miracle music

Does a miracle scale mean that it will produce miracle music? No,
that is dependant on the folks who use it to compose...do they have the
deep technical/emotional/compositional skills necessary to create music
that will last the ages? I guess we'll see...hell, the lowly 12 eq scale
has, with the aid of human ingenuity, been responsible for much
incredible art throughout the ages. It's not a scale that matters...it's
what one does with it...Hstick

--- In tuning@y..., "Neil Haverstick" <STICK@U...> wrote:

/tuning/topicId_22853.html#22853

> Does a miracle scale mean that it will produce miracle music? No,
> that is dependant on the folks who use it to compose...do they have
the deep technical/emotional/compositional skills necessary to create
music that will last the ages? I guess we'll see...hell, the lowly 12
eq scale has, with the aid of human ingenuity, been responsible for
much incredible art throughout the ages. It's not a scale that
matters...it's what one does with it...Hstick

Neil, your point, in general, is well-taken, but you also will have
to admit that on the basis of empirical evidence, 12-tET is a VERY
special scale... Paul's concordance charts show that right away for
the lower ET-s. It's not just coincidence that it became so
predominant... a lot of thinking and experimenting went into it.

Probably the same process that is happening now with the new
advancements... the MIRACLES! Keep "fired up," Monz!!!

_________ ______ ________
Joseph Pehrson

Joseph Pehrson wrote,

<<Paul's concordance charts show that right away for the lower ET-s.
It's not just coincidence that it became so predominant... a lot of
thinking and experimenting went into it. Probably the same process
that is happening now with the new advancements... the MIRACLES!>>

If 12-tET is the model here, then I think natural musical practice
should drive a theory like this, not the other way around. Or they
should at least belly up to the bar on something like speaking terms.
That's pretty much been my point right along.

There's been a lot of folks working with 72 equal for quite a while
now and I would think that there would be some inevitable and repeated
bumping into this if there were anything hopeful afoot (in the
pre-tonal sense that Paul mentioned before).

The modernization of the arts and the world happened... things aren't
so simple. (Though it's neat and often helps to pretend that they
are.)

Neil's absolutely right, the miracle's are in the music not the
scales.

This scale is a theoretical construct with some properties that are
interesting. Not that that's not neat enough in and of itself, but it
has nothing to do with musical miracles.

Theory miracles? Well sure, fair enough then, as some committed folks
here seem to think very highly of all this why not.

--Dan Stearns

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

> There's been a lot of folks working with 72 equal for quite a while
> now and I would think that there would be some inevitable and
repeated
> bumping into this if there were anything hopeful afoot (in the
> pre-tonal sense that Paul mentioned before).

I think that's like saying humankind should have evolved out of
microorganisms in 40 years.
>
> Theory miracles? Well sure, fair enough then, as some committed
folks
> here seem to think very highly of all this why not.
>
Committed . . . as in institutionalized?

Paul Erlich wrote,

<<I think that's like saying humankind should have evolved out of
microorganisms in 40 years.>>

Sure, if you think pre-tonality is to tonality what the microorganism
is to man! (Okay, I'm rolling that upgrade back to 5% now...)

--Dan Stearns

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

/tuning/topicId_22853.html#22876

> Joseph Pehrson wrote,
>
> <<Paul's concordance charts show that right away for the lower ET-s.
> It's not just coincidence that it became so predominant... a lot of
> thinking and experimenting went into it. Probably the same process
> that is happening now with the new advancements... the MIRACLES!>>
>
> If 12-tET is the model here, then I think natural musical practice
> should drive a theory like this, not the other way around. Or they
> should at least belly up to the bar on something like speaking
terms. That's pretty much been my point right along.

Well this is all very fine... but I do get a little tired of the
attitude that 12-tET is something "motley" that the cat brought in.

There is no "Animal Farm" to tuning. Not all scales are "created
equal..." (no pun intended)

Some scales are "more equal" (superior) than others!

