12-tone scales and 9-limit asses

Asses are defined in http://www.cix.co.uk/~gbreed/ass.htm. The two 9-
limit asses are 10:12:15:18 and 12:14:18:21.

In the 12-out-of-22 scale, rotating the pattern 0-3-7-10 through the
scale produces 4 of each of the two 9-limit asses, and 4 dissonant
chords.

In the 12-out-of-meantone scale, rotating the pattern 0-3-7-10
through the scale produces the 10:12:15:18 8 times, the 12:14:18:21 2
times, and 2 dissonant chords.

In the Blackjack scale, the pattern 0-5-12-17 produces 12:14:18:21 7
times, 10:12:15:18 2 times, and 12 dissonant chords.

--- In tuning@y..., paul@s... wrote:
> Asses are defined in http://www.cix.co.uk/~gbreed/ass.htm. The two
9-
> limit asses are 10:12:15:18 and 12:14:18:21.

I call these the (just) minor seventh and sub(minor) seventh chords
respectively. (I call 4:5:6:7 a major sub(minor) seventh chord)
m7,s7,Ms7

> In the Blackjack scale, the pattern 0-5-12-17 produces 12:14:18:21 7
> times, 10:12:15:18 2 times, and 12 dissonant chords.

Cool. Here they are on the chain. Also the dominant seventh and the
major seventh.

Degrees of 72-EDO arranged as a chain of 7-step (116.67c) generators.
2 9 16 23 30 37 44 51 58 65 0 7 14 21 28 35 42 49 56 63 70
+-------------------Blackjack-21-MOS-improper-CS------------+
5----------------15--------------------3-----------------9 m7
7----------------21-----3-----------------9 s7
1/9-------------5-----------------------1-----------------3 dom7
5-------------------15--1-----------------3 M7
3-----------------9-------11----------------33 9:11 ass
7-15-------------21-----3 7:15 ass1
5--------------7-15--------------35 7:15 ass2
2 9 16 23 30 37 44 51 58 65 0 7 14 21 28 35 42 49 56 63 70

Hey Graham, that 7:15 ass1 is asymetrical (not assymetrical :-), so
there's another one which is its inverse. And they both fit in the 10
note MOS twice! Of course Blackjack doesn't render 7:15 quasi-just.

-- Dave Keenan

Dave Keenan wrote:

> Hey Graham, that 7:15 ass1 is asymetrical (not assymetrical :-), so
> there's another one which is its inverse. And they both fit in the 10
> note MOS twice! Of course Blackjack doesn't render 7:15 quasi-just.

I forget if that's unexpected or not. You seem to have some typos as
well. Didn't I cover them all up to the 15-limit? I seem to remember
it's only with 15 that they can be asymmetrical (checked with dictionary).

Erlich-Keenan temperament covers a whole load of pseudo-asses as well, of
which neutral triads are the most well known.

Graham

--- In tuning@y..., graham@m... wrote:
>
> Erlich-Keenan temperament covers a whole load of pseudo-asses as well, of
> which neutral triads are the most well known.
>
Yeah, Dave, although it was great that you included neutral triads (9:11|9:11|3:4), what about
the augmented triad (4:5|7:9|4:5), the magic chord

(4:5|8:9|4:5|7:8) (inner dyads 5:7, 5:7)

and its subsets . . . the neutral triad is just one of many . . .

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_22527.html#22535

> Degrees of 72-EDO arranged as a chain of 7-step (116.67c)
generators.
> 2 9 16 23 30 37 44 51 58 65 0 7 14 21 28 35 42 49 56 63 70
> +-------------------Blackjack-21-MOS-improper-CS------------+
> 5----------------15--------------------3-----------------9 m7
> 7----------------21-----3-----------------9 s7
> 1/9-------------5-----------------------1-----------------3 dom7
> 5-------------------15--1-----------------3 M7
> 3-----------------9-------11----------------33 9:11 ass
> 7-15-------------21-----3 7:15
ass1
> 5--------------7-15--------------35 7:15
ass2
> 2 9 16 23 30 37 44 51 58 65 0 7 14 21 28 35 42 49 56 63 70
>

I'm very sorry, Dave, to be so far behind... but I really don't
understand this chart. Why is "0" of the 72-tET scale in the center??

What does this represent?? Sorry to be such an "ass..."

Could you please "fill me in" a bit in layman's terms??

Thanks!
________ _______ _____
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
>
> /tuning/topicId_22527.html#22535
>
> > Degrees of 72-EDO arranged as a chain of 7-step (116.67c)
> generators.
> > 2 9 16 23 30 37 44 51 58 65 0 7 14 21 28 35 42 49 56 63 70
> > +-------------------Blackjack-21-MOS-improper-CS------------+
> > 5----------------15--------------------3-----------------9 m7
> > 7----------------21-----3-----------------9 s7
> > 1/9-------------5-----------------------1-----------------3
dom7
> > 5-------------------15--1-----------------3 M7
> > 3-----------------9-------11----------------33 9:11
ass
> > 7-15-------------21-----3 7:15
> ass1
> > 5--------------7-15--------------35 7:15
> ass2
> > 2 9 16 23 30 37 44 51 58 65 0 7 14 21 28 35 42 49 56 63 70
> >
>
> I'm very sorry, Dave, to be so far behind... but I really don't
> understand this chart. Why is "0" of the 72-tET scale in the
center??
>
> What does this represent?? Sorry to be such an "ass..."
>
> Could you please "fill me in" a bit in layman's terms??

Gladly.

It's a chord finder. The notes are listed (as steps of 72-EDO) as a
chain of MIRACLE generators. Notice that from left to right they go up
by 7 each time (modulo 72).

Every 11-limit interval spans a constant (unique) number of
generators, so any pattern of intervals that fits within Blackjack may
be slid along to find all the occurrences of that chord (or hexany or
whatever). Paste it into a text editor and insert spaces to slide them
along.

Making the chain have 0 be in the middle is just a convention. A
"standard" 21 of 72 to avoid confusion.

You may want to use this to create a chord chart that instead shows
the notes in pitch order. In that form you can't always just slide the
chords along.

-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

> Making the chain have 0 be in the middle is just a convention. A
> "standard" 21 of 72 to avoid confusion.
>
> You may want to use this to create a chord chart that instead shows
> the notes in pitch order. In that form you can't always just slide
the
> chords along.
>
> -- Dave Keenan

Dave,

Joseph might appreciate this chord chart infinitely more if you used
72-tET notation for it. And gave a few examples of how to use it.

Just a thought,

Paul

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_22527.html#22806
>
> It's a chord finder. The notes are listed (as steps of 72-EDO) as a
> chain of MIRACLE generators. Notice that from left to right they go
up by 7 each time (modulo 72).
>
> Every 11-limit interval spans a constant (unique) number of
> generators, so any pattern of intervals that fits within Blackjack
may be slid along to find all the occurrences of that chord (or
hexany or whatever). Paste it into a text editor and insert spaces to
slide them along.
>
> Making the chain have 0 be in the middle is just a convention. A
> "standard" 21 of 72 to avoid confusion.
>

Hi Dave!

Thanks again... FINALLY, I'm understanding what you mean by finding
chords by "sliding them along..."

Thanks for the help!

_________ _____ ______
Joseph Pehrson