Using Scala, and constant structures (was: about ozan system)

Hi all,

On Tue, 7 Mar 2006, Ozan Yarman wrote:
>
> Splendid suggestion! Although the jump from B to Gb is a little wide for
my
> tastes, one can overlook that particular glitch in this alternative
version
> you suggest:
>
> Run SCALA
>
> File>New>Equal Temperament>33 equal divisions of 4/3
> command prompt>copy (scale number) 0 to (scale number) 1
> File>New>Equal Temperament>13 equal divisions of 9/8
> Modify>Move>raise all pitches after degree 0 by 4/3
> Combine>Merge>With (scale number) 1
> command prompt>copy (scale number) 0 to (scale number) 1
> File>New>Equal Temperament>33 equal divisions of 4/3
> Modify>Move>raise all pitches after degree 0 by 3/2
> Combine>Merge>With (scale number) 1
> command prompt>set nota e79
>
> Voila!

[snip]

One requires 636-tET to approximate all intervals with an error of less than
1 cents.

Here is the cycle:
[snip]

> > Depending on what kinds of F# and Gb you wanted,
> > (assuming you are using this for maqam music, you
> > probably do want these), there are several other
> > ways to fill the 9/8 gap between F and G. The most
> > obvious of these still gives only two step sizes, and
> > divides the 9/8 gap into 13 equal steps each of
> > (701.954 - 498.045)/13 = 203.909/13 = 15.685 cents.
> >
> > a=15.092
> > b=15.685
> > na=66
> > nb=13
> >
> > The step sizes a and b are much closer to each other
> > than in Ozan's tuning.
> >
> > This is symmetrical about 600 cents, which is NOT a
> > scale degree, but falls exactly between degrees 39
> > and 40 of the scale, which are at 592.155 & 607.840
> > cents.
> >
> > The important questions here are: what notes between
> > F and G do you want to approximate well, and how
> > closely?

Oz, I'm glad you're pleased with it. :-)

The jump from Cb to Gb is 699.4 cents, not a bad fifth.
When would you want to jump from B to Gb? 8-0
Speaking for myself, I can't see it as a natural melodic
movement.

I'm also pleased that you supplied the Scala "recipe"
for creating the tuning, as there must be others who,
like me, find Scala a bit daunting to use. For myself,
I have no trouble with using a command-line interface,
or even with scripting - I was the very devil with both
DOS batch files and unix scripts, even writing useful
production systems in the latter. The only difficulties
I really find with Scala are -

1) Knowing which command to use to get the sounds or
info I need; and

2) Understanding what all the info Scala produces
really _means_.

On the latter point, I recently hinted I'd like to
understand the idea of "constant structures" in
tuning better. Can anyone explain this idea simply,
please?

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.375 / Virus Database: 268.2.0/275 - Release Date: 6/3/06

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@...> wrote:

> One requires 636-tET to approximate all intervals with an error of
less than
> 1 cents.

There is no equal temperament of any size that will approximate all
intervals with an error less than a cent in a consistent way. However,
612-et consistently approximates 5-limit consonances with an error
less than 0.045 cents, 7-limit consonances with an error less than
0.204 cents, and 11-limit consonaces with an error less than 0.349 cents.

Yahya,

SNIP

>
>
> Oz, I'm glad you're pleased with it. :-)
>
> The jump from Cb to Gb is 699.4 cents, not a bad fifth.
> When would you want to jump from B to Gb? 8-0
> Speaking for myself, I can't see it as a natural melodic
> movement.
>

But that Gb is also F# next to the lower F#. They can be made enharmonically
equivalent with each other should the need arise.

SNIP

Oz.

On Wed, 08 Mar 2006, Gene Ward Smith wrote:
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@...> wrote:
>
> > One requires 636-tET to approximate all intervals with an error of
> > less than 1 cents.

No, I didn't! That was Oz. Give me some credit ... ;-)

> There is no equal temperament of any size that will approximate all
> intervals with an error less than a cent in a consistent way. However,
> 612-et consistently approximates 5-limit consonances with an error
> less than 0.045 cents, 7-limit consonances with an error less than
> 0.204 cents, and 11-limit consonaces with an error less than 0.349 cents.

And you could go on multiplying instances of EDOs that
approximate all intervals up to any specific prime limit
within a specific margin of error. That being so, it strikes
me that the most convenient EDOs to use would be those
that require only the simplest calculations, eg subdivisions
of today's ubiquitous 12-EDO, or others like the 200- and
400-EDO I recently suggested that make every step a small
integer number of cents. Of those, naturally, some are
going to give better approximations than others.

Here is an equal temperament that approximates all intervals
of any size with an error less than a cent: 1200-EDO.
In a consistent way? Depends what you mean by consistent
here.

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.375 / Virus Database: 268.2.1/277 - Release Date: 8/3/06

612 looks quite good, and imagine would lead to some great subsets being pulled out of it .
also if one wanted to explore11 limit material one could start here until one decides on a specific structure, and if you can't decide, you are still in a good place with lots of optioned

Message: 5 Date: Wed, 08 Mar 2006 06:27:23 -0000
From: "Gene Ward Smith" There is no equal temperament of any size that will approximate all
intervals with an error less than a cent in a consistent way. However,
612-et consistently approximates 5-limit consonances with an error
less than 0.045 cents, 7-limit consonances with an error less than
0.204 cents, and 11-limit consonances with an error less than 0.349 cents.

>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles