Yahoo Tuning Groups Ultimate Backup tuning Schenker

--- In tuning@egroups.com, "John A. deLaubenfels" <jdl@a...> wrote:

http://www.egroups.com/message/tuning/12877

>
> Yes, you did make that clear, and I'm sorry if it seemed as if I was
> barking at you, Joe! It always "pushes my buttons" to hear
> pronouncements from someone with a battery of diplomas on his wall,
> upon an area of his supposed expertise, who obviously expects to be
> taken as seriously by us as he takes himself, but who is talking out
> of ignorance. What are this guy's dates, do you know?
>
> JdL

Hello John!

I surely share your concerns about morons who have advanced degrees
in music. I happen to know some of them rather intimately... It
doesn't take much intelligence to get an advanced degree... but one
does have to know how to sit still in a chair for a very long period
of time. The Germans, as you may know, call this ability
"Sitzenfleisch..."

Heinrich Schenker lived from 1969-1935. There is quite a nice
section about him in Willi Apel's Harvard Dictionary (tres abstruse
source...) I will quote a little of it for people not wishing to take
their eyes from the screen:

"...Schenker's point of departure is "nature," i.e. the overtone
series through the fifth partial, from which man derives not only the
major triad but all the intervals, scales, and basic structures of
music. The overtones (1,2,3,5; i.e., unison, octave, fifth, major
third) constitute the KLANG (sound, sonority) or natural triad, which
may appear in its vertical or horizontal position. The horizontal
projection of the KLANG determines the melody as well as the bass.
In the latter it appears as GRUNDBRECHUNG or BASSBRECHUNG (broken
ground), mainly as a succession of I and V; in the former as URLINIE
(primordial, fundamental line), in which the basic tones, I, III, V,
are filled in with others. URLINIE and GRUNDBRECHUNG together
constitute the URSATZ (fundamental setting), which is the basic
structure, the "background" of the composition...

ACHTUNG! Actually, the experiences I have had with Schenker in music
school were all rather positive. It's a little like "diagramming
sentences." There is a graphic system employed that makes it quite
fascinating. There are "great big" notes... corresponding to the
major points of arrival... yes, generally I, IV or V, and the
diagrammed notes get progressively smaller in size as you map out
linear surface events.

I always found that the real strength in Schenker was the "pitch
height" realizations. One could really see how melodies were
constructed with "expectations" built in for development, depending
on what "pitch height" one had arrived at, and how it corresponded to
the underlying harmony.

So as a "reductional analysis" I always found Schenker superb... but
then, it was not "straight without water" out of Schenker's 1906
harmony book... People have changed the system over the years to suit
analytical ends... In fact, the HARMONY work doesn't even show any
different "sized" noteheads... I'm not even certain that he
developed this feature HIMSELF... It could well be a later addition
(??)

BUT, of course, Schenker had no comparable background in the physical
sciences as someone like Helmholtz... whose SENSATIONS was about 20
years earlier...

Schenker was more your "typical" musiklehrer, as you correctly
guessed. However, given the fact that most people were only
realizing figured basses and doing harmonic exercises with NO thought
of melodic development or "pitch height," his work... and especially
the more "modern" manifestations of it, sprang "light years"
forward...

________ ____ _ __ _
Joseph Pehrson

🔗John A. deLaubenfels <jdl@adaptune.com>

🔗Paul Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Monz <MONZ@JUNO.COM>

🔗John A. deLaubenfels <jdl@adaptune.com>

🔗Joseph Pehrson <josephpehrson@compuserve.com>

🔗John A. deLaubenfels <jdl@adaptune.com>

[I wrote:]
>>Another thing I remember from a quick
>>perusal [of Forte's book ] is a pearl of wisdom,
>>something like, "As to the question of how
>>many major seconds there are, we have only to look at the piano
>>keyboard to know that the answer is one."

[Paul E:]
>What was the context? Probably a particular chord?

Found it. It's on page three of chapter 1, under the heading "Chord
and Interval".

The smallest interval in tonal music is the _second_ (2nd), an
interval which encompasses only two notes. This is the interval we
find between one scale degree and the next - for example, Bb to C
in the Bb major scale. The 2nd has two sizes, a fact easily verified
by looking at a piano keyboard.

That's it. At no point is the harmonic meaning (or near-meaning) of
any interval discussed. No tuning system is discussed (how could it be,
when the theoretical harmonic basis of tuning is omitted?).

