Blackjack ratio approximations

Dave Beardsley wrote:
>I think what really interests me is pitch. What are the near Just ratios?

Hi Dave,

Taking G as 1/1 I've annotated a Scala file for blackjack with some 11-prime-limit ratios and their errors below. But I'm sure to have left out some with larger numbers that would be useful to know in relation to others.

If you're viewing this on Yahoo's dumb web interface you'll need to click on "Message Index" then "Expand Messages" so you see things aligned correctly in the tables.

! blackjack.scl
!
21 note MOS of "MIRACLE" temperament, Erlich & Keenan, TL 2-5-2001
21
! G 1/1
83.33333 ! G#\ 21/20-1.1c 22/21+2.8c
116.66667 ! Ab/ 15/14-2.8c 16/15+4.9c 77/72+0.4c
200.00000 ! A 9/8 -3.9c 28/25+3.8c 55/49+0.0c
233.33333 ! Af 8/7 +2.2c 55/48-2.3c 63/55-1.8c
316.66667 ! Bb/ 6/5 +1.0c
350.00000 ! Bv 11/9 +2.6c 27/22-4.5c 49/40-1.3c 60/49-0.6c
383.33333 ! B\ 5/4 -3.0c 56/45+4.7
466.66667 ! Ct 55/42-0.2c 72/55+0.4c
500.00000 ! C 4/3 +2.0c
583.33333 ! C#\ 7/5 +0.8c 108/77-2.4c
616.66667 ! Db/ 10/7 -0.8c 77/54+2.4c
700.00000 ! D 3/2 -2.0c
733.33333 ! Df 55/36-0.4c 84/55+0.2c
816.66667 ! Eb/ 8/5 +3.0c 45/28-4.7c
850.00000 ! Ev 18/11-2.6c 49/30+0.6c
933.33333 ! Ef 12/7 +0.2c 55/32-4.3c
966.66667 ! Ft 7/4 -2.2c 96/55+2.3c
1050.00000 ! F^ 11/6 +0.6c 90/49-2.6c
1083.33333 ! F#\ 15/8 -4.9c 28/15+2.8c 144/77-0.4c
1166.66667 ! Gt 49/25+1.6c
2/1 ! G 2/1

Notation key:
A to G, # and b are as for 12-tET, and
/ is 1/12 tone up (effectively the 5-comma)
\ is 1/12 tone down
f is 1/6 tone up (effectively the 7-comma)
t is 1/6 tone down
^ is 1/4 tone up (effectively the 11-medium-diesis)
v is 1/4 tone down

>I'm curious to see what others came up with, I think my
>analysis is flawed, trying to shoe horn the 13th harmonic into 72tet,
>
>Any thoughts?

I agree. Forget about the 13th harmonic in 72-tET and its subsets.

A good way to see all the 11-limit relationships in blackjack is with a "slide rule". Don't forget "Message Index" then "Expand Messages" so you see it correctly aligned.

5 4 10 55 18 7 15 1 15 8 11 55 7 3 8 12 11 49 21 9 6
4 3 7 36 11 4 8 1 14 7 9 42 5 2 5 7 6 25 20 8 5
B\ C Db/ Df Ev FtF#\ G Ab/ Af Bv CtC#\ D Eb/ Ef F^ GtG#\ A Bb/
5--------------7-----1-----------------3-----------------9-------11

And here's a utonal slider for it
1/11-----1/9---------------1/3----------------1----1/7------------1/5

The idea is you print it and cut it out and paste it on card, then cut the bottom row away from the rest and slide it along to find 11-limit intervals and chords. Other sliders can be made for other kinds of chords apart from otonal and utonal, such as the various Anomalous Saturated Suspensions and Theoretically Indispensably Tempered Saturations (the "magic" chords that don't work in strict JI). Or a slider can be made for any subset scale so you can see where it can modulate to.

