RE: pure?

SPurman554@aol.com writes:
> Based on the C major scale in
> 12TET, how should each note be tuned to most closely approximate a pure JI
> tuning? Below is a tuning I found in a book:

Gary's guess is almost right, the scale he gave is Ellis's Duodene.
The one from your book is 135/128 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3
9/5 15/8 2/1 but I've never seen it before. The only difference is the
C# of 135/128, flat by a diaschisma from 16/15.
If you transpose the scale by a fifth and then take the octave
inverse, you get a lute tuning from Mersenne.

Manuel Op de Coul coul@ezh.nl

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Gordon Collins wrote:

'' A key is not just a set of notes - it is determined by chordal structure rather than melodic formulae. ''

No, a key is a set of 7 pitches in a (at least nominal) series consecutive
of fifths, octave equivalence assumed, and auxillary accidentals allowed.This contributes the pitch height component of the identification of a mode
of a piece. Our terminology for this is not so transparent, in that
traditionally the tonic is named verbally and the set of pitches identified
by the key signature. Thus the key with two flats gives Bb Major, g minor(with or without auxillaries - a look at Baroque minor key signatures is
instructive), c dorian, d phrygian etc..

Major and minor tonalities have distinctive harmonic possibilities from
harmonized church modes, and these are manifest in particular harmonic
sequences. For example, a phrygian harmonization will have a different
treatment of the second degree from that found in major or minor. (A V ofV
- V - I sequence is very different in these modes and that is exactly thefeature that Schumann or Berlioz or Sibelius grabs onto!).

Since I have had to do some church organ playing of late in a church
(Altkatholische) where Lutheran chorales are used, I have been struck by
the variety of harmonizations. Most settings are modal (i.e. retaining the
dominant/tonic functions of the melodic mode), but some - particularly
those of Bach - put the melody into a Major/minor tonality with elaboratecross relations and usually are slowed down considerably to accommodate the
rapid increase in harmonic rhythm. Indeed, although the congregation onlysings the melody, the ''tonal'' harmonizations make the melody harder to
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>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.
>
Gordon Collins replied:

>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.
>
Well then, clearly we have different definitions of modes or keys. To me a
tonal center is a psychological tendency to hear a certain pitch within the
system as a home base, a gravitational center, however you want to say it.
This tendency is operative in most music whether it has harmony or not. The
tonal center is very often the _finalis_, but not necessarily.

The use of the term "modal" in most theory textbooks as in the distinction
between "modal" and "tonal" counterpoint, is misleading I believe (also
"tonal").

>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!
>
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.

>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.

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.

>>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.
>
Historically, this is true. However, pitch systems change over time. I have
no problem with defining pitch systems in Guido's time as 8/7/0, but I
think it's obvious that diatonic European music since at least the 15th
century has been 12/7/0. 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, but
in any case, once made, the definition of a diatonic mode as a 12-tone
subset became a valid one.

>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.
>
This works for the diatonic set (though I think this definition has come to
be equivalent with a 12-tone tuning system subset). However, there are
other tuning systems that simply are not defined in terms of whole and half
steps. Pelog is one that comes to mind. (Though some have posited a 9TET
superset for pelog, I have yet to see any convincing evidence for this
hypothesis, and much that contradicts it.)

The tuning system that I mentioned I'm working with now has 9 different
sized steps in the octave, ranging from 27 to 204 cents. Perhaps you can
hear some sort of generalized half and whole steps defining a "pattern of
approximate intervals" in such a system. I can't. However, the ability to
do so in a system is part of what I meant by "recognizably diatonic" when
refering to the flexibility of tuning systems in defining modes.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
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Daniel Wolf wrote:

>Gordon Collins wrote:
>
>'' A key is not just a set of notes - it is >
>determined by chordal structure rather than melodic formulae. ''
>
>No, a key is a set of 7 pitches in a (at least nominal) series consecutiv>e
>of fifths, octave equivalence assumed, and auxillary accidentals allowed.>
>This contributes the pitch height component of the identification of a mo>de
>of a piece. Our terminology for this is not so transparent, in that
>traditionally the tonic is named verbally and the set of pitches identifi>ed
>by the key signature. Thus the key with two flats gives Bb Major, g minor>
>(with or without auxillaries - a look at Baroque minor key signatures is
>instructive), c dorian, d phrygian etc..

Well, now. My statement above was taken almost verbatim from Grove's
Dictionary of Music, which also points out the difference between the Ionian
mode and the key of C Major. This also agrees with everything else I have
read on the subject.

You evidently have developed your own definition of "key" - more power to
you, but without common terminology no discussion is possible.

Gordon Collins

From: SMTP%"tuning@eartha.mills.edu" 29-MAY-1997 01:05:51.55
To: manuel.op.de.coul@ezh.nl
CC:
Subj: Re: Modes

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