Here's Forte on parallel fifths (p. 54):

Parallel 5ths are avoided because the 5th formed by scale degree
1 and 5 is the primary harmonic interval, the interval which divides
the scale and thus defines the key. The direct succession of two
5ths raises doubt concerning the key.

The prohibition of parallel 5ths is more than a pedantic dictum.
It is an important negative principle which is responsible for many
harmonic and melodic features of tonal music ... Without the
limitation placed on parallel 5ths and 8ves the art of tonal music
would not have developed the elaborate and intricate forms which
have given it such a unique position.

A couple of thoughts:

. Doubt concerning home key??? That seems bizarre: the distraction,
if any, caused by parallel fifths seems to my ear no greater than
things that DO happen and are encouraged by these rules.

. The art could not have developed? It would not have developed in
exactly the same way, to be sure, but failing to prohibit something
does not mean that it must appear in every composition!

Anyway, the parallel fifths thing is O.T., I suppose, and the idea of
getting the book WAS to learn the sometimes strange rules under which
some music (music I often like, to be sure!) was written, whether or not
I agree with those rules. Trouble is, I have a hard time getting
motivated to read the book when so little of it resonates with me.

JdL

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, "John A. deLaubenfels" <jdl@a...> wrote:

http://www.egroups.com/message/tuning/12914

Hi John!

Actually, I am glad that you _finally_ got the Forte book. I rather
hate to have to inform you of this, but the Forte is actually the
MOST intelligent "conventional" music harmony book around.

They're *THAT* bad! If you want a real joker, try Piston... the
stuff that was jammed down my own esophagus.

>find between one scale degree and the next - for example, Bb to C
>in the Bb major scale. The 2nd has two sizes, a fact easily
verified by looking at a piano keyboard.
>

Here you have my "keyboard harmony" example. Everyone who goes to
music school or conservatory is FORCED to take "keyboard harmony" and
that is the de facto end of it all... unless you are lucky to
encounter a "weirdo" (by the school's standards) enlightened
instructor...

> Here's Forte on parallel fifths (p. 54):
>
>Parallel 5ths are avoided because the 5th formed by scale degree
>1 and 5 is the primary harmonic interval, the interval which
divides the scale and thus defines the key. The direct succession of
two 5ths raises doubt concerning the key.

Yeppir! No thoughts about overtones or tuning. I also hate to
admit, but the recent discussion about the overtones of the parallel
octave timbre cancelling out a second voice is the FIRST TIME I ever
thought about that being one of the main acoustical reasons octaves
have been prohibited. You can see why I hang around on this list!

>
> Anyway, the parallel fifths thing is O.T.,

Um. Not exactly O.T.... since we have been considering various
contrapuntal voices and whether certain timbres with coinciding
overtones "cancel out" horizontal voices... and therefore have
been prohibited by practice... Or at least I think that's what I've
been reading sometimes...

I suppose, and the idea
of getting the book WAS to learn the sometimes strange rules under
which some music (music I often like, to be sure!) was written,
whether or not I agree with those rules. Trouble is, I have a hard
time getting motivated to read the book when so little of it
resonates with me.
>
> JdL

Yeah. Surely. Do look at Piston, though, if you want to see the
THOROUGHLY conventional and WIDESPREAD regurgitated harmony text!!!
This is the book most music students use!! Or used to use, anyway...

[In Piston's defense, though, a fellow who was actually quite a fine
composer... maybe a little on the "academic" side... his
ORCHESTRATION book is quite good. I still use it some.]

I'll tell you where the Forte _Tonal Harmony in Concept and Practice_
is pretty good. There are lots of halfway intelligent figured bass
exercises, and if you have to pass a music theory prelim, this will
do it for ya...

____________ ____ __ __ _
Joseph Pehrson

🔗Carl Lumma <CLUMMA@NNI.COM>

> The smallest interval in tonal music is the _second_ (2nd), an
> interval which encompasses only two notes. This is the interval we
> find between one scale degree and the next - for example, Bb to C
> in the Bb major scale. The 2nd has two sizes, a fact easily verified
> by looking at a piano keyboard.
>
>That's it. At no point is the harmonic meaning (or near-meaning) of
>any interval discussed. No tuning system is discussed (how could it be,
>when the theoretical harmonic basis of tuning is omitted?).

John- you're right that no book on music theory should be without a
discussion on the psycho-acoustic basis of harmony. However, here, the
author may not be committing a crime by assuming a connection between
scale degrees and acoustic intervals, since in the case of the meantone
diatonic scale it exists. Though incomplete without a discussion of
tuning, theory in terms of scale degrees may be the most useful kind for
the practitioner of common-practice-style music -- if I had to have one
without the other, I'd probably take the scale-based theory.

