7-ED(3/2) , 5-ED(4/3) : RE: [tuning] Equally dividing the pure fifth into 7

Hi

I myself use 7-ED(3/2) for Equally dividing the pure fifth into 7 degrees. Now check 5-ED(4/3) with 4/3 and pythagorean 16/9 :

0: 1/1 0.000 unison, perfect prime
1: 99.609 cents 99.609
2: 199.218 cents 199.218
3: 298.827 cents 298.827
4: 398.436 cents 398.436
5: 4/3 498.045 perfect fourth
6: 597.654 cents 597.654
7: 697.263 cents 697.263
8: 796.872 cents 796.872
9: 896.481 cents 896.481
10: 16/9 996.090 Pythagorean minor seventh
11: 1095.699 cents 1095.699
12: 1195.308 cents 1195.308

To get it you must use this formula(C'd'= cent of new degrees of D' of new scale and Cd= cents of D of 12-EDO):
C'd' = Cd-(D*0.391)
0.391= (500-498.045)/5

And about 7-ED(3/2)
you must use this formula(C'd'= cent of new degrees of D' of new scale and Cd= cents of D of 12-EDO):
C'd' = Cd+(D*0.2792)
0.391= (701.955-700)/7

Here we have linear compressing and stretching.

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ??????

My farsi page in Harmonytalk ???? ??????? ?? ??????? ???

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ????

-----Original Message-----
From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Ozan Yarman
Sent: Friday, March 23, 2007 12:51 PM
To: Tuning List
Subject: [tuning] Equally dividing the pure fifth into 7

And extending to the octave yields the following 12-tone system:

0: 1/1 C unison, perfect prime
1: 100.279 cents
2: 200.559 cents D
3: 300.838 cents E
4: 401.117 cents
5: 501.396 cents F
6: 601.676 cents
7: 3/2 G perfect fifth
8: 802.234 cents A
9: 902.514 cents A
10: 1002.793 cents B
11: 1103.072 cents
12: 1203.351 cents C

The fifths remain pure at every degree. Octaves sound fine too.

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This is the pure fourths tuning I hatched up a year ago, remember?

----- Original Message -----
From: "Mohajeri Shahin" <shahinm@kayson-ir.com>
To: <tuning@yahoogroups.com>
Sent: 25 Mart 2007 Pazar 7:58
Subject: 7-ED(3/2) , 5-ED(4/3) : RE: [tuning] Equally dividing the pure
fifth into 7

> Hi
>
> I myself use 7-ED(3/2) for Equally dividing the pure fifth into 7 degrees.
Now check 5-ED(4/3) with 4/3 and pythagorean 16/9 :
>
> 0: 1/1 0.000 unison, perfect prime
> 1: 99.609 cents 99.609
> 2: 199.218 cents 199.218
> 3: 298.827 cents 298.827
> 4: 398.436 cents 398.436
> 5: 4/3 498.045 perfect fourth
> 6: 597.654 cents 597.654
> 7: 697.263 cents 697.263
> 8: 796.872 cents 796.872
> 9: 896.481 cents 896.481
> 10: 16/9 996.090 Pythagorean minor seventh
> 11: 1095.699 cents 1095.699
> 12: 1195.308 cents 1195.308
>
> To get it you must use this formula(C'd'= cent of new degrees of D' of new
scale and Cd= cents of D of 12-EDO):
> C'd' = Cd-(D*0.391)
> 0.391= (500-498.045)/5
>
> And about 7-ED(3/2)
> you must use this formula(C'd'= cent of new degrees of D' of new scale and
Cd= cents of D of 12-EDO):
> C'd' = Cd+(D*0.2792)
> 0.391= (701.955-700)/7
>
> Here we have linear compressing and stretching.
>
> Shaahin Mohajeri
>