Re: Intonational System Earlier Musicians Had in Mind

>I'd like to put in as my opinion that the intonational system
>a great many musicians - theoreticians, composers, and many
>practicing musicians had in mind was just intonation from the
>1400s up until the 1900s.

If you're talking about strict just intonation, where all intervals, melodic or
harmonic, are simple-integer frequency ratios, I'd have to say this is absolutely
false. For but one refutation of this point of view, see Blackwood's _Structure
of Recognizable Diatonic Tunings_.

>Most of the writings I have looked at
>from those times (not comprehensive, but some original writings)
>assume just intonation as being the "true" basis for the pitch
>structure of music,

Just intonation is the true basis for the consonant intervals. That is all.

>with temperament - mean tone and later equal
> temperament - being a necessary but not ideal slight modification
>of the "true harmonies" needed so that the music could be performed
> on instruments having a limited number of fixed pitches.

That is not the case. A simple diatonic, triadic piece in one key may sound
wrong in strict just intonation, because often shifts or drifts of a comma will
occur. We've gone over this myriad times before, but I'd be happy to do so again.
Also, as Margo has been describing in great detail, there were reasons why the
various temperaments were used when they were -- they are not simply alternative
simplifications of just intonation; rather, they are realizations of musical
ideals that varied with the times.

>When I've
>looked at 18th & 19th century books on music - and even some 20th
>century ones, the just ratios of musical intervals are laid out in great
>detail as being the foundation of musical pitch and harmony.

Yes, the just ratios are the foundation of harmonic _consonance_. But there is
more to music than that -- primarily _melody_.

>Some which I remember are Rameau's Treatise on Harmony; Owen's
>Dictionary of the Sciences from the late 1700s quoted in Jorgenson's
>work on tuning in which the author speaks of mean tone tuning as introducing
>small errors into the true musical intervals which are perceptible, but
>still do not harm the music's effect;

Absolutely. But meantone tuning was necessary to allow the _melodic_ structure of
the music to fit with these acceptable _harmonic_ approximations.

>William Pole's Philosophy of Music
>(1879); the first edition of Schoenberg's Harmonielehre of 1911;

Unfortunately, not a paragon of accuracy (historical or mathematical) in
discussion of tuning.

>Also, some of these earlier writings imply that much vocal music
>was performed in closer to just intonation than equal temperament and
>had a different character as a result - a delightful character according
>to some of the authors. No mention was made of singers singing in
>mean tone temperament in things I've read.

Singers may sing in _adaptive_ JI, where each simultaneity is tuned in JI (nearly
enough) but the intervals between successive pitches are irrational. In this way
they may "hide" the commas of strict JI. Ultimately this approach has elements in
common with meantone. However, recent evidence seems to show that the _melody_ in
vocal music tends to be the strongest determinant of intonation -- the melody is
usually performed in something close to 12-equal or Pythagorean, and the other
singers form JI harmonies behind that.

>Recently, some early cylinder recordings of vocal music recorded
>in the late 1800s have been reissued on CD. Many of the early
>recorded quartet songs sound as though the singers were striving for
>just intonation.

Strict JI or adaptive JI?

>I have not made an exhaustive study of the historical literature,
>but most of what I've seen has pointed in the direction of just intonation's
>having been assumed without argument as being the natural basis for
>musical harmony - especially after the discovery of overtones was
>made in the 17th century by Galileo and Mersenne.

The relevance of just intonation for musical _harmony_ is undeniable, although
the psychoacoustic factors at play are quite complex and not at all explicable
merely on the basis of the existence of overtones. But musical tuning is a result
of oftenconflicting influences from harmony (vertical relationships) and _melody_
(horizontal relationships). The combination of these two factors, applied to the
musical language of a given time period, as well as considerations of
convenience (which you note), determined the tuning appropriate to that period's
music.

In the last century, the field of ethnomusicology has shattered many of our naive
presuppositions about musical tuning. Although functional harmony seems to have
been a peculiarly Western development, melody is virtually universal to all
cultures. The scales of a great number of these cultures have been studied (look
up almost any country in the _New Grove_), and very few can be said to represent
or even resemble the "classical" Western ideal of just intonation as put forward
by some of the authors you mention. In the post-Newtonian West, systematization
and numerification became very popular in all fields, which sought to reproduce
the successes of Newtonian theory in physics. Most of the products of this
misguided inspiration have been soundly overturned in the 20th century.