Embat

>From: John Chalmers
>With respect to tuning (embat); Al's posting to the gamelan list in Bahasa
>Indonesia several months back elaborated on some of the possibilities
>inherent in the tuning of a gamelan: (also check out Polansky on
>"Paratactical Tunings" and Wendy Carlos on "Tuning", both in past Computer
>Music Journals for more fruitful musings.)
>
>1. 'mbat Pleng
>2. 'mbat Larasati
>3. 'mbat Sundari

I'll sure admit that my direct experience here comes from a one-time
teacher and gamelan tuner (A.L. Suwardi), but I was under the impression
that at least one or two of these embats referred to the distance between the
wider and narrower intervals - that is, the distance between 1-2, 2-3, etc.
rather than octave stretching or narrowing as such. And I could also be wrong
here, but I'd be surprised to discover that there wasn't some considerable
variation from instrument to instrument among the set of instruments as
well watching A.L. retune out set, something like that sure seemed to me to
be going on....

Selamat pagi,
Gregory

_
I would go to her, lay it all out, unedited. The plot was a simple one,
paraphrasable by the most ingenuous of nets. The life we lead is our only
maybe. The tale we tell is the must that we make by living it. [Richard
Powers, "Galatea 2.2"] Gregory Taylor/Heurikon Corporation/Madison, WI



Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Thu, 18 Jul 1996 18:49 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id JAA15755; Thu, 18 Jul 1996 09:49:40 -0700
Date: Thu, 18 Jul 1996 09:49:40 -0700
Message-Id:
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu

Re Kraehenbuehl and Schmidt: K & B proposed a 12 out of 22 as the next=20
step in Western music and the 4:5:6:7 chord as the basic consonance.=20
Their procedure was to interpolate new notes into the larger intervals
of the older tuning. By this means, which they attribute to Prosdocimus
of Bellemandis, the pentatonic became the diatonic, the diatonic the
chromatic, etc.

See: Kraehenbuehl, David and Christopher Schmidt. "On the Development=20
of Musical Systems," =CAJournal of Music Theory: vol. 6 no. 1,
Spring 1962. pp. 32-65.

Alas, I've never seen the Ogolovets article.

BTW, Yasser lived and worked in Shanghai after leaving Russia during=20
the Revolution. I recommend his "Medieval Quartal Harmony: A Plea
for Restoration" (1938). It also appeared as a three part article in=20
the Musical Quarterly vol 23 (170-197) April 1937, (336-366) July, '37=20
and vol 24 (351-385) July 1938. He wrote about Chinese and Siberian music=
=20
(he spent some time in Siberia on his way to China). In NYC he became
very well-known as an organist and authority on Jewish music, which
he felt was largely pentatonic and should be harmonized with quartal
chords. I think ethnocentric is a somewhat oversimplified judgement,
though perhaps true to some extent. He seemed to feel that Thai music
in particular, was limited by its 7-tet intonation and that going
to 14 was no more of an advance than going to 24 would be for us.

BTW, Yasser did hear a piano in 19 and gave a lecture-demo with it.
I am unclear from what Yasser himself told me and/or from the description=
=20
in the annotated bibliography compiled by Albert Weisser exactly whether
this was two pianos in 19 or one "specially preprared" piano in 19.=20
Weisser states it was the latter. It was done in 1935 at "Steinway and
Sons in their New York studios." The talk was called "Supra-Diatonicsm
in Live Sound." This should satisfy critics who think that Yasser never
heard 19-tet. However, this experiment came 3 years after his book
was published and his theory was in its mature form. Yasser admitted
that it was hard to hear the 12+7 scale "as something inconstesibly
clear and convincing." (The quotes are from the bibliography and are
Yasser's words with or without minor paraphrasis.)=20

Re Hexachord: I've often wondered about the hexachord myself. Some=20
tunings of Wilson's hexany (i.e., the 1.3.5.9) approximate the hexachord,=
=20
but in general, I've found it difficult to generate new scales based=20
on it. Lou Harrison has composed with hexatonic scales.

Refield's scale: This scale has 3 minor triads on the 1/1, 4/3 and 3/2
and two major.Its modes are inversions of the Ptolemaic ones. I wasn't
proposing it as a tuning of the major scale, but pointing out that
Ptolemy's Intense Diatonic generates only half of the major-minor system.
For a more complete discussion of the chordal genesis of the modal
system, see Ellis's additions to Helmholtz. I think this is pretty much
theoretical post-hoc musicology, but it is interesting and suggested to
me at least, a way of harmonically generating scales.

