Yahoo Tuning Groups Ultimate Backup tuning Re: Digest Number 350

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From: tuning@onelist.com [SMTP:tuning@onelist.com]
Sent: Wednesday, October 13, 1999 4:35 AM
To: tuning@onelist.com
Subject: [tuning] Digest Number 350

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There are 16 messages in this issue.

Topics in today's digest:

1. RE: String tension experiment -- Glen's Questions
From: "McDougall, Darren Scott - MCDDS001"
<MCDDS001@students.unisa.edu.au>
2. Cubase
From: patrick pagano <ppagano@bellsouth.net>
3. Re: Cubase
From: "Paul" <paul@i-cue.co.za>
4. Re: Digest Number 349
From: John Starrett <jstarret@math.cudenver.edu>
5. Clavichords, was Invitation
From: "D.C. Carr" <d.c.carr@obgron.nl>
6. RE: micro-guitar-tunings
From: "Canright, David" <dcanright@nps.navy.mil>
7. microguitars buzz
From: David Beardsley <xouoxno@home.com>
8. RE: RE: micro-guitar-tunings
From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
9. Re: Clavichords, was Invitation
From: "D.C. Carr" <d.c.carr@obgron.nl>
10. RE: Re: periodicity blocks algorithm
From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
11. Buzz Feiten intonation adjustments
From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
12. Re: New Haverstick CD
From: Carl Lumma <clumma@nni.com>
13. Re: analog synths & microtuning
From: "Drew Skyfyre" <drew_skyfyre@yahoo.com>
14. Re: 53-note midi sequencing
From: "Drew Skyfyre" <drew_skyfyre@yahoo.com>
15. Re: Re: A readily divisible journey into microtonalism
From: "D.Stearns" <stearns@capecod.net>
16. Kurweil K2600 !
From: "Drew Skyfyre" <drew_skyfyre@yahoo.com>

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Message: 1
Date: Tue, 12 Oct 1999 21:15:13 +0930
From: "McDougall, Darren Scott - MCDDS001"
<MCDDS001@students.unisa.edu.au>
Subject: RE: String tension experiment -- Glen's Questions

> So what you are saying is that your 12tet bass and the one in the
store were
> about 3-5 cents sharp at the first fret, became flatter until they
were in
> tune around the fourth fret, continued to flatten for a few frets,
then
> sharpened back into tune by the 12th fret?
>
Yes. But they also continued to get sharper beyond the 12th fret,
reaching over
18 cents sharp by the 24th fret. I hate fret buzz and have my action
fairly
high, so this does increase the stretching in that area of the neck.

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Message: 2
Date: Tue, 12 Oct 1999 10:41:45 -0700
From: patrick pagano <ppagano@bellsouth.net>
Subject: Cubase

hi folks
does anyone have the documentation for the 3.5 or 3.6 version of
cubase?

i really need them as a friend gave me a copy without the manual and
it
is very difficult to sort right off the bat
Thanks
Pat

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Message: 3
Date: Tue, 12 Oct 1999 16:56:56 +0200
From: "Paul" <paul@i-cue.co.za>
Subject: Re: Cubase

----- Original Message -----
From: patrick pagano <ppagano@bellsouth.net>
To: <algo-comp@onelist.com>; <tuning@onelist.com>
Sent: Tuesday, October 12, 1999 7:41 PM
Subject: [tuning] Cubase

> From: patrick pagano <ppagano@bellsouth.net>
>
> hi folks
> does anyone have the documentation for the 3.5 or 3.6 version of
cubase?

