Reply to Kurt Nelson

Hello there, Kurt! It's exciting to meet another person as crazy as i am!

Well, you came to the right place, as i'm sure you've already gathered now.

I'll attempt to talk about my understanding of the areas you've mentioned.

>I am also quite interested in the notion of Intervals of Equivalence other
than the "octave." I am >undertaking an analysis of spectral concurrences of
pitches in the Farey set of size 16, and using >multidimensional scaling
solution mapping in order to demonstrate that 2:1 is only the first of an
infinite >set of similarity dimensions in pitch space. Since I am doing this
in my "spare time" it is taking quite a >while, so if anyone knows of
previously published papers on this subject please let me know; it would
>save me some work.

In my opinion, octave equivalence has to be confirmed or refuted in
psychoacoustics, not just in mathematics. If you're interested in
psychoacoustics there are some good references on the web such as Ersnt
Terhardt's website. Either way, your work sounds fascinating to me and i've
done a lot of similar work:

on the harmonic entropy list i've displayed 2-d plots of the triads
available in the harmonic series (2-d plots, 1 point for each triad, three
intervals plotted on three axes at 60-degree angles from one another. others
observed fractal periodicities in the design that weren't strictly
octave-repeating -- if you're interested, you can join
harmonic_entropy@yahoogroups.com and look at the archives. To just see the
first octave, look at
/tuning/files/perlich/trimap.jpg. The patterns
repeat at smaller and smaller intervals after the first octave (but you
can't see that here).

I've done multidimensional scalings on the dissonances (interpreted as
distances) of all the dyads in a scale. For example, a pentatonic scale
would have 10 dyads, and a heptatonic scale, 21. Projected into three
dimensions, such MS solutions provide a enlightening portrayal of the
scale's harmonic resources. Robert W., what do you think -- can you lend
your VRML expertise again?

>For instance, 1:1 would be the median of the instrument, extending all the
way to the front edge. Other >"primary" intervals, like 2:1, 2:3, 4:3, are
near the player. As intervals get into more dissonant territory >(like 7:5,
13:8, farther up the Farey tree), they are farther away from the player.
This sounds exactly like Partch's one-footed bride or my dyadic harmonic
entropy curves -- such as
/tuning/files/perlich/ent_006.jpg and
/tuning/files/perlich/tenney/te01_13p2877.jpg,
and more of which, of course, you can see over at
harmonic_entropy@yahoogroups.com.

While you're at it, take a look at
/tuning/files/perlich/triangle_01.jpg.

i have a question, if i may -- will your melodies always be played against a
tonic drone?

Glad again to meet you,
paul

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
> Hello there, Kurt! It's exciting to meet another person as crazy as
i am!

Now Paul, don't be presumptuous! : )

>
> Well, you came to the right place, as i'm sure you've already
gathered now.

Ye Ha!

>
> I'll attempt to talk about my understanding of the areas you've
mentioned.
>
> In my opinion, octave equivalence has to be confirmed or refuted in
> psychoacoustics, not just in mathematics.

Let's don't forget my old favorite - music! This is where I like to
see it "confirmed or refuted". Many possible scales can have an
interval so close to a 2/1 (remember Jeff Scott's scales), that it
will serve the same purpose. Isn't there such a thing as
a "mathematical" and a "perceptual" octave? I've found that the
bonding effect of certain non-octave scales, will provide enough
stability with a near 2/1 (I'm actually writing 6 new pieces without
a 2/1 in sight, to prove the point). The possibilities are infinite!
And I think it's a case by case thing about what these scales can
offer. We'd have to employ a 1000 psychoacousticians to measure it
all! I'm going to go ahead and make some tunes while they work it all
out.

> i have a question, if i may -- will your melodies always be played
against a
> tonic drone?

He provided some clips on his site Paul.

Jacky Ligon

Hello again list,

Thank you for your sincere welcome. I am astonished at the quick
response, and I can tell that this is a unique and well-mannered
community of individuals.

In answer to Paul, yes, I am somewhat crazy.

And my thought on multidimensional scaling analysis of spectra is that
the acoustical part would come first, because I currently have all the
tools. The psychoacoustical part would need to be conducted using a
Shepard-Krumhansl type probe tone study with the Farey set and a randomly
selected panel. I don't have the reference handy, but they used Shepard
tones (which consist of frequency components at powers of two scaled
across the range of human hearing) in 12TET in one octave. Their
analysis consisted, among other things, of a multidimensional scaling
solution of the probe tone data. This resulted in a four dimensional map
of keyspace which can be projected onto a torus (doughnut) in three
dimensions, with two closed circles of fifths spiralling around the
outside (one for major keys and one for minor keys). This is similar to
the Schoenberg grid of key signitures if you wrapped it into a cylinder,
and then wrapped it again into a torus. The problem is, they achieve
this closed result because they used Shepard tones in 12TET, not to
mention they used a panel of less than twenty college students with more
than six years of experience playing an instrument!! I assert that the
result would be quite different if you eliminated the use of Shepard
tones in 12TET and used a statistically significant panel size!

A psychoacoustic understanding would also have to incorporate the notion
of critical bandwidth, of which I understand very little at this point.
Also I am not connected with a research facility or university of any
kind. Well, I have a B.S. in biology, but I got it '94 and haven't even
begun paying off my student loans!

