and 1 steps,
>>respectively.
>
>but where's the drift relative to JI???

Sorry, I meant, "relative to JI within the tuning." But
for relatively accurate tunings (like level-1 consistent
ones, where the concepts differentiate), this should
approximate drift from true JI, as progressions involving
consecutive tritone substitutions or the comma pump in 22
vs. a level-2 consistent 9-limit tuning like 41-tET should
show. Actually, to be fair with step size, the comparo
should probably be 41 and 46. Anyway, the point is, while
the relevant error function for vertical stuff (acoustics)
is smooth (and consistency of any kind doesn't matter), the
relevant one for puns is not. Multi-level consistency makes
it discrete in exactly the way the tunings do. So you say
it doesn't matter, but I say it does matter, and to you; in
general, you like tunings that are lower in consistency.

-Carl

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > > --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> > > > --- In tuning@y..., graham@m... wrote:
> > > > > In-Reply-To: <a3n58p+mcnp@e...>
> > > > > paulerlich wrote:
> > > > >
> > > > > > in case you wanted the specifics on this, you'll find it
at
> > the
> > > > top of
> > > > > >
> > > > > > http://x31eq.com/limit15.txt (thanks graham)
> > > > > >
> > > > > > where you can discover that two 29-equal cycles, tuned
15.563
> > > > cents
> > > > > > apart, would give the 15-limit ogdoads with a maximum
error
> > in
> > > > any
> > > > > > interval of 4.695 cents from just.
> > > > >
> > > > > 29-equal is already 15-limit consistent, so you could get
these
> > > > results by
> > > > > bending the 15.6 cents on an instrument designed for 29-
equal.
> > Or
> > > > even if
> > > > > you could add an extra valve or hole to move the 15.6 cents
> > from
> > > > the
> > > > > default tuning. 29-equal is close to Pythagorean, so this
> > might be
> > > > > practical on a brass instrument.
> > > >
> > > > If we're talking about instruments of flexible pitch, I think
> > we're
> > > > better off just using instruments in 41-EDO. Adjustment of
> > > > intonation by the small amounts (<8.5 cents) required in that
> > system
> > > > is easily achievable by anyone who has learned how to play in
> > tune.
> > >
> > > hmm . . . i don't think you can make such a sweeping statement
> > about "better off". it really depends on what equivalencies the
> > composer wishes to exploit. an adaptive 41-tone system and an
> > adaptive 29-tone system may both be great for vertical 15-limit
> > harmonies, but as you seem to have agreed in a different context,
> > there's far more to a tuning system than the quality of its
vertical
> > harmonies. for example, adaptive 19-tone and adaptive 22-tone are
> > both wonderful for 5-limit, yet a work of common-practice Western
> > music would come out far better in the former than in the latter.
> > >
> >
> > By "better off", I meant that in this particular instance I think
> > that we would be better off with 41-EDO than with two circles of
29-
> > EDO 15.6 cents apart.
>
> what particular instance?

The one (quoted above), where Graham asked what I thought about using
2 cycles of 29-EDO to get 15-limit ogdoads. Inasmuch as he was
asking about implementing this on instruments of flexible pitch, I
don't believe that this application requires the amount of precision
that is offered, especially if we are going to lose the free
modulation allowed by an EDO in the process. Therefore 41-EDO, which
has virtually the same harmonic relationships, would be a better
choice.

--George

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > and the
> > 5-limit, for which [the flute] was designed.
> > >
> > > Similarly, the bassoon is not intended to play in equal
temperament
> > as much
> > > as it is intended to play in tune.
> >
> > Again, in the 5 limit.
>
> george, this is news to me. i thought these instruments were
designed
> to play in 12-equal. what exactly do you mean by saying they were
> designed to play in 5-limit? is it just that the register key (or
> whatever) can give you the fifth overtone? is that all you're
> referring to??