I have the getting started manual for 3.6, as well as the 3.7 update
manual.
both in pdf format. obviously if you don't have 3.7 you don't need
the
update manual.

compressed, the manual is 1.38 mb
I can mail it to you or upload it to a web page if you like.

cheers

Paul

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Message: 4
Date: Tue, 12 Oct 1999 09:08:08 -0600 (MDT)
From: John Starrett <jstarret@math.cudenver.edu>
Subject: Re: Digest Number 349

Glen Peterson:
>There's a fellow named Buzz who I think has a patent on this
technique.
>(really!) He put out a video demonstrating the wonders of his new
>fretting system. He never said how it worked, but it wasn't that
hard to
>figure out that he'd just slid the nut forward a millimeter or two.

Yes, we had a discussion of the Buzz Feiten system here awhile back,
and
while it seems to be effective (my friend Harry Fleishman heard a
side by
side of several different types guitars with and without the Feiten
system
and said the difference was obvious) I have never quite understood
why the
nut should be higher from the first fret than the first fret is from
the
second. With a zero fret, what would the solution to the problem of
differing pitch bends for different string to fret distances be?
Wouldn't
we need to consider where a player plays on average and just tune
the
bridge appropriately?

Judith Conrad:
>One can either have one string per note, as in an 'Unfretted
clavichord',
>and this was really a late-eighteenth century invention, or one can
have
>more than one string per note -- ergo 'fretted'.

You mean "more than one note per string" I think. I have never seen
the
guts of a real clavichord in person, only schematics. I would love
to play
one. Does anyone know of any in the Denver area?

Finally, Chris Mohr of Denver ordered a microtonal button matrix
thing
from Starr Labs, and it is supposed to be delivered in the next
week.
I can't wait to play it. Chris is working on a huge project, a song
cycle
based on the mystical poems of many of the worlds great poets. Man,
I hope
that wasn't suppposed to be a secret and that I got it right.

John Starrett
http://www-math.cudenver.edu/~jstarret

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Message: 5
Date: Tue, 12 Oct 1999 19:33:37 +0200
From: "D.C. Carr" <d.c.carr@obgron.nl>
Subject: Clavichords, was Invitation

Judy's pen seems to have slipped when she wrote:
"One can either have one string per note, as in an 'Unfretted
clavichord',
and this was really a late-eighteenth century invention, or one can
have
more than one string per note -- ergo 'fretted'."

There are indeed clavichords w/ more than one string per note - same
as
pianos in the treble. But she certainly meant it the other way
around:
more than one note per string: more to the point, more than one
note per
key, since the [tangent on the] key determines the pitch of whatever
string
it touches.

A usual way to arrange the frets is to put F and F# [for example] on
the
same string. The fact that these 2 pitches, being on the same
string,
cannot be used in the same harmony, is made irrelevant by the fact
that
musical practice doesn't require it.

Dale C. Carr

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Message: 6
Date: Tue, 12 Oct 1999 11:46:13 -0700
From: "Canright, David" <dcanright@nps.navy.mil>
Subject: RE: micro-guitar-tunings

in TD 343, Message 7, William Sethares wrote:
[snip]
> I also want a JI-style fingerboard, and am having
> trouble visualizing what to do.
[snip]
> Theres two interacting issues here - how to (re)tune
> the strings and how the frets are placed.
> What kinds of solutions have people come up with,
> either in wood or thought?
>
In response:
This question prompted me to put some info about my fretting choices
on my
web site; see:
http://www.mbay.net/~anne/david/frets/index.htm
(As an aside, note that my "blues" scale is the same as Kraig
Grady's
"Centaur" scale, but with an added 21/16.)
Below is an excerpt concerning general issues; the site also shows
diagrams
of 3 fingerboards.

I started with a classical guitar (Giannini) many years ago,
and wrote an article about that guitar. More recently (fewer years
ago), I bought a Martin 00016 steel-string guitar and an
interchangeable fingerboard kit from Mark Rankin, and hired a
luthier
to make the modifications and the fingerboard blanks including a
standard (12-tone equal tempered) fingerboard. After some thought,
I fretted one fingerboard based on the idea of blues in A, using a
7-limit scale. Lately, I'm considering fretting another fingerboard
to
get harmonic scales (8-16) on E and A.

