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

Hi all

First , forget all in previous mail before !!!!

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 24-ADO :

C (24-EDO) ********** (C 24-EDO)/600 **********
24-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
>

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Hi petr

>>>>>>I have to confess I still can't understand why the rational
factors should
>>>>be converted to cents by multipliing them by 600. Why right 600 and
not
>>>something else?

It was an example for edos with cardinality as (2k)-EDO, you can start
from any degree of edo to complete your octave .

Please have a look at my edo to ado.xls file in :

/tuning/files/shaahin/

it shows the relation between edo and ado cardinality and change of ado
cardinality due to degree of edo.i have selected 3 different cardinality
of edo. It shows that there is rational relation between cents of edo
degrees and you can make ado systems acording to these ratioes.

Also it shows that range of ado cardinality is independent from edo
cardinality . but you can consider a range for ado cardinality due to
octave of edo.

It is interesting also that ratio between cents of edo degrees is
independent from them. That is we have constant ratios so if we start
from second degree in

N-EDOs we can construct it.

>>>>>As far as I can understand your concepts, ADOs are in fact regular
parts of
>>>>>the harmonic series, is that right?

The N-ado system is an arithematic series which has a numerary nexus of
N as constant denominators and odentities from N to 2N.

Now consider :

2:5 - 3:5 - 4:5 - 5:5 - 6:5- .........10:5 - 11:5 - 12 :5

Tha 5-ado system is from 5:5 to 10:5 . considering octave equivalency we
have 10-ado from 10:10......20:10 ( 10:5 ........20:5)

>>>>>And if 2^(22/37) and 44/37 are so away from each other, what is the
point in
>>>>>comparing them?

I think the answer is above.

>>>>>>And again, why did you choose to compare right this one to
>>>>>that one?

Which one to which one?edo to ado?ok , the rational relation between edo
degrees was interesting for me !!!

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>

> The N-ado system is an arithematic series which has a numerary
> nexus of N as constant denominators and odentities from N to 2N.

Why didn't you say so?

Denny Genovese calls these "modes" of the harmonic series.
"Mode 5" is 5-10, for example.

-Carl

Can you facilitate these explanations for people like myself who still lack
the fundamentals of Partch's theory?

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 22 Nisan 2006 Cumartesi 19:09
Subject: [tuning] Re: relation between N-ADO and N-EDO : a new revision for
bridge between N-ADO and N-EDORE

> > The N-ado system is an arithematic series which has a numerary
> > nexus of N as constant denominators and odentities from N to 2N.
>
> Why didn't you say so?
>
> Denny Genovese calls these "modes" of the harmonic series.
> "Mode 5" is 5-10, for example.
>
> -Carl
>
>

> > > The N-ado system is an arithematic series which has a numerary
> > > nexus of N as constant denominators and odentities from N to 2N.
> >
> > Why didn't you say so?
> >
> > Denny Genovese calls these "modes" of the harmonic series.
> > "Mode 5" is 5-10, for example.

> Can you facilitate these explanations for people like myself
> who still lack the fundamentals of Partch's theory?

A "numerary nexus" among a group of ratios (denoting pitches
relative to a 1/1) is either a numerator or a denominator they
all share (example: 4/3, 7/3, and 2/3 have a numerary nexus
of 3). An "identity" is the opposite of a nexus -- it's the
number that's different. An odentity (over identity) is such
a number that happens to be a numerator, and a udentity (under
identity) is one that's a denominator.

An otonality is a group of pitches with a numerary nexus in the
denominator, and a utonality is a group with a nexus in the
numerator.

-Carl

And, somehow, it all seems very simple! Thanks very much for the
explanation. So what brother Mohajeri meant is that the denominators of the
ratios of any x-ADO system are all based on the same numbers. Right? Doesn't
that make it a scale based on undertones? Isn't music based on it utonal?

Oz.