Hmmm ... designs vs. intentions, eh? Yes, these instruments were
*designed* to play in 12-EDO, which, in turn, was *intended* to
approximate 5-limit intervals, which, in turn, allows a bassoonist
with a reasonable amount of training and practice to play these
intervals in tune. Yes, the bassoon was *designed* for 12-EDO and
also *intended* for 5-limit harmony.

Quite another matter is what is actually being done out in the real
world, and I quite agree with your observation that most of the time
what we hear from the major orchestras is much closer to 12-ET than
just intonation, meantone temperament, or anything else that might
improve the ratios of 5 from a harmonic standpoint. And when
departures from 12-ET do occur, I think that they are more likely
than not to be in the direction of Pythagorean tuning (for melodic
purposes) rather than just intonation, with the strings in particular.

In reading the digests of the postings of the past 24 hours or so, I
recall seeing a conversation in which a question was raised whether
players (or singers) might tend toward just intonation if they were
performing along with instruments of fixed pitch tuned to rational
intervals. My guess is that for the majority of singers, no, and for
instrumentalists, maybe, but don't count on it. Singers and players
need to be educated about these things, and even a class in musical
acoustics probably isn't going to be enough to give most music
students a sufficient awareness of how to go about achieving "better"
intonation, nor the motivation to do some practical exercises on
their own to develop that awareness.

--George

Regarding the real world: instrumentalists are instructed by private teacher and conductors where to place their pitch. Acoustics classes for students won't change much in that regard.

Johnny Reinhard

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

> Design microtonal woodwinds on one's lunch hour? I didn't think it
> would be this easy! ...

Well, if nobody else is going to comment on this one, then I will.

Driving on the way to work this morning I had an idea how woodwind
instruments intended for multiple tonal systems might be possible
using "logical technology."

In an instrument designed for 72-EDO the pitches would be ~17.7 cents
apart, which means that any pitch required by another tonal system
would depart no more than ~9 cents from one that you already have in
72-EDO, an amount that easily falls within the range of pitch
alterations that are involved in the standard technique known
as "playing in tune." So you could theoretically use that one
instrument for various systems of lower number, such as 19, 22, 31,
41, 46, etc., just as long as you became aware of which tones needed
to be adjusted which way. And the logical technology could even
include provision for a switch to select only the particular subset
of tones applicable to each of these systems. And the employment of
standard (easy-to-remember) fingerings would further simplify the
process.

No extended or extraordinary techniques required! Amateurs welcome!
(Just bring lots of money, because we're still going to have to
figure out how to pay for this -- Patrick, keep filling out those
applications for grants!)

And stay in tune!

--George

Here is a list of ets from 1-100 which have a 15-limit consistent logarithmically flat badness measure less than 1.1:

2 .9030717171
5 1.096829203
7 1.028244534
9 .9807231978
10 .9905023934
15 1.037670842
29 .9520065370
41 1.010934526
46 1.082290028
58 .9018214272
72 1.015331601
94 1.041787396

While 41 scores well, 58 scores better; it has been an object of interest on tuning-math in the last week since it is the first et which can handle the Genesis scale.

Here are the ets from 100-1000 with a badness less than 1.0 by this same measure:

111 .9838918954
130 .9639551321
224 .8736311477
270 .7912887258
311 .8915840783
494 .6885255021

494 divisions of the octave, anyone?

--- In tuning@y..., "clumma" <carl@l...> wrote:
> >>>>() is a good practical measure of how much comma drift
> >>>>you'll experience relative to JI when modulating by
> >>>>common tones in the lattice -- the higher the level of
> >>>>consistency, the less the drift.
> >>>
> >>>not seeing it. examples?
> >>
> >>This comes out of the definition of the measure, no?
> >>Paul Hahn's example of 81:80 and 50:49 in 22-tET comes to
> >>mind. 22 is level-1 consistent at the 9-limit, and
> >>represents these intervals as 1 and 0 steps, respectively.
> >>Their best approximations in the tuning are 0 and 1 steps,
> >>respectively.
> >
> >but where's the drift relative to JI???
>
> Sorry, I meant, "relative to JI within the tuning."

still lost . . .