Here are some issues that arose:

* How close can frets be?

On my Giannini, I chose frets straight across, and lots of 'em (37
in
the first octave). All the frets are playable. The closest frets are
4mm
apart, center to center, and the frets themselves are 2mm wide, so
the gap is a fret-width. With frets this close, one needs to be very
careful to get the fret heights uniform to insure playability and no
buzz.
In my experience, fret separations of 6mm or more are relatively
easy
to play. (The closest frets on my Martin fingerboard are 5mm, but
the
upper note is not in the scale; see below.)

Of course, to play such frets requires precise finger placement, but
no
extra pressure is required. Naturally, wider fret spacing makes for
easier playing, particularly when trying to play chords. Barred
chords
with staggered frets can be tricky.

* Extra frets just above others are not a problem

In some cases on the Martin fingerboard, it was easiest to use a
full
fret where the scale would call for a partial fret with a gap.
Provided
this extra fret was just above (sharp) of the scale fret, the extra
fret
did not get in the way. For example, the 3/2 fret gives a 27/16 on
the
B (9/8) string, just (a comma) above the fret for 5/3. The extra
(27/16) fret does not make the usual fret (5/3) any harder to play,
and because it is so close, it hardly reduces the space to the fret
above (7/4), so that one is really no harder to play either.

This led me to the realization that an "alternate" note will not get
in the
way provided it is a comma sharp of a "standard" note in the scale.
The alternate itself will be harder to play, but the rest of the
scale
won't. (Unfortunately for my blues fingerboard, the alternate D is
21/16, which is below the standard D 4/3, so playing the standard D
4/3 requires particular attention.) I plan to take advantage of this
in
future fingerboards, to throw in a few extra (sharp) notes that I
can
get when I really want them.

* The open strings don't have to be tuned to the scale

I am pretty slow about tuning the strings, in part because I am very
particular about getting it as right as I can, to my ear. (I tune by
harmonics, and it works very well for me. Even when I tune
tempered, I do it based on beats in the harmonics.) In contrast,
changing fingerboards is pretty quick and easy. So for me, the idea
of
using one tuning for more than one fingerboard seems attractive.

But a natural approach is to tune the strings to the scale. For
those
that do a lot with open strings, this makes good sense. (I'm not a
very
good guitarist, but I like to play melodies all over the neck and
don't
always use open strings.) Of course, the choices of scale and string
tuning determine fret positions, which affects the playability (and
navigability too!).

For my first interchangeable fingerboard, I used standard EADGBE
tuning, but all pure fourths (3/2 1/1 4/3 16/9 9/8 3/2, to A440),
even
though the G in the scale is 7/4, not 16/9. This means I can never
play an open G with a fretted G (unless I'm into ugly). But had I
instead chosen an open G 7/4, the frets on the G string would all
have
to go up a bit, resulting in many more partial frets for just the
one
string. Not only would the fingerboard be harder to make, but a bit
harder to play as well. Having all my open fourths perfect makes the
frets simpler, and when they go straight across several strings I
know
those fourths are perfect too, which helps in understanding which
frets are which in the scale. (I may use the same tuning for my next
fingerboard as well, for harmonic scales 8-16.)

Using "dofrets.eps" to visualize the frets helps in exploring the
possibilities...

David Canright http://www.mbay.net/~anne/david/

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Message: 7
Date: Tue, 12 Oct 1999 14:46:12 -0400
From: David Beardsley <xouoxno@home.com>
Subject: microguitars buzz

John Starrett wrote:

> Glen Peterson:
> >There's a fellow named Buzz who I think has a patent on this
technique.
> >(really!) He put out a video demonstrating the wonders of his new
> >fretting system. He never said how it worked, but it wasn't that
hard to
> >figure out that he'd just slid the nut forward a millimeter or
two.
>
> Yes, we had a discussion of the Buzz Feiten system here awhile
back, and
> while it seems to be effective (my friend Harry Fleishman heard a
side by
> side of several different types guitars with and without the
Feiten system
> and said the difference was obvious) I have never quite understood
why the
> nut should be higher from the first fret than the first fret is
from the
> second.

