temperament and 12-tone scale based on ado or edl

Hi all

There are some defenitions about temperament meaning representing
systems near-ji or systems with intervals which are not ratios with
small integer.

Some question :

1- what is exact meaning of temperament , has every arrangement of
intervals a temperament?

2-In edl or ado , we can have 12-tone scales with 12 different fifth ,
what about this?

For example , look at an example in one of my previous mails which is a
simulation of 12-edo in a string with a length of 640 mm (with accuracy
of 1 mm) which belongs to 640-EDL :

0: 1/1 0.000 unison, perfect prime

1: 100.228 cents 100.228

2: 200.532 cents 200.532

3: 300.559 cents 300.559

4: 399.892 cents 399.892

5: 501.655 cents 501.655

6: 598.273 cents 598.273

7: 700.603 cents 700.603

8: 800.750 cents 800.750

9: 897.937 cents 897.937

10: 1000.906 cents 1000.906

11: 1100.144 cents 1100.144

12: 1200.000 cents 1200.000

|640-EDL ( ratioes are simplified) :

0: 1/1 0.000 unison, perfect prime

1: 160/151 100.228

2: 64/57 200.532

3: 320/269 300.559

4: 160/127 399.892

5: 640/479 501.655

6: 640/453 598.273

7: 640/427 700.603

8: 640/403 800.750

9: 640/381 897.937

10: 640/359 1000.906

11: 640/339 1100.144

12: 2/1 1200.000 octave

The maximum and minimum error are 2.062 and - 1.655 cent.this scale has
these fifths :

0: 0.000 cents

7: 700.603 cents

2: 699.929 cents

9: 697.405 cents

4: 701.955 cents

11: 700.252 cents

6: 698.129 cents

1: 701.955 cents

8: 700.522 cents

3: 699.808 cents

10: 700.347 cents

5: 700.750 cents

12: 698.345 cents

Shaahin Mohaajeri

Tombak Player & Researcher , Composer

My web site : http://240edo.tripod.com/index.html
<BLOCKED::http://240edo.tripod.com/index.html>

My tombak musics : www.rhythmweb.com/gdg

My articles in ''Harmonytalk'':

www.harmonytalk.com/archives/000296.html

www.harmonytalk.com/archives/000288.html

My article in DrumDojo:

www.drumdojo.com/world/persia/tonbak_acoustics.htm

--- In tuning@yahoogroups.com, "Mohajeri Shahin" <shahinm@...> wrote:

> 1- what is exact meaning of temperament , has every arrangement of
> intervals a temperament?

Temperament means that intervals are tempered, or adjusted, away from
the theoretical just value so they can play more than one role. For
instance, a whole tone might be employed both as a fifth above a fifth
reduced to an octave, or as a minor third below a fourth.

> 2-In edl or ado , we can have 12-tone scales with 12 different fifth ,
> what about this?

Different sizes for 7 scale steps out of 12 is usual, and may involve
tempering or may not.

> The maximum and minimum error are 2.062 and - 1.655 cent.this scale has
> these fifths :
>
> 0: 0.000 cents
>
> 7: 700.603 cents
>
> 2: 699.929 cents
>
> 9: 697.405 cents
>
> 4: 701.955 cents
>
> 11: 700.252 cents
>
> 6: 698.129 cents
>
> 1: 701.955 cents
>
> 8: 700.522 cents
>
> 3: 699.808 cents
>
> 10: 700.347 cents
>
> 5: 700.750 cents
>
> 12: 698.345 cents

This is a well-temperament, so it's a temperament.