Yahoo Tuning Groups Ultimate Backup tuning 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

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Ozan Yarman
Sent: Saturday, December 24, 2005 9:18 PM
To: tuning@yahoogroups.com
Subject: [tuning] Arithmetic divisions of a string

Dear brother, I have divided not the whole of the string into 72 to parts, but only the distance between the fundamental tone and its octave. This arithmetic division yields the previously mentioned 72-tone rational tuning when you calculate the relative frequencies:

365 hz/360 hz = 73/72,

375 hz/360 hz = 25/24,

480 hz/360 hz = 4/3,

etc...

all independent of a pitch standard, and all derived with 5 hz increments from 360 hz onward.

Can you then calculate what happens when you divide the string's whole lenght into 72? You will arrive at the 36 of the tones within the octave comprised by the 72-tone system I have already given.

Cordially,

Ozan

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

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

To: tuning@yahoogroups.com

Sent: 24 Aralık 2005 Cumartesi 6:45

Subject: RE: [tuning] Bir teli 12 eşit parçaya böldüğümüzde çıkan sonuç

Dear ozan

But the system you mentioned is not system of equally dividing the length of string to 72 part. Also , what is the relationship between frequency-difference of 5 hz and equal divisions of string as you know that relationship between them is stright line :

F1 , f2,f3,.........2f1

F1=f1

F2 = f1 +5

F3=f2+5=f1+10

L (f2f1)= f1/f2 = f1/f1+5

L(f3f2) = f2/f3 = f1+5/f1+10

You know that logic of systems such as 72/72 ..... 72/36 is equally dividing the length of string , which farabi used for his intervallic experiments.

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

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

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

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

🔗Ozan Yarman <ozanyarman@ozanyarman.com>