He's shortening the scale length so all the frets are affected.

> With a zero fret, what would the solution to the problem of
> differing pitch bends for different string to fret distances be?
Wouldn't
> we need to consider where a player plays on average and just tune
the
> bridge appropriately?

What's a zero fret?

--
* D a v i d B e a r d s l e y
* xouoxno@virtulink.com
*
* J u x t a p o s i t i o n N e t R a d i o
*
*
* http://www.virtulink.com/immp/lookhere.htm

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Message: 8
Date: Tue, 12 Oct 1999 14:59:34 -0400
From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
Subject: RE: RE: micro-guitar-tunings

I wrote,

>> Have you heard Eduardo Sabat-Garibaldi's 53-tone (scale of
>> commas) guitarists?

Glen Peterson wrote,

>No. Is there a web site or could you list the ratios and cents?

The notes on one string form a chain of 52 fifths, each diminished
by 1/9
schisma (about 2/9 of 1 cent). It's pretty close to 53-tET. See also
Eduardo's reply from this weekend.

>Leave off a string or two

It just so happens that I have no 2nd string right now! Still,
bending on
the 1st string is limited to a half step; a whole step bend forces
me to
mute the 3rd string.

Thanks for your other suggestions.

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Message: 9
Date: Tue, 12 Oct 1999 21:04:45 +0200
From: "D.C. Carr" <d.c.carr@obgron.nl>
Subject: Re: Clavichords, was Invitation

-----Original Message-----
From: D.C. Carr <d.c.carr@obgron.nl>
To: tuning <tuning@onelist.com>
Date: Tuesday, October 12, 1999 8:39 PM
Subject: Clavichords, was Invitation

|[...] more to the point, more than one note per
|key, since the [tangent on the] key determines the pitch of
whatever string
|it touches. [....]

Now my own pen seems to've slipped! It's just simply 'more than one
note
per string', not 'more than one note per key'.

That's what I get for sticking my tangents into other people's
business.

Dale

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Message: 10
Date: Tue, 12 Oct 1999 15:36:33 -0400
From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
Subject: RE: Re: periodicity blocks algorithm

I wrote,

>> But still, you may have an interval between two
>> notes (say, in opposite halves of the hexagon) that is smaller
than a
unison
>> vector, since the complexity limit is defined only with respect
to the
note at
>> the origin. Isn't that right?

Kees wrote,

>I guess that could happen. But I'm pretty sure it would be a linear
>combination of 'known' unison vectors. So it won't spoil the
'logic' of the
>interpretation inside the complexity limit. (I think)

Well, to me, interpreting a JI pitch set as "closed" seems illogical
in such
a case.

>> One interesting question is whether these alternate numbers lead
to
periodicity
>> blocks with the property I'm looking for (all intervals smaller
than
unison
>> vectors).
>
>I'm still not sure what you mean by 'all intervals of a periodicity
block'.
>Does that concept follow from the Fokker material? Do you mean all
intervals
>inside the parallelogram? From my interpretation a (d determinant)
>periodicity block maps all possible (p-limit) intervals to d
equivalence
>classes. From that point of view there is not _a_ parallelogram,
but lots
of
>possible shapes containing representatives of those classes. Can
you say in
>that context which intervals should be smaller than the unison
vectors ?

I did mention in one post that I don't like "holes" -- so I guess
what I'm
looking for, out of the infinitude of possible shapes, are ones that
are
fully connected in the triangular lattice. If you can find any such
shape in
which all intervals are smaller than the unison vectors, then you
would seem
justified in claiming that a scale of d notes can arise as a
naturally
closed system in JI. I posted a couple of 3-D (3,5,7) lattice
diagrams of
the parallelopiped shape for a few UV triplets. The 27-tone one did
have the
property I'm looking for.

