Re: [tuning] What is Meantone ? Third draft.

To Johnny Reinhard who wrote:

"My only question on the informative
second draft by Daniel is if by the end of the first line, one must still
look up "temperament" and "syntonic" and comma" and "cents" and deal with
numbers, there must be a better way to organize difficult material."

I presume that basic terminology will be treated separately in the FAQ. If each
item in the FAQ is required to re-define basic terms, I believe they will get
hopelessly bogged down, and lose the graces of brevity.

Johnny Reinhard also wrote:

"WHAT IS "MEANTONE"

Meantone is a tuning that was developed in the Renaissance to modulate on a
keyboard instrument."

(1) The time frame in which the development occured is not clear. My item
includes the most crucial dates in the theoretical literature. An association of
the tuning with the Renaissance is plausible (I had it in my initial rough
draft) but arguable.

(2) The purpose "to modulate" is only one attribute, and perhaps rather
secondary to the goal of simply finding a workable compromise between the
product of a(n octave-reduced) series of fifths and a pure major third. For a
great deal of the repertoire we're concerned with, modulation is a negligible
concern, but this basic relationship between intervals is vital. Tuning history
could have gone another way, solving the problem, for example, by a distribution
of the skhisma instead of the syntonic comma. But because music history went in
the meantone (5:4 = up four fifths) direction rather than the skhismatic (5:4 =
down 8 fifths), my draft attempts to respond to that experience.

Johnny Reinhard also wrote:

"Theorists devised a way to split a major third into 2
equal parts (the "mean" whole tones) by flattening the pure fifth
consistently in every key."

(1) Do we know that this was developed by theorists or by practitioners through
trial and error and only later analyzed/desribed by theorists? No.

(2) The mean whole tone is a consequence of this tuning process, and indeed, it
is the atttribute that gave the tuning its name, a point on which my draft is
strict. However, it is far from likely that the mean division of the just major
third was the principle goal of the tuning. I characterize that goal as one of
attempting to relate the interval of the just major third to the product of a
series of fifths.

(2) If you intend it to mean tonality, the term "key" here is inappropriate for
the era in question. Better would have been "flatten each fifth identically."

Johnny Reinhard also wrote:

"This produces variants; quartercomma meantone splits a pure major third
(ratio 5/4 or 386 cents), while sixthcomma meantone was preferred by other
musicians in different times and places."

This is a non-sequitor to your previous sentence. Please note in my third draft
that I follow Barbour and describe the n-th-comma temperaments other than
quarter-comma MT as n-th-comma temperaments (not MTs), in that they do not have
mean-sized wholetones.

Johnny Reinhard also wrote:

"When the pure fifth (formed by the ratio of 3/2) is consistently flattened by
anywhere from 2 cents to 6 cents (with 1200 cents equal to an octave), a set
of identical diatonic keys are set up."

This sentence is empty: A set of identical diatonic keys would be set up by
_any_ uniform size of fifth.

That noted, I'm curious to learn on which grounds you have selected the range
of -2 to -6 cents? (The third-comma temperament would be excluded by your
definition and quarter-comma MT barely makes it).

Please answer me off list. I don't think this discussion is doing anyone else
any good.

Daniel Wolf