> But
> for relatively accurate tunings (like level-1 consistent
> ones, where the concepts differentiate), this should
> approximate drift from true JI, as progressions involving
> consecutive tritone substitutions or the comma pump in 22
> vs. a level-2 consistent 9-limit tuning like 41-tET should
> show.

so don't you really mean 'lack of drift' or something? unlike
physical space, musical pitch is pretty much absolute, so there's no
need to measure motion relative to something else. JI drifts, the
temperament may not. isn't that clearer?

> Actually, to be fair with step size, the comparo
> should probably be 41 and 46. Anyway, the point is, while
> the relevant error function for vertical stuff (acoustics)
> is smooth (and consistency of any kind doesn't matter), the
> relevant one for puns is not.

right.

> Multi-level consistency makes
> it discrete in exactly the way the tunings do.

ech...we have much better ways of characterizing the puns.

> So you say
> it doesn't matter, but I say it does matter, and to you; in
> general, you like tunings that are lower in consistency.

the correlation is far from perfect.

>>But for relatively accurate tunings (like level-1 consistent
>>ones, where the concepts differentiate), this should
>>approximate drift from true JI, as progressions involving
>>consecutive tritone substitutions or the comma pump in 22
>>vs. a level-2 consistent 9-limit tuning like 41-tET should
>>show.
>
>so don't you really mean 'lack of drift' or something? unlike
>physical space, musical pitch is pretty much absolute, so there's
>no need to measure motion relative to something else. JI drifts,
>the temperament may not. isn't that clearer?

Quite possibly.

>>Multi-level consistency makes
>>it discrete in exactly the way the tunings do.
>
>ech...we have much better ways of characterizing the puns.

Where have we been hiding them? We can talk about what commas
vanish in a series of ets, and the like, but I'm not aware of
a general measure.

Besides, for any tuning there may be a huge number of comma
sets that define it. We've had to resort to the notion
Minkowski-reduced basis, just so we have some standard, but
it isn't clear that reduced basi yield the only, or even the
most, musically important basi.

>>So you say it doesn't matter, but I say it does matter, and
>>to you; in general, you like tunings that are lower in
>>consistency.
>
>the correlation is far from perfect.

Maybe so. Can you improve it?

-Carl

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

> > > By "better off", I meant that in this particular instance I
think
> > > that we would be better off with 41-EDO than with two circles
of
> 29-
> > > EDO 15.6 cents apart.
> >
> > what particular instance?
>
> The one (quoted above), where Graham asked what I thought about
using
> 2 cycles of 29-EDO to get 15-limit ogdoads. Inasmuch as he was
> asking about implementing this on instruments of flexible pitch, I
> don't believe that this application requires the amount of
precision
> that is offered, especially if we are going to lose the free
> modulation allowed by an EDO in the process.

you'll still have as much free modulation as in 29-EDO.

> Therefore 41-EDO, which
> has virtually the same harmonic relationships, would be a better
> choice.

it really depends on the music, and what commas it is based on. this
seems to be little different than saying 22 is better than 19, or 19
is better than 22, without a specific musical context.

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

> Hmmm ... designs vs. intentions, eh? Yes, these instruments were
> *designed* to play in 12-EDO, which, in turn, was *intended* to
> approximate 5-limit intervals,

hmm . . . well this may be slightly off-topic, but i'd like to
register my opinion that at best, 12-equal was intended to
approximate meantone, which had in turn been intended to combine 5-
limit harmony with diatonic melody. it's a bit misleading to claim,
as most books on the subject unforntunately do, that the intention
was a direct path between 12-equal and 5-limit.

