Yahoo Tuning Groups Ultimate Backup tuning extended reference? (was RE: Yes)

>>Hmmm... now *there's* something that would make a
>>great tuning analysis project!...
>
>In the case of Yes or Robert Johnson, I have a (IMO) very important
>suggestion for you. Take several alternative performances of the same piece
>and analyze the tuning. You will then have an idea as to what kind of
>accuracy you can meaningfully ascribe to performer intent and what is due
>to random errors.

Paul, forgive me for butting in here, but if one subscribes to extended
reference, as I believe Joe does (his Robert Johnson analysis and Beethovan
Scherzo fragment both qualify as extended reference interpretations), then
your suggestion is a bit misguided. Recall that extended reference has no
way of pairing any single tuning to a given structure -- it's just a set of
rules that may be broken or followed by any number of possible tunings.
Two performances may differ, but each may still be internally consistent.
Of course one could still learn a lot by comparing different performances
of the same structure!!

The notion that only one set of pitches can satisfy JI in melody seems to
me as ignorant as the harmonic version we're now in the process of
debunking with various "adaptive JI" schemes. Blasted California school!

-Carl

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

🔗Joe Monzo <monz@juno.com>

>>> [me, monz, TD 495.2]
>>> Hmmm... now *there's* something [_Close To The Edge_]
>>that would make a great tuning analysis project!...
>>
>> [Paul Erlich, TD 495.15]
>> In the case of Yes or Robert Johnson, I have a (IMO) very
>> important suggestion for you. Take several alternative
>> performances of the same piece and analyze the tuning.
>> You will then have an idea as to what kind of accuracy
>> you can meaningfully ascribe to performer intent and what
>> is due to random errors.

Certainly a reasonable statement. But keep in mind that
I state explicitly on my Robert Johnson webpage
http://www.ixpres.com/interval/monzo/rjohnson/drunken.htm
that I'm using only the first verse of only one take
of only one song.

I do mention that the pitches in the other verses are
slightly different and that overall they function like
'variations on a theme'.

I also note that my choices for the ratios are somewhat
arbitrary, due to limitations of my ear and equipment.

What I'm most interested in is developing software that
can listen to digitized audio samples, tear them apart,
and analyze the tunings of the individual polyphonic voices.
Spectrogram software can already do this with one monophonic
voice; separating the independent voices in the polyphony
is the hard part.

And please keep in mind that in certain circumstances,
I don't hold to an 'extended reference' paradigm; the
most obvious example is probably Partch's compositions.

>
> [Carl Lumma, TD 496.2]
> Paul, forgive me for butting in here, but if one subscribes
> to extended reference, as I believe Joe does (his Robert
> Johnson analysis and Beethovan Scherzo fragment both qualify
> as extended reference interpretations), then your suggestion
> is a bit misguided. Recall that extended reference has no
> way of pairing any single tuning to a given structure -- it's
> just a set of rules that may be broken or followed by any
> number of possible tunings. Two performances may differ, but
> each may still be internally consistent. Of course one could
> still learn a lot by comparing different performances of the
> same structure!!
>
> The notion that only one set of pitches can satisfy JI in
> melody seems to me as ignorant as the harmonic version we're
> now in the process of debunking with various "adaptive JI"
> schemes.

I agree with all of this.
How about a nice, formal definition of 'extended reference'
for my Tuning Dictionary?...

> [Carl]
> Blasted California school!

Presuming myself to be a sort-of member of the
California microtonal 'scene', I'm mystified by
references to this 'California school'.

Is there documentation describing this, or is this
a term Paul Erlich just made up? (I suppose there's
another Dictionary entry lurking here too...)

In my experience, there's as much variey in tuning
among California musicians as there is in New York
(and there's *A LOT* of tuning variety in New York!
- thanks, Johnny!).

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

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🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

🔗Carl Lumma <clumma@nni.com>

>One would still need a way to determine whether the ratios one is ascribing
>are statistically distinguishable from random fluctuations about some
>simpler model.

This might be done by comparing the tuning of like scalar intervals
throughout the piece. Extended reference may allow several intervals to
act as a given scale degree in different spots in a piece, but I would
guess that each choice would attract its own distribution, or at least make
the distribution around the most popular choice non-smooth.

