Re: [MMM] Re: Gene's Tuning

paulerlich wrote:

> --- In MakeMicroMusic@y..., "jacky_ligon" <jacky_ligon@y...> wrote:
>
> > > What you have here is very close to the 18-tone MOS of Gene's
> > > Ennealimmal temperament.
> >
> > This is a neologism and tuning which I'm wholely unfamiliar with.
>
> I assume you understand MOS, yes?
>
> The interval 27/25 is called the "large limma". Gene noticed that it
> equals 1/9 octave almost exactly. So 1/9 octave is used as the period
> of repetition. The MOS proceeds by a generator of 49 cents. If you
> iterate this generator once, you have the 18-tone scale I mentioned
> above (virtually identical to your phi-based one). If you iterate it
> four times, so that there are 5 notes in each period of repetition,
> you get a 45-tone scale. In this scale, there are eighteen 4:5:6:7
> tetrads, and eighteen 1/(7:6:5:4) tetrads, and the intervals in these
> chords are all within 0.2 cent of JI. Astounding accuracy. The scale
> is also wonderful in the 11-limit.
>
> The full 45-tone scale will simply be the pitches
>
> 0
> 35.333
> 49
> 84.333
> 98
>
> repeated over and over again at an interval of 133.333 cents.

Any sound examples of this one?

Regards.

--- In MakeMicroMusic@y..., Alison Monteith <alison.monteith3@w...>
wrote:

> Any sound examples of this one?
>
> Regards.

I'm not too adept at making music with 45 tones per octave,
unfortunately.

How about it Gene?

--- In MakeMicroMusic@yahoogroups.com, Alison Monteith
<alison.monteith3@w...> wrote:
>
>
> paulerlich wrote:
>
> > --- In MakeMicroMusic@y..., "jacky_ligon" <jacky_ligon@y...>
wrote:
> >
> > > > What you have here is very close to the 18-tone MOS of Gene's
> > > > Ennealimmal temperament.
> > >
> > > This is a neologism and tuning which I'm wholely unfamiliar
with.
> >
> > I assume you understand MOS, yes?
> >
> > The interval 27/25 is called the "large limma". Gene noticed that
it
> > equals 1/9 octave almost exactly. So 1/9 octave is used as the
period
> > of repetition. The MOS proceeds by a generator of 49 cents. If you
> > iterate this generator once, you have the 18-tone scale I
mentioned
> > above (virtually identical to your phi-based one). If you iterate
it
> > four times, so that there are 5 notes in each period of
repetition,
> > you get a 45-tone scale. In this scale, there are eighteen 4:5:6:7
> > tetrads, and eighteen 1/(7:6:5:4) tetrads, and the intervals in
these
> > chords are all within 0.2 cent of JI. Astounding accuracy. The
scale
> > is also wonderful in the 11-limit.
> >
> > The full 45-tone scale will simply be the pitches
> >
> > 0
> > 35.333
> > 49
> > 84.333
> > 98
> >
> > repeated over and over again at an interval of 133.333 cents.
>
> Any sound examples of this one?
>
> Regards.

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> How about it Gene?

"The 45000 fingers of Dr. S" is an ennealimmal example in 54 notes to
the octave. The tuning is TOP ennealimmal, but to me it sounds like
JI.

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

Gene Ward Smith wrote:

> "The 45000 fingers of Dr. S" is an ennealimmal example in 54 notes to > the octave. The tuning is TOP ennealimmal, but to me it sounds like > JI.
> > http://66.98.148.43/~xenharmo/gene.html

It sounds remarkably out of tune for something that's been optimized for consonance, but I suppose that's 9-limit harmony for you. I like it, it's got a ghostly feel to it. Picture a supernatural piano playing to itself in a deserted old house somewhere.

Graham

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...>
> wrote:
> > How about it Gene?
>
> "The 45000 fingers of Dr. S" is an ennealimmal example in 54 notes
to
> the octave. The tuning is TOP ennealimmal, but to me it sounds like
> JI.
>
> http://66.98.148.43/~xenharmo/gene.html

Slide piano! Prent, have you checked this out?