> which, in turn, allows a bassoonist
> with a reasonable amount of training and practice to play these
> intervals in tune. Yes, the bassoon was *designed* for 12-EDO and
> also *intended* for 5-limit harmony.

well, you have to be a bit more specific. do you mean *adaptive* 5-
limit harmony, where the melodic intervals are not necessarily simple
ratios? it's important to say so, since a lot of people see '5-limit'
and think 'strict 5-limit JI'. even then, it would only be 'maybe',
because since 1800 or so, musicians have been taught to play sharps
*at least as high* as the enharmonically equivalent flats. this,
unfortunately, does not facilitate adaptive 5-limit harmony.

> Quite another matter is what is actually being done out in the real
> world, and I quite agree with your observation that most of the
time
> what we hear from the major orchestras is much closer to 12-ET than
> just intonation, meantone temperament, or anything else that might
> improve the ratios of 5 from a harmonic standpoint. And when
> departures from 12-ET do occur, I think that they are more likely
> than not to be in the direction of Pythagorean tuning (for melodic
> purposes) rather than just intonation, with the strings in
>particular.

well then, where does that leave the '5-limit' for flutes and
bassoons? neither in design nor in practice . . .

sorry to be so picky, just trying to foster clarity for the sake of
those struggling to follow along . . .

--- In tuning@y..., "clumma" <carl@l...> wrote:

> >ech...we have much better ways of characterizing the puns.
>
> Where have we been hiding them? We can talk about what commas
> vanish in a series of ets, and the like, but I'm not aware of
> a general measure.

it's not a one-dimensional measure. look to the wedgie . . .

> Besides, for any tuning there may be a huge number of comma
> sets that define it. We've had to resort to the notion
> Minkowski-reduced basis, just so we have some standard, but
> it isn't clear that reduced basi yield the only, or even the
> most, musically important basi.

it doesn't matter -- they're all equivalent, and can be derived from
one another.

> >>So you say it doesn't matter, but I say it does matter, and
> >>to you; in general, you like tunings that are lower in
> >>consistency.
> >
> >the correlation is far from perfect.
>
> Maybe so. Can you improve it?

you can't expect a one-dimensional measure like a consistency level
to tell you about the various puns.

>>>ech...we have much better ways of characterizing the puns.
>>
>> Where have we been hiding them? We can talk about what commas
>> vanish in a series of ets, and the like, but I'm not aware of
>> a general measure.
>
> it's not a one-dimensional measure. look to the wedgie . . .

I'm afraid I don't understand wedgies. I'm still waiting for
the gentle introduction.

>>>>So you say it doesn't matter, but I say it does matter, and
>>>>to you; in general, you like tunings that are lower in
>>>>consistency.
>>>
>>>the correlation is far from perfect.
>>
>> Maybe so. Can you improve it?
>
>you can't expect a one-dimensional measure like a consistency level
>to tell you about the various puns.

I don't. I expect it to tell me how much punning is going on.

-C.

--- In tuning@y..., "clumma" <carl@l...> wrote:

> Besides, for any tuning there may be a huge number of comma
> sets that define it. We've had to resort to the notion
> Minkowski-reduced basis, just so we have some standard, but
> it isn't clear that reduced basi yield the only, or even the
> most, musically important basi.

There are an infinite number of bases in general, which sounds pretty huge to me. The MT reduced basis is a good choice, but when a comma is what I whimsically called a "jumping jack", such as 81/80 or 2401/2400, they take on an additional importance (think about Paul's remarkable discovery re 2401/2400, for instance.)

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

> it's not a one-dimensional measure. look to the wedgie . . .

In the case of an et, the wedgie *is* the et, so it doesn't tell you anything you don't already know.

