maqam middle seconds?

This is like choosing 53-EDO and saying that the 6 and 7 Holdrian comma middle seconds are just. Whereas, they are approximations of their JI counterparts 12:11 and 13:12. Cannot you find the "correct" middle seconds in Lucytuning by NOT referring to a chain of fifths, but instead using a formula involving PI?

Oz.
----- Original Message -----
From: Charles Lucy
To: tuning@yahoogroups.com
Sent: 04 Mart 2008 Salı 2:12
Subject: Re: [tuning] Re: "tuning" vs. "temperament" - maqam middle seconds?

Hi Oz;

Yes, I suppose that you could map them using some other pattern (e.g. steps of thirds), yet the resulting intervals will be the same number of cents, just expressed in a slightly different order.

That page shows the interval values as cents from A in terms of number of steps of fourths or fifths.
It shows 21 steps in each direction from A.

Third column from the left for steps of fifths and third column from the right for steps of fourths in ascending number of steps going down the page

http://www.lucytune.com/new_to_lt/pitch_02.html

In your range 130 to 165 cents, the only interval that I find is at:

136.903 which is a double sharp (xI) one. (2L-2s) after 14 steps of fifths.

Since the single sharp i.e. #1 occurs at seven steps (68.45 ¢) it is doubled to get you into the range that you require.

If it doesn't occur there (to sufficient precision) it will require a greater number of steps, which requires me to consult one of my FileMaker or other databases to calculate it.

But you're going to get a result with more than 41 steps.

Hi Oz;

There is not a correct or incorrect solution Oz, it always becomes a
level of precision, and the user has to decide the level of
granularity which is acceptable.

It is inevitable that the interval be found "using a formula involving
PI", yet the formula will contain LucyTuned Large and small intervals,
because that is the method by which the system is mapped. L=approx 191
cents s=approx 122.5 cents

All I am saying is that the intervals that you require between 130 and
165 cents are findable yet do not appear within the first 53 steps in
either direction except as listed below.

The intervals which occur in that range for the fist 53 steps in
either direction are:

136.9 cents after 14 steps of fifths = Ax from A
151.3 cents after 33 steps of fifths = G5# from A
162.3 cents after 36 steps of fourths = A5b's from A
165.6 cents after 52 steps of fifths = F8#'s from A

I have to do some more scripting to get you a more accurate result, as
all my original programs written in Amiga Basic are now stuck on dead
hard drives in my attics either here in London or Hawaii, and it's
about time that I updated to a Mac compatible version.

Which you choose will depend upon the level of precision that you
require.

I shall use your 12:11 (150.6 cents) and 13:12 (138.6 cents) values,
as well as the range 130 to 165 cents and provide you with a more
precise list in the next few days.

I or someone more familiar with the these applications may be able to
do it using Scala, Microtuner, or LMSO X, otherwise it's a case of my
needing to construct a new solution that will run using one of my Mac
Leopard applications e.g. FileMaker.

So patience please Oz.

On 5 Mar 2008, at 22:12, Ozan Yarman wrote:

>
> This is like choosing 53-EDO and saying that the 6 and 7 Holdrian
> comma middle seconds are just. Whereas, they are approximations of
> their JI counterparts 12:11 and 13:12. Cannot you find the "correct"
> middle seconds in Lucytuning by NOT referring to a chain of fifths,
> but instead using a formula involving PI?
>
> Oz.
> ----- Original Message -----
> From: Charles Lucy
> To: tuning@yahoogroups.com
> Sent: 04 Mart 2008 Salı 2:12
> Subject: Re: [tuning] Re: "tuning" vs. "temperament" - maqam middle
> seconds?
>
> Hi Oz;
>
> Yes, I suppose that you could map them using some other pattern
> (e.g. steps of thirds), yet the resulting intervals will be the same
> number of cents, just expressed in a slightly different order.
>
> That page shows the interval values as cents from A in terms of
> number of steps of fourths or fifths.
> It shows 21 steps in each direction from A.
>
> Third column from the left for steps of fifths and third column from
> the right for steps of fourths in ascending number of steps going
> down the page
>
> http://www.lucytune.com/new_to_lt/pitch_02.html
>
> In your range 130 to 165 cents, the only interval that I find is at:
>
> 136.903 which is a double sharp (xI) one. (2L-2s) after 14 steps of
> fifths.
>
> Since the single sharp i.e. #1 occurs at seven steps (68.45 ¢) it is
> doubled to get you into the range that you require.
>
>
>
> If it doesn't occur there (to sufficient precision) it will require
> a greater number of steps, which requires me to consult one of my
> FileMaker or other databases to calculate it.
>
> But you're going to get a result with more than 41 steps.
>
>
>

Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Hi charles

and related to perception , as in 96-EDO ,I love 137.5 cent which is
a good approximation for 13:12.