This is enjoyable, but are you sure it got implemented the way you
wanted it? I hear a lot of pitch-bending of already sounded notes,
which reminds me a lot of various problems I've had with several MIDI
relaying applications. Or if this was intentional, maybe you could
come up with a example of this tuning where each struck note
maintains its sounding pitch throughout its duration, so one might
here what it could sound like on an actual acoustic instrument?

P.S. Using a scale with fewer than 54 notes might make a good selling
point.

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

> It sounds remarkably out of tune for something that's been
optimized for
> consonance, but I suppose that's 9-limit harmony for you.

I think it's horizontal, not vertical. The harmony moves around a lot
in all directions, so to speak.

I like it,
> it's got a ghostly feel to it. Picture a supernatural piano
playing to
> itself in a deserted old house somewhere.

The sinister Dr S!

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:

> This is enjoyable, but are you sure it got implemented the way you
> wanted it? I hear a lot of pitch-bending of already sounded notes,
> which reminds me a lot of various problems I've had with several
MIDI
> relaying applications. Or if this was intentional, maybe you could
> come up with a example of this tuning where each struck note
> maintains its sounding pitch throughout its duration, so one might
> here what it could sound like on an actual acoustic instrument?

This piece started life as a woodwind quintet, but I decided it was
sounding better in a piano version. I don't see the problem with this
myself.

> P.S. Using a scale with fewer than 54 notes might make a good
selling
> point.

To whom? That we have so many notes is I think connected to what
Graham was talking about--the piece is seriously microtonal.

Gene,
I enjoyed the piano piece "Fingers...". The pitches had a very
interesting movement, very fresh and new approach to tonality.

How did you make it? What tools?

Prent Rodgers

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
> I think it's horizontal, not vertical. The harmony moves around a lot
> in all directions, so to speak.
>
> The sinister Dr S!

--- In MakeMicroMusic@yahoogroups.com, "Prent Rodgers"
<prentrodgers@c...> wrote:
> Gene,
> I enjoyed the piano piece "Fingers...". The pitches had a very
> interesting movement, very fresh and new approach to tonality.

Thanks, Prent.

> How did you make it? What tools?

My usual--I used Scala to create a midi file, tinkered with that with
Sibelius, and rendered the midi file to wav with Audio Compositor.
This is a second version--I changed the soundfont to a Steinway after
Aaron complained my font was too effing bright.

The piece is in ennealimmal, with 54 tones to the octave. This allowed
me to move about freely in chord space, and I made use of the
2401/2400 and 4375/4374 commas to make things less static. Ennealimmal
is a microtemperament, which means you can use in in just intonation
(just pretend 2401/2400 and 4375/4374 are unisons) or retune things
very slightly so they actually are. The former some people might
prefer on more or less ideological grounds, but I don't think it has
ever been tried. Maybe I should do it, and blur the distinction
between just and tempered music.

This recording of Lou Harrison's last work, Scenes from Nek Chand, for National Steel Guitar may well be interesting to others on this list. Unlike the performance on the published cd, this strives to be JI.

http://www.archive.org/audio/audio-details-db.php?collectionid=OM8HarrisonScenesfromNikChand&collection=other_minds

Daniel Wolf

thanks for the link Daniel- I like these. The first one sounds more
Hindustani than hawaii'an. I don't understand this in the notes:

Note: This performance employs just intonation. A commercial recording on
the New Albion label (see Other Minds' webstore for availability) presents
the piece in its intended "just" intonation and casts a thoroughly different
light on the music.

Is there a misprint here? Are you saying the published CD version is in ET?

Dante

> -----Original Message-----
> From: Daniel Wolf [mailto:djwolf1@...]
> Sent: Friday, April 30, 2004 7:08 PM
> To: MakeMicroMusic@yahoogroups.com
> Subject: Re: [MMM] Re: Online Harrison recording
>
>
> This recording of Lou Harrison's last work, Scenes from Nek Chand, for
> National Steel Guitar may well be interesting to others on this list.
> Unlike the performance on the published cd, this strives to be JI.
>
> http://www.archive.org/audio/audio-details-db.php?collectionid=OM8
> HarrisonScenesfromNikChand&collection=other_minds
>
> Daniel Wolf
>
>
>
> [MMM info]------------------------------------------------------
> More MMM music files are at http://www.microtonal.org/music.html
> ------------------------------------------------------[MMM info]
> Yahoo! Groups Links
>
>
>
>
>

On Friday 30 April 2004 06:07 pm, Daniel Wolf wrote:
> This recording of Lou Harrison's last work, Scenes from Nek Chand, for
> National Steel Guitar may well be interesting to others on this list.
> Unlike the performance on the published cd, this strives to be JI.
>
>
http://www.archive.org/audio/audio-details-db.php?collectionid=OM8HarrisonScenesfromNikChand&collection=other_minds
>

Wow...... *****WOW***** !!!!!!