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

/tuning/topicId_33601.html#33772

> For the clarinet, I would make the thumb and three fingers down be
a
> C, but instead of sounding B-flat, it would sound C -- same
fingering for the written note, but sounding as written. So now we
no longer
> have the burden of a tranposing instrument! (Isn't that nifty? Who
> wanted to contend with a microtonal transposing instrument
anyway?) And here's something else that puts the frosting on the
cake: the
> extra low-range fingerings would enable you to have an instrument
> with an extended low range (down to concert B-flat, a major third
> lower than at present; no, even lower: that was without counting
what the microtone keys would do!).
>
> Design microtonal woodwinds on one's lunch hour? I didn't think it
> would be this easy! I can't wait to tell Patrick about this!
>
> Stay tuned!
>
> --George

****Hi George. Well you *certainly* make good use of your lunch hour
(!) Personally, I'm lucky if I can just get through part of the
newspaper... :)

Your ideas are fascinating, but, I guess, the question is whether
players would ever want to learn new instruments with radical
designs. It seems however, regrettably, that the "appetite" for
acoustic instruments is actually on the wane, and for "traditional"
art music, although that's just being redefined these days.
Additionally, music education isn't what it used to be in the
schools, as you know, so many people don't even have *band* anymore.
Maybe this will change, or develop into something different, most
probably. Maybe computer classes where suddenly everybody jumps up
with earphones and starts "jammin'" at the computer keyboard... :)

Anyway, I can see the idea of using a foot pedal that is more
a "lever" type, looking more like a classical guitar footstand than
anything, but which cantilevers forward and back. Perhaps there are
*three* "notches" forward which are perceptible clicks and three
backwards. Those would correspond, of course, to your 12th of a
whole tone 6th of a whole tone and quarter tone going in each
direction. The player would have to get used to changing these with
the *one* foot pedal quickly, but it seems that would be much easier
than learning or designing an entirely new instrument!

This would mean, though, that somehow (don't ask *me* this is still
hypothetical! :) ) the sound from the bell would go into some
electronic processing unit that would make the microtonal
inflections, and would still come out sounding like a fine clarinet
sound, or at least a reasonable simulation thereof.

Just an idea... but to me it would seem like more profitable research
than totally redesigning instruments. Players could in this system,
of course, just use the fingerings they already know...

best,

J. Pehrson

Joe and George,

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> Your ideas are fascinating, but, I guess, the question is whether
> players would ever want to learn new instruments with radical
> designs.

I hate to bring this up, but the question really is: where and how
will these instruments be built, and on what kind of scale (i.e. mass-
produced)? In a world where adding microtonality to existing
synthesizers and samplers is, in many cases, simply adding another
bit of code to the firmware, we see... almost nothing. And you would
expect instrumental manufacturers to make large and radical (and
expensive) adjustments to instruments for... a *potential* music?

Frankly, I can't imagine it happening. The only thing I see as
possible are a very, very small number of people altering instruments
(or creating new ones), and that the music being made with those
instruments will be so compelling as to prod manufacturers into at
least investigating the possibility. If you disagree, please let me
know the scenario that you envision for a manufacturer to produce a
new line of microtonally-capable instruments, at an affordable cost,
in a relatively mass-produced manner.

Just look at Starr Labs. Apparantly cool instruments, very high cost,
and almost zero market penetration. Hardly a formula for changing the
world.

In the short run, I definitely think Johnny (and Joe) are on the
right track: if you want acoustic music, work with the existing
instruments to build a body of literature and/or performances. When
the alleged gems appear, a movement *might* begin to create new
instruments to further the music.

(None of this is idle speculation: my dear friend Arlen Fast,
contrabassoon and utility bassoonist with the New York Philharmonic
has recently culminated a years-long project, in conjunction with the
Fox Bassoon Company, for a newly-designed key system for contras. It
has taken a long time, and a lot of effort and expense, to bring to
fruition his system for bettering the contra (in standard 12tet) with
a new key system. I'm sure I could get the gory details of the
journey if people are interested, but I know it was not easy and took
a lot of work to get them interested...)

