Re: [tuning] [MMM] Re: various - any tuning is potentially a goodtuning - for someone.

Most of the scales of Mt. Meru do this in that they all beat by the same
amount, or more exactly the cumulative effect is the same beating. It is a good
goal cause then one needn't worry about con/dis and can concentrate on good
line writing

Kurt Bigler wrote:

>
>
> Goal: to make the *least* consonant intervals in a scale more consonant by
> sacrificing the consonance of some of the more consonant ones. In short to
> reduce the variation in consonance among all the intervals in the scale such
> that the worse ones are less bad and the best ones less good.
>
>

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

[was: various - any tuning is potentially a goodtuning - for someone.]

Kurt wrote:
>> Goal: to make the *least* consonant intervals in a scale more consonant by
>> sacrificing the consonance of some of the more consonant ones. In short to
>> reduce the variation in consonance among all the intervals in the scale such
>> that the worse ones are less bad and the best ones less good.

on 5/3/04 7:49 PM, kraig grady <kraiggrady@anaphoria.com> wrote:
> Most of the scales of Mt. Meru do this in that they all beat by the same
> amount, or more exactly the cumulative effect is the same beating. It is a
> good goal cause then one needn't worry about con/dis and can concentrate on
> good line writing

Thanks, that's an interesting take on it. And the reinforcement of
difference tones with scale tones provides a new take on the whole otonal
thing, and I'm looking forward to trying this.

I never quiet learned Mt. Meru, so I just went back and looked at a thread
on it here from last fall. I still couldn't figure it out, though I only
spent 15 minutes trying.

Looking at meruone.pdf, I can't quite relate the first page to the second in
each set, and I can't relate either one to a scale.

I also don't know anything much yet about CPS either.

I'd love to see a truly beginner-level step-by-step example! Maybe you
could talk monz into putting a Mt. Meru page in the tuning dictionary.

-Kurt

>I'd love to see a truly beginner-level step-by-step example!
>Maybe you could talk monz into putting a Mt. Meru page in the
>tuning dictionary.

Mt. Meru is also known as Pascal's Triangle. I'm not sure if
Erv and Kraig use more than one method to get scales from it...

-Carl

on 5/4/04 5:27 PM, Carl Lumma <ekin@lumma.org> wrote:

>> I'd love to see a truly beginner-level step-by-step example!
>> Maybe you could talk monz into putting a Mt. Meru page in the
>> tuning dictionary.
>
> Mt. Meru is also known as Pascal's Triangle.

Right, I forgot that equivalence, but I understand the PT part of the
process.

> I'm not sure if
> Erv and Kraig use more than one method to get scales from it...

That's the part that I'd like clarified.

-Kurt

>> I'm not sure if
>> Erv and Kraig use more than one method to get scales from it...
>
>That's the part that I'd like clarified.

One thing (there may be others) is that it shows MOS and their
relationships. If you look at...

http://lumma.org/tuning/scale_tree.png

...and find the "12/7" point on the right, it represents the
diatonic scale in 12-tET. The points directly above it (5/3 and
7/4) give bounds on the generator size (the fourth).

See also the Wilson archives at anaphoria.com.

-Carl

General descriptions in the dictionary can be useful i guess , but some of these
which refers to material i have worked with over years leaves me quite perplexed.
These things i believe are best learned by step by step examples for sure, but
each person will grab and understand different things and also ask different
questions.

These scales are derived from these recurrent sequences, most often thought of as
harmonics, but one could think of the numbers as being subharmonic as well. One
can continue as high as one wishes where it will for all practical purposes will
converge on a set relation. Musically though we have found the most interesting
stage of these scales are before they converge and have sequenced long enough that
it begins to approximate the general size. With Meruone each diagonal is followed
by a page showing the MOS the converging interval forms which in most cases will
provide good starting and ending places as far as number of scale tones one might
wish to consider first.
The relationships between the scales themselves, or the diagonals, is not fully
known at this point, although one intuitively sense that there is a connection
there that hasn't been revealed.
Also on the diagonal is listed the recurrent sequence that generates the series
found by the sum of the diagonals. I prefer to use a simpler notation but i need
to go and will pick this up later if interested.

Kurt Bigler wrote:

> I'd love to see a truly beginner-level step-by-step example! Maybe you
> could talk monz into putting a Mt. Meru page in the tuning dictionary.

