intemperate music

To get back to the subject that I really wanted to bring up...


Bill Alves wrote (in response to something else, but providing a good
starting point):

>In my definition of modes in the European tradition, they include at least
>the following defining characteristics:
>
>1) A tuning system, though it may be somewhat flexible as long as the
>general pattern of intervals (below) remains recognizable.

While there has been a fairly strict intonational standard at most times and
places, "somewhat flexible" here is a considerable understatement. The
distinction between n-limit JI, x-comma meantone, well-temperament, and
12TET is *totally irrelevant* to the definition of modes and scales!

Look at a music theory book and its description of musical resources. Where
is there any discussion of pitch or tuning? It just doesn't matter. The
only thing that rules out applying JI or meantone is the circle of fifths
with its enharmonic equivalence of notes.

It also is not sufficient to define "pitch areas" for the notes. There are
Renaissance motets in which, depending on one's interpretation of _musica
ficta_ rules, the range of pitches used for F overlaps that used for E
*within the same piece*. This is not just due to comma shifts, but due to
_ficta_ inflections.



>2) A subset of pitches from that tuning system, or, put another way, a
>pattern of intervals. (In the European tradition this means the diatonic
>set.)

But the notes of the modes were not taken from a larger set. They WERE all
the defined notes. Others were *added* to the set as necessary for
polyphony. They were initially considered as intonational inflections, only
later being accepted as separate notes in their own right as sharps and flats.

I agree with Daniel that modes and scales can only be defined in terms of
whole tones and "half" tones, as a pattern of approximate intervals. I don't
think that those patterns can be described as pitches selected from a
predefined tuning system.



>Number of pitches in the tuning system/number of pitches in the
>subset/number of commonly used auxiliary tones.
>
>[qualification snipped]
>
>Thus traditional diatonic modes are:
>
>12/7/0


In light of the above, the original modes would actually be:

7/7/0

Guido's system formally allowed for:

8/7/0

and the whole system with _musica ficta_ would be:

infinite/7/infinite

as there was no predefined set of available frequencies, and no upper limit
on available auxiliary (_ficta_) pitches.


Reducing this to 12 requires accepting enharmonic equivalence, closing the
circle of fifths. That idea strikes me as one of the most pivotal notions in
the history of Western music, yet as far as I can tell, it grew gradually
over centuries and without much comment, only becoming fully accepted in the
18th century. Only then could 12TET, long understood, be applied. It was
far from being the foundation.

Gordon Collins

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