Yahoo Tuning Groups Ultimate Backup tuning mistake : FW: EDO , EDS , LDO , ADO , ..........RE: [tuning] Arithmetic divisions of a string

Correct : the tetrachord of 12/12 ....12/9 is a species of shur-tetrachordal genous

Shaahin Mohaajeri

Tombak Player & Researcher , Composer

www.geocities.com/acousticsoftombak

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________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Mohajeri Shahin
Sent: Wednesday, December 28, 2005 8:59 AM
To: tuning@yahoogroups.com
Subject: RE: EDO , EDS , LDO , ADO , ..........RE: [tuning] Arithmetic divisions of a string

Merry christmas to all

Dear ozan

As I told before , intervals of LDO system are calculated as R=log10(x) where 10=<x=<100. so as example , consider a scale with 8 degrees as:

X=10 ... 0.000 cent

X=12.5... 160.134 cents

X=15... 280.800 cents

X=20 .... 455.585 cents

X=25 ... 579.963 cents

X=37.5... 785.357 cents

X=50.... 917.592 cents

X=100.... 1200.000 cents

Example of ADO system is like 12/12 ...... 24/12 . we can write it as 12:13:14:......:24 . also you can write EDS as for example : 1/24 : 1/23 : 1/22 : ......... : 1/12

In 12-EDS you mentioned , the pentachord of 12/12 ....12/9 is a species of shur-tetrachordal genous .

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

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Ozan Yarman
Sent: Sunday, December 25, 2005 7:20 PM
To: Tuning List
Subject: Re: EDO , EDS , LDO , ADO , ..........RE: [tuning] Arithmetic divisions of a string

Very good brother, some examples:

53-EDO

relative frequencies=2^({1,2,3...n}/n)

in cents= 1200 * ({1,2,3...n}/n)

(tempering the octave would affect the denominator and make it an irrational number)

12-EDS:

relative frequencies= n/{ n...3, 2, 1}

in cents=1200 * log [n/{ n...3, 2, 1} ] / log 2

12/12 = 0 cents

12/11 = 150.6371 cents

12/10 = 315.6413 cents

12/9 = 498.0450 cents

12/8 = 701.9550 cents

12/7 = 933.1291 cents

12/6 = 1200.0000 cents

12/5 = 1515.6413 cents

12/4 = 1901.9550 cents

12/3 = 2400.0000 cents

12/2 = 3101.9550 cents

12/1 = 4301.9550 cents

Can you give examples along the same line for ADO and LDO?

Oz.

----- Original Message -----

From: Mohajeri Shahin <mailto:shahinm@kayson-ir.com>

To: tuning@yahoogroups.com

Sent: 25 Aralık 2005 Pazar 12:55

Subject: EDO , EDS , LDO , ADO , ..........RE: [tuning] Arithmetic divisions of a string

Dear ozan and other

You are right . if you want to have 72 intevals with equal-string distance you must work with a system 144/144 .......144/72 . the number of degrees in such a system is double of numerary nexus.(as paul mentioned)

Now , I want to propose name of three different systems of octave divisions in 2 categories: ( may be done before by some one)

1- EDO = equal divisions which we had before = based on exponential function : R=2^(K/Y) where y is number of divisions , k is degree .

2- NDO = non-equal divisions of octave :

2-1- EDS = equal divisions of string (or vibrating air column in pipes , I don't know) : 2X/2X .............2X/X for x degrees in system.

2-2- NDS = non-equal divisions of string :

2-2-1- ADO = arithmetic divisions of octave based on arithmetic series : X/X ........ 2X/X for x degrees in system.

2-2-2- LDO = logarithmic divisions of octave : R=log10(x) where 10=<x=<100

.........

And other divisions due to differnt functions.

Any idea?

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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mistake : FW: EDO , EDS , LDO , ADO , ..........RE: [tuning] Arithmetic divisions of a string

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