differencial coherence for double-flute

Hello,

I need some advise to tune my double flutes; if anybody likes to have a new puzzle.

This is two melodic flutes, I play with one hand on each flute. Some notes are missing so we can put bad intervals there.

The flutes are high in pitch and the difference tones are very loud.

That's why I need a "differencial coherence" in my scale.
My lowest flute plays C-D-E-F-G
And the highest flute plays G-A-B-C-D. I would love that all combinations between the 2 flutes would generate beautiful difference tones ;)

As a sum-up:

I would love perfect fifths there:

C-G; D-A;E-B; F-C
And beautiful fourth there:
D-G; E-A
Why not pure major thirds there:
F-A; G-B
And pure minor thirds there:

E-G
and as a conclusion beautiful sixths there:
C-A; D-B; F-D

If anybody can help me on this question, even help me to take the question on the right way...I will be thankful for the rest of my days!
Jerome

--- In tuning@yahoogroups.com, Jérôme Désigaud <jeromedesigaud@...> wrote:
>
> I would love perfect fifths there:
>
> C-G; D-A;E-B; F-C
> And beautiful fourth there:
> D-G; E-A
> Why not pure major thirds there:
> F-A; G-B
> And pure minor thirds there:
>
> E-G
> and as a conclusion beautiful sixths there:
> C-A; D-B; F-D
>
> If anybody can help me on this question, even help me to take the question on the right way...I will be thankful for the rest of my days!
> Jerome
>

If you want F-C-G-D-A-E to be tuned by perfect fifths/fourths, and you also want F-D to be a just major sixth, then meantone tempering is probably your best bet. (May I also suggest superpythagorean tuning as a viable option, which will make F-D closer to the nice 12/7 ratio)

Here are the cents figures for 2/7-comma meantone, which is a decent meantone tuning:

C - 0
D - 191.62
E - 383.24
F - 504.19
G - 695.81
A - 887.43
B - 1079.05
C' - 1200

And frequencies, starting at C (261.63 Hz)

C - 261.63 Hz
D - 292.25 Hz
E - 326.45 Hz
F - 350.07 Hz
G - 391.05 Hz
A - 436.82 Hz
B - 487.94 Hz
C' - 523.25 Hz

Ryan

--- In tuning@yahoogroups.com, "Ryan Avella" <domeofatonement@...> wrote:
>
> --- In tuning@yahoogroups.com, Jérôme Désigaud <jeromedesigaud@> wrote:
> >
> > I would love perfect fifths there:
> >
> > C-G; D-A;E-B; F-C
> > And beautiful fourth there:
> > D-G; E-A
> > Why not pure major thirds there:
> > F-A; G-B
> > And pure minor thirds there:
> >
> > E-G
> > and as a conclusion beautiful sixths there:
> > C-A; D-B; F-D
> >
> > If anybody can help me on this question, even help me to take the question on the right way...I will be thankful for the rest of my days!
> > Jerome
> >
>
>
> If you want F-C-G-D-A-E to be tuned by perfect fifths/fourths, and you also want F-D to be a just major sixth, then meantone tempering is probably your best bet. (May I also suggest superpythagorean tuning as a viable option, which will make F-D closer to the nice 12/7 ratio)
>
>
> Here are the cents figures for 2/7-comma meantone, which is a decent meantone tuning:
>
> C - 0
> D - 191.62
> E - 383.24
> F - 504.19
> G - 695.81
> A - 887.43
> B - 1079.05
> C' - 1200
>
> And frequencies, starting at C (261.63 Hz)
>
> C - 261.63 Hz
> D - 292.25 Hz
> E - 326.45 Hz
> F - 350.07 Hz
> G - 391.05 Hz
> A - 436.82 Hz
> B - 487.94 Hz
> C' - 523.25 Hz

I agree 100% with Ryan; it's obvious that meantone tempering is what you want. With just intonation it would be mathematically impossible to get most of those consonances at the same time.

You shouldn't worry at all that it's temperament rather than just intonation, because meantone is an accurate temperament and it's going to sound more or less pure. In fact, depending on the specific design of the double flute, a phenomenon known as injection locking or injection pulling may occur that causes the two pitches to adjust to each other slightly to make the current interval more pure.

So yeah, meantone is the answer. I personally would have given 1/4-comma meantone but the 2/7-comma meantone given above is nearly indistinguishable; they're both good meantones.

Keenan

On Wed, May 23, 2012 at 6:16 PM, Keenan Pepper <keenanpepper@...>
wrote:
>
> You shouldn't worry at all that it's temperament rather than just
> intonation, because meantone is an accurate temperament and it's going to
> sound more or less pure. In fact, depending on the specific design of the
> double flute, a phenomenon known as injection locking or injection pulling
> may occur that causes the two pitches to adjust to each other slightly to
> make the current interval more pure.
>
> So yeah, meantone is the answer. I personally would have given 1/4-comma
> meantone but the 2/7-comma meantone given above is nearly indistinguishable;
> they're both good meantones.

Yeah, I agree with Keenan here. Also, if you want something a bit more
xenharmonic, you could also try superpyth, which tempers out 64/63
instead of 81/80. Then minor sevenths will be close to 7/4, so
root-fifth-minor 7 triads will be close to 4:6:7. It serves as an
alternate way to intone the usual diatonic scale.

-Mike

Chances are if the holes are equally spaced apart, you have two subharmonic series.
--

/^_,',',',_ //^/Kraig Grady_^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere:
North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

a momentary antenna as i turn to water
this evaporates - an island once again