Yahoo Tuning Groups Ultimate Backup tuning correction for 12-ADO : FW: [tuning] relation between N-ADO and N-EDO : a new revision for bridge between N-ADO and N-EDORE

Please consider 12-ADO instead of 24-ADO

**********

Hi all

First , forget all in previous mail !!!!

We belive in R N-EDO = 2^(M/N) for N-EDO system

Then M/N = log(R N-EDO) / log(2) = CN-EDO /1200 which C stand for cent.

New R' A-EDO of N-ADO system is

2*(M/N) = 2* (log(R N-EDO) / log(2)) = CN-EDO /600

That is :

R'A-EDO = CN-EDO /600

Example , 24-EDO and 12-ADO :

C (24-EDO) ********** (C 24-EDO)/600 **********
12-ADO

0 ********** 0 **********
**********

50 ********** 0.083333333 **********
**********

100 ********** 0.166666667 **********
**********

150 ********** 0.25 **********
**********

200 ********** 0.333333333 **********
**********

250 ********** 0.416666667 **********
**********

300 ********** 0.5 **********
**********

350 ********** 0.583333333 **********
**********

400 ********** 0.666666667 **********
**********

450 ********** 0.75 **********
**********

500 ********** 0.833333333 **********
**********

550 ********** 0.916666667 **********
**********

600 ********** 1 <<
1/1

650 ********** 1.083333333 <<
13/12

700 ********** 1.166666667 <<
7/6

750 ********** 1.25 <<
5/4

800 ********** 1.333333333 <<
4/3

850 ********** 1.416666667 <<
17/12

900 ********** 1.5 <<
3/2

950 ********** 1.583333333 <<
19/12

1000 ********** 1.666666667 <<
5/3

1050 ********** 1.75 <<
7/4

1100 ********** 1.833333333 <<
11/6

1150 ********** 1.916666667 <<
23/12

1200 ********** 2 <<
2/1

You can also change any rational interval to its related in N-EDO. For
example 7 degree of 37-ADO :

44/37 = 1.189189

(44/37) * 600 = 713.513 cent , which is 22 degree of 37-EDO

Shaahin Mohaajeri

Tombak Player & Researcher , Composer

www.geocities.com/acousticsoftombak

My tombak musics : www.rhythmweb.com/gdg

My articles in ''Harmonytalk'':

www.harmonytalk.com/archives/000296.html
<http://www.harmonytalk.com/archives/000296.html>

www.harmonytalk.com/archives/000288.html
<http://www.harmonytalk.com/archives/000288.html>

My article in DrumDojo:

www.drumdojo.com/world/persia/tonbak_acoustics.htm
<http://www.drumdojo.com/world/persia/tonbak_acoustics.htm>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf
Of Paul G Hjelmstad
Sent: Wednesday, April 19, 2006 9:09 PM
To: tuning@yahoogroups.com
Subject: [tuning] Re: a bridge between N-ADO and N-EDO

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

Looks good. How do you come up with 7 as the number to choose for 24-
ADO?

> Hi all
>
>
>
> Assume n^X=2 (for example 3^X=2 which X= 0.356207187)
>
> You want to have N-tone system , you must make a series of N number
(
> 0 X/N 2X/N 3X/N ...........N*X/N )
>
> Now calculate 2/X
>
> Then multiply this 2/X by each number in the series . for every
value
> of N you can have a rational N-ADO system
>
> Remember that if n^X=2 then we have n^(MX/N) = 2^(M/N)
>
>
>
> Example :
>
>
>
> How to take 24-ADO from 24-EDO
>
>
>
> We have 7^ 0.356207 = 2
>
>
>
> A=2/X=5.61471
>
>
>
> For series of ( 0 X/N 2X/N 3X/N ...........N*X/N ) we
> have 24 number :
>
>
>
> 0
>
> 0.014841966
>
> 0.029683932
>
> .
>
> .
>
> .
>
> 0.356207187
>
>
>
> If you calculate formula ( 7^ X/N) and then calculate cents , we
will
> have 24-EDO
>
> Then multiply (A) by each number in the series to have :
>
> 0 *********
>
> 0.083333333 ********* -4301.955001
>
> 0.166666667 ********* -3101.955001
>
> 0.25 ********* -2400
>
> 0.333333333 ********* -1901.955001
>
> 0.416666667 ********* -1515.641287
>
> 0.5 ********* -1200
>
> 0.583333333 ********* -933.1290944
>
> 0.666666667 ********* -701.9550009
>
> 0.75 ********* -498.0449991
>
> 0.833333333 ********* -315.641287
>
> 0.916666667 ********* -150.6370585
>
> 1 ********* 0
>
> 1.083333333 ********* 138.5726609
>
> 1.166666667 ********* 266.8709056
>
> 1.25 ********* 386.3137139
>
> 1.333333333 ********* 498.0449991
>
> 1.416666667 ********* 603.0004086
>
> 1.5 ********* 701.9550009
>
> 1.583333333 ********* 795.5580153
>
> 1.666666667 ********* 884.358713
>
> 1.75 ********* 968.8259065
>
> 1.833333333 ********* 1049.362941
>
> 1.916666667 ********* 1126.319346
>
> 2 ********* 1200
>
>
>
> From 1 to 2 is 24-ADO :
>
>
>
> 0: --- 1/1 ---- 0.000 unison, perfect prime
>
> 1: --- 13/12 ---- 138.573 tridecimal 2/3-tone
>
> 2: --- 7/6 ---- 266.871 septimal minor third
>
> 3: --- 5/4 ---- 386.314 major third
>
> 4: --- 4/3 ---- 498.045 perfect fourth
>
> 5: --- 17/12 ---- 603.000 2nd septendecimal
tritone
>
> 6: --- 3/2 ---- 701.955 perfect fifth
>
> 7: --- 19/12 ---- 795.558 undevicesimal minor
sixth
>
> 8: --- 5/3 ---- 884.359 major sixth, BP sixth
>
> 9: --- 7/4 ---- 968.826 harmonic seventh
>
> 10: --- 11/6 ---- 1049.363 21/4-tone, undecimal
neutral
> seventh
>
> 11: --- 23/12 ---- 1126.319 vicesimotertial major
> seventh
>
> 12: --- 2/1 ---- 1200.000 octave
>
>
>
>
>
>
>
> Shaahin Mohaajeri
>
>
>
> Tombak Player & Researcher , Composer
>
> www.geocities.com/acousticsoftombak
>
> 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
>

You can configure your subscription by sending an empty email to one
of these addresses (from the address at which you receive the list):
tuning-subscribe@yahoogroups.com - join the tuning group.
tuning-unsubscribe@yahoogroups.com - leave the group.
tuning-nomail@yahoogroups.com - turn off mail from the group.
tuning-digest@yahoogroups.com - set group to send daily digests.
tuning-normal@yahoogroups.com - set group to send individual emails.
tuning-help@yahoogroups.com - receive general help information.

________________________________

YAHOO! GROUPS LINKS

* Visit your group "tuning </tuning>
" on the web.

* To unsubscribe from this group, send an email to:
tuning-unsubscribe@yahoogroups.com
<mailto:tuning-unsubscribe@yahoogroups.com?subject=Unsubscribe>

* Your use of Yahoo! Groups is subject to the Yahoo! Terms of
Service <http://docs.yahoo.com/info/terms/> .

________________________________

correction for 12-ADO : FW: [tuning] relation between N-ADO and N-EDO : a new revision for bridge between N-ADO and N-EDORE

🔗Mohajeri Shahin <shahinm@kayson-ir.com>

🔗Petr Parízek <p.parizek@chello.cz>