The variety of possible shapes to consider is still huge. Perhaps
limiting
oneself to the parallelogram/parallelopiped is one way to make the
search
reasonable -- even in that case, you usually still have a few
alternatives
to consider (e.g., vertex on a lattice point, center on a lattice
point,
etc.). Or if you have an alternate suggestion for a consistent
shape-formulation, I'd love to hear it.

Also, I believe your work raises a few other interesting issues that
are
relevant to previous discussions on this list -- I hope you stick
around!

-Paul

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Message: 11
Date: Tue, 12 Oct 1999 16:29:08 -0400
From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
Subject: Buzz Feiten intonation adjustments

John Starrett wrote,

>I have never quite understood why the
>nut should be higher from the first fret than the first fret is
from the
>second. With a zero fret, what would the solution to the problem of
>differing pitch bends for different string to fret distances be?
Wouldn't
>we need to consider where a player plays on average and just tune
the
>bridge appropriately?

Yes. One would not adjust the zero fret. The reason for adjusting
the nut is
that is usually quite a bit higher than the frets. The amount of
extra
pressure required to press a string down to the first fret is
therefore
considerable (try an F minor chord with heavy strings!), and even
with
appropriate bridge adjustment giving, say, a perfect octave at the
12th
fret, notes on the first (and to some degree, second and third) fret
will
tend to be too sharp.

Although the correct adjustment to the fret placements will be some
sort of
complex mathematical function of the nut height, bridge height, and
string
tension/stiffness, adjusting the bridge _and_ nut positions, as well
as the
open string tuning, gives you three parameters (really, two
"interesting"
parameters; the open string tuning is like a constant term) with
which to
approximate that function, which is of course better than one
parameter
(bridge position only). According to Steve Vai, Buzz Feiten's system
involves a separate nut, bridge, and tuning adjustment for each
string.

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Message: 12
Date: Tue, 12 Oct 1999 17:12:58 -0400
From: Carl Lumma <clumma@nni.com>
Subject: Re: New Haverstick CD

Thank you, Dan!

-C.

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Message: 13
Date: Wed, 13 Oct 1999 04:54:13 +0530
From: "Drew Skyfyre" <drew_skyfyre@yahoo.com>
Subject: Re: analog synths & microtuning

Darren, John L., Thanks !

I understand now. I also found some interesting, related articles on
John
Allen's pages (http://web0.tiac.net/users/jsallen/music/ [I
think]).

> Note that digitally controlled analog synths and digitally
emulated analog
> synths may quantize the "voltage control" or keyboard tracking so
that nET
> scales of any degree are not possible.

Most likely, as fas as the info from a controller(keyboard,etc.
goes,
but the "key tracking" parameter that exists in many digi-analog
synths
is documented by all the companies I've seen as capable of of true
nET
microtuning. I've checked at Waldorf, Doepfer, Access, Nord.
Oberheim's OB-Mx, I don't know (too expensive even for my fantasies
:-),
but I know it DOES have tuning tables.

Quasimidi's Polymorph (
http://www.quasimidi.com/englisch/polymorp.htm )
is a groovy synth, but I was unable to determine if it has key
tracking.

My curiousity got me looking around & many (but not all) of the
analog/digital modelling, etc. synths currently available offer
key-tracking, allowing the exploration of myriad Equal Temperaments.
Waldorf's implementation appears to be the best, with the widest
range :
-100% to +200%, with +100% yielding divisions of 1 semitone
(100cents),
being 12EDO (12tET). What's nice is these companies actually include
this
feature, & actually document the potential microtonal use, rather
than just
an "effect".

The synths that don't offer key tracking seem to be mostly the
monophonic
Roland 303 clones, made by numerous companies.

