19 tone just tuning?

Hello. I am doing a research on 19 tone system. I read Joseph Yasser's
book, and he talked about two 19 tone just intonation. What I want to know
is the ratio of tuning of those two system. He gives some of the ratio but
not all of them. I need every ratio of each note for tuning two 19 tone just
scales for my project.

Can anybody recommend any book or website for the tuniing of 19 tone?

Sangmok Lee

--- In tuning@yahoogroups.com, Sangmok Lee <sangmoklee@m...> wrote:

> Hello. I am doing a research on 19 tone system. I read Joseph
Yasser's
> book, and he talked about two 19 tone just intonation. What I want
to
> know
> is the ratio of tuning of those two system. He gives some of the
ratio
> but
> not all of them.

really? i don't recall him leaving anything out . . . i don't have
his book handy, can you post exactly what he gives and maybe we can
figure out the rest?

> I need every ratio of each note for tuning two 19 tone
> just
> scales for my project.

well, there are plenty of 19-tone just scales that make a lot more
sense than yasser's . . . for example see

/tuning/topicId_19050.html#19050

(click on "message index" and then "expand messages" to view the
tables and lattices properly)

and the ensuing discussion in many posts such as

/tuning/topicId_19113.html#19120

also see scala for many other 19-tone just and tempered scales.

can you describe your project in a little more detail?

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

> well, there are plenty of 19-tone just scales that make a lot more
> sense than yasser's . . .

One reasonable approach is simply to use the Fokker block for the TM
basis of commas for the standard 19-et val in the desired prime limit.

In this way we get:

5-limit basis [81/80, 3125/3072]

associated block [1, 25/24, 16/15, 10/9, 75/64, 6/5, 5/4, 32/25, 4/3,
25/18, 36/25, 3/2, 25/16, 8/5, 5/3, 128/75, 9/5, 15/8, 48/25]

7-limit basis [49/48, 81/80, 126/125]

associated block [1, 21/20, 15/14, 10/9, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5,
10/7, 3/2, 14/9, 8/5, 5/3, 12/7, 9/5, 28/15, 40/21]

11-limit basis [45/44, 49/48, 56/55, 81/80]

[1, 21/20, 15/14, 9/8, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, 10/7, 3/2,
14/9, 8/5, 5/3, 12/7, 16/9, 28/15, 40/21]

Other possibilities are to TM reduce the scales themselves, use
superparticular ratios, optimize for harmony, etc etc.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> > well, there are plenty of 19-tone just scales that make a lot more
> > sense than yasser's . . .

Then, of course, there are tempered scales. If you wedge 7-limit h19
with various 7-limit temperaments, you find that negri, kleismic,
hemifourth, meantone, muggles, flattone, magic and semisixths all give
the identity, which means that these "belong" to the 19-tone standard
val and we can expect to find reasonably regular (or in the case of
hemifourth, unreasonably regular) MOS in terms of the ratio of the
large step to the small one (I've chosen generators which are 7-limit
poptimal to show these):

Negri 5/48
[2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3]

Kleismic 14/53
[3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2]

Hemifourth 4/19
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

Meantone 65/112
[7, 7, 4, 7, 7, 4, 7, 7, 4, 7, 4, 7, 7, 4, 7, 7, 4, 7, 4]

Muggles 53/168
[8, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9]

Flattone 37/64
[3, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 3, 4, 3, 4]

Magic 71/224
[16, 11, 11, 11, 11, 11, 16, 11, 11, 11, 11, 11, 16, 11, 11, 11, 11,
11, 11]

Semisixths 17/46
[3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2]

If all of this isn't enough, meantone, flattone, muggles, magic and
semisixths all have the nice value of 49/48 for a chroma (or whatever
the word should be), and we have other just as nice or nicer chromas
giving interesting 19-tone tempered scales: nonkleismic and
superkleismic with 16/15, hemiweurschmidt with 21/20, and hemithird
with 25/24:

Nonkleismic 38/147
[5, 5, 5, 5, 18, 5, 5, 5, 5, 18, 5, 5, 5, 5, 18, 5, 5, 5, 18]

