meantone contrast again

Although meantone, in most historical contexts, does not have key
colour, one could argue that quarter-comma meantone is practically,
among regular tunings, the one with the most contrast in common
practice (post-medieval) music.

The key point is the contrast of pure major thirds with the beating
quarter-comma-impure minor thirds and fifths. In traditional
counterpoint both kinds of thirds are heard in close proximity, so
even ordinary diatonic music is full of strongly contrasted intervals.
When the practically-pure septimal tritones also come into play the
mixture of intervals is fascinating. And all without leaving the tonal
range of the usual, everyday chain of fifths.

Equal temperament, it is true, has a contrast of practically pure
fifths with strongly tempered thirds: but in this case the thirds are
basically so far from 5:4 or 6:5 that one is unable to appreciate them
as slight mistunings of pure intervals. Their beating in most musical
contexts is too rapid to produce any clear effect - and keyboard
instruments of the ET era tend to suppress the relevant partials anyway.

One resulting point is that 2/7 comma and 1/5 comma meantone, although
mathematically not very far from quarter comma, have actually quite
different musical effects. In the first, all thirds are practically
pure so there is less contrast between them, but fifths are strongly
mistuned, to the verge of dissonance. In the second, the diatonic
consonances are more or less equally mistuned, the tuning gives more a
general effect of pretty good intonation without any great contrast
between different chords.

Music conceived in one of these unequal meantones may be relatively
boring (if strong diatonic contrasts are expected), or awkward (if
such contrasts are not expected), in another. The 'historical'
meantones cannot be freely substituted for each other!

~~~T~~~

Excellent post, Tom.

Just for the record, the more common quasi-equivalent EDOs
for the meantones you mention are:

1/4-comma ~= 31-edo
1/5-comma ~= 43-edo
2/7-comma ~= 50-edo

Some of my webpages on these may be found useful:

http://tonalsoft.com/enc/number/1-4cmt.aspx

http://tonalsoft.com/enc/number/31edo.aspx

http://tonalsoft.com/enc/m/meride.aspx

http://tonalsoft.com/enc/number/2-7cmt.aspx

http://tonalsoft.com/monzo/woolhouse/essay.aspx#temp
(50-edo is the third section under this heading)

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> Although meantone, in most historical contexts, does not
> have key colour, one could argue that quarter-comma
> meantone is practically, among regular tunings, the one
> with the most contrast in common practice (post-medieval)
> music.
>
> The key point is the contrast of pure major thirds with
> the beating quarter-comma-impure minor thirds and fifths.
> In traditional counterpoint both kinds of thirds are heard
> in close proximity, so even ordinary diatonic music is
> full of strongly contrasted intervals. When the
> practically-pure septimal tritones also come into play
> the mixture of intervals is fascinating. And all without
> leaving the tonal range of the usual, everyday chain of
> fifths.
>
> <snip>
>
> One resulting point is that 2/7 comma and 1/5 comma
> meantone, although mathematically not very far from
> quarter comma, have actually quite different musical
> effects. In the first, all thirds are practically pure
> so there is less contrast between them, but fifths are
> strongly mistuned, to the verge of dissonance. In the
> second, the diatonic consonances are more or less equally
> mistuned, the tuning gives more a general effect of
> pretty good intonation without any great contrast
> between different chords.
>
> <snip ...> The 'historical' meantones cannot be freely
> substituted for each other!

-monz
http://tonalsoft.com
Tonescape microtonal music software