-- -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, "Carl Lumma" <ekin@l...> wrote:
> >> I'm not sure if
> >> Erv and Kraig use more than one method to get scales from it...
> >
> >That's the part that I'd like clarified.
>
> One thing (there may be others) is that it

What's "it"? I thought you guys were talking about Pascal's triangle.
Now it looks like you've changed the subject to the Stern-Brocot
tree, without warning.

> shows MOS and their
> relationships. If you look at...
>
> http://lumma.org/tuning/scale_tree.png
>
> ...and find the "12/7" point on the right, it represents the
> diatonic scale in 12-tET. The points directly above it (5/3 and
> 7/4) give bounds on the generator size (the fourth).
>
> See also the Wilson archives at anaphoria.com.
>
> -Carl

> > >> I'm not sure if
> > >> Erv and Kraig use more than one method to get
> > >> scales from it...
> > >
> > >That's the part that I'd like clarified.
> >
> > One thing (there may be others) is that it
>
> What's "it"? I thought you guys were talking about Pascal's
> triangle. Now it looks like you've changed the subject to
> the Stern-Brocot tree, without warning.

D'oh! Just ignore everything I say from now on. :)
(I'm loosing my mind.)

-Carl

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

> I never quiet learned Mt. Meru, so I just went back and looked at a
thread
> on it here from last fall. I still couldn't figure it out, though
I only
> spent 15 minutes trying.

The best discussion of this was on the SpecMus list.

on 5/4/04 11:40 PM, kraig grady <kraiggrady@anaphoria.com> wrote:

> These scales are derived from these recurrent sequences, most often thought of
> as harmonics, but one could think of the numbers as being subharmonic as well.
> One can continue as high as one wishes where it will for all practical
> purposes will converge on a set relation. Musically though we have found the
> most interesting stage of these scales are before they converge

Absolutely. Otherwise you just have N-et with an irrational N, right?

Do you usually take an octaves worth of this sequence and then repeat it?
Do you sometimes gerate beyond the limit of the octave without trying to
preserve any kind of octave equivalence?

> and have
> sequenced long enough that it begins to approximate the general size. With
> Meruone each diagonal is followed by a page showing the MOS

MOS, that's what I *meant* to say I also didn't know much about.

Maybe that's the clincher. Do I need to assimilate MOS before I can
approach the question of what a Mt. Meru scale is?

> the converging
> interval forms which in most cases will provide good starting and ending
> places as far as number of scale tones one might wish to consider first. The
> relationships between the scales themselves, or the diagonals, is not fully
> known at this point, although one intuitively sense that there is a connection
> there that hasn't been revealed.

Ah, that's what I didn't get. I was assuming it was a mechanical process to
create one of these scales. So you are saying you start with the sequence
from the diagonal and then you sit down and work out some details
analytically but intuitively and through that process derive a scale? If
so, this is great because it exposes some of the implicit knowledge that
makes the discourse here harder for the newbie to assimilate.

> Also on the diagonal is listed the recurrent
> sequence that generates the series found by the sum of the diagonals. I prefer
> to use a simpler notation but i need to go and will pick this up later if
> interested.

Paul said that SpecMus had a good discussion, but I'd love to see a *single*
scale derivation here, if you are willing. Pick any one of your meruone
examples. If you can explain it from basic principles without needing to
refer to MOS as an existing body of knowledge then all the better. But if
that isn't realistic then maybe I need to assimilate MOS first. But I'd
love to assimilat MOS by *example* here if it is workable.

-Kurt

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

> MOS, that's what I *meant* to say I also didn't know much about.

That's a really basic concept, though some peripheral aspects of the
definition keep changing back and forth . . .

http://www.elvenminstrel.com/music/tuning/horagrams/horagram_intro.htm

http://www.tonalsoft.com/enc/mos.htm

of course there is always the source.
http://www.anaphoria.com/mos.PDF
more later

wallyesterpaulrus wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
> > MOS, that's what I *meant* to say I also didn't know much about.
>
> That's a really basic concept, though some peripheral aspects of the
> definition keep changing back and forth . . .
>
> http://www.elvenminstrel.com/music/tuning/horagrams/horagram_intro.htm
>
> http://www.tonalsoft.com/enc/mos.htm
>
>
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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