Daniel, thanks for sharing this. This is a piece I want to hear again and
again. It's *gorgeous* !!!!

Harrison's (and the sensitive performer, David Tanenbaum's) ability to take
his/his time and use expressive space are exquisite. There is a distinct
sarod- or sitar-like quality to the way Harrison is using the slide guitar
here, giving it a Western US as well as East Indian quality.

Speaking of the Western US, I was flooded with delightfully emotional images
of lonely highways bathed in twilight sun, of the sort one may travel in
Montana, Nevada, Wyoming, etc. Does anyone else have this sort of experience
on hearing this? It's the kind of unsentimental sentimentality that hits my
core and moves me very deeply.

The utter simplicity of the harmonic language, without artiface, is it's
greatest strength, and why it so incredibly moving for me. It's an object
lesson, as most Indian music is, in how to keep a drone interesting. It's
also one of those rare pieces that remind one of music's power.

This is 'late-night-listen-with-candles-and-relax-and-unwind' music, at its
most cosmically beautiful. What a fitting end to Harrison's life on this
'spaceship earth' !!!

10 out of 10 for raw expressive power.

Best,
Aaron Krister Johnson
http://www.dividebypi.com
http://www.akjmusic.com

--- In MakeMicroMusic@yahoogroups.com, "Aaron K. Johnson"
<akjmicro@c...> wrote:
> On Friday 30 April 2004 06:07 pm, Daniel Wolf wrote:
> > This recording of Lou Harrison's last work, Scenes from Nek
Chand, for
> > National Steel Guitar may well be interesting to others on this
list.
> > Unlike the performance on the published cd, this strives to be JI.
> >
> >
> http://www.archive.org/audio/audio-details-db.php?
collectionid=OM8HarrisonScenesfromNikChand&collection=other_minds
> >
>
> Wow...... *****WOW***** !!!!!!
>
> Daniel, thanks for sharing this. This is a piece I want to hear
again and
> again. It's *gorgeous* !!!!
>
> Harrison's (and the sensitive performer, David Tanenbaum's) ability
to take
> his/his time and use expressive space are exquisite. There is a
distinct
> sarod- or sitar-like quality to the way Harrison is using the slide
guitar
> here, giving it a Western US as well as East Indian quality.

As you know, I work in this sort of combined genre as well (for any
newbies, check out
http://www.soundclick.com/bands/3/paulerlichacousticmusic.htm --
unfortunately soundclick truncates after 10 minutes, so you can't
tell that my improvisations have form :))

Thanks for sharing, this was a real pleasure, even if the JI version
is only available on the commercial recording . . .

Gene,

{you wrote...}
>--- In MakeMicroMusic@yahoogroups.com, "Prent Rodgers"
><prentrodgers@c...> wrote:
> > I enjoyed the piano piece "Fingers..."

That's been one of my favorites as well.

> > How did you make it? What tools?
>
>My usual--I used Scala to create a midi file, tinkered with that with
>Sibelius, and rendered the midi file to wav with Audio Compositor.

You left out the part that I happen to find most fascinating: how did you *compose* it? We're in the midst of discussing what tunings to use when making music, and there is everything from plotting out the exact harmonic relationships in a tuning all the way to complete improvisation, and all the stuff in between.

How did you go about writing the piece?

>This is a second version--I changed the soundfont to a Steinway after
>Aaron complained my font was too effing bright.

I believe that should read "elfing" - I think Aaron had just come back from the last of the "Lord of the Rings" movies...

Cheers,
Jon

--- In MakeMicroMusic@yahoogroups.com, "Jonathan M. Szanto"
<JSZANTO@A...> wrote:

> You left out the part that I happen to find most fascinating: how
did you
> *compose* it? We're in the midst of discussing what tunings to use when
> making music, and there is everything from plotting out the exact
harmonic
> relationships in a tuning all the way to complete improvisation, and
all
> the stuff in between.
>
> How did you go about writing the piece?

