Re: [tuning] Re: TD 861 -- Wilson's footprints on plateau! (for Kraig Graidy)

David!
Rest assure that Wilson has always seen it as both a logarithmic and a acoustic tree?
why would you assume one over the other?

David C Keenan wrote:

> Note that Wilson calls it a "scale tree", not an "interval tree". The
> fractions represent fractions of an octave (logarithmic, melodic), not
> frequency ratios (linear, harmonic). Can you confirm this Kraig?

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

David!

David C Keenan wrote:

> For example Noble_Mediant(4:5, 7:9) = (4+7phi):(5+9phi) gives a local
> maximum of dissonance but Noble_Mediant(4:5, 11:14) does not.

The next dotted line is exactly this noble mediant between 5/4 and 14/11 with the number
starting at 1.265125.... the one to the left of that is the one between 5/4 and 19/15 etc.
Note that this structure of the formula (4+7phi):(5+9phi) is the same Wilson formula
structure used to formulate the horagrams

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

David

David C Keenan wrote:

> Nor can I find anything in the egroups tuning archive that
> relates a linear interpretation of noble numbers (or Wilson's diagrams) to
> dissonance maxima, until Margo's and my "Golden Mediant" post at
> http://www.egroups.com/message/tuning/12915

I imagine that Chalmers will back me up on the dual uses of the scale tree. In fact it was him
that pointed it out to me (which brought me back on the list)
I think that Erv's experience is that these are not in fact maximally dissonant when tuned up.

This being only the point of departure that lead to his investigation. I cannot articulate
much more w/o speculating as to what he thinks. too dangerous and not on solid ground. He
might in fact have trouble with m first statement.

> I certainly can't see a linear application of the scale tree in the first
> diagram of http://www.anaphoria.com/tres.html

It seems clear that in this case he is focusing on using the tree to generate epimoric ratios.
Logarithmic formulas have no special use of epimores. It is in relation to the tetrachord. I
find it hard to read as logrithmic. which is possible but not fruitful!

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

I suddenly realized how ironic it is that the current 'hot'
topic on this list is being debated primarily by two members
who took breaks from the list and now, happily for me, are back
(Dave Keenan and Kraig Grady).

I'm beginning to feel uncomfortably warm reading the exchanges
about rational vs. logarithmic in this thread. I just thought
it might be a good idea to post a little reminder to keep this
discussion cordial and to prevent it from bursting into flames.

Be happy.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

Joe Monzo wrote,

> I'm beginning to feel uncomfortably warm reading the exchanges about
rational vs. logarithmic in this thread. I just thought it might be a
good idea to post a little reminder to keep this discussion cordial
and to prevent it from bursting into flames.

Good advice at a good time I think Joe. I was beginning to get a more
than a little honked myself yesterday, though I hadn't slept in nearly
three days either, but today I'm felling a lot less "combustible" <not
to mention manic...>; and all the more so after reading your
"soothing" bit here this morning...

> Be happy.

Yes, I'll try!

--Dan Stearns

David!

David C Keenan wrote:

> What does "epimoric" mean?

oh sorry superparticular. Andrew Barker used epimoric in Greek Musical Writings -

> I should have said that I could not find a logarithmic interpretation of it
> either. I simply cannot figure out what it is trying to show. What is the
> significance of not reducing the 4/4 and so ending up with a tree that does
> not seem to be a section of the Stern-Brocot tree as it claims, since
> fractions connected by lines are not adjacent.

He wanted to use the scale tree to examine the tetrachord. 4/4 being in the same octave,
producing notes whose reduction of terms creates intervals separated by epimores. I need to
look at it more. I am sure that in turn he is aware of the noble numbers that would be created
by such a sequence.

>
> My question is not so much _whether_ Wilson has applied the Stern-Brocot
> tree to both fractions of an octave and frequency ratios, but what musical
> or psycho-acoustic significance he gives to the noble numbers in each case.

This is what I remember of his history with this which I would take with a grain of salt but
at least includes these details . I am sure there is more that i don't know or have forgotten.
Originally I know he was taken by Yasser's sequence and Kornerup's extension. Noticing how the
Indians used a 22 tone scale, he added this part of the tree on to the Yasser zig-zag and saw
how it was related.. After examining different parts of the tree involving other generators
besides the fifth, he finally reconstructed the whole tree, knowing that he could not had been
the first one to create such an object, he first found it described by Pierce.
I will have to ask him about an application of acoustic besides of it just being a good
reference to ratios. It seems that an approach to adding intervals can be done by layers as
opposed to limits. A practice not out of the spirit of some greek and especially Persian
musical thought. I assume your own thoughts might pass along this territory. If the noble
numbers are maximum dissonance then dissonance can be measured by the degree or number of
layers a particular ratio is found as opposed to limit. If nothing else it shows what
intervals offer a good choice if one is inserting a ratio between the two. These are my
thoughts.
Erv as long as I have known him has never really taken any stand as far as consonance and
dissonance. For him ( this is only my experience) the influences of other parameters are so
high that nothing comes as being strong enough in enough cases to warrant him coming up with a
theory. I think Erv is far more concerned with melody than harmony.
Sorry if I digressed, it is not something i can totally answered. When he gave the tree to
me he told me it can be used in both ways. Over the years he has always pointed out when i
failed to see it both sides, reminding me not to be close minded.

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com