wow

man, i thought i had a pretty good grasp on musical tuning theory, but
it sounds to me like you people are speaking Klingon. wow!

not to be guilty of (only) meaningless blather, i'll share my own
personally created 28 tone scale (surely this merely re-creates what
greater minds that mine have done centuries before, but it was new to me):

1/1,21/20,16/15,15/14,10/9,9/8,8/7,7/6,6/5,5/4,9/7,21/16,4/3,7/5,...
10/7,3/2,32/21,14/9,8/5,5/3,12/7,7/4,16/9,9/5,28/15,15/8,40/21,2/1

i've been making instruments using sub-sets of this scale, and they
sound pretty cool. most fascinating is how people can tell when an
instrument is tuned right and when a note is mis-tuned. they can spot
the mis-tuned notes, even when the correctly tuned note is (for
example) 7/6, something not even closely available in our 12 tone
tempered scale.

rj

--- In tuning@yahoogroups.com, "R. J. Perz-Edwards" <rrrhythm@a...> wrote:
> man, i thought i had a pretty good grasp on musical tuning theory, but
> it sounds to me like you people are speaking Klingon. wow!

And what's more, they make it up as they go along! Papaya, anyone?

--- In tuning@yahoogroups.com, "R. J. Perz-Edwards" <rrrhythm@a...>
wrote:

> not to be guilty of (only) meaningless blather, i'll share my own
> personally created 28 tone scale (surely this merely re-creates what
> greater minds that mine have done centuries before, but it was new
to me):

I doubt it; 27 (which seems to be the actual number) tone scales with
7-limit intervals of low complexity exist in mind-bogglingly vast
numbers. Scala knows of nothing much like your scale, at any rate.

Scala does know all the intervals involve superparticular ratios, that
these vary widely in size, (from 225/224 up to 21/20), that it has 10
major/otonal tetrads and 10 minor/utonal ones, and many other facts.
What it can't tell me is what plan you used for creating it, and what
you were looking for in a scale. It has a number of notes off from 9-
limit consonances by 225/224 or 1029/1024; if we temper out both of
these (called "miracle" in these parts) we get a 25 note scale;
whether or not you would find that interesting depends on your
philosophy about scales.

Here's your scale in Scala scale file format:

! perz.scl
Perz-Edwards 27 note 7-limit scale
27
!
21/20
16/15
15/14
10/9
9/8
8/7
7/6
6/5
5/4
9/7
21/16
4/3
7/5
10/7
3/2
32/21
14/9
8/5
5/3
12/7
7/4
16/9
9/5
28/15
15/8
40/21
2

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> I doubt it; 27 (which seems to be the actual number)

indeed, a 27 note scale. my mistake.

tone scales with
> 7-limit intervals of low complexity exist in mind-bogglingly vast
> numbers. Scala knows of nothing much like your scale, at any rate.

how nice, maybe i've invented something truly new, although it
certainly feels old to me. pardon a newcomers ignorance, but who, or
what, is "Scala".
>
> Scala does know all the intervals involve superparticular ratios, that
> these vary widely in size, (from 225/224 up to 21/20),

yes, yes, very clever that Scala, can't pull one over on him/her/it.

that it has 10
> major/otonal tetrads and 10 minor/utonal ones, and many other facts.

yes. in fact there are 14 quintads (complete to 9, 7 otonal, 7
utonal), and 6 tetrads (complete to 7, again half of them utonal and
half otonal). there are also 2 tetrads of the 1-3-5-9 type, and 2 of
the 1-3-7-9 type, two 1-3-5 triads and two 1-3-7 triads. among all
these, every note acts as the root of some chord, with the exception
of 10/9, 9/7, 14/9 and 9/5.

> What it can't tell me is what plan you used for creating it, and what
> you were looking for in a scale.

actually, it came to me slowly and in pieces until it revealed itself
in it's full glory. initially, it started from taking the ptolameic
scale and thinking about how to add 7 to it, which is conspicuously
missing. in hind sight, i've realized that there is an easy way to
it. for starters, consider the ptolameic scale and it's inverse:
1/1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2/1 and 1/1, 16/15, 6/5, 4/3, 3/2,
8/5, 16/9, 2/1.

put those together and divide/multiply away all those factors of 2 and
you get:

1, 1/15, 9, 3/5, 5, 1/3, 3, 1/5, 5/3, 1/9, 15,

these are just all the possible ways of combining 2 or fewer members
of the set (1,3,5), with an arbitrary limit of 15, ordered as they
would fall within the octave. this 11 note scale, is really two
6-note scales which are the inverse of one another.