Superkleismic 106/395
[10, 19, 29, 29, 19, 10, 19, 29, 29, 19, 10, 19, 29, 29, 19, 10, 19,
29, 19]

Hemiwuerschmidt 37/229
[23, 7, 7, 23, 7, 7, 23, 7, 7, 23, 7, 7, 23, 7, 7, 23, 7, 7, 7]

Hemithird 43/267
[25, 9, 9, 25, 9, 9, 25, 9, 9, 25, 9, 9, 25, 9, 9, 25, 9, 9, 9]

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Superkleismic 106/395
> [10, 19, 29, 29, 19, 10, 19, 29, 29, 19, 10, 19, 29, 29, 19, 10, 19,
> 29, 19]

Note that this is not a MOS nor even an NMOS, yet it's nicely
organized anyhow. Some sort of theory for this sort of thing would be
nice; it seems clear the MOS concept needs to be generalized somehow.
It might be clearer in 41-et (which is 11-limit poptimal anyway):

[1, 2, 3, 3, 2, 1, 2, 3, 3, 2, 1, 2, 3, 3, 2, 1, 2, 3, 2]

Superkleismic can be defined (in the 7-limit) from its mapping,
[[1, 4, 5, 2], [0, -9, -10, 3]]; from its TM basis
[875/864, 1029/1024]; or of course its wedgie
[9, 10, -3, -5, -30, -35].

Here are what the approximations to the major tetrad [1,5/4,3/2,7/4]
and the minor tetrad [1,6/5,3/2,12/7] turn into, using corresponding
scale steps, as we traverse the circle of minor thirds:

[1, 4/3, 8/5, 7/4] [1, 6/5, 8/5, 50/27]
[1, 4/3, 8/5, 7/4] [1, 6/5, 8/5, 50/27]
[1, 4/3, 8/5, 7/4] [1, 6/5, 8/5, 50/27]
[1, 4/3, 8/5, 7/4] [1, 6/5, 8/5, 50/27]
[1, 4/3, 8/5, 7/4] [1, 6/5, 8/5, 50/27]
[1, 4/3, 8/5, 7/4] [1, 6/5, 8/5, 50/27]
[1, 4/3, 8/5, 7/4] [1, 6/5, 8/5, 50/27]
[1, 4/3, 8/5, 7/4] [1, 6/5, 8/5, 50/27]
[1, 4/3, 8/5, 7/4] [1, 6/5, 8/5, 50/27]
[1, 4/3, 3/2, 7/4] [1, 6/5, 3/2, 50/27]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 50/27]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 50/27]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 7/4] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 80/49] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 80/49] [1, 6/5, 3/2, 12/7]
[1, 5/4, 3/2, 80/49] [1, 9/8, 3/2, 12/7]

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Here are what the approximations to the major tetrad [1,5/4,3/2,7/4]
> and the minor tetrad [1,6/5,3/2,12/7] turn into, using corresponding
> scale steps, as we traverse the circle of minor thirds:

While it might seem this is really only interesting from a 5-limit
point of view, here is what they convert to using 13-limit
approximations for the 41-et:

> [1, 4/3, 8/5, 7/4] [1, 6/5, 8/5, 50/27]

[1, 6/5, 8/5, 50/27] ~ [1, 6/5, 8/5, 11/6]

> [1, 5/4, 3/2, 80/49] [1, 6/5, 3/2, 12/7]

[1, 5/4, 3/2, 80/49] ~ [1, 5/4, 3/2, 13/8]
(or [1, 5/4, 3/2, 18/11] in the 11-limit, but the above seems more to
the point.)

----- Original Message -----
From: "Gene Ward Smith" <gwsmith@svpal.org>

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> > <wallyesterpaulrus@y...> wrote:
> >
> > > well, there are plenty of 19-tone just scales that make a lot more
> > > sense than yasser's . . .
>
> Then, of course, there are tempered scales.

Sangmok Lee wan't asking about tempered scales.

* David Beardsley
* microtonal guitar
* http://biink.com/db

--- In tuning@yahoogroups.com, David Beardsley <davidbeardsley@b...>
wrote:

> Sangmok Lee wan't asking about tempered scales.

And I wasn't replying to him. Do you have a point?