Fred in Toronto wrote:



> I have been hiding behind my ignorance for a bit on this thread - I don't
> understand the usage of the term "comma" (I hope I am not alone in this)
>
> Fred in Toronto
>

So far, noone has responded to this basic bit of info.

The comma is the amount of tuning error you will accumulate if you tune
(perfectly) through the circle of fifths until you reach an octave. The
octave will not agree with the note from which you started, thus any tuning
system requires adjustment (temperament) of the intervals to be useful.
Equal temperament evens out the error uniformly through all the notes of the
octave, making all the semitones the same size (100 cents/semitone, 1200
cents/octave). ET could also be expressed, then, as 12th comma meantone,
though it isn't so expressed, except humorously.

To get your bearings, it's helpful to describe 1/4 comma meantone, the
native temperament of most "early" music. To set the temperament, one tunes
C, G, D, A, E three times as fast as in equal temperament, so that E is a
pure major third. The remaining notes are tuned as pure major thirds (or
minor sixths) according to how they are used: C#-A, Eb-G, F-A, F#-D, G#-E,
Bb-D, B-G. This yields a temperament with two sizes of semitone. Those that
are used as leading tones in the "good" keys (to 3 sharps or 2 flats) are
wide, the others narrow. Thus there is no tuning color distinction between
the different good keys - they all share the same progression of interval
size. Some will argue with this statement, but they are no more right or
wrong than those who make the same argument for ET.

1/5 th comma and sixth comma yield milder versions of meantone. Spreading
the comma by another fifth to B yields a temperament (1/5th comma) where all
the leading tones are just, ie B is a pure fifth and a pure major third (by
temporary tuning) from C. 1/6 th comma is, then, a bit milder yet.

Well tempered tunings fall into two broad categories. Several are similar to
1/5 and 1/6 comma and can therefore fairly be described as compromise
tunings, ie they give a bit of the flavor of original meantone tunings,
while being less destructive of the ET repertoire.

Others go off in entirely different directions and, IMHO, are utterly
worthless, since they tend to make ET repertoire sound odd to bizarre and do
nothing towards faithfully presenting the character of the QC repertoire.
Indeed the QC rep often fares worse than the ET rep in some of these
tunings.

Hope that this is somewhat helpful to those who would like to understand a
bit of what this discussion is about.

Dick H.

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