"complete" Blackjack progression posted

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I've just posted the "complete" Blackjack progression I was working
on, as described by Dave Keenan in the following post:

/tuning/topicId_31354.html#31354

Don't forget... in order to view this "sliderule" correctly go:

"Message Index," "Expand Messages" (it's not all left aligned.. :) )

The .mp3 file is in my "Pehrson" directory:

/tuning/files/Pehrson/

Blackjack extended prog3.mp3

So... this progression, essentially, goes through 28 chords and then
can't be repeated in the Blackjack lattice.

Now... I was just wondering why that was...

Isn't Blackjack set up in multiples of 10??

Why, then, are we getting 28 chords before the "break..."

Any help from Dave Keenan or Paul Erlich on this would be *greatly*
appreciated...

Hope people enjoy the "full cycle..." I intend to use it in my
piece, but in some "musical" context, of course.

Joseph

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> I've just posted the "complete" Blackjack progression I was working
> on, as described by Dave Keenan in the following post:
>
> /tuning/topicId_31354.html#31354
>
> Don't forget... in order to view this "sliderule" correctly go:
>
> "Message Index," "Expand Messages" (it's not all left
aligned.. :) )
>
> The .mp3 file is in my "Pehrson" directory:
>
> /tuning/files/Pehrson/
>
> Blackjack extended prog3.mp3
>
> So... this progression, essentially, goes through 28 chords and
then
> can't be repeated in the Blackjack lattice.
>
> Now... I was just wondering why that was...
>
> Isn't Blackjack set up in multiples of 10??
>
> Why, then, are we getting 28 chords before the "break..."

Think of the diatonic scale. Think of how each chord type can be
transposed by fifths a certain number of times within the diatonic
scale. Think of how the number of times is a function of the type of
chord you choose.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_31512.html#31537
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> >
>
> Think of the diatonic scale. Think of how each chord type can be
> transposed by fifths a certain number of times within the diatonic
> scale. Think of how the number of times is a function of the type
of chord you choose.

Thanks, Paul!

Well then, the next question :)

is whether *every* tempered periodicity block has the same properties
of "limited transposition..."

My guess would be yes...

Joseph

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> Thanks, Paul!
>
> Well then, the next question :)
>
> is whether *every* tempered periodicity block has the same
properties
> of "limited transposition..."
>
> My guess would be yes...
>
> Joseph

Not if you temper out _all_ the unison vectors. Then you have an ET,
or at least a "well-temperament".

If you leave untempered only one of the commas (in the diatonic case,
25:24, or in the Blackjack case, 36:35), you have the nice MOS
property that any chord you find has all its transpositions "near" to
it within the chain of generators, and none elsewhere.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_31512.html#31558

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > Thanks, Paul!
> >
> > Well then, the next question :)
> >
> > is whether *every* tempered periodicity block has the same
> properties of "limited transposition..."
> >
> > My guess would be yes...
> >
> > Joseph
>
> Not if you temper out _all_ the unison vectors. Then you have an
ET, or at least a "well-temperament".

Oh sure... well that makes sense. So, that would, essentially,
differentiate between the limited transpositions of the diatonic set
and, let's say, the full transpositions of the traditional 12-tET
chromatic, for example... (??)

Thanks, Paul!

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> Oh sure... well that makes sense. So, that would, essentially,
> differentiate between the limited transpositions of the diatonic
set
> and, let's say, the full transpositions of the traditional 12-tET
> chromatic, for example... (??)

Right . . . now, in my answer, I forgot to mention that if you leave
_more than one_ of the unison vectors untempered, you don't get the
nice transposability properties of _either_ . . .

I wrote,

> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>
> > Oh sure... well that makes sense. So, that would, essentially,
> > differentiate between the limited transpositions of the diatonic
> set
> > and, let's say, the full transpositions of the traditional 12-tET
> > chromatic, for example... (??)
>
> Right . . . now, in my answer, I forgot to mention that if you
leave
> _more than one_ of the unison vectors untempered, you don't get the
> nice transposability properties of _either_ . . .

. . . the diatonic set or the 12-tET chromatic.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_31512.html#31562

> I wrote,
>
> > --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> >
> > > Oh sure... well that makes sense. So, that would, essentially,
> > > differentiate between the limited transpositions of the
diatonic
> > set
> > > and, let's say, the full transpositions of the traditional 12-
tET
> > > chromatic, for example... (??)
> >
> > Right . . . now, in my answer, I forgot to mention that if you
> leave
> > _more than one_ of the unison vectors untempered, you don't get
the
> > nice transposability properties of _either_ . . .
>
> . . . the diatonic set or the 12-tET chromatic.

Well, that would, essentially, be Just Intonation, yes, and the land
of howlin' wolf??

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
?)
> > >
> > > Right . . . now, in my answer, I forgot to mention that if you
> > leave
> > > _more than one_ of the unison vectors untempered, you don't get
> the
> > > nice transposability properties of _either_ . . .
> >
> > . . . the diatonic set or the 12-tET chromatic.
>
>
> Well, that would, essentially, be Just Intonation, yes, and the land
> of howlin' wolf??

In 5-limit or any other "two-dimensional" system, yes, it would.

But in 7-limit, you could have two unison vectors untempered, and only
one tempered out. In 11-limit, one could have two unison vectors
untempered, and two tempered out. These are examples of _planar_
temperaments, and an example of the latter case was in fact the
predecessor to MIRACLE in Dave Keenan's research.