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Re: [MMM] Re: mixing Equal Temperaments of 11 & 7

🔗Phil Collins <pmcomp@...>

2/3/2007 9:11:32 AM

hi monz,
Thank you for replying to my posting. Unfortunately, I am very new to
the intricacies of tuning jargon and the math end of it is an obstinate
impediment. I have become accustomed with some of the just ratios and
the cents-o-meter, but not much further than that.
I'm not familiar with EDO. When I went to the site you gave me, I found
a series of numbers and signs that I don't understand.
anyway, I appreciate it. I'm going to NZ to give talk about the matter
this week and I've at least got some hands-on experiementation under my
belt.

Phil


monz wrote:Hi Phil,


--- In MakeMicroMusic@yahoogroups.com, "fikolanzo" <pmcomp@...> wrote:
>
> I am working on ways to combine and integrate 7-tone
> Thai Equal Temperament with Western 11-tone Equal Temperament.
> I would like advise from anyone who has experience and/or
> solutions regarding the possibilities and problems of this
> matter. thank you. I am not interested in altering either
> system, except to have the Thai instruments tune to
> Bb=466.165, according to western equal temperament.
> thank you,
> Phil


It took me about 2 minutes to create a Tonescape
.tuning file of this:

/makemicromusic/files/monz/7-and-11-edo-combined_phil_mmm15852.tuning



On the Lattice, i have 11-edo on the horizontal axis and
7-edo on the vertical, and each step along a Lattice axis
represents one degree of the EDO, with the origin at the
center.

I wasn't sure if you wanted the origin to be tuned
to the Bb 466.165 Hz, so i left it at the default
A 440. You can go to "File | Reference Pitch" to
change that ... but BE SURE TO TYPE THE KEYBOARD
'ENTER' KEY WHILE THE MOUSE IS POSITIONED OVER
THE SLIDER! in order to have Tonescape accept the change.


You can download Tonescape from my website homepage.


-monz
http://tonalsoft.com
Tonescape microtonal music software








🔗monz <monz@...>

2/3/2007 10:03:20 AM

Hi Phil,

EDO is an acronym for "Equal Division of the Octave".
Basically it just means the same thing as "Equal Temperament",
but because an equal temperament can be an equal division
of some other interval instead of an octave, EDO makes
it more definite.

I set up your tuning as a Tonescape file in such a
simple way that you really don't need to understand
anything more than you already do, in order to play
around with it and compose some music. So to help avoid
the confusion, here's the direct link to the software:

http://tonalsoft.com/downloads/redist/Tonescape_Studio_Den_Haag.exe

If you have a Windows XP system with the necessary
hardware, you can download Tonescape, load your tuning,
and start composing!

Tonescape has two main windows:

. one called Pitch-Height which is similar to the
familiar "piano-roll" view found on most MIDI sequencers,
except that it's quantized to whatever spacing your
tuning has (instead of the standard 12-EDO); and

. the Lattice window, which shows the harmonic
relationships between the notes of your tuning.

From your first post i knew that you're a newbie
to all this, so i kept the Lattice of your tuning
simple by just putting 11-EDO along one axis and
7-EDO along the other, and using the step-size of
each tuning as the axis steps on the Lattice.

Hopefully you can get Tonescape working and try it out.

PS -- Are you the Phil Collins who was a superstar
in the '80s?