I used the technique I've been mentioning; I composed a sort of
outline of it in 4-equal, then added harmony to that. Even 4-equal is
capable of musical qualities, strange to relate; though it has all the
features I complain of in 5-equal, only worse. But 4 or 5 equal means
you can concentrate on the broad outlines.

Gene,

{you wrote...}
>I used the technique I've been mentioning; I composed a sort of outline of >it in 4-equal, then added harmony to that. Even 4-equal is capable of >musical qualities, strange to relate; though it has all the features I >complain of in 5-equal, only worse. But 4 or 5 equal means you can >concentrate on the broad outlines.

I swear, I've never even remotely seen anything like this mentioned! I realize you do a lot of harmonization, but many people find the composition/performance of multiple-pitch tunings to be difficult with a traditional kbd layout, and I had no idea this is the tack you were following.

So, you work up pieces, a little at a time in a sequencer? Small phrases, melodies, etc? and then apply ideas of harmony on top of that.

I find it a fascinating approach, one I'll bet is virtually singular to your use. We are certainly seeing a variety of approaches to the task of composition/creation.

Thanks - honestly, I think it would be very cool to see/hear a short piece that has been finished, and be able to juxtapose it with a rendering of the original sketch...

Cheers,
Jon

--- In MakeMicroMusic@yahoogroups.com, "Jonathan M. Szanto"
<JSZANTO@A...> wrote:

> So, you work up pieces, a little at a time in a sequencer? Small
phrases,
> melodies, etc? and then apply ideas of harmony on top of that.

I go back and forth between Maple and Scala, and to some extent
imitate common-practice examples. Because I have vastly more chords to
work with, it's not exactly the same sort of thing, but I usually keep
things decidely tonal, though without emphaszing V/I; I sometimes pick
on another chord relationship and put it in something of the role of
dominant tonic, however. I don't always do this 4 or 5 equal thing,
though, or try to follow any examples for that matter.

> Gene wrote...
> >I used the technique I've been mentioning; I composed a sort of outline of
> >it in 4-equal, then added harmony to that. Even 4-equal is capable of
> >musical qualities, strange to relate; though it has all the features I
> >complain of in 5-equal, only worse. But 4 or 5 equal means you can
> >concentrate on the broad outlines.
>
> To which Jon replied...
> I swear, I've never even remotely seen anything like this mentioned! I
> realize you do a lot of harmonization, but many people find the
> composition/performance of multiple-pitch tunings to be difficult with a
> traditional kbd layout, and I had no idea this is the tack you were following.

I'm with Jon here. This is a very interesting and unique way of
working. It had never occurred to me to use one tuning (4-tet or 5-tet in your
example) as a vehicle for composing in another (say 15-tet).

In a way, this is kind of the reverse of the Schenker method of
analysis, but applied to non-I-V-I music. The 5-tet forms the harmonic skeleton
which can then be fleshed out using the full harmonic resources of the larger
tuning.

It is making me think that I should take one of my new 5-tet pieces
and see if there is a way to rehamonize it in 10-tet, 15-tet,ormaybe 20-tet...

Thanks!

--Bill Sethares

Gene,

{you wrote...}
>I go back and forth between Maple and Scala, and to some extent imitate >common-practice examples.

I guess that is one of the things that is not very obvious - neither program is a 'music' program. IOW, *where* are you adding notes to a track? How are you actually adding the counterpoint/harmony lines? (Some people create music in a notation program and export, some play 'live' into a sequencer, or use step/note input).

>I don't always do this 4 or 5 equal thing, though, or try to follow any >examples for that matter.

Right. I would think if you only worked with the 4/5 tack, you'd never have a chance of creating an interesting melody.

Cheers,
Jon

--- In MakeMicroMusic@yahoogroups.com, "Bill Sethares" <sethares@e...>
wrote:

> In a way, this is kind of the reverse of the Schenker method of
> analysis, but applied to non-I-V-I music. The 5-tet forms the
harmonic skeleton
> which can then be fleshed out using the full harmonic resources of
the larger
> tuning.