so, my 27 note scale, is all possible ways of combining 3 or fewer
members of the set (1,3,5,7) with an arbitrary limit of 21, ordered
within the octave. this is not how i initially approached this,
coming at this problem from many different directions as i was, but
it's a good working definitinition i quickly realized with hindsight.

similar to the ptolameic scale, i tend to think of the 27-note scale
as being 2 14-note scales, which are the inverse of one another, and
interpenetrate, one being major (in the sense that it has 1/1
otonality to the 9 limit) the other being minor (in the sense that it
has 1/1 utonality). which notes belong to which scale? just take
every other note, so:
1, 21/5, 15/7, 9, 7/3, 5, 21, 7/5, 3, 7/9, 5/3, 7, 9/5, 15
and 1, 1/15, 5/9, 1/7, 3/5, 9/7, 1/3, 5/7, 1/21, 1/5, 3/7, 1/9 7/15, 5/21
(sorry if this notation drives folks crazy, but i like to get rid of
all the factors of 2 because it keeps me from making math mistakes
when looking at invervals between notes. it's pretty easy to back
express them within the octve when i need, eg. 5/9 = 10/9).

like the ptolamaic scales, the intervals of the 2 individual scales
are all supernumerary. unlike the ptolameic, when you combine them
into a single scale, all of the intervals of the scale are also
supernumary.

the art of inventing scales is clearly the art of getting from 1 to 2,
and there are an infinite number of ways to do that. what i set out
to do was just take a very small step beyond what music is today
(almost all based on the ptolameic scale). i wasn't looking for
anything very radical or weird, i just wanted something that was new
but familiar. bringing 7 into the fold was the obvious way to go, and
that's what i set out to do.

if i were Bach, i'd have an organ built, with 14 keys to the octave,
and two rows of keys, one for each scale. then i could explore the
full depth of the scale. too bad i'm not! i'm just me, with very
little musical talent. but i do what i can. i'm a drummer, trained
in west african percussion, so i've been making xylophones and
kalimbas. it's fun. the kalimbas are selling pretty well, and it's
great fun to see people's reaction to them. in general, it's exactly
what i was looking for: familiar and yet different. and people (even
those with no training) instinctively recognize them as being "in
tune" even when they are not notes available in our western scale.
likewise, they can spot a key that has gotten knocked about and is
out of tune.

It has a number of notes off from 9-
> limit consonances by 225/224 or 1029/1024; if we temper out both of
> these (called "miracle" in these parts) we get a 25 note scale;
> whether or not you would find that interesting depends on your
> philosophy about scales.

oh, let us not speak of tempering. that's my philosophy at least.

one last story: there was a time when i was feverishly working all
this out, muttering under my breath and constantly scribbling numbers
on scraps of papers like a possessed man. at the moment that it was
finally showing it's full form to me, i was sitting there slightly
stunned with this chorus of angels singing in my head, reeling with
how big it seemed. at that moment my (very tolerant) wife asks,
"honey, what exactly are you doing?" when i replied, "i think i've
just invented music," she just smiled and said, "that's nice dear.
but i think it's already been done."

cheers!
rj

--- In tuning@yahoogroups.com, "R. J. Perz-Edwards" <rrrhythm@a...>
wrote:

> 1/1,21/20,16/15,15/14,10/9,9/8,8/7,7/6,6/5,5/4,9/7,21/16,4/3,7/5,...
> 10/7,3/2,32/21,14/9,8/5,5/3,12/7,7/4,16/9,9/5,28/15,15/8,40/21,2/1

Welcome!

I'm going to draw a lattice diagram of this scale, which should help
anyone using it see all its 'consonant' harmonies at a glance. The 7-
limit tetrads look like tetrahedra, etc. However, since yahoo sucks,
the lattice may look like a total mess unless you click on "reply"
and view it in quoted form in your typing window. If you still don't
see it as a nice symmetrical crystal, let me know, and I can upload
it somewhere . . .