Funny thing is, the non-analog Ensoniq ASR-X pro has a parameter
called
"key track", with a range of fractional negative & positive options
:

" Off, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, normal,
9/8, 5/4, 11/8, 3/2, 13/8, 7/4, 15/8, 2, Pitch Table "

With 1/1 (8/8) being "normal", & the option to just select the pitch
table
(tuning table) of the synth.

I suppose this means that there's a whole bunch of ET options
available, in
addition to the presets in the tuning table ?

___________________________________________________________________________
Virus Access "analog" synth
http://www.access-music.de/index.html

From the PDF manual :

KEY FOLLOW (EX)
Determines the intensity of the pitch control via the keyboard: At
the value
+32 (standard setting) the oscillator is controlled normally, i.e.
the
octave you play is identical to the octave of the oscillator; at +63
every
ascending octave you play transposes the oscillator upwards by two
octaves
(whole tone scale); +15 transposes the oscillator upwards by one
octave for
every two ascending octaves you play (quarter tone scale); at 0 the
keyboard
control option is off.
Negative values generate opposite control intensities.

____________________________________________________________________________

BTW, I've been looking at the demo of the latest SuperCollider
release
(2.2.1), http://www.audiosynth.com , & it just gets better all the
time !
PowerMac only, btw.

It is so easy to work microtonally & in real time ! There r a few
microtonal
examples included. James, I don't know if you're on this list, but
trust me,
if I had the money, I'd have sent you the $250 a while ago !
Meantime, I'll
try to learn how to use it.

Personally I believe SC2 is the ONLY software synth worth using,
with the
exception of the icon-based Max-MSP, though SC is more powerful & is
more
efficient.

____________________________________________________________________________

Salut,
Drew

__________________________________________________
Do You Yahoo!?
Bid and sell for free at http://auctions.yahoo.com

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Message: 14
Date: Wed, 13 Oct 1999 05:22:10 +0530
From: "Drew Skyfyre" <drew_skyfyre@yahoo.com>
Subject: Re: 53-note midi sequencing

Ben, a few random thoughts :

1) Lime (notation software, @$60.00, Win/Mac)
http://datura.cerl.uiuc.edu/Lime/WhatsNew.html

But you'll need a way to convert(map) the MIDI output to allow
your synth to actually play microtonally, perhaps Max on a Mac.

2) Common Music (Win/Mac/etc.)
http://ccrma-www.stanford.edu/CCRMA/Software/cm/cm.html

You'll have to change the way u work to use CM, since it involves
specifying your music in a text file program of sorts, somewhat
like
Csound. But CM is NOT a synthesis program. It is a built for
composition,
is OMS savvy & well suited to MIDI use.

This may be the easiest (& a more rewarding) way to work with
microtonality, especially when dealing with tunings with
more than 12 notes. Personally I'm trying to break away from the
conventional linear approach to composing music, mainly inspired
by
playing with the SuperCollider demo ( & glorious lack of formal
training
!:-)

3) Use a sequencer that allows u to create "note name" lists, such
as the
kind that shows up for percussion tracks, with the name of ea.
instrument
beside the appropriate MIDI note no. So u can make a note name
lis
featuring anything u need.

Try : MidiGraphy (Mac)
http://ux01.so-net.ne.jp/~mmaeda/indexe.html

------------------------------------------------------
Interesting reading can be found here :
http://home.t-online.de/home/j.ingram/index.htm

The home page of James Ingram, the chap who does work for
Stockhausen.
See his info about his work for the big S. & The Notation of Time
(Essay, 1985)

------------------------------------------------------

I came across a couple of neat Brian McLaren posts from a while
back. Not
sure where I found them, but the subject of ea. is :