I think of the 5-et as forming a non-harmonic skeleton, with no
harmonic data carried by it; harmonic data comes from a second,
separately created source the way I work it.

> It is making me think that I should take one of my new 5-tet pieces
> and see if there is a way to rehamonize it in 10-tet, 15-tet,ormaybe
20-tet...

That would be quite different, but I think it would be worth persuing.
One possibility would be to start with 3; for each note you next
decide if it should get a +1, a 0, or a -1; this gives you 9-et. Doing
it again gives you 27-et, and again 81-et--all of which have their
uses, though if you planned to make use of meantone in 81 after all of
this I'd say good luck. I'd not recommed persuing 5-et all the way up
to 3125, either. :)

--- In MakeMicroMusic@yahoogroups.com, "Jonathan M. Szanto"
<JSZANTO@A...> wrote:
> Gene,
>
> {you wrote...}
> >I go back and forth between Maple and Scala, and to some extent
imitate
> >common-practice examples.
>
> I guess that is one of the things that is not very obvious - neither
> program is a 'music' program. IOW, *where* are you adding notes to a
track?

I'm afraid I do that in a text editor. Pretty pitiful, but it works
for my style. Even I can manage noodling around in 4 and 5, but I've
never thought about using a program to save the results. Hmmm...

> How are you actually adding the counterpoint/harmony lines? (Some
people
> create music in a notation program and export, some play 'live' into a
> sequencer, or use step/note input).

I just notate things in a text editor and create a file that Maple can
read. I can then use Maple to work with it, and print to a file that
is in a format I can add header material to by hand, converting it
into a Scala seq file. Manuel has been improving Scala, and now it has
less tendency to choke and die, and is an even more powerful
compositional tool because of that. It's still limited by midi, which
I have to turn the seq file into in order for Audio Compositor or
Timidity to do anything with the score.

>
> >I don't always do this 4 or 5 equal thing, though, or try to follow
any
> >examples for that matter.
>
> Right. I would think if you only worked with the 4/5 tack, you'd
never have
> a chance of creating an interesting melody.

What I've found surprising is how much horizontal interest one can get
even out of the seemingly pitiful 4-equal; that 5-et can sound like
music we've had examples of here recently. It's amazing but true,
though you won't morph into Tchaikovsky doing this sort of thing to be
sure. Maybe I'll try 3-equal some time, though right now I'm back
doing a 5.

Paul Erlich wrote:

> > here, giving it a Western US as well as East Indian quality.
>
> As you know, I work in this sort of combined genre as well (for any
> newbies, check out
> http://www.soundclick.com/bands/3/paulerlichacousticmusic.htm --

Paul,

This is just a suggestion, not a criticism: You might consider using something similar to the formal controls that Lou used in his pieces. Traditional forms of modal improvisation (maqam, alapana, etc) depend highly on having a reserve of known melodic figures to hold the impovisation together rhetorically for the listener. I believe that Lou was acutely aware of this and used very strict formal methods as, effectively, a substitute for the deep cultural background that he could not bring to new materials. If you are committed to your project as an improvisational one, I can not immage any reason why improvisation should not be compatible with such formal controls, indeed, I suspect it might give you more opportunity to attend to the surface (ornaments, articulation) of your improvisation.

>
> Thanks for sharing, this was a real pleasure, even if the JI version
> is only available on the commercial recording . . .
>
The websites are completely confused about which performance is JI and which is not. Is anyone on the list familiar enough with the piece to sort this out?

DJW

--- In MakeMicroMusic@yahoogroups.com, Daniel Wolf <djwolf1@a...>
wrote:
> Paul Erlich wrote:
>
> > > here, giving it a Western US as well as East Indian quality.
> >
> > As you know, I work in this sort of combined genre as well (for
any
> > newbies, check out
> > http://www.soundclick.com/bands/3/paulerlichacousticmusic.htm --
>
>
> Paul,
>
> This is just a suggestion, not a criticism: You might consider
using
> something similar to the formal controls that Lou used in his
pieces.
> Traditional forms of modal improvisation (maqam, alapana, etc)
depend
> highly on having a reserve of known melodic figures to hold the
> impovisation together rhetorically for the listener. I believe
that Lou
> was acutely aware of this and used very strict formal methods as,
> effectively, a substitute for the deep cultural background that he
could
> not bring to new materials.
>
> If you are committed to your project as an improvisational one, I
can
> not immage any reason why improvisation should not be compatible
with
> such formal controls, indeed, I suspect it might give you more
> opportunity to attend to the surface (ornaments, articulation) of
your
> improvisation.