10/9-------5/3-------5/4------15/8
/|\`. ,'/|\`. ,'/|\`. ,'/|\
/ | \40/21/ | \10/7-/-|-\15/14/ | \
/14/9-------7/6-------7/4------21/16\
/,' \`.\|/,'/ \`.\|/,'/ \`.\|/,'/ `.\
16/9-----\-4/3-/---\-1/1-/---\-3/2-/-----9/8
\`. /,\/|\/.\ /,\/|\/.\ /,\/|\/.\ ,'/
\32/21/\|/\-8/7-/\|/\12/7-/\|/\-9/7-/
\ | /28/15\ | / 7/5 \ | /21/20\ | /
\|/,' `.\|/,' `.\|/,' `.\|/
16/15------8/5-------6/5-------9/5

In this, one can explicitly see the 10 Utonal tetrads (three in the
top row, four in the bottom row, and three sticking out in the middle
row) and the 10 Otonal tetrads (four in the top row, three in the
bottom row, and three hiding behind the Utonals in the middle). Any
other 'consonant' chords or intervals are easily found as well.

Am I making any sense to you?

-Paul

RJ,

--- In tuning@yahoogroups.com, "R. J. Perz-Edwards" <rrrhythm@a...> wrote:
> pardon a newcomers ignorance, but who, or
> what, is "Scala".

Man, I can't believe *I'm* the one getting you this info, but here it
is: Scala is a freeware program for Windows, Mac, and Linux (I *think*
all three) written by list member Manuel Op de Coel, and it is one of
the true wonders of the world. It not only encompasses a HUGE library
of tunings and scales, but you can create your own and then transform
and analyze the bloody thing until the end of the universe. And it
seems every time one of the Klingons around here comes up with some
new way to mutate tunings, Manuel finds a way to add it into the program.

You can hear the scales, chords, etc. You can even bundle it with
another freeware program from another list member, Robert Walker,
called Fractal Tune Smithy, which can take Scala information directly
and generate real-time, algorithmic music.

One of the great things is that developers are now using both Scala
file formats and .tun formats (a similar format for storing tuning
information) to enable software synthesizers to actually use these
tunings for recording/sequencing/performing. A lot of this aspect is
discussed over at another forum, MMM.

Get Scala here:
http://www.xs4all.nl/~huygensf/scala/

Cheers,
Jon

Hi Jon I thought i would download it for the future but i got stuck when i
got the following directions

- go into Terminal window, use the cd command to go to the folder where the
Scala files are: cd /Applications/ScalaX
- start Scala using the command: ./scala

I could not find anything resembling a cd command nor typing that in did
anything
just in case anyone know s OS X

Jon Szanto wrote:

> RJ,
>
> --- In tuning@yahoogroups.com, "R. J. Perz-Edwards" <rrrhythm@a...> wrote:
> > pardon a newcomers ignorance, but who, or
> > what, is "Scala".
>
> Man, I can't believe *I'm* the one getting you this info, but here it
> is: Scala is a freeware program for Windows, Mac, and Linux (I *think*
> all three) written by list member Manuel Op de Coel, and it is one of
> the true wonders of the world. It not only encompasses a HUGE library
> of tunings and scales, but you can create your own and then transform
> and analyze the bloody thing until the end of the universe. And it
> seems every time one of the Klingons around here comes up with some
> new way to mutate tunings, Manuel finds a way to add it into the program.
>
> You can hear the scales, chords, etc. You can even bundle it with
> another freeware program from another list member, Robert Walker,
> called Fractal Tune Smithy, which can take Scala information directly
> and generate real-time, algorithmic music.
>
> One of the great things is that developers are now using both Scala
> file formats and .tun formats (a similar format for storing tuning
> information) to enable software synthesizers to actually use these
> tunings for recording/sequencing/performing. A lot of this aspect is
> discussed over at another forum, MMM.
>
> Get Scala here:
> http://www.xs4all.nl/~huygensf/scala/
>
> Cheers,
> Jon

-- -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 tuning@yahoogroups.com, "R. J. Perz-Edwards" <rrrhythm@a...>
wrote:

pardon a newcomers ignorance, but who, or
> what, is "Scala".

It's a program of numerous talents, which you almost certainly will
want to own. Here is the download page:

http://www.xs4all.nl/~huygensf/scala/downloads.html

> so, my 27 note scale, is all possible ways of combining 3 or fewer
> members of the set (1,3,5,7) with an arbitrary limit of 21, ordered
> within the octave.

Similar ideas are bounding the Tenney height (product of numerator
and denominator) or odd height (with the 2s taken out) or Hahn size,
etc. etc.