>How about a nice, formal definition of 'extended reference' for
>my Tuning Dictionary?...

A method of notating a melody in which consecutive pitches are given in
order, by their distance from a previously-tuned note. The frequency of
the first note is arbitrary, and it serves as the reference point for the
second note, after which either the first or second note may be the
reference, and so on.

Like classical melodic JI, extended reference holds that melodic intervals
are ideally tuned according to ratios of small whole numbers. But extended
reference differs from the classical application in two important ways:

1. Rather than mapping notes of the scale to a fixed pitch set and
performing modal transpositions on the pitch set, extended reference
interprets modal transposition as a change of reference point (tonic) --
maps scale degrees to intervals instead of pitches.

2. Rather than map a single just ratio to each scale degree, extended
reference may allow several tunings of a given scalar interval, so long as
all occurances of that interval are tuned with the same ratio _within a
given reference point_. [The model borrows from conventional music theory
the idea that harmonic progressions function in a sort of
"parenthesis-checking" hierarchy, where one must first resolve to the local
tonic, then to the next tonic up, and so on up to the master tonic (first
note).]

<---Throw in references, credit B & C...--->

-Carl

🔗Joe Monzo <monz@juno.com>

>> [me, monz]
>> How about a nice, formal definition of 'extended reference' for
>> my Tuning Dictionary?...

> [Carl Lumma, TD 498.3]
> A method of notating a melody in which consecutive pitches
> are given in order, by their distance from a previously-tuned
> note. The frequency of the first note is arbitrary, and it
> serves as the reference point for the second note, after which
> either the first or second note may be the reference, and so on.
> <...etc., snip>
>
> <---Throw in references, credit B & C...--->

Thanks, Carl!

http://www.ixpres.com/interval/dict/extref.htm

The 'B & C' refers to:

REFERENCES
----------

Boomsliter, Paul C. and Warren Creel. 1961.
"The Long Pattern Hypothesis in Harmony and Hearing",
_Journal of Music Theory_, vol. 5 no. 2, April 1961, pp. 2-30.

Boomsliter, Paul C. and Warren Creel. 1962a.
_Interim Report on the Project on <B>Organization in Auditory
Perception</B> at the State University College.
Albany, New York_,
(with recorded illustrations), February 1962.

Boomsliter, Paul C. and Warren Creel. 1962b.
"Ratio Relationships in Melody",
_Journal of the Acoustical Society of America_,
vol. 34 no. 9, part 1, September 1962, pp. 1276-1277.

Boomsliter, Paul C. and Warren Creel. 1963.
"Extended Reference: An Unrecognized Dynamic in Melody",
_Journal of Music Theory_, vol. 2 no. 1, spring 1963, pp. 2-22.

-monz

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

Monz wrote,

>>How about a nice, formal definition of 'extended reference' for
>>my Tuning Dictionary?...

Carl Lumma wrote,

>A method of notating a melody in which consecutive pitches are given in
>order, by their distance from a previously-tuned note. The frequency of
>the first note is arbitrary, and it serves as the reference point for the
>second note, after which either the first or second note may be the
>reference, and so on.

>Like classical melodic JI, extended reference holds that melodic intervals
>are ideally tuned according to ratios of small whole numbers. But extended
>reference differs from the classical application in two important ways:

>1. Rather than mapping notes of the scale to a fixed pitch set and
>performing modal transpositions on the pitch set, extended reference
>interprets modal transposition as a change of reference point (tonic) --
>maps scale degrees to intervals instead of pitches.

>2. Rather than map a single just ratio to each scale degree, extended
>reference may allow several tunings of a given scalar interval, so long as
>all occurances of that interval are tuned with the same ratio _within a
>given reference point_. [The model borrows from conventional music theory
>the idea that harmonic progressions function in a sort of
>"parenthesis-checking" hierarchy, where one must first resolve to the local
>tonic, then to the next tonic up, and so on up to the master tonic (first
>note).]

Then I don't see how you could justify your statement that Monz' JI
Beethoven and Robert Johnson interpretations are extended-reference ones.

🔗Carl Lumma <clumma@nni.com>

>Then I don't see how you could justify your statement that Monz' JI
>Beethoven and Robert Johnson interpretations are extended-reference ones.