- Approaches to microtonal notation

- Xenharmonic scores (this one is neat with this enlightening intro
:
" After hearing my music, most people ask: "Do you have scores?"
The answer is always: "Yes--the scores are MIDI files."
To which the inevitable reply is,
"No, I mean do you have actual *scores*?"
"Yes. Here are the MIDI files."
"do you have actual *scores*?"
"Yes. Here are the MIDI files."
"No, I mean SCORES. Real SCORES."
"The MIDI files are the scores."
"No, I mean *SCORES*..."
And so on. "
------------------------------------------------------

- Drew

__________________________________________________
Do You Yahoo!?
Bid and sell for free at http://auctions.yahoo.com

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Message: 15
Date: Tue, 12 Oct 1999 20:34:38 -0700
From: "D.Stearns" <stearns@capecod.net>
Subject: Re: Re: A readily divisible journey into microtonalism

[Paul Erlich:]
> 3. The number of exceptions to strict propriety would be numerous.
While the diatonic scale in 12-equal has one exception (aug. 4th =
dim. 5th), and both decatonic scales in 22-equal as well as the
"diatonic pentatonic" in whatever have none,

Yes, I guess you could say that 12 (and its successive multiples) is
a
sort of the propriety borderline when mapping a 2L & 8s step
structure, as everything > would be strictly proper (though less and
less meaningfully so, the higher and further you go), and everything
<
would be improper... there seems to be a lot of pretty nice 2L & 8s
strictly proper decatonics that fall between the 12 and the 22,
where
the equal division of the octave isn't either too large, or, so
close
to the 12 that a difference between the largest interval of one
class
and the smallest interval of the next class approaches triviality.
Once you start to exceed 22*n, where n is the n of L=s+n, you can
work
the 2nds & 7ths closer to 16/15 & 8/7, and 15/8 & 7/4, but you'd
also
be working everything else closer and closer to 10e, hence, nearer
to
neutral 3rds & 6ths, and 5e 5ths & 4ths... Here are some of those
that
I was referring to where the 2L & 8s is <22*n & >12*n (and the
additional chromatic step is therefore >0 & <L-s).

L=5 s=3
0 3 6 11 14 17 20 25 28 31 34

L=7 s=4
0 4 8 15 19 23 27 34 38 42 46

L=8 s=5
0 5 10 18 23 28 33 41 46 51 56

L=11 s=7
0 7 14 25 32 39 46 57 64 71 78

L=12 s=7
0 7 14 26 33 40 47 59 66 73 80

L=13 s=8
0 8 16 29 37 45 53 66 74 82 90

L=14 s=9
0 9 18 32 41 50 59 73 82 91 100

L=17 s=11
0 11 22 39 50 61 72 89 100 111 122

etc.

Dan

PS - This list doesn't include 2L 8s decatonics like 58, 70 & 82e,

L=9 s=5 0 5 10 19 24 29 34 43 48 53 58
L=11 s=6 0 6 12 23 29 35 41 52 58 64 70
L=13 s=7 0 7 14 27 34 41 48 61 68 75 82,

where the difference between the largest interval of one class and
the
smallest interval of the next aren't necessarily so bad, but are
growing successively smaller than a syntonic comma - in other words
I
used the 81/80 as a cut off point (and I think that all of the
approximate ratio interpretations of the interval classes in your
22e
decatonic are also separated by at least an 81/80?).

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Message: 16
Date: Wed, 13 Oct 1999 13:36:23 +0530
From: "Drew Skyfyre" <drew_skyfyre@yahoo.com>
Subject: Kurweil K2600 !

o.k. how many of u knew Kurzweil had a K2600 out !?

http://www.youngchang.com/kurzweil/html/k2600.html

Mega bucks :
Suggested List Price -
K2600R $5,175.00
K2600RS $5,950.00

But there it is !

- Drew

__________________________________________________
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Re: Digest Number 350

🔗John Starrett <jstarret@xxxx.xxxxxxxx.xxxx>

🔗Stearns, Greg <STEARNSG@xxx.xxxx.xxxx>