Re: 14 EDO

>
I wonder if the 9 note scale
0 2 3 5 6 8 9 11 13 (0 has any folk counterparts. This scale is like a diatonic or pentatonic scale in that it has 14 unique transpositions or 'keys'

Mark

> ____________________________________________________
>
> Message: 6
> Date: Tue, 10 Jan 2006 08:04:11 +0330
> From: "Mohajeri Shahin" <shahinm@kayson-ir.com>
> Subject: music in 14-edo
>
> Hi
>
> Link of a small mp3- file in 14-edo with some taste of iranian > chahargah
> mode:
>

--- In tuning@yahoogroups.com, Mark Gould <mark@e...> wrote:
>
> >
> I wonder if the 9 note scale
> 0 2 3 5 6 8 9 11 13 (0 has any folk counterparts. This scale is like a
> diatonic or pentatonic scale in that it has 14 unique transpositions or
> 'keys'

This can be interpreted as the 14-et version of a temperament called
"beep" (or bug.) Beep proceeds on the optimistic theory that 8/7, 7/6
and 6/5 are all more or less the same thing and can be equated.
Whether something so far from just is really tempering is an
interesting philosophical question, but if you allow such high degrees
of error, beep stands out as an important temperament. It's
theoretically by far the most interesting linear temperament for 14-et
in the 7-limit, again if you are willing to accept that 14 equal is
tempering. A curious feature of beep is that the commas of beep
(21/20, 27/25, 36/35) are exactly the same as the generators for
ennalimmal. Ennealimmal+beep = the seven limit, which has some
interesting applications.

Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, Mark Gould <mark@e...> wrote:
> >>I wonder if the 9 note scale
>>0 2 3 5 6 8 9 11 13 (0 has any folk counterparts. This scale is like a >>diatonic or pentatonic scale in that it has 14 unique transpositions or >>'keys'
> > > This can be interpreted as the 14-et version of a temperament called
> "beep" (or bug.)

I like to make the distinction between "beep" (the 7-limit temperament) and "bug" (the 5-limit temperament), which have distinct TOP tunings (historically, "bug" seems to have been the earlier name, and was applied to the 27/25 temperament.)

> Beep proceeds on the optimistic theory that 8/7, 7/6
> and 6/5 are all more or less the same thing and can be equated.
> Whether something so far from just is really tempering is an
> interesting philosophical question, but if you allow such high degrees
> of error, beep stands out as an important temperament. It's
> theoretically by far the most interesting linear temperament for 14-et
> in the 7-limit, again if you are willing to accept that 14 equal is
> tempering. A curious feature of beep is that the commas of beep
> (21/20, 27/25, 36/35) are exactly the same as the generators for
> ennalimmal. Ennealimmal+beep = the seven limit, which has some
> interesting applications.

"Beep" seems to me as a pretty marginal 7-limit temperament; the tetrads sound like sixth chords. But this scale can also be interpreted as a 9-note MOS of superpelog temperament (which has a generator of a similar size to "beep" / "bug" and von Hornbostel's "type b" pelog tuning, which is pelog_pb.scl in the Scala archive).

generators 5.....1..6.....2..7.....3..8.....4.....0..5
degree of 14-ET 0..1..2..3..4..5..6..7..8..9.10.11.12.13.14

Back when I was playing around with what I thought was "beep" temperament, I realized that I was actually using a different mapping, which I named "superpelog" after the Indonesian pelog scale which it resembles.

http://www.io.com/~hmiller/music/superpelog.html

The mapping of superpelog temperament is like this:

<1, 2, 1, 3], <0, -2, 6, -1]

Beep has a similar mapping, but the prime 5 is mapped differently.

<1, 2, 3, 3], <0, -2, -3, -1]

The CD "Music of the Gambuh Theater" uses a number of scales that are subsets of a 9-note tuning; while it's not very clear exactly what tuning is used, it sounds very similar to this 9-note scale.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> The mapping of superpelog temperament is like this:
>
> <1, 2, 1, 3], <0, -2, 6, -1]

You could also try that in 5/23 or 8/37. It also makes sense to ignore
5, calling it a {2,3,7} system tempering out 49/48, or else map 5
differently. Then 19, 24, 29, or 34 are possibilities. 29 or 34-et
using the <0 -2 -13 -1| map would be reasonable.

Just trying other EDOs that contain the 9-note, here's another three:

0 3 4 7 8 11 12 15 18 (0 19EDO
0 3 5 8 10 13 15 18 21 (0 23EDO
0 5 8 13 16 21 24 29 34 (0 37EDO

just by following patterns here...

Mark

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
>
> > The mapping of superpelog temperament is like this:
> >
> > <1, 2, 1, 3], <0, -2, 6, -1]
>
> You could also try that in 5/23 or 8/37. It also makes sense to
ignore
> 5, calling it a {2,3,7} system tempering out 49/48, or else map 5
> differently. Then 19, 24, 29, or 34 are possibilities. 29 or 34-et
> using the <0 -2 -13 -1| map would be reasonable.
>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, Mark Gould <mark@e...> wrote:
> >
> > >
> > I wonder if the 9 note scale
> > 0 2 3 5 6 8 9 11 13 (0 has any folk counterparts. This scale is
like a
> > diatonic or pentatonic scale in that it has 14 unique
transpositions or
> > 'keys'
>
> This can be interpreted as the 14-et version of a temperament called
> "beep" (or bug.) Beep proceeds on the optimistic theory that 8/7,
7/6
> and 6/5 are all more or less the same thing and can be equated.
> Whether something so far from just is really tempering is an
> interesting philosophical question,

Make the partials of the sounds you're using inharmonic --
particularly, map them to their Bug approximations -- and it gets
somewhat less philosophical. The beating can be eliminated, but do
the timbres cohere as single pitches?