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Hi Oz;
>
> There is not a correct or incorrect solution Oz, it always becomes
a
> level of precision, and the user has to decide the level of
> granularity which is acceptable.
>
> It is inevitable that the interval be found "using a formula
involving
> PI", yet the formula will contain LucyTuned Large and small
intervals,
> because that is the method by which the system is mapped. L=approx
191
> cents s=approx 122.5 cents
>
> All I am saying is that the intervals that you require between 130
and
> 165 cents are findable yet do not appear within the first 53 steps
in
> either direction except as listed below.
>
> The intervals which occur in that range for the fist 53 steps in
> either direction are:
>
> 136.9 cents after 14 steps of fifths = Ax from A
> 151.3 cents after 33 steps of fifths = G5# from A
> 162.3 cents after 36 steps of fourths = A5b's from A
> 165.6 cents after 52 steps of fifths = F8#'s from A
>
> I have to do some more scripting to get you a more accurate result,
as
> all my original programs written in Amiga Basic are now stuck on
dead
> hard drives in my attics either here in London or Hawaii, and it's
> about time that I updated to a Mac compatible version.
>
>
> Which you choose will depend upon the level of precision that you
> require.
>
> I shall use your 12:11 (150.6 cents) and 13:12 (138.6 cents)
values,
> as well as the range 130 to 165 cents and provide you with a more
> precise list in the next few days.
>
> I or someone more familiar with the these applications may be able
to
> do it using Scala, Microtuner, or LMSO X, otherwise it's a case of
my
> needing to construct a new solution that will run using one of my
Mac
> Leopard applications e.g. FileMaker.
>
> So patience please Oz.
>
>
>
>
>
>
> On 5 Mar 2008, at 22:12, Ozan Yarman wrote:
>
> >
> > This is like choosing 53-EDO and saying that the 6 and 7
Holdrian
> > comma middle seconds are just. Whereas, they are approximations
of
> > their JI counterparts 12:11 and 13:12. Cannot you find
the "correct"
> > middle seconds in Lucytuning by NOT referring to a chain of
fifths,
> > but instead using a formula involving PI?
> >
> > Oz.
> > ----- Original Message -----
> > From: Charles Lucy
> > To: tuning@yahoogroups.com
> > Sent: 04 Mart 2008 Salı 2:12
> > Subject: Re: [tuning] Re: "tuning" vs. "temperament" - maqam
middle
> > seconds?
> >
> > Hi Oz;
> >
> > Yes, I suppose that you could map them using some other pattern
> > (e.g. steps of thirds), yet the resulting intervals will be the
same
> > number of cents, just expressed in a slightly different order.
> >
> > That page shows the interval values as cents from A in terms of
> > number of steps of fourths or fifths.
> > It shows 21 steps in each direction from A.
> >
> > Third column from the left for steps of fifths and third column
from
> > the right for steps of fourths in ascending number of steps
going
> > down the page
> >
> > http://www.lucytune.com/new_to_lt/pitch_02.html
> >
> > In your range 130 to 165 cents, the only interval that I find is
at:
> >
> > 136.903 which is a double sharp (xI) one. (2L-2s) after 14 steps
of
> > fifths.
> >
> > Since the single sharp i.e. #1 occurs at seven steps (68.45 ¢)
it is
> > doubled to get you into the range that you require.
> >
> >
> >
> > If it doesn't occur there (to sufficient precision) it will
require
> > a greater number of steps, which requires me to consult one of
my
> > FileMaker or other databases to calculate it.
> >
> > But you're going to get a result with more than 41 steps.
> >
> >
> >
>
> Charles Lucy
> lucy@...
>
> - Promoting global harmony through LucyTuning -
>
> for information on LucyTuning go to:
> http://www.lucytune.com
>
> For LucyTuned Lullabies go to:
> http://www.lullabies.co.uk
>