FW: Re:Free sample of new tuning theory I've been working on...and any idea

Hi dear Michael , How are you?

Your 12-Tone scale is ,in its best approximation ,12 degrees of 1000-ADO
. For ADO you can see
http://240edo.googlepages.com/arithmeticrationaldivisionsofoctave .
There you see that these decimals indicates relations between something
like frequencies and show arithmetic sequence
<http://www.richland.edu/james/lecture/m116/sequences/arithmetic.html>
.Also you can see http://240edo.googlepages.com/ADO-EDL.XLS to test any
scales based on decimals.In 1000-ADO we have :

A5 1----------0 degree
B5 1.125----------125---203.91 cent
C5 1.142----------142---229.8752
D5 1.187----------187---296.7839
E5 1.212----------212---332.8676
F5 1.245----------245---379.3749
G5 1.3333----------334--497.6121~4/3
H5 1.5----------500---701.955
I5 1.615----------615---829.841
J5 1.6666----------667---884.7049~5/3
K5 1.8----------800---1017.596~9/5
L5 1.89777----------898 , you can use 897,898 or 900 ---(898,1109.376
cent ....... a deviation of +0.203 cent with 1109.173 cent)
A6 2----------1000---1200

1000-ADO shows a common difference between degrees as .001 and as an
example ,for 125 degree you must calculate (125*0.001)+1 which is 1.125.

and what about your 12-tone approximation in 440-ADO which shows
frequncies according to A=440 Hz:

0 55- 495 62-502 82-522 93-533 108-548
147-587 220-660 270-710 293-733 352-792 440-880

The first number befor (-) is degree and the second number after (-) is
the frequency

For decimals use for example (55/440)+1=1.125 or (93/440)+1=1.211

Test it.If you want to have decimals for frequencies , use 4400 or
44000-ADO then select your decimal places.

In http://240edo.googlepages.com/ADOandEDO.xls , you can select your EDO
and ADO to approximate any EDO by any ADO. and also you can approximate
and see the differences between 12-EDO and the best 12-tone subset of
any ADO approximating it.For example in 1000-ADO we have these degrees
to approximate 12-EDO the best:

Degree*******************Ratio***********************Cent

0****** 1 / 1******
0

59****** 1059 / 1000******
99.2431072

122****** 561 / 500******
199.2872111

189****** 1189 / 1000******
299.6984581

260****** 63 / 50******
400.1084805

335****** 267 / 200******
500.2076903

414****** 707 / 500******
599.7385442

498****** 749 / 500******
699.6451486

587****** 1587 / 1000******
799.5625538

682****** 841 / 500******
900.2132467

782****** 891 / 500******
1000.196804

888****** 236 / 125******
1100.230518

1000****** 2 / 1******
1200

Best wishes for you

Shaahin mohajeri , Tombak player and microtonalist

My web site <http://240edo.googlepages.com/>

My farsi page in harmonytalk <http://www.harmonytalk.com/mohajeri>

Irandrumz ensemble

*********

www.kayson-ir.com <http://www.kayson-ir.com/>

2288 Iranzamin bldg Iranzamin Ave.

Shahrak Qods, Tehran 14656, Iran
Telephone: (9821) 88072501-9

Fax: (9821) 88072500
Email: shahinm@...

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