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?