-- Dave Keenan
Brisbane, Australia
http://dkeenan.com/

----- Original Message -----
From: "David C Keenan" <D.KEENAN@UQ.NET.AU>

> Dave Beardsley wrote:
> >I think what really interests me is pitch. What are the near Just ratios?
>
> Hi Dave,
>
> Taking G as 1/1 I've annotated a Scala file for blackjack with some
> 11-prime-limit ratios and their errors below. But I'm sure to have left
out
> some with larger numbers that would be useful to know in relation to
others.
>
> If you're viewing this on Yahoo's dumb web interface you'll need to click
> on "Message Index" then "Expand Messages" so you see things aligned
> correctly in the tables.
>
> ! blackjack.scl
> !
> 21 note MOS of "MIRACLE" temperament, Erlich & Keenan, TL 2-5-2001
> 21
> ! G 1/1
> 83.33333 ! G#\ 21/20-1.1c 22/21+2.8c
> 116.66667 ! Ab/ 15/14-2.8c 16/15+4.9c 77/72+0.4c
> 200.00000 ! A 9/8 -3.9c 28/25+3.8c 55/49+0.0c
> 233.33333 ! Af 8/7 +2.2c 55/48-2.3c 63/55-1.8c
> 316.66667 ! Bb/ 6/5 +1.0c
> 350.00000 ! Bv 11/9 +2.6c 27/22-4.5c 49/40-1.3c 60/49-0.6c
> 383.33333 ! B\ 5/4 -3.0c 56/45+4.7
> 466.66667 ! Ct 55/42-0.2c 72/55+0.4c
> 500.00000 ! C 4/3 +2.0c
> 583.33333 ! C#\ 7/5 +0.8c 108/77-2.4c
> 616.66667 ! Db/ 10/7 -0.8c 77/54+2.4c
> 700.00000 ! D 3/2 -2.0c
> 733.33333 ! Df 55/36-0.4c 84/55+0.2c
> 816.66667 ! Eb/ 8/5 +3.0c 45/28-4.7c
> 850.00000 ! Ev 18/11-2.6c 49/30+0.6c
> 933.33333 ! Ef 12/7 +0.2c 55/32-4.3c
> 966.66667 ! Ft 7/4 -2.2c 96/55+2.3c
> 1050.00000 ! F^ 11/6 +0.6c 90/49-2.6c
> 1083.33333 ! F#\ 15/8 -4.9c 28/15+2.8c 144/77-0.4c
> 1166.66667 ! Gt 49/25+1.6c
> 2/1 ! G 2/1
>
> Notation key:
> A to G, # and b are as for 12-tET, and
> / is 1/12 tone up (effectively the 5-comma)
> \ is 1/12 tone down
> f is 1/6 tone up (effectively the 7-comma)
> t is 1/6 tone down
> ^ is 1/4 tone up (effectively the 11-medium-diesis)
> v is 1/4 tone down
>
> >I'm curious to see what others came up with, I think my
> >analysis is flawed, trying to shoe horn the 13th harmonic into 72tet,
> >
> >Any thoughts?
>
> I agree. Forget about the 13th harmonic in 72-tET and its subsets.

Yep.

> A good way to see all the 11-limit relationships in blackjack is with a
> "slide rule". Don't forget "Message Index" then "Expand Messages" so you
> see it correctly aligned.
>
> 5 4 10 55 18 7 15 1 15 8 11 55 7 3 8 12 11 49 21 9 6
> 4 3 7 36 11 4 8 1 14 7 9 42 5 2 5 7 6 25 20 8 5
> B\ C Db/ Df Ev FtF#\ G Ab/ Af Bv CtC#\ D Eb/ Ef F^ GtG#\ A Bb/
> 5--------------7-----1-----------------3-----------------9-------11
>
> And here's a utonal slider for it
> 1/11-----1/9---------------1/3----------------1----1/7------------1/5
>
> The idea is you print it and cut it out and paste it on card, then cut the
> bottom row away from the rest and slide it along to find 11-limit
intervals
> and chords. Other sliders can be made for other kinds of chords apart from
> otonal and utonal, such as the various Anomalous Saturated Suspensions and
> Theoretically Indispensably Tempered Saturations (the "magic" chords that
> don't work in strict JI). Or a slider can be made for any subset scale so
> you can see where it can modulate to.

Thanks, I'm not sure I'll need to go that far with Blackjack. My music
doesn't need that much modulation. At least not now.

And thanks for the ratios!

* David Beardsley
* microtonal guitar
* http://biink.com/db

--- In tuning@yahoogroups.com, "David Beardsley" <db@b...> wrote:

/tuning/topicId_45270.html#45290

>
> Thanks, I'm not sure I'll need to go that far with Blackjack. My
music
> doesn't need that much modulation. At least not now.
>
> And thanks for the ratios!
>
> * David Beardsley
> * microtonal guitar
> * http://biink.com/db

***Actually, the more people writing in Blackjack or Blackjust, the
better! There might even be some longevity and recognition of this
microtonal direction...

J. Pehrson