Re: [tuning] Digest Number 1747

> From: "paulerlich" <paul@stretch-music.com>
> Subject: Re: Digest Number 1744
>
> --- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>
> > I have certainly been exploring MOS and MOS offspring so I'm
> > interested in this topic. Recently I have been looking at
> > mappings from one ed2 to another. For instance, this weekend
> > I played with
> >
> > 31 : 4414414441
> > 41 : 5525525552
>
> Is it clear to you what I mean if I say the generator of this system
> is the neutral third?

I believe so. If I take the neutral third in these two systems and
repeat it over and over, I can arrive at these scales as one of the
stopping points.

> There has been quite a bit of investigation on
> chain-of-neutral third tunings . . . might I ask Gene and Graham to
> chime in with some comments, cloaked in as little obscure theoretical
> terminology as possible, so that Robert will view them as "musical"?
>

Hi Paul, sorry to have used the "m" word. Talking about music is like
dancing about architecture so, yes, there will be disconnects
between how different people choose to express understanding of
certain phenomena.

As I alluded to, the thing I was more interested in was the meantone
vs pythagorean mapping that was going on. For instance...

44 1441 44 41
55 2552 55 52

show the minor seventh chords, in one case, 5-odd-limit, in the
other 3-prime-limit. Perhaps this is a bit pedestrian, but although
some the neutral thirds and a variety of crumpled near-fifths are
available in both, I was just looking at a new scale with major and
minor modes. In fact, its probably even easier to see what I
was thinking of by writing it out in note names

C Cx Eb Dx F Fx G Gx Bb B#
C Fbbb Eb Gbbb F Bbbbb G Cbbb Bb Ebbbb

(basing note names on chain-of-fifth diatonics 5535553 and
7737773).

Here the traids, pentatonics, stacks of fourths, etc in the
two systems are clear, and the warped connections to the two
spirals of fifths is also clear (showing that the similar
resources are doing different things on the 'big crystal').

One of the reasons I haven't gotten too 'into' the 72
discussion is because bicycle chains require a different way
of thinking than this. Some would say its easier and liberating,
I'll get there when I get there.

Bob Valentine

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

> As I alluded to, the thing I was more interested in was the meantone
> vs pythagorean mapping that was going on.

Yes -- since both systems have a fifth equal to two neutral thirds,
you're going to get quite a lot of this. If you extended the system
to 14 notes per octave, you'd have exactly two diatonic scales in it.
It's interesting to see where the 7-limit and other intervals pop
up . . . though neither of these scales excels at producing them.

> One of the reasons I haven't gotten too 'into' the 72
> discussion is because bicycle chains require a different way
> of thinking than this.

Not necessarily. For example, the MIRACLE tuning is a chain of fifths
too, except that now the fifth is equal to _six_ generators, not just
two. I don't see any conceptual difference here: the period of
repetition is still an octave in this scale; you could tune it in
some tuning where the chain of fifths doesn't close on itself if you
so desired; etc.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> Not necessarily. For example, the MIRACLE tuning is a chain of
fifths
> too, except that now the fifth is equal to _six_ generators, not
just
> two.

Hmm. That could easily be misunderstood. What this means is that
MIRACLE tuning is _six_ chains of fifths, NOT _a_ chain of fifths.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > Not necessarily. For example, the MIRACLE tuning is a chain of
> fifths
> > too, except that now the fifth is equal to _six_ generators, not
> just
> > two.
>
> Hmm. That could easily be misunderstood. What this means is that
> MIRACLE tuning is _six_ chains of fifths, NOT _a_ chain of fifths.

I guess I meant "contains a chain of fifths" rather than "is a chain
of fifths". Well whatever, it was in the context of whatever Robert
V. wrote, which I have forgotten by now.