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In MakeMicroMusic@yahoogroups.com, Phil Collins <pmcomp@...> wrote:
>
> hi monz,
> Thank you for replying to my posting. Unfortunately,
> I am very new to the intricacies of tuning jargon and
> the math end of it is an obstinate impediment. I have
> become accustomed with some of the just ratios and
> the cents-o-meter, but not much further than that.
> I'm not familiar with EDO. When I went to the site
> you gave me, I found a series of numbers and signs
> that I don't understand. anyway, I appreciate it.
> I'm going to NZ to give talk about the matter this
> week and I've at least got some hands-on experiementation
> under my belt.
>
> Phil
> 
>
> monz wrote:Hi Phil,
> 
>
> --- In MakeMicroMusic@yahoogroups.com, "fikolanzo" <pmcomp@> wrote:
> >
> > I am working on ways to combine and integrate 7-tone
> > Thai Equal Temperament with Western 11-tone Equal Temperament.
> > I would like advise from anyone who has experience and/or
> > solutions regarding the possibilities and problems of this
> > matter. thank you. I am not interested in altering either
> > system, except to have the Thai instruments tune to
> > Bb=466.165, according to western equal temperament.
> > thank you,
> > Phil
> 
>
> It took me about 2 minutes to create a Tonescape
> .tuning file of this:
>
>
/makemicromusic/files/monz/7-and-11-edo-combined_phil_mmm15852.tuning
>
> 
>
> On the Lattice, i have 11-edo on the horizontal axis and
> 7-edo on the vertical, and each step along a Lattice axis
> represents one degree of the EDO, with the origin at the
> center.
>
> I wasn't sure if you wanted the origin to be tuned
> to the Bb 466.165 Hz, so i left it at the default
> A 440. You can go to "File | Reference Pitch" to
> change that ... but BE SURE TO TYPE THE KEYBOARD
> 'ENTER' KEY WHILE THE MOUSE IS POSITIONED OVER
> THE SLIDER! in order to have Tonescape accept the change.
>
>
> You can download Tonescape from my website homepage.

🔗Rick McGowan <rick@...>

2/3/2007 10:08:20 AM

> I am working on ways to combine and integrate 7-tone
> Thai Equal Temperament with Western 11-tone Equal Temperament.

Are you all sure the question was really about "11"? And that "11" isn't
really a typo for "12"? After all, "11" isn't the ordinary western tuning,
and I don't know why someone would be interested in integrating 11 and 7
together, unless they have some orchestra of non-Western instruments in 11
tones/octave.

Rick

🔗Phil Collins <pmcomp@...>

2/3/2007 10:25:03 AM

monz,
that is very nice to know. One impediment, I'm a Mac-guy. I will be copy
your info and take it to NZland, where I surely will be able to avail
myself upon a PC person to try it out. If you can recommend a Mac-way to
get there, I'd love to know.
Thanks for your time and effort.
Phil

monz wrote:

> Hi Phil,
> 
>
> EDO is an acronym for "Equal Division of the Octave".
> Basically it just means the same thing as "Equal Temperament",
> but because an equal temperament can be an equal division
> of some other interval instead of an octave, EDO makes
> it more definite.
>
> I set up your tuning as a Tonescape file in such a
> simple way that you really don't need to understand
> anything more than you already do, in order to play
> around with it and compose some music. So to help avoid
> the confusion, here's the direct link to the software:
>
> http://tonalsoft.com/downloads/redist/Tonescape_Studio_Den_Haag.exe
> 
>
> If you have a Windows XP system with the necessary
> hardware, you can download Tonescape, load your tuning,
> and start composing!
>
> Tonescape has two main windows:
>
> . one called Pitch-Height which is similar to the
> familiar "piano-roll" view found on most MIDI sequencers,
> except that it's quantized to whatever spacing your
> tuning has (instead of the standard 12-EDO); and
>
> . the Lattice window, which shows the harmonic
> relationships between the notes of your tuning.
> 
>
> >From your first post i knew that you're a newbie
> to all this, so i kept the Lattice of your tuning
> simple by just putting 11-EDO along one axis and
> 7-EDO along the other, and using the step-size of
> each tuning as the axis steps on the Lattice.
> 
>
> Hopefully you can get Tonescape working and try it out.
> 
>
> PS -- Are you the Phil Collins who was a superstar
> in the '80s?
> 
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
> 
> 
>
> --- In MakeMicroMusic@yahoogroups.com, Phil Collins <pmcomp@...>
> wrote:
> >
> > hi monz,
> > Thank you for replying to my posting. Unfortunately,
> > I am very new to the intricacies of tuning jargon and
> > the math end of it is an obstinate impediment. I have
> > become accustomed with some of the just ratios and
> > the cents-o-meter, but not much further than that.
> > I'm not familiar with EDO. When I went to the site
> > you gave me, I found a series of numbers and signs
> > that I don't understand. anyway, I appreciate it.
> > I'm going to NZ to give talk about the matter this
> > week and I've at least got some hands-on experiementation
> > under my belt.
> >
> > Phil
> >
> >
> > monz wrote:Hi Phil,
> >
> >
> > --- In MakeMicroMusic@yahoogroups.com, "fikolanzo" <pmcomp@> wrote:
> > >
> > > I am working on ways to combine and integrate 7-tone
> > > Thai Equal Temperament with Western 11-tone Equal Temperament.
> > > I would like advise from anyone who has experience and/or
> > > solutions regarding the possibilities and problems of this
> > > matter. thank you. I am not interested in altering either
> > > system, except to have the Thai instruments tune to
> > > Bb=466.165, according to western equal temperament.
> > > thank you,
> > > Phil
> >
> >
> > It took me about 2 minutes to create a Tonescape
> > .tuning file of this:
> >
> >
> h
> tp://launch.groups.yahoo.com/group/makemicromusic/files/monz/7-and-11-edo-combined_phil_mmm15852.tuning
>
> >
> >
> >
> > On the Lattice, i have 11-edo on the horizontal axis and
> > 7-edo on the vertical, and each step along a Lattice axis
> > represents one degree of the EDO, with the origin at the
> > center.
> >
> > I wasn't sure if you wanted the origin to be tuned
> > to the Bb 466.165 Hz, so i left it at the default
> > A 440. You can go to "File | Reference Pitch" to
> > change that ... but BE SURE TO TYPE THE KEYBOARD
> > 'ENTER' KEY WHILE THE MOUSE IS POSITIONED OVER
> > THE SLIDER! in order to have Tonescape accept the change.
> >
> >
> > You can download Tonescape from my website homepage.
> 
> 
> 
> 
> 
> 
> 