On one of my web pages,

http://66.98.148.43/~xenharmo/sevlat.htm

you will find an explanation (or my idea of one, at any rate) of
among other things a way of naming 7-limit tetrads in terms of
triples of integers. Using that syste, your scale has the 20 tetrads

[[0, 0, -1], [-1, 1, 0], [-1, 1, 1], [0, -2, -1], [0, -1, -2],
[0, -1, -1], [0, 0, 1], [0, -1, 0], [-1, 0, -1], [0, 1, 0],
[0, 1, 1], [-1, 0, 0], [-1,-2, -2], [-1, -1, 0], [-1, 0, 1],
[-1, -1, -2], [-1, -1, -1], [-1, -2, -1], [0, 0, 0], [0, -2, -2]]

which is actually another way of defining it. One of my favorite
scales along these lines is the cubic chord block consisting of all
chords [a1,a2,a3] with |a1|<=1. I wrote my piece "Bodacious Breed" in
this scale, tuned to 441-equal (which has the effect of tempering out
2401/2400.)

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

Now that I've got my new computer I should try to fix
the "performance" of this piece, but I think it's got a lot worth
listening to unless like some it drives you nuts merely to try.
Anyway it gives an idea of what can be done with 7-limit scales of
around this size.

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> You can hear the scales, chords, etc. You can even bundle it with
> another freeware program from another list member, Robert Walker,
> called Fractal Tune Smithy, which can take Scala information
directly
> and generate real-time, algorithmic music.

You should add one of Scala's most useful features--it can take an
ascii score in a particular format, a Scala .seq file, and convert
that into the midi file; of course that includes *microtonal* midi
files. Moreover, it can take a midi file and transform it into a .seq
file, though unfortunately if it is a microtonal file which uses
pitch bends (and almost certainly pitch bends will be what it uses)
that information will be lost.

I've not given up hope, however, since Manuel keeps improving the
program. I'd suggest either having the user define what equal
temperament he wants it translated into, or translating it
automatically into 49152-equal, or both, making 49152 a default.

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> You should add one of Scala's most useful features--it can take an
> ascii score in a particular format, a Scala .seq file, and convert
> that into the midi file; of course that includes *microtonal* midi
> files.

Unless I'm mistaken, and it is doing it other than splitting a line up
onto separate midi channels and using pitch bend to alter the notes,
most of what I hear done this way comes out unmusical (or non-musical)
in that it is not possible then to process the lines for dynamics,
touch, etc.

I don't work this way, but sometime soon when I have some extra time
I'll make up a short example that includes all kinds of nice nuance
and see what happens when I do the Scala trip.

I'm not saying it can't be done, but I am not happy with the channel
splitting idea, at least when applied to nuanced music.

Cheers,
Jon

hi R.J. and Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> Welcome!
>
> I'm going to draw a lattice diagram of this scale,
>
> <snip>

i've made a graphic of Paul's lattice and put it here:

http://launch.groups.yahoo.
com/group/tuning_files/files/perz-edwards/perz-edwards_scale.gif

delete the line-break in that URL to make the link work,
or just use this instead:

http://tinyurl.com/2t65l

-monz

Sorry Monz and R. J., I was missing some lines on the lattice.

Here's the corrected version.

Would you replace your graphic with this, Monz?

Thanks!

10/9-------5/3-------5/4------15/8
/|\`. ,'/|\`. ,'/|\`. ,'/|\
/ | \40/21/ | \10/7-/-|-\15/14/ | \
/14/9-------7/6-------7/4------21/16\
/,' \`.\|/,'/ \`.\|/,'/ \`.\|/,'/ `.\
16/9-----\-4/3-/---\-1/1-/---\-3/2-/-----9/8
\`. /,\/|\/.\ /,\/|\/.\ /,\/|\/.\ ,'/
\32/21/\|/\-8/7-/\|/\12/7-/\|/\-9/7-/
\ | /28/15------7/5------21/20\ | /
\|/,' `.\|/,' `.\|/,' `.\|/
16/15------8/5-------6/5-------9/5

done.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Sorry Monz and R. J., I was missing some lines on the lattice.
>
> Here's the corrected version.
>
> Would you replace your graphic with this, Monz?
>
> Thanks!
>
>
> 10/9-------5/3-------5/4------15/8
> /|\`. ,'/|\`. ,'/|\`. ,'/|\
> / | \40/21/ | \10/7-/-|-\15/14/ | \
> /14/9-------7/6-------7/4------21/16\
> /,' \`.\|/,'/ \`.\|/,'/ \`.\|/,'/ `.\
> 16/9-----\-4/3-/---\-1/1-/---\-3/2-/-----9/8
> \`. /,\/|\/.\ /,\/|\/.\ /,\/|\/.\ ,'/
> \32/21/\|/\-8/7-/\|/\12/7-/\|/\-9/7-/
> \ | /28/15------7/5------21/20\ | /
> \|/,' `.\|/,' `.\|/,' `.\|/
> 16/15------8/5-------6/5-------9/5

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> Unless I'm mistaken, and it is doing it other than splitting a line
up
> onto separate midi channels and using pitch bend to alter the notes,
> most of what I hear done this way comes out unmusical (or non-
musical)
> in that it is not possible then to process the lines for dynamics,
> touch, etc.