Thanks so much Daniel. Is there any information on the Web about
these formal controls? At the moment we're mainly working on playing
in odd meters such as 5 and 7, but it would certainly be a great time
for us to inject *form* as a conscious object of training.

[PS: I'm keenly aware that the examples up there are "noodling" in
the main (you even hear me fixing the tuning several times), and the
little formal structure that they do have is chopped off by the 10-
minute time limit, so you can't hear it. The percussionist and I
happened to be invited, without warning, into a recording studio, and
the inspiration that leads to memorable (or maybe just remembering)
melodic figures, or spontaneously tight formal structures, was
clearly lacking that day. As you hear me say on the
recording, "Where's your heart" -- in a search for the suprapersonal
musical spirit that sometimes does inhabit our explorations . . .
instead, the recording captured some robotic machinations. This is my
impression, but so many people responded so positively to the
recording that I felt obliged to put it up on the web . . .]

Arabic music often uses rhythm as the unifying element, often by
determining accented and unaccented beat within such meters as these, but
then india uses both rhythm and pitch contour.
Paul Erlich wrote:

> At the moment we're mainly working on playing
> in odd meters such as 5 and 7, but it would certainly be a great time
> for us to inject *form* as a conscious object of training.

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In MakeMicroMusic@yahoogroups.com, Daniel Wolf <djwolf1@a...>
wrote:
> Paul Erlich wrote:
>
> > > here, giving it a Western US as well as East Indian quality.
> >
> > As you know, I work in this sort of combined genre as well (for
any
> > newbies, check out
> > http://www.soundclick.com/bands/3/paulerlichacousticmusic.htm --
>
>
> Paul,
>
> This is just a suggestion, not a criticism: You might consider
using
> something similar to the formal controls that Lou used in his
pieces.

Hi Daniel,

Is there anything on the web that describes these formal controls?
Can you describe them?

Our duo performed in front of hundreds of people at a festival
Saturday. We had to play for an hour. By my reckoning, compositional
sense was pretty much lost after half an hour. I don't know if anyone
noticed that, though . . . the response was really something . . .

Paul Erlich wrote:

>
>
> Hi Daniel,
>
> Is there anything on the web that describes these formal controls?
> Can you describe them?
>
As far as I know, nothing is online. You should buy a copy of Lou's book -- it's a work of art in itself. There are two editions, by the way, the first is available from Peters Edition, the second, bilingual (English-Japanese) from Frog Peak, with a few added items, including a contribution by Kraig Grady.

DJW

Daniel,

{you wrote...}
>... buy a copy of Lou's book -- it's a work of art in itself.

Absolutely. I could throw away virtually everything but that little book.

>There are two editions, by the way, the first is available from Peters >Edition, the second, bilingual (English-Japanese) from Frog Peak, with a >few added items, including a contribution by Kraig Grady.

This is really great to know, I'll be contacting Frog Peak. I recently gave Larry P. a dose of s**t for the tag line they use in their emails, but to each his own! :)

Cheers,
Jon

Jonathan M. Szanto wrote:

> This is really great to know, I'll be contacting Frog Peak. Another treasure at Frog Peak is Clarence Barlow's _Bus Journey to Parametron_ (actually 3 volumes of the journal "Feedback Papers"), which is crazy to look at (imagine an Ivor Darreg tome laid out on a PDP-11), controversial on many points, but a great insight into how a composer works (including how a composer arrives at a particular tuning system) and a work of some comic literary genius, full of puns, suggestive misspellings and grammar in freefall. Also, I'm fairly certain it's the only work of music theory including bibliographic entries for L. Lovelace and S. Milligan. I have advocated this book for years, to no avail. (My impression is that people just want to argue about his formulae without seeing the more vital context in which they appear).

Speaking of Barlough, if anyone still has an Atari ST in working condition, Bahrlo has put most of his "autobusk" software online at

http://www.mynetcologne.de/~nc-barlowcl/

DJW

Yes, the spelling of Klarenz Bhaaloh's name is variable.