🔗Phil Collins <pmcomp@...>

2/3/2007 10:39:23 AM

Rick,
you are correct, sir!
it's a misnomer (number) that evolved over time following a friend's
likening my situation to modern conveniance of 7-11
I do indeed mean 12.

your mentioning of it is a welcome cautioning before I get too hung up
on marketing.
Phil

Rick McGowan wrote:
> I am working on ways to combine and integrate 7-tone
> Thai Equal Temperament with Western 11-tone Equal Temperament.

Are you all sure the question was really about "11"? And that "11" isn't

really a typo for "12"? After all, "11" isn't the ordinary western
tuning,
and I don't know why someone would be interested in integrating 11 and 7

together, unless they have some orchestra of non-Western instruments in
11
tones/octave.

 Rick



🔗Gene Ward Smith <genewardsmith@...>

2/3/2007 10:42:54 AM

--- In MakeMicroMusic@yahoogroups.com, "monz" <monz@...> wrote:

> EDO is an acronym for "Equal Division of the Octave".
> Basically it just means the same thing as "Equal Temperament",
> but because an equal temperament can be an equal division
> of some other interval instead of an octave, EDO makes
> it more definite.

EDO does not entail that it is a temperament.

🔗monz <monz@...>

2/3/2007 11:10:04 AM

Hi Phil,

No, sorry -- Tonescape is Windows-only, unless the new
Mac-with-Windows will run it, which i'm not sure of.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In MakeMicroMusic@yahoogroups.com, Phil Collins <pmcomp@...> wrote:
>
> monz,
> that is very nice to know. One impediment, I'm a Mac-guy.
> I will be copy your info and take it to NZland, where I
> surely will be able to avail myself upon a PC person to
> try it out. If you can recommend a Mac-way to get there,
> I'd love to know.
> Thanks for your time and effort.
> Phil

🔗monz <monz@...>

2/3/2007 11:24:02 AM

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "monz" <monz@> wrote:
>
> > EDO is an acronym for "Equal Division of the Octave".
> > Basically it just means the same thing as "Equal Temperament",
> > but because an equal temperament can be an equal division
> > of some other interval instead of an octave, EDO makes
> > it more definite.
>
> EDO does not entail that it is a temperament.

Yes, of course i should have added that comment myself.

-monz

🔗monz <monz@...>

2/3/2007 11:23:17 AM

Hi Phil,

Darn, and i thought you were doing something *really* new!

OK, it will only take me a couple of minutes to make
a new Tonescape .tuning file for you ... voila:

/makemicromusic/files/monz/mixed-7-edo-and-12-edo_2d_degree-space.tuning

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In MakeMicroMusic@yahoogroups.com, Phil Collins <pmcomp@...> wrote:
>
> Rick,
> you are correct, sir!
> it's a misnomer (number) that evolved over time following
> a friend's likening my situation to modern conveniance
> of 7-11 I do indeed mean 12.
>
> your mentioning of it is a welcome cautioning before I
> get too hung up on marketing.
> Phil

🔗Rick McGowan <rick@...>

2/3/2007 12:14:23 PM

Hi Phil,

> it's a misnomer (number) that evolved over time following
> a friend's likening my situation to modern conveniance of 7-11

Yes, I thought you were probably talking 7 with 12 equal.