Personally, I think the tritriadic genesis of the major and minor
scales to be post-hoc theorizing, but the fact that it is possible and
largely agrees with musical usage, is further evidence for the
"fitness" of the major and minor modes for tonal music. The challenge
is to find analogues and homologues, as well as convincing new formations=
=20
for xenharmonic music.

--John


Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Sat, 30 Nov 1996 09:55 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA12617; Sat, 30 Nov 1996 09:57:41 +0100
Received: from eartha.mills.edu by ns (smtpxd); id XA12024
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id AAA19117; Sat, 30 Nov 1996 00:57:38 -0800
Date: Sat, 30 Nov 1996 00:57:38 -0800
Message-Id:
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu

John,

I believe it was Gary who said that. I've not yet used that scale.

Johnny Reinhard
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@ios.com

On Sat, 25 Jan 1997, John Chalmers wrote:

> >From Kami:
> > The only other time I saw this interval was in
> > the scale :
> > 7/7 8/7 9/7 10/7 11/7 12/7 13/7 14/7.
>
> >From Johnny Reinhard:
>
> > That's a really fun, ear-scorcher tuning! I've written a bit with it
> > and enjoyed doing so.
>
> Ear-scorcher? It's just the harmonic series from 7 to 14... The
> inversion, Kathleen Schlesinger's diatonic Mixolydian harmonia, sounds
> a bit odd, however.
>
> --John
>
>


Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Sun, 26 Jan 1997 06:04 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA15316; Sun, 26 Jan 1997 06:04:38 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA15197
Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id SAA18308; Sat, 25 Jan 1997 18:31:21 -0800
Date: Sat, 25 Jan 1997 18:31:21 -0800
Message-Id:
Errors-To: madole@mills.edu
Reply-To: tuning@ella.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@ella.mills.edu

Brian McLaren phoned me and said that mail is now being delivered
properly to his home in Oregon and that he will send out things
he's promised people earlier. Also, Brian also offered to send some
introductory materials to newcomers to the list if they would write him
at 2462 S.E. Micah Place, Corvallis, OR 97333 USA.

BTW, an excellent introduction to Just Intonation is David Doty's
Just Intonation Primer, available through the Just Intonation
Network. See the web page at http://www.dnai.com:80/~jinetwk/other.html.

>From Kami:
> The only other time I saw this interval was in
> the scale :
> 7/7 8/7 9/7 10/7 11/7 12/7 13/7 14/7.

>From Johnny Reinhard:

> That's a really fun, ear-scorcher tuning! I've written a bit with it
> and enjoyed doing so.

Ear-scorcher? It's just the harmonic series from 7 to 14... The
inversion, Kathleen Schlesinger's diatonic Mixolydian harmonia, sounds
a bit odd, however.

--John


Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Sun, 26 Jan 1997 18:00 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA15399; Sun, 26 Jan 1997 18:00:13 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA15356
Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id JAA00719; Sun, 26 Jan 1997 09:00:09 -0800
Date: Sun, 26 Jan 1997 09:00:09 -0800
Message-Id: <199701261156_MC2-1033-FD3@compuserve.com>
Errors-To: madole@mills.edu
Reply-To: tuning@ella.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@ella.mills.edu

> > 7/7 8/7 9/7 10/7 11/7 12/7 13/7 14/7.
> > That's a really fun, ear-scorcher tuning! I've written a bit with it
> > and enjoyed doing so.
> Ear-scorcher? It's just the harmonic series from 7 to 14... The
> inversion, Kathleen Schlesinger's diatonic Mixolydian harmonia, sounds
> a bit odd, however.

As with any matter of art appreciation, that's a matter of perspective.


From the perspective of most tuning-listers, it's probably only a little
more freaky than average. From the perspective of the average Western
(culture) ear, I guarantee ya, it'll get'em screamin' in six notes flat!

But whatever your perspective, it's definitely CONCENTRATED xenharmony.
It could perhaps be described as the simplest formulation of just 7 steps,
and goes all the way up to a 13-limit.

Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Mon, 27 Jan 1997 23:27 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA16799; Mon, 27 Jan 1997 23:27:28 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA16707
Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id OAA08491; Mon, 27 Jan 1997 14:27:20 -0800
Date: Mon, 27 Jan 1997 14:27:20 -0800
Message-Id: <970127180257_74744.443_EHL128-1@CompuServe.COM>
Errors-To: madole@mills.edu
Reply-To: tuning@ella.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@ella.mills.edu

RE ether: Whether Einstein or other theorists still needed the
concept of the ether in 1920 is irrelevant to physics today.
The concept is not needed for current theories. Einstein never
accepted quantum mechanics in full and ignored the strong and
weak nuclear forces in formulating his abortive unified field
theory. He made essentially no contribution to physics after General
Relativity.

Re Rydberg states of H: Spectra of atoms more complex than hydrogen do
not have these simple relations. However, other number series than
n^2 (n 1, 2, 3 etc.) may be used for defining chords, scales
and intervals. Fokker made use of the Fibonacci and Lucas series.
Brian McLaren has proposed a number of other series. Erv Wilson has
generated many too.

Dominant 7th: While one might add the 8 to the 4:5:6:7, it is not
mandatory and makes the chord unnecessarily dense. One might add
the 9 to make a dom major 9th or 17 (8:10:12:14:17 as a minor 9th.
The 10:12:14:17 part is Ellis's diminished 7th. Other chords such
as 11:13:15:17 have been used too.

Re Aristoxenos: I think Jonathan's suggestion that reluctance to
extract the 5th root of 4/3 explains the failure of Greek theorists
to interpret Aristo correctly is a wonderful piece of insight.
I too was seduced by the octave...

Paul E: I have constructed a number of positive systems with good
Harmonic 7ths. Will post a few later when I have formatted them.
--John



Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Tue, 11 Mar 1997 03:21 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01105; Tue, 11 Mar 1997 03:21:16 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA01103
Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
id SAA16638; Mon, 10 Mar 1997 18:19:40 -0800
Date: Mon, 10 Mar 1997 18:19:40 -0800
Message-Id:
Errors-To: madole@mills.edu
Reply-To: tuning@ella.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@ella.mills.edu

-------------------- Begin Original Message --------------------

Message text written by INTERNET:tuning@ella.mills.edu

"Einstein never
accepted quantum mechanics in full and ignored the strong and
weak nuclear forces in formulating his abortive unified field
theory. He made essentially no contribution to physics after General
Relativity. "


-------------------- End Original Message --------------------

Or perhaps he planned to deal with them later.

But, that's off the subject I suppose...

Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Fri, 14 Mar 1997 07:07 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA14020; Fri, 14 Mar 1997 07:07:57 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA14019
Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
id WAA13255; Thu, 13 Mar 1997 22:06:31 -0800
Date: Thu, 13 Mar 1997 22:06:31 -0800
Message-Id: <199703140100_MC2-1291-D7D6@compuserve.com>
Errors-To: madole@mills.edu
Reply-To: tuning@ella.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@ella.mills.edu

I'll be a digest out of date by the time I send this.
Anyway, there are some things I want to say and I'll say
them all in one message. Apologies if I seem to be repeating
or ignoring someone.


LATTICES
--------

Joseph L Monzo wrote:

> Picking a particular set of pitches arbitrarily, and
> Going back to Tuning Digest 1315, here's the 7-Limit
> "Tonality Diamond" in Graham Breed's Triangular Lattice
> Diagram, which is of the type used by Erlich:

It would be more correct to say "Paul Erlich's Triangular
Lattice Diagram, which is of the type used by Breed". Paul
was using them before me, definitely extended them to the
7-limit first, and drew them in ASCII first. He also named
them "triangular". As I say on my website (and have said
before on this list) _I_ would have called them hexagonal,
like I was taught in Condensed Matter Physics.

I don't know how much, if anything, is original to Paul.
He can speak for himself on that.

> First comment: I've many times wished that we humans could
> work with more than 3 dimensions when up against the problem
> of visualizing and representing more than 3 prime dimensions
> in music. Fortunately, 7-limit systems _can_ be represented
> in three dimensions.

We can, of course, work with as many dimensions as we like
by using coordinate geometry. It is easer to "understand"
scales when you can visualise them, though. You can specify
ambiguous chords as a superposition of different matrices.
I think this has application in a dynamic tuning program.

