hi david b. and alison m.

hey guys,

you've both alluded to the question of a ji version of blackjack in the past.

after checking with kraig grady, i think perhaps the most solid answer is this:

/tuning/files/perlich/scales/blackjust4.gif

the consonances that are 'broken' in the ji tuning are shown in gray. they're
broken by the ratios indicated -- 224:225, 16875:16807, and 2400:2401, which
are only 7.7, 7.0, and 0.7 cents, respectively. if you can live with these
errors, this ji rendition gives you the full 7-limit resources of the tempered
blackjack (where the maximum error is 3 cents).

for convenience, here is 'blackjust4' in order (note that 1/1 is what we're
tuning to B[ (a quarter-tone below B) in the 'standard key') along with some
approximated ratios (differing from the main ratio by 7.7, 7.0, or 0.7 cents):

ratios cents approx. ratios

1/1 0.00
50/49 34.98 49/48 (35.70), 64/63 (27.26)
15/14 119.44 16/15 (111.73)
49/45 147.43 35/32 (155.14)
8/7 231.17
7/6 266.87
60/49 350.62 49/40 (351.34)
5/4 386.31
98/75 463.07 64/49 (462.35), 21/16 (470.78)
4/3 498.04
7/5 582.51
10/7 617.49
3/2 701.96
75/49 736.93 49/32 (737.65), 32/21 (729.22)
8/5 813.69
49/30 849.38 80/49 (848.66)
12/7 933.13
90/49 1052.57 64/35 (1044.86)
28/15 1080.56 15/8 (1088.27)
49/25 1165.02 96/49 (164.30), 63/32 (1172.74)
2/1 1200.00

enjoy!

paul@stretch-music.com wrote:

> hey guys,
>
> you've both alluded to the question of a ji version of blackjack in the past.
>
> after checking with kraig grady, i think perhaps the most solid answer is this:
>
> /tuning/files/perlich/scales/blackjust4.gif
>
> the consonances that are 'broken' in the ji tuning are shown in gray. they're
> broken by the ratios indicated -- 224:225, 16875:16807, and 2400:2401, which
> are only 7.7, 7.0, and 0.7 cents, respectively. if you can live with these
> errors, this ji rendition gives you the full 7-limit resources of the tempered
> blackjack (where the maximum error is 3 cents).
>
> for convenience, here is 'blackjust4' in order (note that 1/1 is what we're
> tuning to B[ (a quarter-tone below B) in the 'standard key') along with some
> approximated ratios (differing from the main ratio by 7.7, 7.0, or 0.7 cents):
>
>
> ratios cents approx. ratios
>
> 1/1 0.00
> 50/49 34.98 49/48 (35.70), 64/63 (27.26)
> 15/14 119.44 16/15 (111.73)
> 49/45 147.43 35/32 (155.14)
> 8/7 231.17
> 7/6 266.87
> 60/49 350.62 49/40 (351.34)
> 5/4 386.31
> 98/75 463.07 64/49 (462.35), 21/16 (470.78)
> 4/3 498.04
> 7/5 582.51
> 10/7 617.49
> 3/2 701.96
> 75/49 736.93 49/32 (737.65), 32/21 (729.22)
> 8/5 813.69
> 49/30 849.38 80/49 (848.66)
> 12/7 933.13
> 90/49 1052.57 64/35 (1044.86)
> 28/15 1080.56 15/8 (1088.27)
> 49/25 1165.02 96/49 (164.30), 63/32 (1172.74)
> 2/1 1200.00
>
> enjoy!

Mmmm - that's a nice graphic. Thanks.

Regards