But if this kind of thing gets your goat, as it did mine after 13 years
of music education (including a year of composition, theory, and piano
at the Conservatory of Music at Indiana University) without one mention of
tuning, you'd probably like Doty's JI Primer as much as I did. It totally
busts these Schenker types (with appologies to Schenker for the term).

>Here's Forte on parallel fifths (p. 54):
>
> Parallel 5ths are avoided because the 5th formed by scale degree
> 1 and 5 is the primary harmonic interval, the interval which divides
> the scale and thus defines the key. The direct succession of two
> 5ths raises doubt concerning the key.

An important point, in addition to the one Paul mentioned.

> The prohibition of parallel 5ths is more than a pedantic dictum.
> It is an important negative principle which is responsible for many
> harmonic and melodic features of tonal music ... Without the
> limitation placed on parallel 5ths and 8ves the art of tonal music
> would not have developed the elaborate and intricate forms which
> have given it such a unique position.

He's dreaming. As Paul pointed out, this is a reversal of history.
Self-important music theory at its best.

>A couple of thoughts:
>
> . Doubt concerning home key??? That seems bizarre: the distraction,
> if any, caused by parallel fifths seems to my ear no greater than
> things that DO happen and are encouraged by these rules.

Though the existence of parallel fifths alone is hardly enough, sections
of tonal music harmonized in parallel fifths can easily run into problems,
since this kind of music often relies on a steady pace of tonal motion,
and as Rothenberg points out, the diatonic scale is highly efficient, so
it takes some work to achieve this. Take an hour, and set a hymn to 4-part
harmony in three different ways, and you'll see for yourself immediately.
Paul Erlich presents a reasonable version of all of this in his paper, with
characteristic disonances, and so on. Rothenberg's sufficient sets are
another approach.

> . The art could not have developed? It would not have developed in
> exactly the same way, to be sure, but failing to prohibit something
> does not mean that it must appear in every composition!

Of course. I would also like to point out that, with mastery of the tonal
style, harmonizing in parallel fifths is fine. The rule that Forte so
highly recommends is, in fact, a rule given to beginners, since learning
to leave enough anchor points in a progression requires some subtlety.
Beethovan didn't have a problem with it, though. Or, you can skip the
anchor points, and return to a more modal style, as in Jazz (harmonizing
in parallel fifths is almost standard in some voicings).

If these rules of music theory really did dictate the behavior of composers,
rather than describing it as Paul and I suggest, then perhaps they could
also take credit for setting up a hegemony for great music to break! (This
may sound funny, but if you read your liner notes, you'll find nothing
but praise for rule-breaking from Forte's colleagues. With appologies to
Forte for the term.)

>Anyway, the parallel fifths thing is O.T., I suppose, and the idea of
>getting the book WAS to learn the sometimes strange rules under which
>some music (music I often like, to be sure!) was written, whether or not
>I agree with those rules. Trouble is, I have a hard time getting
>motivated to read the book when so little of it resonates with me.

John, I would recommend you F all that. Get yourself some basic tools --
a polyphonic instrument, do a little ear training every time you warm
up, a good score-entry package (paper ain't bad), and play (literally).

-Carl

🔗Monz <MONZ@JUNO.COM>

In the discussion about Forte's _Tonal Harmony in Concept and
Practice_, Joe Pehrson's response to John deLaubenfels included:

> http://www.egroups.com/message/tuning/12917
>
> ... I rather hate to have to inform you of this, but the Forte
> is actually the MOST intelligent "conventional" music harmony
> book around.
>
> They're *THAT* bad! If you want a real joker, try Piston... the
> stuff that was jammed down my own esophagus.
>
> ... Do look at Piston, though, if you want to see the
> THOROUGHLY conventional and WIDESPREAD regurgitated harmony
> text!!!
> This is the book most music students use!! Or used to use,
> anyway...
>
> ... I'll tell you where the Forte _Tonal Harmony in Concept and
> Practice_ is pretty good. There are lots of halfway intelligent
> figured bass exercises, and if you have to pass a music theory
> prelim, this will do it for ya...

Talk about _practica vs. theoretica_!

Joe, there is some value to be found in Forte's, Piston's, and
any other harmony textbook.

The *big* problem - and it's a huge one - is that none of the
'traditional' books bother to explain that theirs is but *one*
perspective based in *one* particular tuning; instead they
present that perspective as *the* one-and-only framework without
any acknowledgment whatsoever of the vast universe of intonational
possibilities that exist outside of 12-tET/meantone.

