(d / O * F) * f

One option for converting* unit numbers** to ratios
__________________________________________________________

1tET
1/1[i]2/1

2tET
1/1, (7/5[i]10/7), 2/1

3tET
1/1, 5/4[i]8/5, 2/1

4tET
1/1, 13/11, (7/5[i]10/7), 22/13, 2/1

5tET
1/1, 8/7, 17/13[i]26/17, 7/4, 2/1

6tET
1/1, 9/8, 19/15, (10/7[i]7/5), 30/19, 16/9, 2/1

7tET
1/1, 21/19, 11/9, 23/17[i]34/23, 18/11, 38/21, 2/1

8tET
1/1, 12/11, 25/21, 13/10, (27/19[i]38/27), 20/13, 42/25, 11/6, 2/1

9tET
1/1, 27/25, 7/6, 29/23, 15/11[i]22/15, 46/29, 12/7, 50/27, 2/1

10tET
1/1, 15/14, 31/27, 16/13, 33/25, (17/12[i]24/17), 50/33, 13/8, 54/31, 28/15,
2/1

11tET
1/1, 33/31, 17/15, 35/29, 9/7, 37/27[i]54/37, 14/9, 58/35, 30/17, 62/33, 2/1

12tET
1/1, 18/17, 37/33, 19/16, 39/31, 4/3, (41/29[i]58/29), 3/2, 62/39, 32/19,
66/37, 17/9, 2/1

13tET
1/1, 39/37, 10/9, 41/35, 21/17, 43/33, 11/8[i]16/11, 66/33, 34/21, 70/41,
9/5, 74/39, 2/1

14tET
1/1, 21/20, 43/39, 22/19, 45/37, 23/18, 47/35, (24/17[i]17/12), 70/47,
36/23, 74/45, 19/11, 78/43, 40/21, 2/1

15tET
1/1, 45/43, 23/21, 47/41, 6/5, 49/39, 25/19, 51/37[i]74/51, 38/25, 78/49,
5/3, 82/47, 42/23, 86/45, 2/1

16tET
1/1, 24/23, 49/45, 25/22, 51/43, 26/21, 53/41, 27/20, (55/39[i]78/55),
40/27, 82/53, 21/13, 86/51, 44/25, 90/49, 23/12, 2/1

17tET
1/1, 51/49, 13/12, 53/47, 27/23, 11/9, 14/11, 57/43, 29/21[i]42/29, 86/57,
11/7, 18/11, 46/27, 94/53, 24/13, 98/51, 2/1

18tET
1/1, 53/51, 27/25, 55/49, 7/6, 57/47, 29/23, 59/45, 15/11,(61/43[i]86/61),
22/15, 90/59, 46/29, 94/57, 12/7, 98/55, 50/27, 102/53, 2/1

19tET
1/1, 28/27, 57/53, 29/26, 59/51, 6/5, 61/49, 31/24, 63/47, 32/23[i]23/16,
94/63, 48/31, 98/61, 5/3, 102/59, 52/29, 106/57, 27/14, 2/1

etc�

Dan

*Conversion formula:

N (s+1�d / 2 {r.5>} [i]�2D)
[(d / O * F) * f] {rni(.5>)} = ----------------------------------------
D (s-1�d / 2 {r.5>} [i]�N)

n
**Any -----
d

Dan Stearns wrote:
>*Conversion formula:
>
> N (s+1�d / 2 {r.5>} [i]�2D)
>[(d / O * F) * f] {rni(.5>)} = ----------------------------------------
> D (s-1�d / 2 {r.5>} [i]�N)

I'm interested Dan, but I don't understand your notation. Can you explain?

-- Dave Keenan
http://dkeenan.com

d is "d"ivision (any so defined equidistant division of the octave)� O is 12
("O"ctave), F is 7 ("F"ifth), and f is 5 ("f"ourth)� rni simply stands for
"r"ound to the "n"earest "i"nteger (and .5>; round exact halves down)� N is
"N"umerator, D "D"enominator� s stands for the "s"equential + and -, and [i]
stands for ["i"]nversion�

Apparently I had come across this a couple of years ago, but as I wasn�t
exactly looking for �it�, I consequently never really stopped to �see it'...
I have a couple more of these, but this one is probably the least convoluted
(as well as the one that least distorts the actual equidistant divisions of
the octave; for better or worse...).

Dan

-----Original Message-----
From: Dave Keenan <d.keenan@uq.net.au>
To: tuning@onelist.com <tuning@onelist.com>
Date: Monday, February 15, 1999 6:25 PM
Subject: [tuning] Re: (d / O * F) * f