> Graham leaves his 7-factor-ratios unconnected by
> any lines to the 3- and 5-limit ratios. If I replace
> the ratios with the prime-factor notation that I use,
> and connect the 7-ratios in a manner similar to others,

Usually, I connect all 5-limit planes in this fashion. I
don't usually do that with three planes in a diagram, because
it gets too cluttered with lines. If I were to, it would
look something like this:


B-----------F#
/ \ / \
/ \ Ab / \
/ \ / \ / \
/ E#----------B# \
/ \ / \ / \ / \
G-------\---D---/-------A
\ / \ / \ / \ /
\ Fb--\---/---Cb /
\ / \ / \ /
\ / G# \ /
\ / \ /
Bb----------F

>From the way the lines cross, you can see which plane is
supposed to be the highest, and so reconstruct it in three
dimensions in your mind. Ideally, each plane would be a
different colour. The structure is a regular dodecahedron,
or something like that.

I find it easier to understand the scales with conventional
names. There's no need for prime factorisation, because it's
implied by the lattice.


PRIME VS ODD LIMIT
------------------

The most paradoxical chord from an odd limit perspective I
find is 4:6:9. I think of it as extended 3-limit, because
it's the fifths that give it it's character. It is also
highly octave specific. It sounds more consonant
(concordant) than a major triad in root position, but
transpose it to 8:9:12 and it's clearly more dissonant.

There may be ways the ear relates to prime factors. Different
overtones will be reinforced, and the difference tone pattern
may change. This is strongly linked to timbre, though, and
breaks down before you get to 81/64.

The good intervals in equal temperaments don't usually
constitute anything like an odd limit. It's generally more
efficient to say how well different primes are approximated.
For exactness, state the signed errors, and you can work
other intervals out from that.

Incidentally, it seems to me that the concept of level-n
consistency is closely related to the recently defined
radius of the scale. If you want to use all the notes in
a radius 2 scale, it helps if it's level-2 consistent as well.


OCTAVE INVARIANCE
-----------------

There are (at least) three different concepts involved here,
which need to be distinguished for the discussion to progress:

1) The idea that harmony is unchanged if notes are transposed
independently in octaves.

2) The practice of giving notes related by octaves the same name.

3) The practice of defining scales within an octave, and
repeating them in other octaves.

In all cases the choice of the octave as an invariant interval
is not an arbitrary one. (1) I would argue with, if taken as a
fundamental principle. I won't do so in detail today, as it is
outside the brief of this list (we all now how to tune octaves!)

If the ear/brain complex has a hard-wired mechanism for
octave reduction, this would relate to the 10:12:15 vs
16:19:24 tuning of a minor triad.

Personally, I see no way in which intervals an octave apart
can be considered "the same" and my brother agrees with me.
I'm sure people can convince themselves otherwise, the same
way they learn to hear the "3-ness" in a sharp major third.


TEMPERAMENT
-----------

Joe Monzo again:

> I think a large part of the reason Schoenberg stuck with the
> 12-Eq scale was because he realized intuitively that within the
> vastly expanded resources of his implied 13-Limit, were he to
> work in just-intonation, the number-play involved could quickly
> become a bottomless pit from which his musical inspiration would
> never again emerge into the light of day. Then again, I also
> think he wanted to make use of the ambiguities made possible
> by a comparison of so many close ratios on the one hand and
> their nearby 12-Eq equivalents on the other.

Then again, perhaps Schoenberg had a piano.

> I refuse to accept an equal-temperament because it makes
> modulation "easy" or (excuse me while I laugh) "possible".

Where were you when Gregg Gibson was stomping all over the
list? Temperaments do make modulation easier, and this is
important. If this is a personal decision, though, it's fair
enough.

> The only reasons I can see for accepting any equal-temperament
> is that it is easier to play on most instruments, and, as I stated
> in another post to this issue, the study of the interplay between
> JI and ET in the same piece is becoming more and more interesting
> to me.

That sounds too dogmatic to me, perhaps it wasn't intended
to be. Other reasons are:

1) You like the sound of it.

The only reason you need.

2) It simplifies notation.

If a piece of music makes sense in JI, good musicians will
work this out from staff notation, if you point out the
difference between G# and Ab. (If there are a lot of
Pythagorean intervals, Erv Wilson's positive notation is more
useful.) Bad musicians won't be helped by precise tuning
indications. If the music doesn't make sense, who cares
how it's played?