What's *really* interesting to me about the 'traditional'
harmony-books is that they *do* mix various different aspects of
both 12-tET and meantone in their presentation, again without any
acknowledgement whatsoever!

The traditional Euro-centric music-notation has its origins in
3-limit Pythagorean JI. In Pythagorean tuning, 'A' was obviously
the first reference pitch; now it's 'middle-C' - there's a
harmonic reason for that which I explore in my book and at:
http://www.ixpres.com/interval/monzo/article/article.htm

The notes designated by 'sharps' are a Pythagorean comma higher
in pitch than the 'enharmonic equivalents' designated by 'flats'.
e.g., if A = n^0 = 0 Semitones = 1/1, then Ab == 3^-7 = ~10.86
Semitones, and G# == 3^5 = ~11.10 Semitones. (I use '==' to
mean '8ve'-equivalent; i.e., powers of 2 are ignored.)

Originally, 'accidentals' really had a meaning close to what
the word's etymology would suggest: used only as _musica ficta_,
they indicated a mutation into a hexachord outside the 'regular'
tuning (_musica recta_).

This awkward system developed as a result of the diatonic basis
of the slowly-evolving European gamut, and is also a residue of
the ancient Greek theory of conjuct vs. disjunct tetrachords.

Theorists and composers realized that chromatic pitches were being
used, and they were groping for a way to represent them within the
established diatonic framework. This was around 800 to 1300 AD in
the Frankish Holy Roman Empire.

The meanings of accidentals as absolute pitch-values solidified
around the 1400s, just when 5-limit harmonies were being accepted
in theory (c.f. Ramos) and ancient Greek texts describing all
sorts of rational tunings (c.f. Ptolemy) were being rediscovered
by the Western Europeans after the Ottoman conquest of
Constantinople.

- see my Dictionary entry for 'mutation' for more background:
http://www.ixpres.com/interval/dict/mutation.htm

The twist is that in 5-limit JI theory and in the associated
meantones that were its practical extensions, the situation
is almost exactly the reverse of the Pythagorean.

I'll demonstrate:

By adding the Ab to this typical 5-limit 12-tone scale:

5:3 5:4 15:8
F# ------ C# ------- G#
/ \ / \ / \
/ \ / \ / \
/ \ / \ / \
4:3 ----- 1:1 ---- 3:2 ----- 9:8
D A E B
/ \ / \ / \ /
/ \ / \ / \ /
/ \ / \ / \ /
16:15 --- 8:5 ---- 6:5 ---- 9:5
Bb F C G
\ / \ /
\ / \ /
\ / \ /
48:25 --- 36:25
Ab Eb

we again get two so-called 'enharmonically equivalent' notes:
Ab == 48/25 = ~11.29 Semitones, and G# == 15/8 = ~10.88 Semitones.
This is almost precisely the reverse of the Pythagorean system
described above.

In two important meantones, 1/4-comma (by far the most common)
and 2/7-comma (advocated by Zarlino), we get the following pairs:

Ab == (3^-7)/((81/80)^(-7*(1/4))) = 11.24 Semitones
G# == (3^ 5)/((81/80)^( 5*(1/4))) = 10.83 Semitones

Ab == (3^-7)/((81/80)^(-7*(2/7))) = 11.29 Semitones
G# == (3^ 5)/((81/80)^( 5*(2/7))) = 10.79 Semitones

Enharmonic discrepancies for all meantones will be pretty close
to the 5-limit JI equivalents, as these two demonstrate.

So here, just as the meaning of accidentals in notation solidified,
they came to represent the opposite of their old Pythagorean
transformations. 'Sharps' were now *lower* in pitch than the
enharmonically equivalent 'flats'.

Of course, over the years as meantone became firmly established,
the textbooks ceased to mention the old Pythagorean version of
the accidentals, and the 5-limit/meantone version became standard.
The revival of appropriate Pythagorean tuning for pre-1500 music
is very much a modern development.

Then, with the advent of near-universal acceptance of 12-tET
in Euro-centric musicology, the harmony books struggled to
describe the 'common-practice' repertoire by retaining use
of the 5-limit/meantone accidentals in the notation, while
at the same time insisting in theory that the enharmonic
differences could be ignored.

A truly confusing situation was the legacy, and it still
plagues lots of trained musicians who either don't even
realize their imprisonment within these contradictory
limitations, or who do realize it and long to escape this
confinement but don't know how. The lucky few are those
of us who have discovered the world of microtonality.