_________ _______ ______
Joseph Pehrson

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Paul Erlich wrote,
>
> <<I think that's like saying humankind should have evolved out of
> microorganisms in 40 years.>>
>
> Sure, if you think pre-tonality is to tonality what the microorganism
> is to man! (Okay, I'm rolling that upgrade back to 5% now...)
>
No, that's not what I'm saying at all! But I live in Boston, and I know what Maneri and friends are
after. Like my friend Steve Lantner who plays two 12-tET keyboards, sometimes 1/4-tone
apart, sometimes 1/6-tone apart. And Maneri himself, who sits in with the jam-jazz group Club
d'Elf and whose book you're familiar with. What are they after? It sure ain't consonance! (and if it
were relevant, I'd add that it sure ain't tonality either)

Paul Erlich wrote,

<<I live in Boston, and I know what Maneri and friends are
after. [SNIP] What are they after? It sure ain't
consonance! (and if it were relevant, I'd add that it sure ain't
tonality either)>>

It's not that simple. Modernism happened (quite a while ago in fact).
The liberation happened. Music grew up. These things are no longer
seditious crimes against music!

If you and Dave K's scales, aesthetics and advice were going out to
some staunch but forward looking "back to tonality" guys and gals,
rather than say Joseph Pehrson, I'd probably have little to squawk
about here. It would make sense.

But this movement ain't happening, not here anyway. And the closest
things to it are probably to be found in the diehard JI camp, and they
probably aren't going to fancy the paradigm getting "corrupted" by an
equal temperament. But wherever these guys and gals are, and I think
it would be neat if they were somewhere, well that's the place for the
miracle scale et al.

--Dan Stearns

--- In tuning@y..., "Neil Haverstick" <STICK@U...> wrote:
> Does a miracle scale mean that it will produce miracle music? No,
> that is dependant on the folks who use it to compose...do they have
the
> deep technical/emotional/compositional skills necessary to create
music
> that will last the ages? I guess we'll see...hell, the lowly 12 eq
scale
> has, with the aid of human ingenuity, been responsible for much
> incredible art throughout the ages. It's not a scale that
matters...it's
> what one does with it...Hstick

Hi Neil,

I personally think you are stating the obvious. But thanks.

Scales do however impose limitations. I happen to think that the
miracle (Many Integer Ratios Approximated Consistently Linearly and
Evenly) subsets have fewer limitations than many other scales, for the
same number of notes. Instead of a 31-EDO guitar you might have had
one with a very even 31 frets per octave that is way closer to
11-limit JI. How often did you need to modulate all the way around the
cycle of 31?

But if that's wrong and they don't have fewer limitations, they at
least have interesting _new_ limitations.

Of course limtations can actually be good for creativity, but it's
easy to _impose_ limitations (e.g. just use fewer notes), but some
limitations have proven very difficult to remove until now.

Regards,
-- Dave Keenan

Hi Dave,

I'm quoting you in reverse order:

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
/tuning/topicId_22853.html#22899

> Of course limtations can actually be good for creativity,
> but it's easy to _impose_ limitations (e.g. just use
> fewer notes), but some limitations have proven very
> difficult to remove until now.

What a great succint way of describing why some of us
are so excited about this MIRACLE.

> Scales do however impose limitations. I happen to think
> that the miracle (Many Integer Ratios Approximated
> Consistently Linearly and Evenly) subsets have fewer
> limitations than many other scales, for the same number
> of notes.

(BTW, in case no-one else noticed, Dave's fleshing-out
of MIRACLE is a bit different from the one Paul originally
posted. I took the best of both and put it in my Dictionary
<http://www.ixpres.com/interval/dict/miracle.htm>: Multitudes
of Integer Ratios Approximated Consistently Linearly and Evenly.)

> Instead of a 31-EDO guitar you might have had one with a
> very even 31 frets per octave that is way closer to
> 11-limit JI.

Ah, THANKS DAVE!

This reminded me of something I had thought of this morning
while not at the computer, and had by now forgotten about
in the course of a very busy day.