3) It allows ambiguous chords.

I remember you (Monzo, TD1403) agreeing that the chord
below only works in meantone. Did you really mean to imply
(above) that this isn't a use for temperament?

A---E---B
\ / \
G---D---A

4) You can't be bothered to work out the ratios.

As implied in the Schoenberg paragraph, most
composers don't want to worry about ratios. They want a
resourceful scale to compose in. Give them a meantone, and
they'll find good harmonies in it. They might even give
them to musicians who'll render them in JI. Do you really
expect the composer to sit and work out where the commas
should be?


POPULAR MUSIC
-------------

Drew Skyfyre wrote:

> In an interview I just saw on TV,in which they discussed briefly,their
> middle eastern/oriental explorations,Jimmy Page said of their new
> album,Walking into Clarksdale,(I quote from memory)
> "The Oriental stuff was done by a guy called Tim from Transglobal
> Underground (a British dance music outfit) who plays an Oriental keyboard
> that plays microtones."

Cool! I've got one TGU album (Psychic Karaoke) and I've
always wondered if it's strictly 12-equal. There's no mention
of a Tim in the booklet, though. Alex Kasiek and Hamid Mantu
are both credited, among other things, with "Keyboards".

> Could this be one of those General Music "Arabian" keyboards ?

Unlikely, I'd have thought. Perhaps they just mean a tunable
synth. There's seem's to be more of an Indian than Arabic
influence in TGU, along with the dance, rap and reggae. There
are Indian Classical vocals on one track.

When I was looking for a MIDI keyboard, one of the shops I
went to said, after I asked about tuning capability, that
there'd been some Arabs in before after the same thing. I
think they use normal synths with tuning tables.

Technically, it was someone in the shop who said that, rather
than the shop itself. Anyway, you get the idea.

Also, there's an "Eno" credited on this TGU album. Probably
Brian, although could be Roger. I think Brian was mentioned
before as having used microtonality, wasn't he? Maybe there's
a connection.


BTW, anyone familiar with Nassim Maalouf?


LUCYTUNING
----------

Gary Morrison wrote:

> The semitruth: LucyTuning definitely can stack up more fifths above a tonic
> before approximately closing the circle than either quarter-comma or third-
> comma meantone. Third-comma meantone comes "close enough" at 19 fifths,
> and quarter-comma at 31 fifths. LucyTuning doesn't get there until about
> 88 fifths. But this is only a semitruth, because taken in absolutes, the
> circle of fifths never closes in ANY typical meantone tuning.

The most irrational meantone in this respect is Kornerup's
phi based tuning. Is that right? I think of it as the
standard melodic meantone.


GUITAR TUNING
-------------

Drew Skyfyre:

> I'm having a sort of eureka thing .Two recent/current threads got me
> thinking about how it is possible to put together a microtonal guitar
> (even non-tempered) and be able to modulate through quite a few keys,etc..
> The possibilities are extensive so,I'll just let you use your imagination.

> All it entails is combining a guitar with any microtonal fretting system
> (including JI) and a Steinberger TransTrem.

This is pitch shifting, presumably? It's something I had in
mind when I went for a non-equal fretting. Unfortunately,
my Zoom 505 isn't good enough to be useful in this respect.
Actually, modulation hasn't been a problem so far, as it's
common to use keys with open strings anyway. The solution
would be to tune the strings around the set of keys desired.

Incidentally, having different notes on different strings is
a _good_ thing. It means you get more chords than you would
otherwise.


John Starrett:

> If someone
> can give me a valid reason why the nut should not be treated as the 0th
> fret, I will eat a bug (I get to choose the bug and the method of
> preparation).

Fretting a note will slightly lengthen the string, and so
increase it's tension. I worked out that, to a first order
approximation, this effect is independent of where on the
fingerboard you put your finger. So, move the nut a bit
nearer the bridge than if it were the zeroth fret.

Independently movable bridges probably work for this reason,
except they're at the wrong end of the guitar!

For a guitar's tuning to be good enough to make just intonation
relevant, we do have to think about this sort of thing. The
tuning pegs are the most imprecise bit according to my ST900.
Good enough for meantone, but no better. Also, the thickest
string varies about 10 cents depending on how hard I pluck it.


Your unloveble young nutcase,

Graham Breed
www.cix.co.uk/~gbreed/