> > > > The N-ado system is an arithematic series which has a numerary
> > > > nexus of N as constant denominators and odentities from N to 2N.
> > >
> > > Why didn't you say so?
> > >
> > > Denny Genovese calls these "modes" of the harmonic series.
> > > "Mode 5" is 5-10, for example.
>
> > Can you facilitate these explanations for people like myself
> > who still lack the fundamentals of Partch's theory?
>
> A "numerary nexus" among a group of ratios (denoting pitches
> relative to a 1/1) is either a numerator or a denominator they
> all share (example: 4/3, 7/3, and 2/3 have a numerary nexus
> of 3). An "identity" is the opposite of a nexus -- it's the
> number that's different. An odentity (over identity) is such
> a number that happens to be a numerator, and a udentity (under
> identity) is one that's a denominator.
>
> An otonality is a group of pitches with a numerary nexus in the
> denominator, and a utonality is a group with a nexus in the
> numerator.
>
> -Carl
>
>

> So what brother Mohajeri meant is that the denominators of the
> ratios of any x-ADO system are all based on the same numbers.
> Right? Doesn't that make it a scale based on undertones? Isn't
> music based on it utonal?

The opposite. If the denominators are all the same, then they
would all share the same undertone relation, making them
harmonics. If the numerators were the same, they would be
utonal.

-Carl

I see, I got it the other way round then. Thanx.

Oz.

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 25 Nisan 2006 Salï¿½ 18:24
Subject: [tuning] Re: relation between N-ADO and N-EDO : a new revision for
bridge between N-ADO and N-EDORE

> > So what brother Mohajeri meant is that the denominators of the
> > ratios of any x-ADO system are all based on the same numbers.
> > Right? Doesn't that make it a scale based on undertones? Isn't
> > music based on it utonal?
>
> The opposite. If the denominators are all the same, then they
> would all share the same undertone relation, making them
> harmonics. If the numerators were the same, they would be
> utonal.
>
> -Carl
>
>

> > > So what brother Mohajeri meant is that the denominators of the
> > > ratios of any x-ADO system are all based on the same numbers.
> > > Right? Doesn't that make it a scale based on undertones? Isn't
> > > music based on it utonal?
> >
> > The opposite. If the denominators are all the same, then they
> > would all share the same undertone relation, making them
> > harmonics. If the numerators were the same, they would be
> > utonal.
>
> I see, I got it the other way round then. Thanx.

Perhaps best is an example. 1/1 3/1 9/1 21/1 are clearly
all harmonics. So are 9/5 12/5 13/5 17/5 (numerary nexus = 5).
In the same way, 12/1 12/2, 12/3... are subharmonics (nexus = 12).

-C.

I'm beginning to remember... so, how does ADO differ from EDSL?

SNIP

>
> Perhaps best is an example. 1/1 3/1 9/1 21/1 are clearly
> all harmonics. So are 9/5 12/5 13/5 17/5 (numerary nexus = 5).
> In the same way, 12/1 12/2, 12/3... are subharmonics (nexus = 12).
>
> -C.
>

My dear brother ozan

According to my previous mail about EDSL , ......:

The difference between ADO and EDL is in position of their numerary
nexus and their odentity and udentity.

In two equal degree edl and ado , the cardinality of them are so :

Cardinality of edl = 2* Cardinality of ado

So 24-edl and 12-ado have 12 tone per system.

But In 12-ado , numerary nexus is undertones and overtones are odentity
so it acts otonal. But 24-edl acts utonal.

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

-----Original Message-----
From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf
Of Ozan Yarman
Sent: Saturday, April 29, 2006 5:10 AM
To: tuning@yahoogroups.com
Subject: Re: [tuning] Re: relation between N-ADO and N-EDO : a new
revision for bridge between N-ADO and N-EDORE

I'm beginning to remember... so, how does ADO differ from EDSL?

SNIP

> Perhaps best is an example. 1/1 3/1 9/1 21/1 are clearly

> all harmonics. So are 9/5 12/5 13/5 17/5 (numerary nexus = 5).

> In the same way, 12/1 12/2, 12/3... are subharmonics (nexus = 12).

> -C.

