Definition Question for Paul Erlich: "True" Interval

Paul,

Hi!

I've been reading your "On Harmonic Entropy", and would like to ask
for clarification on what you mean by "True Intervals".

Thanks for your unending patience,

Respectfully,

Jacky Ligon

--- In tuning@egroups.com, "Jacky Ligon" <jacky_ekstasis@y...> wrote:

> I've been reading your "On Harmonic Entropy", and would like to ask
> for clarification on what you mean by "True Intervals".

I think I just mean the actual interval being played, with a precise
cents value, rather than the various just ratios that the brain tries
to hear it as. What was the context in which the term confused you?

Paul,

Good Morning!

Thanks for your answer to my question! This is what I thought you
meant when you wrote "true" interval - I was just seeking
clarification.

I was reading from: "The harmonic entropy is based on the concept
that the critical band represents a certain degree of uncertainty in
the perception of pitch, and for any "true" interval, the auditory
system will perceive a range of intervals spanning a number of simple-
integer ratios."

So the ear could percieve a 5/4 as a 9/7 or 16/13 etc...?

Also: "Combination tones complicate the matter but with a knowledge
of the amplitudes and frequencies of all combination tone components,
Plomp's algorithm can be still applied. "

Do the harmonic entropy computations include first, second ,third
(etc..) order combination and difference tones supplied by
neurological processing of intervals, or is anything beyond the first
order negligible?

What are some compositional uses of this theory?

Thanks kindly,

Jacky

--- In tuning@egroups.com, "Paul Erlich" <PERLICH@A...> wrote:
> --- In tuning@egroups.com, "Jacky Ligon" <jacky_ekstasis@y...>
wrote:
>
> > I've been reading your "On Harmonic Entropy", and would like to
ask
> > for clarification on what you mean by "True Intervals".
>
> I think I just mean the actual interval being played, with a
precise
> cents value, rather than the various just ratios that the brain
tries
> to hear it as. What was the context in which the term confused you?

--- In tuning@egroups.com, "Jacky Ligon" <jacky_ekstasis@y...> wrote:
>
> So the ear could percieve a 5/4 as a 9/7 or 16/13 etc...?

Hi Jacky,

Just thought I'd take a stab at clarifying this. Yes, Paul's
harmonic entropy theory does say that 'the ear could percieve
a 5/4 as a 9/7 or 16/13 etc...'. So you are correct, to a
point...

But what's *more* important, the theory says that the ear
(more accurately, the ear/brain system) will *tend* to do
the opposite: it will tend to perceive the 9/7, 16/13, etc.,
as a 5/4, because the 5/4 falls at the point of one of the
lower (i.e., more powerful) minima. The minima describing
the other intervals are higher (less powerful), so perception
will gravitate towards the 5/4.

Hmmm... will all the 'planetary' ideas bouncing around here
lately, the analogy of gravity is actually a pretty good
way to understand harmonic entropy. The biggest dips in the
graph are the ones which tend to pull the ear in.

(Big post on more spacey stuff coming soon!... but this time
it really is musical!)

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

Monz and Paul,

Hi!

Ok - it's starting to click with me. I think this has the potential
to answer a question that I have long pondered about how our hearing
tends to round off intervals.

You know, when I'm mapping intervals to my synths and samplers, and I
wish to bring them all in to the same tuning system, I have to make a
compromise in that some of my modules are limited to a +50, -50 cents
adjustment. This forces me to map and classify intervals to a certain
pitch name if they fall within 1/4 tone above or below the 12 tET
pitch name. This is really a horrible compromise too, because as we
all know, that even though you may map a ratio to a certain key and
call it a certain pitch name, what the ear percieves this as is
entirely another thing altogether.

For example, in a 12 pitch tuning in a "C to C" octave, if I map a
12/11 to "D" (which I must do if I want to tune it to 151 cents), and
I'm wanting to classify this in a scale as a "whole tone" - well, my
ear tells me something entirely different - I'm still hearing this as
a minor second (obviously pitch naming/mapping/classification and the
experience of "major and minor" scale degrees are two mutually
exclusive things). Another example is: if I map a 13/10 to "F", which
I must do if I want to tune it to 454 cents - well I certainly don't
hear this interval as a 4/3 - I hear it as a very wide major 3rd. So
you see the paradoxical problem with this.

This leads to the following question: How far beyond the simple
integer ratios does this band of classification extend in light of
the reality of what the ear/neurological processing perceives? From
what I've been able to deduce from the Harmonic Entropy threads, the
width of this is different for each interval, with the gravitational
pull of the 3/2 being the most strong. So am I correct to assume that
there is a sort of gradient scale of tonal gravity for each interval
in terms of where it falls in integer size? If true, then the
harmonic series would provide the order of gravitational pull: 1/1,
2/1, 3/1, 4/1, 5/1 etc...right - wrong?

It is an honor to learn from you guys - thanks!!!

Jacky

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
> --- In tuning@egroups.com, "Jacky Ligon" <jacky_ekstasis@y...>
wrote:
> >
> > So the ear could percieve a 5/4 as a 9/7 or 16/13 etc...?
>
>
> Hi Jacky,
>
>
> Just thought I'd take a stab at clarifying this. Yes, Paul's
> harmonic entropy theory does say that 'the ear could percieve
> a 5/4 as a 9/7 or 16/13 etc...'. So you are correct, to a
> point...
>
> But what's *more* important, the theory says that the ear
> (more accurately, the ear/brain system) will *tend* to do
> the opposite: it will tend to perceive the 9/7, 16/13, etc.,
> as a 5/4, because the 5/4 falls at the point of one of the
> lower (i.e., more powerful) minima. The minima describing
> the other intervals are higher (less powerful), so perception
> will gravitate towards the 5/4.
>
> Hmmm... will all the 'planetary' ideas bouncing around here
> lately, the analogy of gravity is actually a pretty good
> way to understand harmonic entropy. The biggest dips in the
> graph are the ones which tend to pull the ear in.
>
>
> (Big post on more spacey stuff coming soon!... but this time
> it really is musical!)
>
>
>
> -monz
> http://www.ixpres.com/interval/monzo/homepage.html