Cheers,
Jon

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

/tuning/topicId_33601.html#33829

>
> In reading the digests of the postings of the past 24 hours or so,
I
> recall seeing a conversation in which a question was raised whether
> players (or singers) might tend toward just intonation if they were
> performing along with instruments of fixed pitch tuned to rational
> intervals. My guess is that for the majority of singers, no, and
for instrumentalists, maybe, but don't count on it. Singers and
players
> need to be educated about these things, and even a class in musical
> acoustics probably isn't going to be enough to give most music
> students a sufficient awareness of how to go about
achieving "better" intonation, nor the motivation to do some
practical exercises on their own to develop that awareness.
>
> --George

****This statement by George Secor seems particularly apt, and it's
*exactly* why I would like to keep the "major third" the 12-tET
(wrong) "major third."

It's not that the players don't *know* any better... it's just that
music is about more than *thinking* In fact, it's bad to think too
much about music... :) (joke)

It's about *playing* and playing involves (sometimes)*practicing* and
practicing involves getting used to a certain set of *conventions.*

They may even be "lame-brained" but the *are* conventions and if you
don't start with those conventions you're running "against the grain"
or "swimming upstream" or "going against the tide" or just "wading in
the water..." Or maybe just sunbathing??

JP

I tend to think that given the proper cues singers will sing in tune. This was Wilson conclusion
working with two and also more recently with some hymn singers. Also there is also the work of
boomliter and creel that support such possibility.
Instrumentalist it would seem to be restricted by there instruments "natural " inclination to
play in what they were designed to do.
We underestimate the ear as if it is limited to what we can map and place within a fixed
system. Western culture has developed maybe 20 different major thirds in its history ( i may be
way underestimating this) that are decided upon intuitively out of the learn subconscious response
of playing the music and hearing others do it. Such things as cadences appear to my ear to have
unique intonations determined by it meaning. In fact i would speculate that that where ever we can
perceive an different musical meaning i would imagine a different intonation. All we can really
accomplish is to use as many as possible with the less amount of inventory.
Also it appears to my ear just as different singers develop their own "intonation' i sense
different composers imply different intonations.
To finally end, it seems that given random intervals performers will gravitate to the closest
acoustical phenomenon possible.

jpehrson2 wrote:

> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> /tuning/topicId_33601.html#33829
>
> >
> > In reading the digests of the postings of the past 24 hours or so,
> I
> > recall seeing a conversation in which a question was raised whether
> > players (or singers) might tend toward just intonation if they were
> > performing along with instruments of fixed pitch tuned to rational
> > intervals. My guess is that for the majority of singers, no, and
> for instrumentalists, maybe, but don't count on it. Singers and
> players
> > need to be educated about these things, and even a class in musical
> > acoustics probably isn't going to be enough to give most music
> > students a sufficient awareness of how to go about
> achieving "better" intonation, nor the motivation to do some
> practical exercises on their own to develop that awareness.
> >
> > --George
>
> ****This statement by George Secor seems particularly apt, and it's
> *exactly* why I would like to keep the "major third" the 12-tET
> (wrong) "major third."
>
> It's not that the players don't *know* any better... it's just that
> music is about more than *thinking* In fact, it's bad to think too
> much about music... :) (joke)
>
> It's about *playing* and playing involves (sometimes)*practicing* and
> practicing involves getting used to a certain set of *conventions.*
>
> They may even be "lame-brained" but the *are* conventions and if you
> don't start with those conventions you're running "against the grain"
> or "swimming upstream" or "going against the tide" or just "wading in
> the water..." Or maybe just sunbathing??
>
> JP

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

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

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > Hmmm ... designs vs. intentions, eh? Yes, these instruments were
> > *designed* to play in 12-EDO, which, in turn, was *intended* to
> > approximate 5-limit intervals,
>
> hmm . . . well this may be slightly off-topic, but i'd like to
> register my opinion that at best, 12-equal was intended to
> approximate meantone, which had in turn been intended to combine 5-
> limit harmony with diatonic melody. it's a bit misleading to claim,
> as most books on the subject unforntunately do, that the intention
> was a direct path between 12-equal and 5-limit.