OK, so what you're trying to do is play some Thai instruments that are
tuned to 7 equal, with some ordinary Western instruments that are tuned to
12-equal. Not too hard.

The Thai instruments give more-or-less 1200 / 7 = 171.42857 cents per
step, resulting in intervals of approximately:

171.42857 * 2 = 342.8 cents
171.42857 * 3 = 514.3 cents
171.42857 * 4 = 685.7 cents
171.42857 * 5 = 857.1 cents
171.42857 * 6 = 1028.5 cents
...and then the octave.

So, if you play on the Western instruments in B-flat, you'll
sort-of-maybe-a-little-bit sync up at:

E-flat: the perfect 4th, or 514 cents Thai, 500 cents Western,
F: the perfect 5th, or 685.7 cents Thai, 700 cents Western,
A-flat: the minor 7th, or 1028.5 cents Thai, 1000 cents Western

That's about the best you can hope for in terms of being pretty close in
the unisons. Your Thai 3rd won't match D or D-flat, but you can probably
use either of those for "inflections" in the Western instruments and be OK.
Pentatonic stuff works pretty well.

Let's see how this works in practice. Here is short musical example. A
kind of xylphone-like sound in 7-equal coupled with a reed-like thing in
12-equal. First the xylo plays its 7-tone scale, then the reed plays a
7-tone diatonic scale, then they play a bit of so-called music together:

http://rm-and-jo.laughingsquid.org/temp/Test-7-12.mp3

This is in "C", but by the same principle, if your Thai instruments are
tuned to a B-flat, and you play in B-flat, this is the kind of sound you'll
get if you play in a sort of pentatonic way. Your mileage may vary.

Rick

🔗Kraig Grady <kraiggrady@...>

2/3/2007 12:32:03 PM

the idea that the Thailand used 7 equal was introduced by Europeans in the 19th century. .What the term equal means to them and us , like in many parts of Africa,means different things.

Rick McGowan wrote:
> Hi Phil,
>
> >> it's a misnomer (number) that evolved over time following
>> a friend's likening my situation to modern conveniance of 7-11
>> >
> Yes, I thought you were probably talking 7 with 12 equal.
>
> OK, so what you're trying to do is play some Thai instruments that are > tuned to 7 equal, with some ordinary Western instruments that are tuned to > 12-equal. Not too hard.
>
> The Thai instruments give more-or-less 1200 / 7 = 171.42857 cents per > step, resulting in intervals of approximately:
>
> 171.42857 * 2 = 342.8 cents
> 171.42857 * 3 = 514.3 cents
> 171.42857 * 4 = 685.7 cents
> 171.42857 * 5 = 857.1 cents
> 171.42857 * 6 = 1028.5 cents
> ...and then the octave.
>
> So, if you play on the Western instruments in B-flat, you'll > sort-of-maybe-a-little-bit sync up at:
>
> E-flat: the perfect 4th, or 514 cents Thai, 500 cents Western,
> F: the perfect 5th, or 685.7 cents Thai, 700 cents Western,
> A-flat: the minor 7th, or 1028.5 cents Thai, 1000 cents Western
>
> That's about the best you can hope for in terms of being pretty close in > the unisons. Your Thai 3rd won't match D or D-flat, but you can probably > use either of those for "inflections" in the Western instruments and be OK. > Pentatonic stuff works pretty well.
>
> Let's see how this works in practice. Here is short musical example. A > kind of xylphone-like sound in 7-equal coupled with a reed-like thing in > 12-equal. First the xylo plays its 7-tone scale, then the reed plays a > 7-tone diatonic scale, then they play a bit of so-called music together:
>
> http://rm-and-jo.laughingsquid.org/temp/Test-7-12.mp3
>
> This is in "C", but by the same principle, if your Thai instruments are > tuned to a B-flat, and you play in B-flat, this is the kind of sound you'll > get if you play in a sort of pentatonic way. Your mileage may vary.
>
> Rick
>
>
> > Yahoo! Groups Links
>
>
>
>
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗Phil Collins <pmcomp@...>