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I don't know what EDSL is, and frankly the alphabet soup
makes me dizzy.

-C.

> I'm beginning to remember... so, how does ADO differ from EDSL?
>
> SNIP
>
> >
> > Perhaps best is an example. 1/1 3/1 9/1 21/1 are clearly
> > all harmonics. So are 9/5 12/5 13/5 17/5 (numerary nexus = 5).
> > In the same way, 12/1 12/2, 12/3... are subharmonics (nexus = 12).
> >
> > -C.

Dear j1

Forgive me , I forgot to delet this question in my previous mail , I
never ask anybody why to use this or that scale or system? 22-edl sounds
good to me ,too.

But about EDSL :

Please refer to my previous mail about EDL and EDSL.

We may realy need to have new terms but must consider :

1- if act of string and pipe is the same (which I don't think so ) , EDL
is used for both ,

2- if not , and if there were any relations between hole distance and
length equal dividing system , we must use another term.

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 J.Smith
Sent: Sunday, April 30, 2006 7:58 AM
To: tuning@yahoogroups.com
Subject: [tuning] Re: relation between N-ADO and N-EDO : a new revision
for bridge between N-ADO and N-EDORE

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> I don't know what EDSL is, and frankly the alphabet soup
> makes me dizzy.
>
> -C.

Carl, I believe EDSL is Equal Divisions of String Length...which
yields an Undertone series.

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Mohajeri Shahin wrote:
> Dear j1
>
> Forgive me , I forgot to delet this question in my previous mail , I
> never ask anybody why to use this or that scale or system? 22-edl sounds
> good to me ,too.
>
> But about EDSL :
>
> Please refer to my previous mail about EDL and EDSL.
>
> We may realy need to have new terms but must consider :
>
> 1- if act of string and pipe is the same (which I don’t think so ) , EDL
> is used for both ,
> > 2- if not , and if there were any relations between hole distance and
> length equal dividing system , we must use another term.

Think of a pipe as somewhere between a string and an ocarina. For a
string, the length pretty much translates directly into a frequency. For
an ocarina, something similar (but probably less direct) goes for the
relation of inclosed volume and the open area. For the pipe, both
principles are at work to some extent, which depends on the shape
(cylindrical/conical flaring towards the mouthpiece or the bell/with a
"waist" like some saxophones, and whatever else variations there may
be), the flare of the bell, the size of the holes and even how high the
lids of the holes can be lifted. How do you want to take all that into
account?

I'd prefer sticking to otonal and utonal as the basic principles, even
though I do welcome any thoughts about the ways these can be realized on
a given instrument.

klaus

Klaus wrote:

>Think of a pipe as somewhere between a string and an ocarina. For a
>string, the length pretty much translates directly into a frequency.
For
>an ocarina, something similar (but probably less direct) goes for the
>relation of inclosed volume and the open area. For the pipe, both
>principles are at work to some extent, which depends on the shape
(>cylindrical/conical flaring towards the mouthpiece or the bell/with a
">waist" like some saxophones, and whatever else variations there may
>be), the flare of the bell, the size of the holes and even how high the

>lids of the holes can be lifted. How do you want to take all that into
>account?

So,It is obvious that the term EDL is best fitted to strings and EDSL is
the same , and for pipes we can have equal distance holes with the same
diameter but not related to EDL.

>I'd prefer sticking to otonal and utonal as the basic principles, even
>though I do welcome any thoughts about the ways these can be realized
on
>a given instrument.

Yes , EDL and ADO system is a way to use otonality and utonality.

Yahoo! Groups Links

> > I don't know what EDSL is, and frankly the alphabet soup
> > makes me dizzy.
> >
> > -C.
>
> Carl, I believe EDSL is Equal Divisions of String Length...which
> yields an Undertone series.

Wasn't that EDL just a few posts back?

-Carl

Dear brother, as far as I recollect, udentity is having the same numerary nexus as the numerator:

12/12
12/11
12/10
etc...
12/1

and odentity is having the same numerary nexus as the denominator:

12/12
13/12
14/12
15/12
etc...
24/12

So, the first example is EDSL, and the second is ADO (or ADSL when going all the way to 24/1)?

