If you want to understand and/or try MT (1/4 or 1/6/ comma) on your
Renaissance lute, here is a small DIY I wote some years ago:
[1]https://davidvanooijen.wordpress.com/mean-tone-temperament-for-lute/
I did something similar for Pythagorean tuning (pure fifths, good for
Medieval music) too. It somehow is only visible on my old website:
[2]http://home.kpn.nl/ooije006/david/writings/pythagoras_f.html
David
*******************************
David van Ooijen
[3]davidvanooi...@gmail.com
[4]www.davidvanooijen.nl
*******************************
On Mon, 14 May 2018 at 22:38, Tristan von Neumann
<[5]tristanvonneum...@gmx.de> wrote:
Thanks Martin, this is really one of the most concise tuning
explanations I have read to date!
As for lute fretting:
In Lüdtke/Schlegel's book it is shown why there are problems with
different tunings on the lute, resulting in offset frets on
different
courses.
What I have seen lutists do is make the frets queer so they are a
mean
of the offset positions desired. I don't know what the result is, as
I
have never consciously seen/heard someone play with queer frets in
close
up, and I haven't tried yet because I'm happy that my frets are
staying
in place just now and that I got used to these positions.
For which cases would this solution be advised?
What are the disadvantages?
Am 14.05.2018 um 21:12 schrieb Martin Shepherd:
> Hi All,
>
> Without wishing to prolong a kind of flame war on ET versus
everything
> else, having written the following by way of explanation to
someone it
> occurred to me that it might be useful for others (I've noticed
that
> some people seem to assume that the fifths and even thirds are
perfect
> in ET, for example):
>
> If you were to imagine a keyboard instrument, and you start on C,
and
> tune a pure 5th to the G above. Then you tune that G to the D
above,
> also a perfect 5th. Then the D to the A above, and so on. (In
practice,
> you run out of octaves so you have to tune up a 5th, down an
octave, up
> a 5th, and so on.) Eventually you arrive at B#, which should be
the
> same as the C you started off with, but it isn't. It's horribly
sharp.
>
> That is the basis of temperaments. If you tune all those 5ths
just a
> little bit flat (i.e. "temper" them), you will indeed end up at
the C
> you started off with, and the B# will indeed be the same as C.
That is
> called equal temperament (ET), where each 5th is 2 cents flat and
every
> semitone is the same size - so C# to D is the same distance as D
to Eb.
> This is the tuning system in universal use in modern times, and is
the
> basis for all piano tuning and setting of fret distances on
guitars.
> This kind of tuning was known (theoretically) in medieval times,
but was
> not used for various reasons, most of which involved the
"impurity" of
> various intervals. In the renaissance, major thirds assumed a
new
> importance and so temperaments tended to favour them over other
intervals.
>
> Of course keyboard instruments (and to some extent lutes and
viols)
> always had this problem of trying to reconcile irreconcilable
ratios,
> but singers and players of wind instruments were able to "cheat"
by
> changing some of their intervals but not others - whereas someone
tuning
> a keyboard instrument (then as now) would have to make definite
choices
> about how to "temper" the intervals. In the renaissance, music
was
> played at a wide variety of pitches (in the absolute sense, there
was no
> such thing as a'=440) but in a very limited variety of "keys" as
we
> would call them. Of course they had no notion of "key" in the
modern
> sense and their understanding was in terms of hexachords and
modes. So
> if you were tuning a keyboard you could tune all the usual thirds
pure
> (C to E, F to A, G to B, and so on) because intervals like C# to
E#
> simply didn't exist. If you tune these important major thirds
pure you
> end up with a tuning in which the 5ths are quite narrow. Tuning
C-G,
> G-D, D-A, A-E you should end up with an E which is a pure major
third
> above the C you started with. This is called "1/4 comma
meantone"
> temperament, and it was probably the most common kind of tuning of
> keyboard instruments for at least 1500-1600, and well beyond.
Those
> major thirds sound wonderful, but you do have to decide how to
tune some
> of the "black" notes. Should you tune that key to G# or Ab? Bb
or A#?
> They're very different, so you have to make a choice. Usually,
if you
> tune to Bb rather than A#, Eb rather than D#, C# rather than Db,
F#
> rather than Gb, you will have a tuning which works in all the keys
you
> are likely to use. But of course if you decide to play in E
minor,
> you're going to need a D# instead of an Eb, so you have a problem.
Many
> early keyboards have "split" sharps/flats, where for one or more
of the
> "black" keys there are actually two keys, one for Eb and one for
D#, for
> example. You can also think about using a compromise pitch in
which the
> Eb is a bit flat and the D# is a bit sharp, but there's a limit to
how
> far this works.
>
> In the 18th century, although you could still use these "meantone"
> temperaments to good effect, especially if you make the major
thirds a
> little bit wider than pure (as in 1/6 comma meantone), there came
a
> point where you had to be able to play in any "key" (in the modern
> sense) and various "circular" temperaments were devised where the
fifths
> and thirds varied in size, so all keys were playable, but they
sounded
> different. These "circular" temperaments are probably what Bach
had in
> mind when he wrote the WTC - after all, what is the point of
writing
> music in every conceivable key if a piece in C# sounds the same as
a
> piece in C, but a semitone higher?
>
> The lute's frets, because they cover all the strings, limit our
room for
> manoeuvre. We can put the first fret in a position which gives
us Ab on
> the first course, Eb on the second course, Bb on the third course,
and
> so on, and it's all fine except that Gb on the fourth course,
which we
> really want to be an F#. We can (and I often do) put a "tastino"
there
> to give a proper F# - since the Gb is never needed. But there
are other
> places where we might want a tastino, and it soon gets very
complicated.
>
> Having grappled with these problems for many years, I now feel
that it's
> important to remember that the old lutenists did not play in any
> particular temperament (though in fact the fretting instructions
of Hans
> Gerle (1533, repeated by John Dowland in 1610, and evidenced in
> surviving citterns suggest something like 1/6 comma meantone) -
they
> used their ears. Everyone likes a perfect 5th, everyone likes a
perfect
> 3rd, but the two are mathematically incompatible, so it comes down
to
> what sort of compromise you are willing to make, and how far your
> strings and frets can be persuaded to give you what you want.
Insisting
> on equal temperament, or a specific meantone temperament, is hard
to
> reconcile with either the historical evidence or the
practicalities of
> tuning. I should also say that many modern proponents of equal
> temperament on the lute tend to assume that all positions on all
frets
> must be in tune (e.g. first fret fourth course to fourth fret
second
> course) - which if true would indeed rule out anything except
equal
> temperament - when in practical terms there are some course/fret
> combinations which are never used and therefore don't need to be
in tune
> with each other.
>
> Best wishes,
>
> Martin
>
>
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References
1. https://davidvanooijen.wordpress.com/mean-tone-temperament-for-lute/
2. http://home.kpn.nl/ooije006/david/writings/pythagoras_f.html
3. mailto:davidvanooi...@gmail.com
4. http://www.davidvanooijen.nl/
5. mailto:tristanvonneum...@gmx.de
6. https://www.avast.com/antivirus
7. http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