I wrote:

/tuning/topicId_22793.html#22793

> I've come up with a mapping of Canasta to the Ztar keyboard
> which does that *and* amazingly gives an approximation that
> preserves something something very familiar to string players,
> altho here it's the bowed string family and not the guitar:
>
> If each key (or Ztar "fret") to the right is one 7/72-"octave"
> higher than the one to its left, and we duplicate every 7th
> "fret" on the next "string", each "string" will be a 12-EDO
> "perfect 5th" higher than the previous one!
>
> [no > used below so as to not break the lines]
>
F^ 5&1/2
Bb^10&1/2 C< 11&2/3 C#- 5/6 D 2 Eb+ 3&1/6 E> 4&1/3 F^ 5&1/2
Eb^ 3&1/2 F< 4&2/3 F#- 5&5/6 G 7 G#+ 8&1/6 A> 9&1/3 Bb^10&1/2
G#^ 8&1/2 Bb< 9&2/3 B- 10&5/6 C 0 C#+ 1&1/6 D> 2&1/3 Eb^ 3&1/2
C#^ 1&1/2 Eb< 2&2/3 E- 3&5/6 F 5 F#+ 6&1/6 G> 7&1/3 G#^ 8&1/2
F#^ 6&1/2 G#< 7&2/3 A- 8&5/6 Bb 10 B+ 11&1/6 C> 1/3 C#^ 1&1/2
>
>

I realized that this would work just fine for a regular guitar
fretboard, since the frets would go straight across the neck.

... Thus bringing a MIRACLE to guitar fretboards. :)

I'll try to get around to making the calculations and posting
them some time.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Paul Erlich wrote,
>
> <<I live in Boston, and I know what Maneri and friends are
> after. [SNIP] What are they after? It sure ain't
> consonance! (and if it were relevant, I'd add that it sure ain't
> tonality either)>>
>
> It's not that simple. Modernism happened (quite a while ago in
fact).
> The liberation happened. Music grew up. These things are no longer
> seditious crimes against music!

Who said they are?
>
> If you and Dave K's scales, aesthetics and advice were going out to
> some staunch but forward looking "back to tonality" guys and gals,
> rather than say Joseph Pehrson, I'd probably have little to squawk
> about here. It would make sense.

Are you saying we've misled/deceived Joseph Pehrson?
>
> But this movement ain't happening, not here anyway. And the closest
> things to it are probably to be found in the diehard JI camp, and
they
> probably aren't going to fancy the paradigm getting "corrupted" by
an
> equal temperament.

72-tET has been used by James Tenney, and something very similar
(also using 12-tET fifths) by Harald Waage. Kraig Grady doesn't seem
to have a problem with 72-tET's approximations. Anyway, assuming
you're right that "the closest things to it are probably to be found
in the diehard JI camp", does that mean that this "camp" has an
exclusive right to dictate the methods that can be used to
achieve "it"? That's a rather bizarre view of the world, I'd say.

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> Instead of a 31-EDO guitar you might have had
> one with a very even 31 frets per octave that is way closer to
> 11-limit JI. How often did you need to modulate all the way around
the
> cycle of 31?

Actually I disagree. The Canasta scale won't even support a single
meantone diatonic scale, while the 31-tET guitar has, of course, 31
of them.

Paul,

I'm tired of banging my head against this. The replies I keep giving
are just more and more strained reiterations of the points I've been
trying to make from the beginning.

Perhaps they meant something to somebody to whatever extent it all
possibly matters. If not, no further amount of yapping on my part is
gonna change that at this point.

<<Are you saying we've misled/deceived Joseph Pehrson?>>

That's not for me to say. I said what I said and that's that!

<<Anyway, assuming you're right that "the closest things to it are
probably to be found in the diehard JI camp", does that mean that this
"camp" has an exclusive right to dictate the methods that can be used
to achieve "it"? That's a rather bizarre view of the world, I'd say.>>

Well I never said that. In fact what I said was that it would be nice
if some talented folks were taking up these scales along the lines of
which they are designed, etc. To your credit I think, the only piece
of music that I've heard of yours is at least very much in sync with
the theoretical intentions and designs.

--Dan Stearns

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> To your credit I think, the only piece
> of music that I've heard of yours is at least very much in sync with
> the theoretical intentions and designs.

I hope you get to hear more on Friday's webcast.