The exceptions in the 12-tET harmony books are the more
modern ones, evolving ultimately from Schoenberg's theories,
which present the 12-tET '8ve'-equivalent pitch-classes
in a sensible method using the integers 0 to 11 to represent
the 12 degrees. If you're going to expound on 12-tET theory,
you might as well use a notation that reflects the tuning
you've accepted!

In fact, I would argue that these modern 12-tET theories should
more accurately be called 12-EDO, while the older, more confusing
theories are very aptly called 12-tET. The distinction is a
very subtle one, but based on the fact that the older theory
was very much meant to be a temperament used to describe harmonic
practice grounded in 5-limit JI theory, wheras the newer theories
are grounded firmly in the properties inherent in 12-EDO tuning
itself.

There's been much interesting strictly-12-EDO theory presented in
the pages of _Journal of Music Theory_ and _Perpectives of New
Music_. Some if it is even an attempt to ground theories of
diatonicism in the 12-EDO scale, and much recent work makes use
of the kinds of lattices we draw here, but twisted in various ways
to reflect 12-EDO properties.

I have never read the Forte book under discussion, but I have
his _The Structure of Atonal Music_; in this book, he too likes
to make diagrams which represent tonal structures, again grounded
in 12-EDO. Many theorists today are taking concepts developed
by Forte, Babbitt, and the rest of the 'academic crowd' and
applying them to microtonal pitch-sets, with interesting results.

In a weird sort of way, I see Erv Wilson's work as related to
this too. (This time I *do* hope that Kriag Grady isn't reading
this... I think he'd be pissed...)

I bet you never realized how much information was locked away
between the covers of old music manuscripts and more recent
books and scores! It's a journey into the past (and future)
that I've found fascinating.

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

🔗Joseph Pehrson <pehrson@pubmedia.com>

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

http://www.egroups.com/message/tuning/12963

> The *big* problem - and it's a huge one - is that none of the
> 'traditional' books bother to explain that theirs is but *one*
> perspective based in *one* particular tuning; instead they
> present that perspective as *the* one-and-only framework without
> any acknowledgment whatsoever of the vast universe of intonational
> possibilities that exist outside of 12-tET/meantone.
>
> What's *really* interesting to me about the 'traditional'
> harmony-books is that they *do* mix various different aspects of
> both 12-tET and meantone in their presentation, again without any
> acknowledgement whatsoever!
>

I want to thank you so much for this nice, concise explanation of our
"traditional" accidentals! I have copied it and added it to my
permanent "store" of info.

Theory texts really *NEED* this kind of "preamble" to their
discussions but my guess is that most of the conventional
theory text authors don't know much about it... or at least don't
*care* enough to include it! Perhaps with the recent interest in
alternate tunings -- at least in the realm of meantone and historical
temperaments for earlier musics, more of this kind of material will
find its way into the conventional textbooks!

>
> Originally, 'accidentals' really had a meaning close to what
> the word's etymology would suggest: used only as _musica ficta_,
> they indicated a mutation into a hexachord outside the 'regular'
> tuning (_musica recta_).
>

This is a fascinating and frequently "overlooked" etymology!

>
> The twist is that in 5-limit JI theory and in the associated
> meantones that were its practical extensions, the situation
> is almost exactly the reverse of the Pythagorean.
>

Yes, Paul Erlich had explained this to me, and I understand that with
the application of the "diesis" the situation becomes reversed. But,
like I said, before I came on this list I knew none of this!

>
> In fact, I would argue that these modern 12-tET theories should
> more accurately be called 12-EDO, while the older, more confusing
> theories are very aptly called 12-tET. The distinction is a
> very subtle one, but based on the fact that the older theory
> was very much meant to be a temperament used to describe harmonic
> practice grounded in 5-limit JI theory, wheras the newer theories
> are grounded firmly in the properties inherent in 12-EDO tuning
> itself.
>

I guess this really would make some sense, since in a 12-tone
universe *nothing* really is "tempered" -- the structure is a "given."

Thanks so much for this handy "recap." I have filed it in a
prominent and easily-accessible place.

Oh... and on another topic... I'm still "crying" over my cut onion
debacle. Surely, I had no intention to deprecate your tuning
efforts! I should have said the Beatles' piece was "fun," not
"funny."
Just a miswrite... I appreciate the serious work that went into it!

Best,
__________ ____ __ _
Joseph Pehrson