Cordially,
Oz.
----- Original Message -----
From: Mohajeri Shahin
To: tuning@yahoogroups.com
Sent: 29 Nisan 2006 Cumartesi 10:51
Subject: RE: [tuning] Re: relation between N-ADO and N-EDO : a new revision for bridge between N-ADO and N-EDORE

My dear brother ozan

According to my previous mail about EDSL , ……:

The difference between ADO and EDL is in position of their numerary nexus and their odentity and udentity.

In two equal degree edl and ado , the cardinality of them are so :

Cardinality of edl = 2* Cardinality of ado

So 24-edl and 12-ado have 12 tone per system.

But In 12-ado , numerary nexus is undertones and overtones are odentity so it acts otonal. But 24-edl acts utonal.

Shaahin Mohaajeri

Indeed so. If one would ask what the difference between that and utonality
is, I would refer them to compare EDO with tET or EQ.

----- Original Message -----
From: "J.Smith" <jsmith9624@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 30 Nisan 2006 Pazar 6:28
Subject: [tuning] Re: relation between N-ADO and N-EDO : a new revision for
bridge between N-ADO and N-EDORE

> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
> >
> > I don't know what EDSL is, and frankly the alphabet soup
> > makes me dizzy.
> >
> > -C.
>
>
> Carl, I believe EDSL is Equal Divisions of String Length...which
> yields an Undertone series.
>
>

I feel one must make the distinction between EDSL and EDPL. Nevertheless, EDL could work as long as you specify for which type of instrument you wish to utilize the method. For all it matters, I could obtain the cheapest garden hose and start punching equally-spaced holes in order to make a domestic instrument.

Oz.
----- Original Message -----
From: Mohajeri Shahin
To: tuning@yahoogroups.com
Sent: 30 Nisan 2006 Pazar 9:10
Subject: RE: [tuning] Re: relation between N-ADO and N-EDO : a new revision for bridge between N-ADO and N-EDORE

Dear j1

Forgive me , I forgot to delet this question in my previous mail , I never ask anybody why to use this or that scale or system? 22-edl sounds good to me ,too.

But about EDSL :

Please refer to my previous mail about EDL and EDSL.

We may realy need to have new terms but must consider :

1- if act of string and pipe is the same (which I don’t think so ) , EDL is used for both ,

2- if not , and if there were any relations between hole distance and length equal dividing system , we must use another term.

Shaahin Mohaajeri

Adolphe Sax, here's lookin' atcya!

The whole point in EDL is, it is not limited to utonality or otonality. You
can punch equally spaced holes all over a sewer tube aerated by giant
ventilation fans and invent the largest canalization instrument ever thought
of... that is, if you don't mind the smell!

Oz.

----- Original Message -----
From: "klaus schmirler" <KSchmir@online.de>
To: <tuning@yahoogroups.com>
Sent: 30 Nisan 2006 Pazar 21:42
Subject: Re: [tuning] Re: relation between N-ADO and N-EDO : a new revision
for bridge between N-ADO and N-EDORE

Mohajeri Shahin wrote:
> Dear j1
>
> Forgive me , I forgot to delet this question in my previous mail , I
> never ask anybody why to use this or that scale or system? 22-edl sounds
> good to me ,too.
>
> But about EDSL :
>
> Please refer to my previous mail about EDL and EDSL.
>
> We may realy need to have new terms but must consider :
>
> 1- if act of string and pipe is the same (which I donï¿½t think so ) , EDL
> is used for both ,
>
> 2- if not , and if there were any relations between hole distance and
> length equal dividing system , we must use another term.

I'd prefer sticking to otonal and utonal as the basic principles, even
though I do welcome any thoughts about the ways these can be realized on
a given instrument.

klaus

relation between N-ADO and N-EDO : a new revision for bridge between N-ADO and N-EDORE

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

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

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🔗klaus schmirler <KSchmir@online.de>

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

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