pythagorean third

brett; i would still have to say, in MY opinion, that
polyphony really didn't exist in medeval times....

that is to say, much as microtonality doesn't exist for 99.9% of amerikans................

to call the pythagorean third dissonant is to call the
12 tone major third dissonant, at just 8 cents difference, most instruments STILL aren't capable of that resolution. i would say that anyone who believes that a stringed or wind instrument is up to the job, needs a
REALITY CHECK. I regularly see deviations of up to 20 cents in 'in tune' instruments.............

best, buzzy^

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>buzzy^ wrote,

>brett; i would still have to say, in MY opinion, that
>polyphony really didn't exist in medeval times....

I'm sure that would come as a shock to Margo, who has spent much of her life
studying medieval polyphony.

(By the way, that was me posting from Brett's computer)

>to call the pythagorean third dissonant is to call the
>12 tone major third dissonant, at just 8 cents difference, most instruments
STILL aren't capable >of that resolution. i would say that anyone who
believes that a stringed or wind instrument is up >to the job, needs a
>REALITY CHECK. I regularly see deviations of up to 20 cents in 'in tune'
instruments.............

To a modern ear, the pythagorean major third still sounds like a 5:4 ratio,
so it can function as a consonance, but it is rather rough. The 8-cent
improvement offered by 12-tET is quite audible and significant.

My point, however, was that the musical language of Gothic times (yes, it
was polyphonic) had accepted only fifths, fourths, and octaves as stable
consonances. This is quite well documented. The 5:4 ratio is consonant in
the context of the thicker harmonic language of today, but in those days,
thirds, however tuned, functioned as unstable sonorities and had to resolve.

Professional brass ensembles especially tend toward just rather than
pythagorean thirds, even in keys where the opposite would be easier. Yes, a
20-cent margin of error is normal, but certain styles and instruments
necessitate finer control for professional-level performances.