Pajara[10]

This is a 25/24 chroma system, as well as being a 28/27 and 49/48
chroma system, so I don't give circles for major and minor tetrads,
but rather another circle for subminorish stuff.

Pajara[10]

[2, -4, -4, -11, -12, 2]
[1, 15/14, 8/7, 5/4, 4/3, 7/5, 3/2, 8/5, 7/4, 15/8]
[[7/4, 4/3, 1, 3/2, 8/7], [5/4, 15/8, 7/5, 15/14, 8/5]]

Circles of fifths
[1, 6/5, 3/2, 12/7] [1, 8/7, 3/2, 8/5]
[1, 6/5, 3/2, 12/7] [1, 8/7, 3/2, 8/5]
[1, 5/4, 3/2, 7/4] [1, 8/7, 3/2, 8/5]
[1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
[1, 5/4, 14/9, 7/4] [1, 7/6, 14/9, 5/3]

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> This is a 25/24 chroma system, as well as being a 28/27 and 49/48
> chroma system,

as shown in "the forms of tonality"

> so I don't give circles for major and minor tetrads,
> but rather another circle for subminorish stuff.

i don't get the logic of the "so". what implies what, exactly?

>
> Pajara[10]
>
> [2, -4, -4, -11, -12, 2]
> [1, 15/14, 8/7, 5/4, 4/3, 7/5, 3/2, 8/5, 7/4, 15/8]
> [[7/4, 4/3, 1, 3/2, 8/7], [5/4, 15/8, 7/5, 15/14, 8/5]]
>
> Circles of fifths
> [1, 6/5, 3/2, 12/7] [1, 8/7, 3/2, 8/5]
> [1, 6/5, 3/2, 12/7] [1, 8/7, 3/2, 8/5]
> [1, 5/4, 3/2, 7/4] [1, 8/7, 3/2, 8/5]
> [1, 5/4, 3/2, 7/4] [1, 7/6, 3/2, 5/3]
> [1, 5/4, 14/9, 7/4] [1, 7/6, 14/9, 5/3]

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > This is a 25/24 chroma system, as well as being a 28/27 and 49/48
> > chroma system,
>
> as shown in "the forms of tonality"

Didn't you tell me you were sending me some stuff, BTW?

> > so I don't give circles for major and minor tetrads,
> > but rather another circle for subminorish stuff.
>
> i don't get the logic of the "so". what implies what, exactly?

The major and minor circles are the same.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> > --- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...>
> > wrote:
> > > This is a 25/24 chroma system, as well as being a 28/27 and
49/48
> > > chroma system,
> >
> > as shown in "the forms of tonality"
>
> Didn't you tell me you were sending me some stuff, BTW?

i'm sending a lot of people a lot of stuff. last call for snail-mail
addresses -- i'm sending out a paper my a "famous music theorist",
and if you need a copy of _the forms of tonality_ too, let me know.

> > > so I don't give circles for major and minor tetrads,
> > > but rather another circle for subminorish stuff.
> >
> > i don't get the logic of the "so". what implies what, exactly?
>
> The major and minor circles are the same.

is this the antecedent or the consequent?

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> > > i don't get the logic of the "so". what implies what, exactly?
> >
> > The major and minor circles are the same.
>
> is this the antecedent or the consequent?

It's a consequence of 25/24 and 49/48 both being chromas. Didn't we
get into this once?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning-math@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> > > > i don't get the logic of the "so". what implies what, exactly?
> > >
> > > The major and minor circles are the same.
> >
> > is this the antecedent or the consequent?
>
> It's a consequence of 25/24 and 49/48 both being chromas. Didn't we
> get into this once?

not sure . . . the major and minor circles are the same as a
consequence of 25/24 and 49/48 both being chromas . . . hmm . . . can
you give the "for dummies" explanation of this? i mean, i know that
25/24 and 49/48 both being chromas implies that 50/49 is a comma,
which implies that there will be a half-octave period . . . are you
saying something beyond that?