I agree, Rainer, I think it's accepted there's no _perfect_ way to
introduce meantone or its variants to lute. The trade off of 2 or 3
cents (which I will barely --if at all-- notice) in a 5th or octave for
10 cents for nicer thirds is acceptable to me.
- nb. If one is using gut strings all bets are off after a week or so
anyway, esp'ly anything above the 5th fret. This related to the age of
the gut, weather, finger oils, overstrumming/plucking/fingering wear.
- nb2. The act of pressing or over pressing a digit behind a fret will
also affect that tuning.
- nb3. The attempted meantone fretting of fixed fret instruments like
citterns and orpharions shows that it was given at the very least lip
service and, at most, worth spending money on and a real pursuit at the
time.
To my ear, a gut strung instrument that stays in perfect equal
temperament for any length of time is equally a chimera. ... unless
you're wealthy.
This is my 2 cents and you may continue with your mathematics now.
Sean
On Sun, May 13, 2018 at 12:30 PM, Rainer
<[1]rads.bera_g...@t-online.de> wrote:
A clarification:
Suppose you want to place the frets on a lute so that:
1) All unisons are pure. That means the f on the second course has
the same frequency as the open 1. course, the g on the second string
has the same pitch as the b on the 1. course, ... over all courses.
2) All octaves are pure. The c on the fourth course has half the
frequency of the first course,
Then you have no choice left except equal temperament.
The reason is that lutes cannot be tuned in any meantone
temperament. You always have to accept false unisons or octaves.
Rainer
PS
I use 1/6 comma meantone. However, I have no Baroque lutes nor have
I ever tried accord nouveaux...
On 13.05.2018 21:04, Ralf Mattes wrote:
Am Sonntag, 13. Mai 2018 20:43 CEST, Ron Andrico
<[2]praelu...@hotmail.com> schrieb:
Ralf and Rainer, I believe you are in agreement. Octaves,
fourths and
fifths are pure and other intervals are an approximation.
No, that's not what I (or Rainer) said. And it's wrong: Octaves are
alway pure in all (western) tuning
systems. Fifth/forth can be pure but then will be incomensurable
with octaves (i.e. you can't stack
fifth/forth and ever end up with pure octaves. As a matter of fact
no pure intervals are comensurable.
That IS a mathematic fact).
Cheers, RalfD
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