a bridge between N-ADO and N-EDO

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

--- 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
>

Hi Shaahin,

> 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

I'm afraid you lost me. Can you tell us what ADO stands for?

-Carl

I think that should be "arithmetic division of an octave", shouldn't it?

Petr

I often forget what the difference between ADL and EDL is...

----- Original Message -----
From: "Petr Par�zek" <p.parizek@chello.cz>
To: <tuning@yahoogroups.com>
Sent: 20 Nisan 2006 Per�embe 0:38
Subject: Re: [tuning] Re: a bridge between N-ADO and N-EDO

> I think that should be "arithmetic division of an octave", shouldn't it?
>
> Petr
>
>

> I think that should be "arithmetic division of an octave",
> shouldn't it?

In that case, is it different from the harmonic series?

-Carl