Re: [tuning] A new piece of music -- about the scale

Hi there.

Well, for those of you who may be interested, I promissed to say a few words about the tuning I've used in the new recording of mine, which I'll do now. It's a linear temperament with a period of 1200 cents and a generator of about ~357.076 cents. The point here is that this generator is fairly close to 16/13, which makes it possible to approximate 13-limit intervals nicely. What's more, three of these neutral thirds are close to 13/7 and therefore 7-limit intervals can be mapped here as well. And even better (the most interesting thing of all), this particular generator is actually the 9th root of 32/5, which means that also 5-limit intervals can be played there. So in this scale, I can, in fact, easily play chords very close to 4:5:7:13 or something like this. The one that I used so often at the beginning of the celesta part was an approximation to 1:4:7:10:13:16 which sounds particularly attractive to me because of the difference tones all of them being three times the common fundamental. That's why I finally called the piece "13-limit Spectrum" as it reminds me of the old strange synthetic timbre whose harmonics go 1:4:7:10:13:16:19:22 ...

Petr

PS: As you can hear from the music, although I also tried to play something like fifths, it was not one of the best choices -- they are about 12 cents away from pure.

PP

--- In tuning@yahoogroups.com, Petr Pařízek <p.parizek@...> wrote:
>
> Hi there.
>
> Well, for those of you who may be interested, I promissed to say a
few words about the tuning I've used in the new recording of mine,
which I'll do now. It's a linear temperament with a period of 1200
cents and a generator of about ~357.076 cents. The point here is that
this generator is fairly close to 16/13, which makes it possible to
approximate 13-limit intervals nicely. What's more, three of these
neutral thirds are close to 13/7 and therefore 7-limit intervals can
be mapped here as well. And even better (the most interesting thing
of all), this particular generator is actually the 9th root of 32/5,
which means that also 5-limit intervals can be played there. So in
this scale, I can, in fact, easily play chords very close to 4:5:7:13
or something like this. The one that I used so often at the beginning
of the celesta part was an approximation to 1:4:7:10:13:16 which
sounds particularly attractive to me because of the difference tones
all of them being three times the common fundamental. That's why I
finally called the piece "13-limit Spectrum" as it reminds me of the
old strange synthetic timbre whose harmonics go
1:4:7:10:13:16:19:22 ...
>
> Petr

Chords in which consecutive pitches are separated by a common first-
order difference tone were identified by the term "isoharmonic" in
Leigh Gerdine's translation of a book on 31-ET by A. D. Fokker. I
don't know what German (or Dutch) term Fokker may have originally
used, but at any rate, it's a very effective way to build relatively
consonant-sounding chords using higher prime numbers.

I also observed that your linear temperament may be reasonably
approximated by edo's 94, 111, and 205.

--George