Yes, there is a path that led us to where we are, and to lose sight
of that can result in an oversimplification of the whole matter, by
which we lose sight of our historical intentions.
>
> > which, in turn, allows a bassoonist
> > with a reasonable amount of training and practice to play these
> > intervals in tune. Yes, the bassoon was *designed* for 12-EDO
and
> > also *intended* for 5-limit harmony.
>
> well, you have to be a bit more specific. do you mean *adaptive* 5-
> limit harmony, where the melodic intervals are not necessarily
simple
> ratios? it's important to say so, since a lot of people see '5-
limit'
> and think 'strict 5-limit JI'. even then, it would only be 'maybe',
> because since 1800 or so, musicians have been taught to play sharps
> *at least as high* as the enharmonically equivalent flats. this,
> unfortunately, does not facilitate adaptive 5-limit harmony.

Any player of an instrument of fixed pitch that is attempting to
play "in tune" (whatever that means) is by nature employing
*adaptive* intonation (of whatever sort). As we both pointed out,
the objective is often (if not usually) not the attainment of more
consonant 5-limit harmony.
>
> > Quite another matter is what is actually being done out in the
real
> > world, and I quite agree with your observation that most of the
> time
> > what we hear from the major orchestras is much closer to 12-ET
than
> > just intonation, meantone temperament, or anything else that
might
> > improve the ratios of 5 from a harmonic standpoint. And when
> > departures from 12-ET do occur, I think that they are more likely
> > than not to be in the direction of Pythagorean tuning (for
melodic
> > purposes) rather than just intonation, with the strings in
> >particular.
>
> well then, where does that leave the '5-limit' for flutes and
> bassoons? neither in design nor in practice . . .
>
> sorry to be so picky, just trying to foster clarity for the sake of
> those struggling to follow along . . .

I believe that, in an ideal performance, the players should have the
sensitivity to alter their intonation in both ways -- toward the
Pythagorean in a resolving chord, and toward (5-limit) just
intonation in the resolution. A high leading tone in a dominant
chord will accomplish both harmonic tension (or dissonance) and
melodic effectiveness in its resolution to a tonic chord with the
third of the chord adjusted for high consonance. The effectiveness
of the resolution is twofold: employment of 1) a more melodically
effective (i.e. smaller) semitone and 2) increased contrast in
sonance between the resolving chord and its resolution.

This, I submit, is how 5-limit intonation should be taught.

--George

On 2/13/02 1:54 PM, "tuning@yahoogroups.com" <tuning@yahoogroups.com> wrote:

> Message: 14
> Date: Wed, 13 Feb 2002 20:24:15 -0000
> From: "gdsecor" <gdsecor@yahoo.com>
> Subject: Re: Digest Number 1890
>
> --- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:
>> On 2/12/02 11:07 AM, "tuning@y..." <tuning@y...>
>> wrote:
>>
>>>
>>> Message: 22
>>> Date: Tue, 12 Feb 2002 18:26:16 -0000
>>> From: "gdsecor" <gdsecor@y...>
>>> Subject: Re: Extended techniques (Was: Patrick Ozzard-Low)
>>>
>>>
>>> I believe that, in an ideal performance, the players should have
> the
>>> sensitivity to alter their intonation in both ways -- toward the
>>> Pythagorean in a resolving chord, and toward (5-limit) just
>>> intonation in the resolution. A high leading tone in a dominant
>>> chord will accomplish both harmonic tension (or dissonance) and
>>> melodic effectiveness in its resolution to a tonic chord with the
>>> third of the chord adjusted for high consonance. The
> effectiveness
>>> of the resolution is twofold: employment of 1) a more melodically
>>> effective (i.e. smaller) semitone and 2) increased contrast in
>>> sonance between the resolving chord and its resolution.
>>>
>>> This, I submit, is how 5-limit intonation should be taught.
>>>
>>> --George
>>
>> I certainly agree in principle, George. However, in my experience,
> the
>> tension in the dominant seventh chord is further enhanced when 7-
> limit is
>> employed. Contrary to what my teachers believed, the seventh
> partial is not
>> "unusable." Combine a "high third" with a super-flat seventh over a
> dominant
>> root and you've got tension that *cries* for resolution.
>
> Tension is definitely the word, although, as a couple others also
> noted, some of us might judge the interval between the third and
> seventh of the chord to be so small as to be interpeted as something
> other than a diminished fifth (which is why I used the term "5-limit"
> above).

