Fred writes
I frankly don't think dividing a 12th evenly into 19 is
significantly different from dividing an octave evenly into 12
Actually it is... tho the distinction in the temperament area is a bit
subtle. If you require that D3 and A4 have a pure 3:1 relationship...
then require that A4 and A3 have a pure 6:3 relationship then your 3:2
D3 and A3 is not necessarily going to work out quite like you want it...
and you may be forced to fudge. Course that kind of thing develops
around the temperament octave as you go.
But more then this, and evenly divided 12ths temperament extended into
the treble so that all notes above this area are tuned to pure 3:1 to
their respective 12ths below then the treble curve around the F5 - F6
area is significantly different then in an Octave type based curve. Jim
Coleman commented on this when my own P 12ths for Tune Lab was released
back around the turn of the century. Indeed, it was a characteristic he
liked quite abit.
Stoppers approach, if it indeed does use the Perfect 12th the whole way
will do exactly what Fred states... by definition all 12ths are tuned
pure and some middle area 12th interval must be used as a temperament
basis. I have not heard it...but if his device works well.. then it
simply must stretch the bass as described briefly in my last or as Fred
mentions, (and Jim Coleman confirmed years ago) the bass will simply be
too narrow to sound good. I suspect Stopper knows this and uses 12th
types in some fashion or another consciously or otherwise to provide an
appropriate stretch.
Fred is also correct in saying that the very top will be a conservative
stretch. Whether or not one thinks any particular stretch anywhere is
pleasing or not in the end falls into the realm of personal
preference.... subjectivity. That said... I think most folks if viewed
statistically would find a strict P-12th relationship in the low bass in
bigger pianos to be a bit to....tense.
Cheers
RicB
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