Re: Intervals around 467 cents -- a certain famous post

Hello, there, everyone, and as long as a certain set of scales is
still a rather amply discussed topic on this List, I'd like to honor a
very important contributor by recalling a famous post which may be of
special relevant to one of the resources of this kind of tuning:

/tuning/topicId_11922.html#11922

An interval of around 467 cents (e.g. 28/72 octave) is quite close to
21:16, and I wonder how the message I've cited about sonorities where
one interval contributes a greater amount of "harmonic entropy" than
all the others combined might apply to certain recent developments.

To be specific, as our famous contributor suggested, how about
something like 0-467-700-967 cents? Maybe this has already been
discussed, but at least it's an opportunity to honor a great post --
and maybe season things with a bit of "ice cold raw green pepper."

Most respectfully,

Margo Schulter
mschulter@value.net

> ----- Original Message -----
> From: mschulter <MSCHULTER@VALUE.NET>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, June 07, 2001 10:58 PM
> Subject: [tuning] Re: Intervals around 467 cents -- a certain famous post
>

>
> /tuning/topicId_11922.html#11922
>
> at least it's an opportunity to honor a
> great post -- and maybe season things with a bit
> of "ice cold raw green pepper."

"Ice cold raw green pepper"... that lad sure is clever!...

-monz
http://www.monz.org
"All roads lead to n^0"

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--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:
> Hello, there, everyone, and as long as a certain set of scales is
> still a rather amply discussed topic on this List, I'd like to honor
a
> very important contributor by recalling a famous post which may be
of
> special relevant to one of the resources of this kind of tuning:
>
> /tuning/topicId_11922.html#11922
>
> An interval of around 467 cents (e.g. 28/72 octave) is quite close
to
> 21:16, and I wonder how the message I've cited about sonorities
where
> one interval contributes a greater amount of "harmonic entropy" than
> all the others combined might apply to certain recent developments.

Thanks for that Margo!

> To be specific, as our famous contributor suggested, how about
> something like 0-467-700-967 cents? Maybe this has already been
> discussed, but at least it's an opportunity to honor a great post --
> and maybe season things with a bit of "ice cold raw green pepper."

Not already discussed (except the one I mention at the end of this
post). I think we've stayed pretty much with the soggy chords so far.
Thanks for reminding us about the crunchy universe.

That particular crunchy chord, which might be called a
subminor-seventh suspended subfourth, sm7sus-s4, (I'm using
"suspended" here to imply the absence of the third, is that acceptable
usage?), is very compact on the Miracle chain. It only spans 8
generators, so even in Miracle-10 there are two of them, and 13 of
them in Blackjack.

1/1:9/8:7/6:3/2:7/4, if revoiced as 1/1:7/6:3/2:7/4:9/4, might be
called a subminor seventh ninth, sm79. It spans 20 Miracle generators,
so there is only one of them in Blackjack.

I suspect that Keenan Pepper's "ice cold raw green pepper" chord is
already with us as the major seventh chord 1/1:5/4:3/2:15/8 (or
4:5:6:15/2), which I think is quite crunchy, even in 12-tET. These
span 13 Miracle generators so there are 8 in Blackjack.

We were crying out for a name for that concept but didn't know it.
"Crunchy" is just great.

Regards,
-- Dave Keenan

Hello, there, Dave Keenan, and thank you for your response on the
small fourth around 467 cents or 21:16, which raises an interesting
question of nomenclature:

> That particular crunchy chord, which might be called a
> subminor-seventh suspended subfourth, sm7sus-s4, (I'm using
> "suspended" here to imply the absence of the third, is that
> acceptable subminor-seventh suspended subfourth, sm7sus-s4, (I'm
> using "suspended" here to imply the absence of the third, is that
> acceptable usage?), is very compact on the Miracle chain. It only
> spans 8 generators, so even in Miracle-10 there are two of them, and
> 13 of them in Blackjack.

Here I would say that use of "suspended" is fine either in a setting
where that subfourth would often resolve down to a major third (a
variant on the 4-3 suspension of Renaissance-Romantic practice); or in
a kind of "popular" notation where "sus4" has come to mean "a fourth
without a third," whether or not it actually resolves as a suspension.

The main implication of the "suspended" terminology for me is that of
a style where thirds and sixths are stable intervals, and the fourth
is appearing "in place of" a third, with at least some implication
that it _might_ resolve to this third. Here's an example of such a
resolution to a 4:5:6:7 tetrad:

Fv4
D4
Cv4 B4
G3

Here the voice at the 21:16 subfourth (~470.78 cents) resolves to a
5:4 (~386.31 cents), moving downward by a semitone of 21:20 (~84.47
cents), a step equal to a 16:15 less the 64:63 comma.

Since a Miracle-type tuning is very likely to be used mainly for
styles of a "7-limit or higher" variety, with 5:4 as an element in
many stable sonorities, the "suspended" terminology would seem to me
as fitting as it is in popular guitar chord nomenclatures, for
example.

In styles such as neo-Gothic where thirds and sixths are unstable, or
fifths and fourths are regarded as the primary concords, we'd want to
use a different kind of terminology. As you point out in your
discussion of interval names,

http://www.uq.net.au/~zzdkeena/Music/IntervalNaming.htm.

it's more generally at best difficult to come up with a single set of
conventions to fit all tunings or styles.

However, with the kind of setting a Miracle-style tuning is likely to
imply, "sm7sus-s4" has the advantage of familiarity for people used to
"sus4," etc.

Kennan Pepper, by the way, himself refers to 1:1-21:16-3:2-7:4 or
0-471-702-969 cents as a "3-7 square chord," maybe suggesting this
kind of geometry:

4:3
Cv4 ----------- Fv4
| |
21:16 | | 7:6
| |
G3 ----------- D4
3:2

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:

> Kennan Pepper, by the way, himself refers to 1:1-21:16-3:2-7:4 or
> 0-471-702-969 cents as a "3-7 square chord," maybe suggesting this
> kind of geometry:
>
> 4:3
> Cv4 ----------- Fv4
> | |
> 21:16 | | 7:6
> | |
> G3 ----------- D4
> 3:2
>
I would guess that Keenan P. was instead suggesting a geometry in which you'd switch the
positions of Cv4 and Fv4, so that you'd have 7:4 intervals on both sides of the square -- which
shows how the chord would appear on a square lattice with a 3-axis horizontally and a 7-axis
vertically.