2/3/2007 1:05:26 PM

hi Rick,
Thanks for the information, the mp3 file, and advice. I already have my
virginal tuned to Bb, 7-tone ET and am familiar with the comparative
ratios on paper as well as by ear. The explorations of late have been
more about the special relationships that suggest special musical
possibilities/contexts to my ear.
I am curious what, if any, musical constructs have occurred. I will try
your mp3 in a little bit.
The instruments of Thai culture have different ways of elaborating upon
the 7-tone ET. I should mention that the Thai and Cambodian music I've
encountered is not exactingly true to 171.42 per step; the confluence of
Western and other musical sources have had diverse affects on their
tuning practices.

again, thank you very much,
Phil

Rick McGowan wrote:
Hi Phil,

> it's a misnomer (number) that evolved over time following
> a friend's likening my situation to modern conveniance of 7-11

Yes, I thought you were probably talking 7 with 12 equal.

OK, so what you're trying to do is play some Thai instruments that are
tuned to 7 equal, with some ordinary Western instruments that are tuned
to
12-equal. Not too hard.

The Thai instruments give more-or-less 1200 / 7 = 171.42857 cents per
step, resulting in intervals of approximately:

171.42857 * 2 = 342.8 cents
171.42857 * 3 = 514.3 cents
171.42857 * 4 = 685.7 cents
171.42857 * 5 = 857.1 cents
171.42857 * 6 = 1028.5 cents
...and then the octave.

So, if you play on the Western instruments in B-flat, you'll
sort-of-maybe-a-little-bit sync up at:

 E-flat: the perfect 4th, or 514 cents Thai, 500 cents Western,
 F: the perfect 5th, or 685.7 cents Thai, 700 cents Western,
 A-flat: the minor 7th, or 1028.5 cents Thai, 1000 cents Western

That's about the best you can hope for in terms of being pretty close in

the unisons. Your Thai 3rd won't match D or D-flat, but you can probably

use either of those for "inflections" in the Western instruments and be
OK.
Pentatonic stuff works pretty well.

Let's see how this works in practice. Here is short musical example. A
kind of xylphone-like sound in 7-equal coupled with a reed-like thing in

12-equal. First the xylo plays its 7-tone scale, then the reed plays a
7-tone diatonic scale, then they play a bit of so-called music together:

http://rm-and-jo.laughingsquid.org/temp/Test-7-12.mp3

This is in "C", but by the same principle, if your Thai instruments are
tuned to a B-flat, and you play in B-flat, this is the kind of sound
you'll
get if you play in a sort of pentatonic way. Your mileage may vary.

 Rick



🔗Phil Collins <pmcomp@...>

2/3/2007 1:08:37 PM

hi Rick,
Thanks for the information, the mp3 file, and advice. I already have my
virginal tuned to Bb, 7-tone ET and have been experimenting in
complicity with my standard synthesizer. Also, composer Jeff Harrington
has been extremely generous by providing me a Bb-based 7-tone ET scale
from which to tune from.
I am familiar with the comparative ratios between Thai and I on paper as
well as by ear. They are sinking in through practice and (rather oddly)
my dreams.

The explorations of late have been more about the special relationships
that suggest special musical possibilities/contexts to my ear.
I am curious what, if any, musical constructs have occurred. I will try
your mp3 in a little bit.
The instruments of Thai culture have different ways of elaborating upon
the 7-tone ET. I should mention that the Thai and Cambodian music I've
encountered is not exactingly true to 171.42 per step; the confluence of
Western and other musical sources have had diverse affects on their
tuning practices.

again, thank you very much,
Phil

Rick McGowan wrote:
Hi Phil,

> it's a misnomer (number) that evolved over time following
> a friend's likening my situation to modern conveniance of 7-11

Yes, I thought you were probably talking 7 with 12 equal.

OK, so what you're trying to do is play some Thai instruments that are
tuned to 7 equal, with some ordinary Western instruments that are tuned
to
12-equal. Not too hard.

The Thai instruments give more-or-less 1200 / 7 = 171.42857 cents per
step, resulting in intervals of approximately:

171.42857 * 2 = 342.8 cents
171.42857 * 3 = 514.3 cents
171.42857 * 4 = 685.7 cents
171.42857 * 5 = 857.1 cents
171.42857 * 6 = 1028.5 cents
...and then the octave.