Wow! That bends my brain, George. I guess I've been influenced by
major/minor system too long. Evidently you have broken the umbilical chord
to the world of Beethoven. I'm still stuck in that tradition.
>
>> The "high third" that "locks" in such a chord, however, seems to me
> *not* to
>> be a Pythagorean third--which to my ear is too high. (Again, not to
> re-open
>> past discussion, but simply to keep it in mind.)
>
> By contrast, the 17-tone well-temperament "revolution" that Margo
> Schulter and I have been conducting involves leading tones
> considerably higher than this -- in the neighborhood of 14:11 to 9:7
> above the dominant -- and "semitones" in the range of 63 to 78
> cents. These resolve either to open fifths (in Margo's neo-Medieval
> style) or subminor (6:7:9) triads, either way achieving a huge
> contrast in sonance in the harmonic resolution, in combination with
> intervals that are (in my estimation) unsurpassed in their melodic
> effectiveness. Margo and I are submitting papers for the next issue
> of Xenharmonikon that will go into considerable detail about this
> (and other things as well).
>
> Which goes to show you that there are more than a few ways to exploit
> the interplay between the melodic and harmonic elements.
>
> --George

No problem, George. I'm sure there are myriad ways. How does that relate to
my post?

Gerald Eskelin
>

--- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:
> On 2/13/02 1:54 PM, "tuning@y..." <tuning@y...> wrote:
>
> > Message: 14
> > Date: Wed, 13 Feb 2002 20:24:15 -0000
> > From: "gdsecor" <gdsecor@y...>
> > Subject: Re: Digest Number 1890
> >
> > --- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:

> >> The "high third" that "locks" in such a chord, however, seems to
me
> > *not* to
> >> be a Pythagorean third--which to my ear is too high. (Again, not
to
> > re-open
> >> past discussion, but simply to keep it in mind.)
> >
> > By contrast, the 17-tone well-temperament "revolution" that Margo
> > Schulter and I have been conducting involves leading tones
> > considerably higher than this -- in the neighborhood of 14:11 to
9:7
> > above the dominant -- and "semitones" in the range of 63 to 78
> > cents. These resolve either to open fifths (in Margo's neo-
Medieval
> > style) or subminor (6:7:9) triads, either way achieving a huge
> > contrast in sonance in the harmonic resolution, in combination
with
> > intervals that are (in my estimation) unsurpassed in their melodic
> > effectiveness. Margo and I are submitting papers for the next
issue
> > of Xenharmonikon that will go into considerable detail about this
> > (and other things as well).
> >
> > Which goes to show you that there are more than a few ways to
exploit
> > the interplay between the melodic and harmonic elements.
> >
> > --George
>
> No problem, George. I'm sure there are myriad ways. How does that
relate to
> my post?
>
> Gerald Eskelin

You mentioned a Pythagorean third as being too high to "lock in a
chord" for a certain purpose. This was my way of saying "a
Pythagorean third is too high? You ain't heard nothin' till you've
locked onto dominant triads with thirds in the range of 417 to 435
cents (inspired by Marchettus of Padua)."

I was about to say that Margo could write a book on this, except that
that's pretty much what she's been up to for the past couple of
months -- and now she's going to be tempted to give you a memory dump
when she's supposed to be busy writing (Margo, no more than two
paragraphs, please!).

--George