Yahoo Tuning Groups Ultimate Backup tuning-math Beep isn't useless....

http://www.io.com/~hmiller/midi/egress/egress-beep.mid

It doesn't sound as bad as I was imagining it would. It really warps the
melody and harmony, but it could have its uses. Compare with the
superpelog version, which I originally thought was beep before I figured
out the mapping.

http://www.io.com/~hmiller/midi/egress/egress-superpelog.mid

I still think the best use of extreme temperaments like beep and father
is for their exotic melodic and harmonic properties, and not as
approximations of JI. But the beep version doesn't seem as extreme as
the father version:

http://www.io.com/~hmiller/midi/egress/egress-father.mid

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> http://www.io.com/~hmiller/midi/egress/egress-beep.mid
>
> It doesn't sound as bad as I was imagining it would. It really warps the
> melody and harmony, but it could have its uses. Compare with the
> superpelog version, which I originally thought was beep before I figured
> out the mapping.
>
> http://www.io.com/~hmiller/midi/egress/egress-superpelog.mid
>
> I still think the best use of extreme temperaments like beep and father
> is for their exotic melodic and harmonic properties, and not as
> approximations of JI. But the beep version doesn't seem as extreme as
> the father version:
>
> http://www.io.com/~hmiller/midi/egress/egress-father.mid

What qualifies this tune as a good test of a temperament's
approximation of 7-limit JI? It seems the tune was not composed for
7-limit JI and you are even unsure of how it should be mapped to
7-limit JI.

The Canon was ideal for 5-limit as there was no such doubt.

Can't we find some "classic" 7-limit-JI piece that demonstrates a lot
of different 7-limit consonances and cadences, and warp that?

🔗Herman Miller <hmiller@IO.COM>

Dave Keenan wrote:

> What qualifies this tune as a good test of a temperament's
> approximation of 7-limit JI? It seems the tune was not composed for
> 7-limit JI and you are even unsure of how it should be mapped to
> 7-limit JI.

I don't think of it so much as a test of how well a temperament approximates JI (you can look at the numbers for that). My original thought was that the ambiguity inherent in 14-ET would allow me to choose a different mapping for each temperament that would suit the individual temperament. Then I found a mapping that seemed to work well for a lot of different temperaments, so I decided to use that as a basis for comparison. But I still think I'm going to want to use different JI mappings to illustrate the characteristic features of the different temperaments. A scale that works well in meantone won't be much good for kleismic or magic. If I had an original piece that was unambiguous, I wouldn't have that flexibility. But I need to translate it to some version of 7-limit JI to begin with so that I can apply the temperament.

In any case, the point is that a tuning that seemed useless, after a bit of experimentation, turned out to have some attractive features after all.

> The Canon was ideal for 5-limit as there was no such doubt.
> > Can't we find some "classic" 7-limit-JI piece that demonstrates a lot
> of different 7-limit consonances and cadences, and warp that?

It's hard enough to find "classic" 5-limit JI! It's not hard to find something that could imply 7-limit harmony, but finding something that doesn't at the same time exploit the meantone comma is going to be tricky. Possibly Beethoven's Moonlight Sonata (minus the second movement) might do the trick. Actually, I've thought about doing a Warped Moonlight page, but never got around to it.

I'm sure if I could find some piece that was written with 7-limit JI in mind (assuming that one could be found that's in the public domain), it'd be better suited for tuning comparison than something awkwardly written in 14-ET by a programmer who likes music (not that there's a long tradition of well-written composition in 14-ET to compare with). What I'm more interested in right now is figuring out which temperaments seem the most useful for new music, and the Warped Egress page is a bit of fallout from the sort of experimentation that I'm doing with these tunings to get a general feel for what they sound like (in the same way that Porcupines in the Moonlight was a spinoff of my Zireen kleismic scale experimentation).

But then, maybe I'd be better off putting together a page on Zireen music theory, with fragments of actual Zireen music to illustrate the different temperaments......

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Paul Erlich <perlich@aya.yale.edu>

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
> --- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...>
wrote:
> > http://www.io.com/~hmiller/midi/egress/egress-beep.mid
> >
> > It doesn't sound as bad as I was imagining it would. It really
warps the
> > melody and harmony, but it could have its uses. Compare with the
> > superpelog version, which I originally thought was beep before I
figured
> > out the mapping.
> >
> > http://www.io.com/~hmiller/midi/egress/egress-superpelog.mid
> >
> > I still think the best use of extreme temperaments like beep and
father
> > is for their exotic melodic and harmonic properties, and not as
> > approximations of JI. But the beep version doesn't seem as
extreme as
> > the father version:
> >
> > http://www.io.com/~hmiller/midi/egress/egress-father.mid
>
> What qualifies this tune as a good test of a temperament's
> approximation of 7-limit JI? It seems the tune was not composed for
> 7-limit JI and you are even unsure of how it should be mapped to
> 7-limit JI.
>
> The Canon was ideal for 5-limit as there was no such doubt.
>
> Can't we find some "classic" 7-limit-JI piece that demonstrates a
lot
> of different 7-limit consonances and cadences, and warp that?

Cadences are too tied to particular scales and temperaments.