Megastaff JI notation

Before I leave TL for a while I would like to give some clues about JI notation on the megastaff.

1) There are various limits available, and markings increase in complexity with higher limits:

5-limit
11-limit
23-limit
47-limit

Any higher prime limit increasing as shown in the form (3 x 2^n) can be shown although only the limits above are directly advocated as practical

2) Every note, and the key (1/1), is expressible in what I call 'combinatorial intonation':

x = a:b / c:d

where x is a tone, and a:b and c:d are integer ratios where a > b and c > d and 1 < a:b < 2 and 1 < c:d < 2.

3) Although higher limits are more difficult to read, the JI markings are all preattentively perceptible and can also act directly as tableture.

I hope this helps give at least a general idea, for now. Until later...

Cheers,
Aaron Hunt
H-Pi Instruments

--- In tuning@yahoogroups.com, Aaron Andrew Hunt <aahunt@...> wrote:
>
> Before I leave TL for a while I would like to give some clues about
> JI notation on the megastaff.
>
> 1) There are various limits available, and markings increase in
> complexity with higher limits:
>
> 5-limit
> 11-limit
> 23-limit
> 47-limit
>
> Any higher prime limit increasing as shown in the form (3 x 2^n) can
> be shown although only the limits above are directly advocated as
> practical
>
> 2) Every note, and the key (1/1), is expressible in what I call
> 'combinatorial intonation':
>
> x = a:b / c:d
>
> where x is a tone, and a:b and c:d are integer ratios where a > b and
> c > d and 1 < a:b < 2 and 1 < c:d < 2.
>
> 3) Although higher limits are more difficult to read, the JI markings
> are all preattentively perceptible and can also act directly as
> tableture.
>
> I hope this helps give at least a general idea, for now. Until later...
>
> Cheers,
> Aaron Hunt
> H-Pi Instruments
>

These naming concepts make sense, but how this relates to notation on
the score isn't clear. If it is just implied that any JND is rounded
to the simplest JI within its JND range, as specified by the 1/1 and
the prime limit, then that sounds good to me...

--- In tuning@yahoogroups.com, Aaron Andrew Hunt <aahunt@...> wrote:
> 1) There are various limits available, and markings increase in
> complexity with higher limits:
>
> 5-limit
> 11-limit
> 23-limit
> 47-limit

Interesting choice of limits. Were you smoking crack before
you came up with this?

> I hope this helps give at least a general idea, for now.

It doesn't...

-Carl

Carl Lumma wrote:
> --- In tuning@yahoogroups.com, Aaron Andrew Hunt <aahunt@...> wrote:
> >>1) There are various limits available, and markings increase in >>complexity with higher limits:
>>
>>5-limit
>>11-limit
>>23-limit
>>47-limit
> > Interesting choice of limits. Were you smoking crack before
> you came up with this?

I'm guessing these are the points where the system naturally becomes more complex.

Graham

Carl,

Interesting wise-Crack!

Mark

--- Carl Lumma <carl@lumma.org> wrote:

> --- In tuning@yahoogroups.com, Aaron Andrew Hunt
> <aahunt@...> wrote:
> > 1) There are various limits available, and
> markings increase in
> > complexity with higher limits:
> >
> > 5-limit
> > 11-limit
> > 23-limit
> > 47-limit
>
> Interesting choice of limits. Were you smoking
> crack before
> you came up with this?
>
> > I hope this helps give at least a general idea,
> for now.
>
> It doesn't...
>
> -Carl
>
>

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