--- In tuning@y..., paul@s... wrote:
> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> > Instead of a 31-EDO guitar you might have had
> > one with a very even 31 frets per octave that is way closer to
> > 11-limit JI. How often did you need to modulate all the way around
> the
> > cycle of 31?
>
> Actually I disagree. The Canasta scale won't even support a single
> meantone diatonic scale, while the 31-tET guitar has, of course, 31
> of them.

Good point. Canasta only supports a few JI diatonics. But if you only
wanted lots of meantone diatonics you wouldn't need 31 frets (max even
19 of 31 is plenty).

-- Dave Keenan

On 5/15/01 4:11 PM, "paul@stretch-music.com" <paul@stretch-music.com> wrote:

>> There's been a lot of folks working with 72 equal for quite a while
>> now and I would think that there would be some inevitable and
> repeated
>> bumping into this if there were anything hopeful afoot (in the
>> pre-tonal sense that Paul mentioned before).
>
> I think that's like saying humankind should have evolved out of
> microorganisms in 40 years.

I think playing in 12, after awhile,
since there's only so much you can do with it,
there's only so much anyone can *say* about it.

Corollary: the more notes in the temperament,
the more possibilities you have,
the more you can do with it,
so the *more* there is to say about it.

And no I wouldn't say that there's 6 times as much
you can say about 72 than you can about 12.
Maybe some power of 6 though.

I think the bumping into anything would be inevitable also.
But I think it would take a LOTTT longer.

"DIVERGENT microtonality" eh...

As Peter Schickele (a.k.a. P.D.Q. Bach) quotes on his syndicated radio program, "If it sounds good, it is good." One could just as well say, "If it sounds better, it is better." Or, "If it sounds worse, it is worse." But apart from those composers like Paul Dukas who were so self critical that they deliberately destroyed some of their scores, there is probably no piece of music that somebody didn't like, even if it was only its composer.

>>> jpehrson@rcn.com 05/15/01 05:46PM >>>
--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

/tuning/topicId_22853.html#22876

> Joseph Pehrson wrote,
>
> <<Paul's concordance charts show that right away for the lower ET-s.
> It's not just coincidence that it became so predominant... a lot of
> thinking and experimenting went into it. Probably the same process
> that is happening now with the new advancements... the MIRACLES!>>
>
> If 12-tET is the model here, then I think natural musical practice
> should drive a theory like this, not the other way around. Or they
> should at least belly up to the bar on something like speaking
terms. That's pretty much been my point right along.

Well this is all very fine... but I do get a little tired of the
attitude that 12-tET is something "motley" that the cat brought in.

There is no "Animal Farm" to tuning. Not all scales are "created
equal..." (no pun intended)

Some scales are "more equal" (superior) than others!

_________ _______ ______
Joseph Pehrson

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--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22853.html#22886

> --- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> > Paul Erlich wrote,
> >
> > <<I think that's like saying humankind should have evolved out of
> > microorganisms in 40 years.>>
> >
> > Sure, if you think pre-tonality is to tonality what the
microorganism
> > is to man! (Okay, I'm rolling that upgrade back to 5% now...)
> >
> No, that's not what I'm saying at all! But I live in Boston, and I
know what Maneri and friends are
> after. Like my friend Steve Lantner who plays two 12-tET keyboards,
sometimes 1/4-tone
> apart, sometimes 1/6-tone apart. And Maneri himself, who sits in
with the jam-jazz group Club
> d'Elf and whose book you're familiar with. What are they after? It
sure ain't consonance! (and if it
> were relevant, I'd add that it sure ain't tonality either)

Well, this is a good point... and I would have to say that the kind
of rudimentary ear training I am after would not necessarily be from
the Maneri school. Nor would it probably be from Ezra Sims...

So where *would* one find it?? Is anybody doing it? (It being
developing a whole new "grundsatz" for harmony using 72-tET)

___________ _______ _____
Joseph Pehrson

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> I think playing in 12, after awhile,
> since there's only so much you can do with it,
> there's only so much anyone can *say* about it.
>
> Corollary: the more notes in the temperament,
> the more possibilities you have,
> the more you can do with it,
> so the *more* there is to say about it.
>
> And no I wouldn't say that there's 6 times as much
> you can say about 72 than you can about 12.
> Maybe some power of 6 though.

A silly calculation:

How many ways can you order the 12 pitches (not counting
transpositions)?
Answer: 11! ~= 40,000,000

How many ways can you order the 72 pitches (not counting
transpositions)?
Answer: 71! ~=
850,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00
0,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

So perhaps there is over 2 * 10^94 times as much you can say about 72
than you can about 12.
>
> I think the bumping into anything would be inevitable also.
> But I think it would take a LOTTT longer.

Agreed!!

On 5/18/01 6:23 PM, "paul@stretch-music.com" <paul@stretch-music.com> wrote:

>> And no I wouldn't say that there's 6 times as much
>> you can say about 72 than you can about 12.
>> Maybe some power of 6 though.
>
> A silly calculation:
>
> How many ways can you order the 12 pitches (not counting
> transpositions)?
> Answer: 11! ~= 40,000,000
>
> How many ways can you order the 72 pitches (not counting
> transpositions)?
> Answer: 71! ~=
> 850,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,00
> 0,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Well yeah... that... wow... it's so amazing to see
the math center of THIS brain shut off for awhile. ::POOF::

Hehhhhhhhhh ... man funny me laugh.

Seriously though Paul that's a good reference point to make a point.
I was imagining more that, well,
music isn't just 12 or 72 notes in a row,
it's lots and lots of notes,
which if you have 6 times as many to choose from,
then you have 6 to the power of how many notes
you wind up playing in a piece of music,
that any increase from 12 or any other number
is going to be infinite, give or take a few.

BRAINBRAINBRAIN

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> I was imagining more that, well,
> music isn't just 12 or 72 notes in a row,
> it's lots and lots of notes,
> which if you have 6 times as many to choose from,
> then you have 6 to the power of how many notes
> you wind up playing in a piece of music,

Good point!

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

/tuning/topicId_22853.html#22961

>
> <<Are you saying we've misled/deceived Joseph Pehrson?>>
>
> That's not for me to say. I said what I said and that's that!
>

My understanding is that the miracle family,
including "blackjack," "canasta" and the 41-tone variant, translated
into 72-tET notation is such an incredible set of scales, so,
miraculous, in fact, that I will use them, and only them for the rest
of my life.

In addition, because of the fortuitous and exceptional properties of
these scales they will eventually replace 12-tET as an acceptible new
tuning and at some point in the future, the "miracle family" will
become the one and only tuning, as Joe Monzo states, for centuries to
come....

How could I *possibly* be deceived?

__________ _______ _____ _______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

/tuning/topicId_22853.html#23234

> In addition, because of the fortuitous and exceptional
> properties of these [MIRACLE] scales they will eventually
> replace 12-tET as an acceptible new tuning and at some
> point in the future, the "miracle family" will become
> the one and only tuning, as Joe Monzo states, for centuries
> to come....
>
> How could I *possibly* be deceived?
>
> __________ _______ _____ _______
> Joseph Pehrson

Come on now, Joe, that's not what I "stated", and you know
it. If you're being sarcastic (which is how I'm reading
your post), then a smiley-face or some such indication
would be appropriate.

I'm saying that these scales have properties that emulate
so many different tuning systems that they very well *could*
(*not* "will") take over the role that 12-EDO has had for
a century.

*I* would *never* be the person to talk about any "one and
only tuning"... one reason I'm so interested in tuning theory
is the vast diversity of different tunings.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_22853.html#23262

>
> --- In tuning@y..., jpehrson@r... wrote:
>
> /tuning/topicId_22853.html#23234
>
>
> > In addition, because of the fortuitous and exceptional
> > properties of these [MIRACLE] scales they will eventually
> > replace 12-tET as an acceptible new tuning and at some
> > point in the future, the "miracle family" will become
> > the one and only tuning, as Joe Monzo states, for centuries
> > to come....
> >
> > How could I *possibly* be deceived?
> >
> > __________ _______ _____ _______
> > Joseph Pehrson
>
>
> Come on now, Joe, that's not what I "stated", and you know
> it. If you're being sarcastic (which is how I'm reading
> your post), then a smiley-face or some such indication
> would be appropriate.
>
> I'm saying that these scales have properties that emulate
> so many different tuning systems that they very well *could*
> (*not* "will") take over the role that 12-EDO has had for
> a century.
>
> *I* would *never* be the person to talk about any "one and
> only tuning"... one reason I'm so interested in tuning theory
> is the vast diversity of different tunings.
>
>
> -monz
> http://www.monz.org
> "All roads lead to n^0"

I can't believe you misread my little "joke" and, in fact, it was
directed mostly at Paul Erlich and Dave Keenan in response to Dan
Stearns' suggestion that I had been "misled..." (For this, once, you,
Joe were rather an "afterthought...")

