Subject: Definitions of JI (was: Digest Number 3539)

Of course there is !. JI like ET fills and produces a continuum as does recurrent sequences, as does MOS
Just look at the scale tree!

Is there any context in which a 75 cent interval could be considered just?

-- Dave Keenan

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

> Is there any context in which a 75 cent interval could be considered
just?
>
> -- Dave Keenan

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> Of course there is !. JI like ET fills and produces a continuum as
does recurrent sequences, as does MOS
> Just look at the scale tree!

Well yes, I can see that is a logical conclusion from taking "just" to
mean "rational".

So if someone says to you that some interval is Just, this would tell
you absolutely nothing about it? For example, if asked to play a just
major third, you'd be just as likely to play a 12-equal major third,
or to ask which of the infinite number of possible rational major
thirds they would like you to aim for?

What ratio do you consider 75 cents to be?

-- Dave Keenan

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> What ratio do you consider 75 cents to be?

My vote goes to 1:2^(1/16)

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > What ratio do you consider 75 cents to be?
>
> My vote goes to 1:2^(1/16)

Sure, but I think Kraig knows I'm asking him (or anyone else for whom
JI = rational) which particular ratio of whole numbers he considers it
to be. Or maybe it can be several. e.g.

Ratio Difference in cents (to 75 cents)
22:23 -2.0
23:24 1.3
45:47 -0.3
68:71 0.3
113:118 0.04
158:165 -0.05
271:283 -0.01
384:401 0.005
655:684 -0.002
1039:1085 0.0007
1694:1769 -0.0002
... an infinite number of them getting progressivley closer but never
quite reaching.

-- Dave Keenan

I believe the JI ratios are only those first two on top of the list, and maybe, just maybe the third.

Cordially,
Ozan
----- Original Message -----
From: Dave Keenan
To: tuning@yahoogroups.com
Sent: 07 Haziran 2005 Salı 6:59
Subject: [tuning] Re: Subject: Definitions of JI (was: Digest Number 3539)

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> > What ratio do you consider 75 cents to be?
>
> My vote goes to 1:2^(1/16)

Sure, but I think Kraig knows I'm asking him (or anyone else for whom
JI = rational) which particular ratio of whole numbers he considers it
to be. Or maybe it can be several. e.g.

Ratio Difference in cents (to 75 cents)
22:23 -2.0
23:24 1.3
45:47 -0.3
68:71 0.3
113:118 0.04
158:165 -0.05
271:283 -0.01
384:401 0.005
655:684 -0.002
1039:1085 0.0007
1694:1769 -0.0002
... an infinite number of them getting progressivley closer but never
quite reaching.

-- Dave Keenan