If you have 128 or fewer notes, it is preferable to use midi tuning
standard instead, at least if you don't care whether a midi player
can play your midi file.

5 1-3-5-7-9 harmonic and subharmonic pentads

monz wrote:

> done.
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> > Sorry Monz and R. J., I was missing some lines on the lattice.
> >
> > Here's the corrected version.
> >
> > Would you replace your graphic with this, Monz?
> >
> > Thanks!
> >
> >
> > 10/9-------5/3-------5/4------15/8
> > /|\`. ,'/|\`. ,'/|\`. ,'/|\
> > / | \40/21/ | \10/7-/-|-\15/14/ | \
> > /14/9-------7/6-------7/4------21/16\
> > /,' \`.\|/,'/ \`.\|/,'/ \`.\|/,'/ `.\
> > 16/9-----\-4/3-/---\-1/1-/---\-3/2-/-----9/8
> > \`. /,\/|\/.\ /,\/|\/.\ /,\/|\/.\ ,'/
> > \32/21/\|/\-8/7-/\|/\12/7-/\|/\-9/7-/
> > \ | /28/15------7/5------21/20\ | /
> > \|/,' `.\|/,' `.\|/,' `.\|/
> > 16/15------8/5-------6/5-------9/5
>
>

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

Actually, Kraig, R.J. himself wrote

"yes. in fact there are 14 quintads (complete to 9, 7 otonal, 7
utonal),"

And he's right, there are 7 of each, not 5 of each.

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> 5 1-3-5-7-9 harmonic and subharmonic pentads
>
> monz wrote:
>
> > done.
> >
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > > Sorry Monz and R. J., I was missing some lines on the lattice.
> > >
> > > Here's the corrected version.
> > >
> > > Would you replace your graphic with this, Monz?
> > >
> > > Thanks!
> > >
> > >
> > > 10/9-------5/3-------5/4------15/8
> > > /|\`. ,'/|\`. ,'/|\`. ,'/|\
> > > / | \40/21/ | \10/7-/-|-\15/14/ | \
> > > /14/9-------7/6-------7/4------21/16\
> > > /,' \`.\|/,'/ \`.\|/,'/ \`.\|/,'/ `.\
> > > 16/9-----\-4/3-/---\-1/1-/---\-3/2-/-----9/8
> > > \`. /,\/|\/.\ /,\/|\/.\ /,\/|\/.\ ,'/
> > > \32/21/\|/\-8/7-/\|/\12/7-/\|/\-9/7-/
> > > \ | /28/15------7/5------21/20\ | /
> > > \|/,' `.\|/,' `.\|/,' `.\|/
> > > 16/15------8/5-------6/5-------9/5
> >
> >
>
> -- -Kraig Grady
> North American Embassy of Anaphoria Island
> http://www.anaphoria.com
> The Wandering Medicine Show
> KXLU 88.9 FM WED 8-9PM PST

Hi Paul!
I stand corrected. but i think i noticed another feature of it. it is 3
tetradic diamonds transposed on three successive fifths.
4/3, 1/1 and 3/2. Something i have recommended to do with Partch's
diamond.

wallyesterpaulrus wrote:

