Re: Decatonic scales: temperaments with relatively just thirds and fifth?
- --- In email@example.com, Torsten Anders <torstenanders@...>
> Thank you all very much for your replies!! I had no time yet to
> all your recommendations, but I definitely will :)Hi Torsten,
I thought it was about time I replied directly to one of your
messages about a couple of things that weren't completely answered.
> On Mar 27, 2008, at 6:28 AM, Petr Parízek wrote:get
> > If you want thirds and fifths to be closer to just, then you'll
> > only a very poor approximation to 7/4 because the same intervalis
> > also used here to approximate 16/9.septimal
> Does there also exist a variant where the intonation of the
> intervals is optimised (possibly to the detriment of thirds andIt looks as if that would have to be something very close to 22-
> fifths) like the (major) thirds are optimised in meantone (to the
> detriment of the fifths)?
equal. Because ~7/5 is fixed at 600 cents in pajara (with pure
octaves; but, in any case, something very close to that), further
decreasing the error of 7/4 (by lowering it) causes the error of 5/4
(which also must go lower) to increase further in error. A major 3rd
that's narrower than in 22-equal is not very good melodically, which
I suspect is one of the things that caused you to look for
alternatives to 22-equal (in addition to the heavily tempered fifths).
> ...some "gentle
> On Mar 27, 2008, at 7:37 AM, Graham Breed wrote:
> > Well temperament -- make the tuning more lumpy. You can
> > make some chords better in tune at the expense of others.
> > Naturally you'll probably want the most important chords to
> > be well tuned. As a bonus you can get the temperament to
> > circulate, so that you can modulate over a fixed number of
> > notes. 22 and 34 are the most obvious choices.
> I have never created a well temperament yet -- is there
> introduction" to this subject available I could read?Please do check out the 34-tone well-temperament that I discussed
here, because (in its dozen or so best keys) it doesn't damage 7/4
nearly as much as does 34-equal:
I've tried (on several occasions) to construct some sort of 22-tone
well temperament, but I wasn't able to come up with anything
On Mar 28, 2008, at 4:20 PM, Carl Lumma wrote:
Original Subject: Re: [tuning] Re: Decatonic scales: temperaments
with relatively just thirds and fifth?
> George Secor wants to preserve the common usage of these terms.
> However, since the common usage isn't precise (uses these
> terms interchangeably), I don't think that's a good idea.
Just remembered that we were discussing this terminology already a
year ago. In summary I feel instead of redefining established terms
it might be a better idea to use new terms or common terms with
additional qualifiers in order to avoid confusion.
Interdisciplinary Centre for Computer Music Research
University of Plymouth