Happy microtoning.
Sincerely,
Kurt

--- In tuning@y..., Kurt S Nelson <
kurtnelson2@j...> wrote:

> And my thought on multidimensional scaling analysis of spectra is that
> the acoustical part would come first, because I currently have all the
> tools. The psychoacoustical part would need to be conducted using a
> Shepard-Krumhansl type probe tone study with the Farey set and a randomly
> selected panel. I don't have the reference handy, but they used Shepard
> tones (which consist of frequency components at powers of two scaled
> across the range of human hearing) in 12TET in one octave. Their
> analysis consisted, among other things, of a multidimensional scaling
> solution of the probe tone data. This resulted in a four dimensional map
> of keyspace which can be projected onto a torus (doughnut) in three
> dimensions, with two closed circles of fifths spiralling around the
> outside (one for major keys and one for minor keys). This is similar to
> the Schoenberg grid of key signitures if you wrapped it into a cylinder,
> and then wrapped it again into a torus.

This is exactly the same 4-dimensional
result I got for 12-tET (pitches, not keys) by
using a simple model for dissonance (in
which octave equivalence was imposed) and
_no_ empirial data! You can get the key-map
from this pitch-map by simply locating each
key near the center of mass of its pitches,
with the tonic pitch weighted more heavily.

The problem is, they achieve
> this closed result because they used Shepard tones in 12TET, not to
> mention they used a panel of less than twenty college students with more
> than six years of experience playing an instrument!! I assert that the
> result would be quite different if you eliminated the use of Shepard
> tones in 12TET and used a statistically significant panel size!

Well, if I still have my statistical software
licence (it may have expired but I can
probably renew it), I can run some MS
solutions using a non-octave equivalent
dissonance model and _any_ pitch set you
choose.

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:

/tuning/topicId_21346.html#21346

> Hello there, Kurt!

>
> Glad again to meet you,
> paul

Hi Paul!

Something is wrong with lots of the links that you have given Kurt...
they won't work.

I've seen many of these diagrams, but perhaps he hasn't...

Do you know what could be doing this?? Was something moved??

_______ ______ ___ _
Joseph Pehrson

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

> Hi Paul!
>
> Something is wrong with lots of the links that you have given
Kurt...
> they won't work.

You're right! But it's easy to get around this problem -- just go to
the website, click on "files", then click on "perlich", then click on
the file you want . . . all should be well . . . does that work for
you?

--- In tuning@y..., ligonj@n... wrote:
> --- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:> > i
have a question, if i may -- will your melodies always be played
> against a
> > tonic drone?
>
> He provided some clips on his site Paul.
>
Well, it appears that for the piece in question, _Farey Music_, there
indeed was a tonic drone. Glad we're on the same page, Kurt!

--- In tuning@y..., PERLICH@A... wrote:

/tuning/topicId_21346.html#21445

> --- In tuning@y..., jpehrson@r... wrote:
>
> > Hi Paul!
> >
> > Something is wrong with lots of the links that you have given
> Kurt...
> > they won't work.
>
> You're right! But it's easy to get around this problem -- just go
to
> the website, click on "files", then click on "perlich", then click
on
> the file you want . . . all should be well . . . does that work for
> you?

Yes it does... so I suppose, in this case, it's better to post just
the directory rather than the specific file in the link... (??)

_______ ______ _____ ____
Joseph Pehrson

> --- In tuning@y..., ligonj@n... wrote:
> > --- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:> > i
> have a question, if i may -- will your melodies always be played
> > against a
> > > tonic drone?
> >
> > He provided some clips on his site Paul.
> >
> Well, it appears that for the piece in question, _Farey Music_,
> there
> indeed was a tonic drone. Glad we're on the same page, Kurt!

Dear Paul, et al:

"Farey Music" is my very first rendering of anything in JI. You see, I
have a situation similar to the person who posted a question about sound
cards a while ago. My machine is a 425mHz with sound built in, and it
experiences drastic latency when running Direct Csound with even the
simplest orchestras. Furthermore, my MIDI keyboard is an old Casio,
which will never be able to support sysex tuning dumps. Consequently, I
have no way of playing with non-12tET scales in real time! "Farey Music"
is the CSound rendering of some tone row scores algorithmically generated
by a BASIC program I wrote, which assesses the probability of branching
to a harmonically or subharmonically adjacent pitch based on a simple
distance model of sonance. I added the drone so that I could hear JI
harmonies for the first time (it was a drone that was sitting around from
an earlier project). My plans are considerably more contrapunctal! As
in twelve-tone serialsm, no two rows are equivalent in their fludity or
musical usefulness. My next step is to hand pick the most useful and
interesting Farey rows (a Farey row, by my definition, is a phrase
beginning and ending on 1/1, and moving, in between, by harmonic and
subharmonic steps), and treat them to various kinds of transpositions,
retrogressions, inversions, and hemiolas.

My plan is develop my skills, in other words, by emulating in microcosm
the historical development from monophony to polyphony to counterpoint
and beyond. (A good JI instrument or two would certainly speed this
development.)

Happy microtoning,
Kurt

Kurt S Nelson wrote:

> My plan is develop my skills, in other words, by emulating in microcosm
> the historical development from monophony to polyphony to counterpoint
> and beyond. (A good JI instrument or two would certainly speed this
> development.)
>
> Happy microtoning,
> Kurt
>

Have you tried your voice and a guitar for a drone? Certainly a good start and it drives home the
pure low ratio intervals.

--- In tuning@y..., Kurt S Nelson <kurtnelson2@j...> wrote:

> based on a simple
> distance model of sonance

Are you familiar with Tenney's Harmonic Distance function? It has
some amazingly nice properties and seems quite accurate (if you don't
assume octave-equivalence) for simple ratios.