re: Using Scala, and constant structures

Hi Shaahin,

On Thu, 9 Mar 2006, Mohajeri Shahin wrote:
> 1- I always do my calculations in excell spreadsheet with copy-paste the
> results to scala.for example for working on ozan system , instead of
> using commands of scala , I designed the system in excell very simple.

Thank you for your suggestion! This might reduce
the pain somewhat .. :-)

> 2- you propoesd 13 equal intervals in f-g. For na=132 and nb=26 we have
> interval of 600 cent as symmetry center.

True. But my intention was simply to offer Ozan an
idea for a small adjustment to his preferred tuning
system that might improve it for his use. That idea
preserved his 79 steps per octave, whereas this one
doubles them to 158 steps per octave. Given that he
feels the 79 steps already approaches the limits of
the abilities of his qanun-maker, I'm fairly sure that
doubling the number of steps is not really an option.
Besides, even if it could be made, could it be played?

> 3- consider fifth as 700 and fourth as 500 cent then f-g with nb=26 is a
> part of 156-edo and c-f and g-c' with na=66 are part of 158-edno or
> 159-edno based on 66-ed(500c)

> So we see that we have a hybrid structure of edo and nedo systems with 2
> different packages . if we had na=65 then we could have only 156-edo .

A 500-cent fourth and 160-odd steps seems a poor
compromise when we can have a 498-cent fourth
using half the steps ...

[snip]

[Ozan:]
> > One requires 636-tET to approximate all intervals with an error of less
> > than 1 cents.
> >
> > Here is the cycle:
[snip]

[Yahya, earlier:]
> > > 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?

[Yahya:]
> 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?

Are you able to help me with "constant structures"?

Regards,
Yahya
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