To be honest, I'd have trouble defending that statement. Part of the
problem is the time I'm unwilling to spend to do it.

On the surface my statement seems way off, since the examples are both
notated as pitch sets with a single fixed tonic. But I can't help but
feel, having spoken with Joe about his approach, that he's using the
principles of extended reference to come up with these pitch sets
(especially the Beethovan). His prime factor notation sounds suspiciously
like his way of dealing with the huge ratios that arise when expressing an
E.R. melody from a single tonic. Joe has often spoken about how he likes
the way P.F.N. shows simple, local relationships, which would occur in E.R.
but not necessarily in classical JI melodies (of course it would be better
still to simply use multiple tonics).

Joe's page on the Beethovan fragment speaks about tuning pitches 3:2's away
from other pitches, rather than some "classical JI" ratio away from the
fixed tonic. The whole bit about how this mysteriously sounds "right" to
him, despite the insanely complex ratios involved, reads like straight out
of a Boomsliter and Creel paper. He also specifically mentions "classical
JI" as being an poor application of just intonation to melody...

"...which are too frequently assumed in a just-intonation analysis of
classical music."

"I must take issue with the methods of analysis to which Paul refers, and
which have been used by almost all JI theorists."

-Carl

🔗Joe Monzo <monz@juno.com>

> [Paul Erlich, TD 499.15, to Carl Lumma]
> Then I don't see how you could justify your statement that
> Monz' JI Beethoven and Robert Johnson interpretations are
> extended-reference ones.

I accepted Carl's characterization without really
thinking too hard about it. What exactly is wrong
with calling my interpretations extended-reference?

The approaches I took in these two examples are quite
different. For Robert Johnson, I was starting with an
actual recording that provided microtonal pitches which
it was then my task to analyze. For Beethoven, I could
only start with Beethoven's score and its meantone-based
notation; the microtonal subtleties there are entirely
my own.

When selecting ratios for what I heard in the Robert Johnson
example, I was guided not so much by extended-reference
but rather by the desire to keep the ratios as close as
possible in lattice-space to 1/1 while keeping the prime-limit
fairly low and still coming within a few cents of what he
actually sang (at least as I hear it).

My immediate guess is that (by Boomsliter/Creel's
definitions) extended-reference is a good way to describe
what I did here, but in my own mind when I made the
analysis, Partch's idea of Monophony was really my guideline.

For the Beethoven example, I let my imagination go and
simply substituted (extended-reference?) commatically-shifted
ratios for the simple JI ones that didn't sound right to me.

With the Beethoven fragment, I was consciously *not*
seeking small-number ratios in many cases, which upon
reflection seems to contradict the extended-reference
idea. My method here was to tune the 'roots' of the
chords to small-integer JI, then to tune other notes
with commatic substitutions of small-integer JI wherever
small-integer JI didn't sound right to me, and where
I imagined Beethoven might want those commatic substitutions
for harmonic or melodic reasons.

So is that extended reference or not?

-monz

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

Joe Monzo wrote,

>When selecting ratios for what I heard in the Robert Johnson
>example, I was guided not so much by extended-reference
>but rather by the desire to keep the ratios as close as
>possible in lattice-space to 1/1 while keeping the prime-limit
>fairly low and still coming within a few cents of what he
>actually sang (at least as I hear it).

>My immediate guess is that (by Boomsliter/Creel's
>definitions) extended-reference is a good way to describe
>what I did here, but in my own mind when I made the
>analysis, Partch's idea of Monophony was really my guideline.

>For the Beethoven example, I let my imagination go and
>simply substituted (extended-reference?) commatically-shifted
>ratios for the simple JI ones that didn't sound right to me.

>With the Beethoven fragment, I was consciously *not*
>seeking small-number ratios in many cases, which upon
>reflection seems to contradict the extended-reference
>idea. My method here was to tune the 'roots' of the
>chords to small-integer JI, then to tune other notes
>with commatic substitutions of small-integer JI wherever
>small-integer JI didn't sound right to me, and where
>I imagined Beethoven might want those commatic substitutions
>for harmonic or melodic reasons.

>So is that extended reference or not?

No. Carl, care to back me up on this?