It was a sardonic treatment of the fact that Dan thought I had been
taken in "hook line and sinker..."

But I guess now is not the time to be sardonic on this list. Too
many bad vibes...

________ _______ ______
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

/tuning/topicId_22853.html#23264

> I can't believe you misread my little "joke" and, in fact,
> it was directed mostly at Paul Erlich and Dave Keenan in
> response to Dan Stearns' suggestion that I had been "misled..."
> (For this, once, you, Joe were rather an "afterthought...")
>
> It was a sardonic treatment of the fact that Dan thought I had been
> taken in "hook line and sinker..."

Sorry, Joe... as I said, I had a feeling you were being
sarcastic, but when in doubt, I always choose to assume
sincerity.

>
> But I guess now is not the time to be sardonic on this list. Too
> many bad vibes...

Yeah, you're right about that. Not a good time for sarcastic
jokes.

Did you or anybody else take the trouble to try out my
JustMusic computer keyboard mapping of Canasta? I'd certainly
love to get some feedback on it.

-monz
http://www.monz.org
"All roads lead to n^0"

Joseph Pherson wrote,

<<I can't believe you misread my little "joke" and, in fact, it was
directed mostly at Paul Erlich and Dave Keenan in response to Dan
Stearns' suggestion that I had been "misled..." (For this, once, you,
Joe were rather an "afterthought...") It was a sardonic treatment of
the fact that Dan thought I had been taken in "hook line and
sinker...">>

Now now... if your going to use quotes and my name then you might want
to try quoting what I actually did say and not something that you
might've thought I said!

smiley smiley happy happy joy joy,

--Dan Stearns

--- In tuning@y..., "monz" <joemonz@y...> wrote:
> Did you or anybody else take the trouble to try out my
> JustMusic computer keyboard mapping of Canasta? I'd certainly
> love to get some feedback on it.

Sounds like a neat idea. How about a quick reminder of where to get
the required software for those of us who haven't the time to follow
the long and winding thread?

David F.

--- In tuning@y..., "David J. Finnamore" <daeron@b...> wrote:

> --- In tuning@y..., "monz" <joemonz@y...> wrote:
> > Did you or anybody else take the trouble to try out my
> > JustMusic computer keyboard mapping of Canasta? I'd certainly
> > love to get some feedback on it.
>
> Sounds like a neat idea. How about a quick reminder of where to
get
> the required software for those of us who haven't the time to
follow
> the long and winding thread?
>
> David F.

Wow, I can't believe there have been over 80 posts today
since I posted the message about JustMusic this morning!
(And most of them dealing not with tuning, but with flak
over Paul's being banned...)

All the relevant info is here:
/tuning/topicId_23193.html#23193
and in the follow-up links.

Hope you like it.

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., jpehrson@r... wrote:

>
> In addition, because of the fortuitous and exceptional properties of
> these scales they will eventually replace 12-tET as an acceptible new
> tuning and at some point in the future, the "miracle family" will
> become the one and only tuning, as Joe Monzo states, for centuries to
> come....
>
You forgot the little smiley face, Joseph.

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_22853.html#23303

> --- In tuning@y..., jpehrson@r... wrote:
>
> >
> > In addition, because of the fortuitous and exceptional properties
of
> > these scales they will eventually replace 12-tET as an acceptible
new
> > tuning and at some point in the future, the "miracle family" will
> > become the one and only tuning, as Joe Monzo states, for
centuries to
> > come....
> >
> You forgot the little smiley face, Joseph.

Yeah, I know. We went over that. Sorry again, Monz!

_________ _______ ______
Joseph Pehrson