modes vs keys (was: JI modes)

Daniel Wolf wrote:

>Although the art repertoire indeed became Major/minor, the training with
>the church modes remained quite traditional. Composers learned with Fux
>well into the nineteenth century (and again in the late twentieth century:
>indeed, the fashionable Schenkerian training is fundamentally Fuxian)

The rules of counterpoint certainly continued to be taught (and still are,
no?), but most apply equally well to tonal music. The Well-Tempered Clavier
is not modal! And surely the concepts of chord progressions and key
relationships have been far more fundamental in musical training.


>(I don't know quite what to say about the German chorale
>tradition where old, distinctively modal melodies are harmonized tonally -

.. thereby producing tonal music!! Perhaps we're using different
definitions of tonality, but the one I know defines it in terms of key
centers, chord progressions, and modulation, not melody. Since you often put
"modal" in quotes, I'm not sure what you mean by it. Are you saying that
Schumann wrote pieces that do not modulate or use chordal (tonal) harmony?

I do need to beat a retreat from my hasty generalization about the use of
modes ("well, hardly ever"...), especially regarding 20th century music, but
I remain unconvinced that modes have ever returned as the *basis* of music
theory or compositional styles in the Western classical tradition.



Bill Alves wrote:

>I don't see why refering to major and minor as modes is misleading. In my
>definition of modes in the European tradition, they include at least the
>following defining characteristics:
>[...snip...]
>3) A tonal center within that subset.

Are you just referring to the _final_ of the mode, or do you really mean
"tonal center" defined harmonically? Because that is the defining
distinction between modes and keys. A key is not just a set of notes - it is
determined by chordal structure rather than melodic formulae.


Gordon Collins

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Bill Alves wrote:

>Well, right now I have my synth tuned in a very interesting 11-limit
>lattice, and when I play the white keys from C to C it certainly doesn't
>sound like any kind of major scale I would recognize.

What you've got there is not a major scale. But a major scale is a major
scale is a major scale whether a whole tone is 9/8, 10/9, (5/4)^(1/2),
2^(1/6), or something in between.

Or whether the scale is 1/1 9/8 44/35 4/3 3/2 176/105 66/35 2/1.
This is 11-limit according to at least one definition I've seen (yet another
terminology problem plaguing this list). (Actually, I haven't had a chance
to listen to this one, but all the ratios are within the ranges bounded by
5-limit JI and 12TET for the corresponding notes.)


>This is one real problem with most theory books (by which I assume you
>primarily mean harmony books) but I won't get into that. The reason that
>they don't go into it is because 12TET is assumed as a standard now. They
>don't go into a lot of the "why's," not because they aren't important, but
>just because they want to take a lot of things as given in order to get on
>to the business of augmented sixth chord arcana. However, in many theory
>books of pre-12TET period, tuning is discussed as a prerequisite to the
>study of harmony.

The point is, those augmented sixth chord arcana are more important *to
understanding the music* than are the details of the tuning. In an era when
everyone tuned their own way, composers did not specify tuning instructions
with their music. That's why you see raging debates about J. S. Bach's
desires for the WTC.

Rameau, for instance, wrote his Treatise on Harmony when JI was not in use.
Yet he gave integer ratios for the various intervals - not one, but *two*
ratios for most of them. He then went on to say that the (syntonic) comma is
inaudible and proceeded to ignore the difference in the rest of his
Treatise. Later (if I recall correctly) he advocated ET without, presumably,
any effect on his theories. It is clear that the ratios themselves were
merely an explanation for the origin of consonance and dissonance.

Modern players don't play in 12TET *per se*, they play *in tune* with each
other. Most of the time that results in 12TET because a piano is being
used. But a good choir will experience comma shifts when a capella and if
string players are playing along with a 1/4CMT harpsichord, they'll match it
without thinking about it.


>Yes, perhaps accepting enharmonic equivalence was
>an important step in European music. Personally, I think it was a step
>conceptually taken long before the 18th century and the use of 12TET [....]

The idea was certainly considered earlier, but the persistence of
non-circulating tunings and of split-key keyboards through the 17th century
prove that it was not accepted until then.


>[T]he ability to [hear a diatonic scale] in a system is part of what I
>meant by "recognizably diatonic" when refering to the flexibility of
>tuning systems in defining modes.

Your idea of "recognizably diatonic" is interesting, and deserves
quantification. As in, "What is the ideal and how far from it can a scale be
to be recognized as diatonic?"

But treating 3-limit JI and 12TET as variations within the same tuning
system.... Well, I have the definite impression that most list contributors
consider them to be fundamentally different.

Gordon Collins

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CC:
Subj: modes vs keys (was: JI modes)

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Bill Alves wrote:

>My point was to counter an earlier claim I had thought you made:
>
>>The distinction between n-limit JI, x-comma meantone, well-temperament,
and
>>12TET is *totally irrelevant* to the definition of modes and scales!
>
>with a counter-example. Of course it's not a major scale, because the
>tuning system no longer makes it recognizably diatonic.

It's not 11-limit JI but your selection of pitch classes therefrom that
prevents your particular scale from being diatonic. You can find seven
pitch classes in 12TET that don't make a diatonic scale.


>>But treating 3-limit JI and 12TET as variations within the same tuning
>>system.... Well, I have the definite impression that most list
contributors
>>consider them to be fundamentally different.
>>
>As would I, but I never claimed that pythagorean and 12TET were
>"variations" of the same tuning system. I think that subsets of both can
>reasonably represent diatonic modes.

Your definition of mode started out with "1) A tuning system, though it
may be somewhat flexible". What would you say is the (flexible) tuning
system for, say, the Aeolian mode? If 3-limit JI and 12TET are not
variations of it, how can they both represent that mode?

My whole point is that the flexibility that is required is greater than
the difference between these tuning systems. Heck, most singers and
string players have vibratos wider than that!


>I think the value of tuning
>knowledge for the understanding of music is greatly underrated in
general.
>(As Lou Harrison says: You haven't heard a piece until you've heard it
in
>the tuning that the composer intended or expected.)

.. and on the intended instruments, with the intended performance
technique, with the intended phrasing, etc. These are all important
performance considerations - change any one of them and the performance
suffers. The particular tuning used, however, is probably the least
noticeable of these. How many people can tell the difference between
12TET and 5-limit JI in a string quartet played with the usual vibrato?

Change any of these considerations (to a point, of course) and the piece
is still considered to be the same piece. Change the melodies and
harmonies - the *notes* - and it is not. (The concept of *note* here is
not as precise as that of *pitch*.)

In many cases, the most difficult of these considerations for a
historically informed performer to determine is which tuning the composer
intended.


>To those students who unquestionably accept 12TET as the
>words of the Prophet, an understanding of tuning systems is, I think,
just
>as valuable as how to resolve a Neapolitan sixth chord, if not more so.

I agree that it would greatly enrich any student's musical education, not
only to increase understanding of non-common-practice music, but also to
increase understanding of the tuning systems that have been used *within*
that tradition. But those students you mention are not accepting 12TET -
they're only accepting that there are 12 notes in an octave, *roughly*
evenly distributed in pitch. How many of them even know what 12TET is?
To most of them, "tuning" is a verb, not a noun, and "temperament" is a
psychological term.

Gordon Collins
(going off-line for a week....)

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