ET data file

There is a new version of
ftp://ella.mills.edu/ccm/tuning/papers/et_data.zip
It contains one text file with many mathematical properties of equal
temperaments from 5 to 612 tones per octave. For example sizes of
semitones and commas in number of steps, best approximations to
5/4, 3/2 and 7/4, various subscales of 7, 12 and 19 tones, consistency
limits, numbers of cycles of fifths, etc.
Unzipping is best done with the -a option for ASCII file to prevent
problems with the carriage-return character.

Manuel Op de Coul coul@ezh.nl

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Certain important musical terms regularly employed by microtonalists have
multiple meanings, including mode, pentatonic, and enharmonic.

Though coming off the recent AFMM series, the above distinctions are a
welcome diversion. (I'm really enjoying David Beardsley's report.)

Re: modes with Greek-area names, they have changed mightily since the dawn
of Greek culture. Phrygian, Lydian, Aeolian, etc. were distinct peoples
with cultural models for their modes. This information is lost. The
Greeks recognized a healthy diversity in combining the characteristics of
these prehistoric ethnic scales into a modulating 2-octave infrastructure,
a scalar system. The Church modes of the middle ages looking backwards
over a spate of centuries relabelled modes in practice with earlier
nomenclature (e.g. Phrygian, Lydian, etc.) Modern useage is limited to
12-TPO well-temperaments.

Pentatonic tuning can be in just intonation, pythagorean tuning,
12ET, 5-ET, and presumeably any other 5-note scale (including
auxillaries). Might we not include Indonesian Pelog, quartertone
deriveatives, and any other series of relationships of 5 notes that can
modulate to any one of its members?

Enharmonic meant an ancient Greek genus that primarily featured a just
major third (5/4) and 2 distinct, but different "quartertones." Euripides
was said to favor it in his tragedies, for which he composed music. It
lost out historically to more equally spaced Diatonic scales. Composers
like Nicolo Vicentino in the Renaissance revisited it. By the Baroque,
enharmonic intervals were a comma in size, this reflecting a distinction
between a C# and a Db. G.F. Handel is reported to have had split-black
keys on his organ, allowing for 14 note per octave capability. Gradually,
the enharmonic difference transmuted into an identity, thanks largely to
the piano's tuning compromise.

It may be best for the list to be very clear on the above distinctions.
Harry Partch's "monophony" as the fabric of his O- and U-tonality is
certainly a stretch from the homophonic or heterophonic lines of the
Middle Ages.

Johnny Reinhard
Director
American Festival of Microtonal Music - MicroMay '97 (May 16, 21-23)
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@idt.net
http://www.echonyc.com/~jhhl/AFMM/

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> Am I correct in deducing that say Dorian mode uses exactly the same
>note frequencies at which say Ionian mode was tuned in just intonation,
>i.e. 9/8 5/4 4/3 3/2 5/3 15/8 2 9/4 ?

That is definitely NOT true if you're taking those ratios relative to
the tonic rather than to a C in particular.

If you're taking those ratios relative specifically to a C, then that's
as true as for any other tuning mode. By that I mean that there will be
variations in what tuning for any particular tone is best for the
particular situation. Comma differences are probably the most celebrated
example of this. In some contexts tuning the D to 10:9 relative to C makes
more sense than 9:8.

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On Fri, 30 May 1997 15:53:12 -0400 (EDT) Daniel Wolf
wrote:

>A close study of that alto voice will probably reveal motion that is
>uncharacteristic of a lydian melody.

Not certain what a "Lydian melody" is. Are you saying that the Lydian
mode has characterstics melodic motions, as would say, an Indian raga?

>Simply playing dorian as d to d' on a just
>major C scale won't work due to the comma shy fifth d - a;

It not clear to me how the imperfect 5th (40/27) can be avoided.
Even if the tonic is 'd', the 5th above must be 'a' at an interval
of 40/27ths, yes? We cannot transpose the Dorian mode to begin
with the interval 9/8 instead of 10/9.

>in pythagorean
>the opposite is often the case due to the ditone above the tonic,
>resolution to which is demanded by the diminished fifth b - f.

Again, in monophonic music, which the ancient Greek mode was,
would the 'f' need to lowered to avoid the tritone, or would the
729/512ths jump be made?

Thanks.

Polychronios N. Moniodis
upb_moniodis@online.emich.edu

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Let me try to answer both of your questions at once. Medieval music theory
for the motion of melodic voices is based upon the assumption that the
scale is pythagorean. Therefore the dorian is going to have a 3/2 fifth at
the interval d - a. A combination of this tuning and the standard rules for
melodic motion leads logically to something like a raga with a distinct
identity for each mode, albeit obligatory ornamentation (like gamakas) must
remain a matter of conjecture. There is simply too little evidence one way
or another, and the difference over time and in different places must have
been enormous (as is true for South Indian music, for example.) Later polyphonic music may or may not require just thirds and comma shifts
to accomodate these, or the whole matter may be rendered moot by a
temperament (i.e. equal on fretted strings, meantone on keyboards). In any
case, a 40/27 on the dorian tonic would only be the consequence of a justhexachord on c (assuming that just hexachords ever were current), but could
be corrected to 3/2 by RE on the hexachord on G. Ancient greek music is another matter altogether. There is no theoreticalevidence one way or another of rules regarding tritone leaps - or of any
rules about melodic motion except for the labeling of certain common
motions. If I recall correctly, however, some of the preserved fragments do
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