> Actually, Kraig, R.J. himself wrote
>
> "yes. in fact there are 14 quintads (complete to 9, 7 otonal, 7
> utonal),"
>
> And he's right, there are 7 of each, not 5 of each.
>
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> > 5 1-3-5-7-9 harmonic and subharmonic pentads
> >
> > monz wrote:
> >
> > > done.
> > >
> > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> > > > Sorry Monz and R. J., I was missing some lines on the lattice.
> > > >
> > > > Here's the corrected version.
> > > >
> > > > Would you replace your graphic with this, Monz?
> > > >
> > > > Thanks!
> > > >
> > > >
> > > > 10/9-------5/3-------5/4------15/8
> > > > /|\`. ,'/|\`. ,'/|\`. ,'/|\
> > > > / | \40/21/ | \10/7-/-|-\15/14/ | \
> > > > /14/9-------7/6-------7/4------21/16\
> > > > /,' \`.\|/,'/ \`.\|/,'/ \`.\|/,'/ `.\
> > > > 16/9-----\-4/3-/---\-1/1-/---\-3/2-/-----9/8
> > > > \`. /,\/|\/.\ /,\/|\/.\ /,\/|\/.\ ,'/
> > > > \32/21/\|/\-8/7-/\|/\12/7-/\|/\-9/7-/
> > > > \ | /28/15------7/5------21/20\ | /
> > > > \|/,' `.\|/,' `.\|/,' `.\|/
> > > > 16/15------8/5-------6/5-------9/5
> > >
> > >
> >
> > -- -Kraig Grady
> > North American Embassy of Anaphoria Island
> > http://www.anaphoria.com
> > The Wandering Medicine Show
> > KXLU 88.9 FM WED 8-9PM PST
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
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-- -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 tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> Hi Paul!
> I stand corrected. but i think i noticed another feature of it. it
is 3
> tetradic diamonds transposed on three successive fifths.
> 4/3, 1/1 and 3/2.

Exactly. It's the union of the 7-limit diamonds centered on 4/3, 1/1,
and 3/2. In fact, you barely even need the middle one -- it only
provides two notes that the others don't: 7/5 and 10/7. I was going
to point this out to R. J., but I wanted to wait and get an initial
response from him first.

well, like i said, i THOUGHT i had a pretty firm grasp on theory until
i found this group of folks. i think i can work out what you mean by
"tetradic diamonds transposed on three successive fifths", but i'll
have to think about it. obviously, that's not something i've
considered before. i'm not a composer, so i just thought i'd post the
scale to see what folks make of it. very fascinating so far.

and i woke up last night thinking that the 2 ptolameic scales are
7-note scales, not 6-note scales which is what i wrote i think.
having trouble counting in my excitement i guess.

are there any other instrument makers out there, or do most folks go
the electronic route?

cheers,
rj

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> > Hi Paul!
> > I stand corrected. but i think i noticed another feature of it. it
> is 3
> > tetradic diamonds transposed on three successive fifths.
> > 4/3, 1/1 and 3/2.
>
> Exactly. It's the union of the 7-limit diamonds centered on 4/3, 1/1,
> and 3/2. In fact, you barely even need the middle one -- it only
> provides two notes that the others don't: 7/5 and 10/7. I was going
> to point this out to R. J., but I wanted to wait and get an initial
> response from him first.

Hello R.J.!
Not many instrument builders, but one here. Although i do quite a bit
of modifying existing instruments as it saves time and money.
Some of my instruments can be seen on this page, some of these are in the
process of being expanded
http://www.anaphoria.com/musinst.html
I imagine you ask due to being concerned how one could lay out your
tuning.
but if you have a pattern already , i would be curious to see it

"R. J. Perz-Edwards" wrote:

>
>
> are there any other instrument makers out there, or do most folks go
> the electronic route?
>
> cheers,
> rj
>

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

rj,

--- In tuning@yahoogroups.com, "R. J. Perz-Edwards" <rrrhythm@a...> wrote:
> are there any other instrument makers out there, or do most folks go
> the electronic route?

Alison Monteith took a bunch of theory gleaned here and has built a
nice ensemble of instruments and has both composed and gotten
commissions. Unfortunately, the web site appears to be down. I'll
write back.

OTOH, although this guy has no connection with the tuning list, here's
a great example of instrument design/building of a current nature:

http://www.anarchestra.net/

Cheers,
Jon

--- In tuning@yahoogroups.com, "R. J. Perz-Edwards" <rrrhythm@a...>
wrote:

> are there any other instrument makers out there,

Quite a few. Thanks to one of them (John Starrett), I have a couple
of microtonal guitars.

> or do most folks go
> the electronic route?

Many do, though there's very little that makes me (and those around
me) happier than a warm guitar . . . :)

--- In tuning@yahoogroups.com, "R. J. Perz-Edwards" <rrrhythm@a...>
wrote:
> well, like i said, i THOUGHT i had a pretty firm grasp on theory
until
> i found this group of folks. i think i can work out what you mean
by
> "tetradic diamonds transposed on three successive fifths", but i'll
> have to think about it.

I'm not sure if it'll help or not, but here's a definition
of "diamonds":

http://tonalsoft.com/enc/tondiam.htm

By "tetradic diamond" Kraig meant "7-limit diamond". The 5-limit
diamond would be "triadic", the 9-limit diamond "pentadic", and the
11-limit diamond, "hexadic".