Patrick Frye asked:
> So---I began at the beginning and found myself here:
> Does this seem a good site to research this aspect of the subject, as
> there is much to read and discover, I don't care to be misled.
Well...for starters, the analytical table of meantone makes the
musically impossible choices of Db, Eb, F#, G#, and A# for the five
accidentals. (What, we're supposed to pick the notes so we have five
wolves instead of one? Db-G#, G#-Eb, F#-Db, A#-F, and Eb-A#? And this
selection of accidentals reduces our set of usable major triads from
eight to only four!)
There is no section about modified meantone schemes (_temperament
The section about "well temperament" is so superficial as to say almost
nothing. Furthermore, that section relies on almost nothing for its
background, except a (good) medievalist article.
Better to start with the _New Grove_ "Temperaments" article than that
web essay at midicode.com.
Here's my own little summary of the different keyboard-temperament
strategies, from this article (originally for _BBC Music Magazine_, 2006):
Reference: Other keyboard tuning strategies, historically
Keyboard tuning methods fall historically into several competing styles,
as to the size(s) of 5ths used to generate the notes. All of these
styles have been brought back into use in the 20th and 21st centuries,
for reasons that are variously historical, aesthetic, or practical.
* Pythagorean (before the 17th century): Eleven pure 5ths or 4ths
are easily tuned in succession. The resulting major 3rds are very wide.
The cycle of 5ths does not meet itself exactly; a dissonance results
between the twelfth note and the first note.
* Just intonation (15th century forward): All the notes are related
to one another variously by pure 5ths or pure major 3rds. The available
intervals and chords are outstandingly resonant within the single home
key, but strong dissonances arise in other keys (thereby restricting
modulations). Melodies are bumpy, as the steps within the scale are of
vastly different sizes.
* Equal temperament (16th century forward, but not a universal
"standard" until the 20th): The same amount of tempering is given to
each of the eleven 5ths, so the beginning and end meet with a twelfth
5th of the same size. All twelve notes are equally spaced, and all
scales have the same character. The tempering of the 5th is so slight
that it is difficult to control with precise equality, in practice.
* Quasi-equal (18th century forward): These variously subtle
methods make a neutral effect similar to equal temperament's, without a
strongly recognizable character to any key. Some of these are easier to
tune than equal temperament, as they have several pure 5ths spaced
symmetrically among their tempered 5ths.
* Meantone or "regular" systems (16th-19th centuries): Each tone
(whole step) is placed at an exact mean (geometric average) position
within the major 3rd, whatever its size. For example, C-D and D-E are
equally spaced within C-E. All of these meantone systems are generated
by tuning eleven identical (regular) 5ths of some selected size, until
there are twelve different notes. There is a leftover gap, or "wolf"
diminished 6th, from the twelfth back to the first note; this rift is
usually placed at G#-Eb, D#-Bb, or C#-Ab. Notes such as Db, A#, and E#
usually do not exist in this scheme; and they sound rough if they occur
in the music. The most common meantone system had a strongly tempered
5th so that the usable major 3rds worked out to be pure; but from the
early 17th century forward this was gradually relaxed toward slightly
sharper major 3rds and gentler 5ths, as practical compromises.
* Modified meantone, or "circulating" or "irregular" or "ordinary"
(17th-19th centuries): The series of 5ths is regular in the midsection
(on the natural notes of the C major scale, ...C-G-D-A-E...), but
increasingly wide toward the outsides. This sharpens the sharps and/or
flattens the flats gradually, so they can serve passably as one another,
and it reduces or eliminates the "wolf" intervals. Some of these schemes
also have a flattened F or a raised B, as transition into the flats or
* Split keys (15th century forward): Extra key-levers are added
within the octave, e.g., having two separate keys to play G# and Ab.
Such keyboards are usually tuned in a meantone style, taking advantage
of excellent major 3rds.