Re: blackjack "problem" solved

In 28752 Paul Erlich wrote:

<< why not think of Blackjack as basically a 10-tone scale >>

I suppose that Paul has always thought so and it is a pure
coincidence if he express that only after my post 1000 on the
tuning-math list where I linked

<http://www.aei.ca/~plamothe/sys72/ib1215.htm>

and after I wrote in 28120:

<< --------------------------------------------------------

I would suggest a reinterpretation of the Blackjack set
using incidentally a decatonic gammier.

-- snip --

As alternative to the Blackjack set seen as the scale 0 2
7 9 14 16 21 23 28 30 35 37 42 44 49 51 56 58 63 65 70 72
having alternatively steps 2 and 5, let us work on this
approach where the same set would be seen as

9 16 23 30 37 44 51 58 65
0 72
7 14 21 28 35 42 49 56 63

where 2 and 70 are missing for being considered as unison
vectors.

-- snip --

we obtain this JI lattice having all low sonance excepted
the two using odd 105.

| 35/32 | 21/20 | 35/32 |

--- ( 1 )----35/32
| |
16/15 | |
| |
--- 16/15-----7/6
| |
15/14 | |
| |
--- 8/7------5/4-----21/16
| | |
16/15 | | |
| | |
--- 128/105----4/3------7/5
| |
15/14 | |
| |
--- 10/7------3/2----105/64
| | |
16/15 | | |
| | |
--- 32/21-----8/5------7/4
| |
15/14 | |
| |
--- 12/7-----15/8
| |
16/15 | |
| |
--- 64/35----( 2 )

So, rather than that

9---16---23---30---37---44---51---58---65
/ / / / / / / / / \
0 / / / / / / / / 72
\ / / / / / / / / /
7---14---21---28---35---42---49---56---63

we have that

9---16---23---30---37---44 51---58---65
/ / / \ / \ \ \ / / / \
0 / / \ \ \ \ / / 72
\ / / / \ \ \ / \ / / /
7---14---21 28---35---42---49---56---63

-----

I add simply that 9 as a step has to correspond to 35/32 here
to give consistency while it may appear as 12/11 in chord.

----------------------------------------------------------- >>

Now, in 28790 Paul Erlich wrote:

<< Well, then, I'm glad I kept beating my head against you in
this! Also, try every fourth note -- that's "Slendro" . . . >>

Nice, but since I use maths with so few sense for the music I
suppose it is totally unsignificant to add there exist four
pentatonic substructure in ib1215, the chinese one, the slendro
one, a pelog one using 11 (the other using 13) and the japanese
one. You could "discovered" also many hexatonic structures like
the blues one, many heptatonic like the arabic one, the Zarlino
one, the lydian one, and so many others ... up to the decatonic
structures ib1183 and ib1215 itself.

I loss motivation to publish on that.

Pierre (who?)

--- In tuning@y..., Pierre Lamothe <plamothe@a...> wrote:
>
> In 28752 Paul Erlich wrote:
>
> << why not think of Blackjack as basically a 10-tone scale >>
>
> I suppose that Paul has always thought so and it is a pure
> coincidence if he express that only after my post 1000 on the
> tuning-math list where I linked
>
> <http://www.aei.ca/~plamothe/sys72/ib1215.htm>
>
> and after I wrote in 28120:
>
> << --------------------------------------------------------
>
> I would suggest a reinterpretation of the Blackjack set
> using incidentally a decatonic gammier.

Thanks for the implication of plagiarism, Pierre, but we had already
mentioned this on MakeMicroMusic, and Graham Breed implied it even
earlier with his initial conception of "Decimal" here in April or May.

> Now, in 28790 Paul Erlich wrote:
>
> << Well, then, I'm glad I kept beating my head against you in
> this! Also, try every fourth note -- that's "Slendro" . . . >>
>
> Nice, but since I use maths with so few sense for the music I
> suppose it is totally unsignificant to add there exist four
> pentatonic substructure in ib1215, the chinese one, the slendro
> one, a pelog one using 11 (the other using 13) and the japanese
> one. You could "discovered" also many hexatonic structures like
> the blues one, many heptatonic like the arabic one, the Zarlino
> one, the lydian one, and so many others ...

This has all already been done, by Dave Keenan, who posted all the
subsets of blackjack that are named scales in Scala, to within 5
cents.