So, if you play on the Western instruments in B-flat, you'll
sort-of-maybe-a-little-bit sync up at:

 E-flat: the perfect 4th, or 514 cents Thai, 500 cents Western,
 F: the perfect 5th, or 685.7 cents Thai, 700 cents Western,
 A-flat: the minor 7th, or 1028.5 cents Thai, 1000 cents Western

That's about the best you can hope for in terms of being pretty close in

the unisons. Your Thai 3rd won't match D or D-flat, but you can probably

use either of those for "inflections" in the Western instruments and be
OK.
Pentatonic stuff works pretty well.

Let's see how this works in practice. Here is short musical example. A
kind of xylphone-like sound in 7-equal coupled with a reed-like thing in

12-equal. First the xylo plays its 7-tone scale, then the reed plays a
7-tone diatonic scale, then they play a bit of so-called music together:

http://rm-and-jo.laughingsquid.org/temp/Test-7-12.mp3

This is in "C", but by the same principle, if your Thai instruments are
tuned to a B-flat, and you play in B-flat, this is the kind of sound
you'll
get if you play in a sort of pentatonic way. Your mileage may vary.

 Rick



🔗monz <monz@...>

2/3/2007 1:20:23 PM

Hi Phil and Rick,

--- In MakeMicroMusic@yahoogroups.com, Rick McGowan <rick@...> wrote:

> So, if you play on the Western instruments in B-flat, you'll
> sort-of-maybe-a-little-bit sync up at:
>
> E-flat: the perfect 4th, or 514 cents Thai, 500 cents Western,
> F: the perfect 5th, or 685.7 cents Thai, 700 cents Western,
> A-flat: the minor 7th, or 1028.5 cents Thai, 1000 cents Western
>
> That's about the best you can hope for in terms of being
> pretty close in the unisons. Your Thai 3rd won't match
> D or D-flat, but you can probably use either of those
> for "inflections" in the Western instruments and be OK.

The simplest notation to use to see how they intersect
is 84-edo (7*12=84). The pitches of each tuning in
ascending order in 84-edo notation are:

. 7-edo: 0, 12, 24, 36, 48, 60, 72, 84=0

. 12-edo: 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84=0

The two close ones are the E-flat and F, which are only
one step away in 84-edo. The A-flats are the same distance
apart as the Ds: 2 steps of 84-edo. The union of the
two is a perfectly symmetrical tuning.

In steps of 84-edo, the comparison of close intervals is:

E-flat:
Thai: 3/7 = 36/84, Western: 5/12 = 35/84

F:
Thai: 4/7 = 48/84, Western: 7/12 = 49/84

If you are looking at this in Tonescape, click on the
blue Lattice background, "Select Notation" from the pop-up
menu, choose "Logarithmic" from the list, leave
"Interval Magnitude" set at 2.000, and type "84" into
the "Divisions" box, then click the "OK" button.
Your Lattice will give all pitches in steps of 84-edo.

link to the Tonescape .tuning file:
/makemicromusic/files/monz/mixed-7-edo-and-1\
2-edo_2d_degree-space.tuning

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Herman Miller <hmiller@...>

2/3/2007 7:35:10 PM

Phil Collins wrote:
> monz,
> that is very nice to know. One impediment, I'm a Mac-guy. I will be copy
> your info and take it to NZland, where I surely will be able to avail
> myself upon a PC person to try it out. If you can recommend a Mac-way to
> get there, I'd love to know.
> Thanks for your time and effort.
> Phil

Scala is available for Mac, and it's great for figuring out properties of different scales.

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

You can start by typing "equal 12" to get a 12-note scale, then add the extra notes of the 7-note scale and sort.

! 7-and-12.scl
!
7-note and 12-note equal temperament, coinciding on Bb
18
!
100.00000
142.85714
200.00000
300.00000
314.28571
400.00000
485.71429
500.00000
600.00000
657.14286
700.00000
800.00000
828.57143
900.00000
1000.00000
1100.00000
1171.42875
2/1

You can see that there are some very small intervals in this scale, including two small steps of 14.286 cents. There's also a good minor third at 314.286 cents. Scala can show you a complete list of intervals by typing "show intervals".