6 note proper scales in 12 and 19

This note has less to do about tuning that I hoped it would. This is
because I had hoped to get 19-et strictly proper scales corresponding
to 12-et proper scales in the same way as works for 7-note scales, and
they just aren't talking to each other.

The 6-note proper scales in 12-et are mostly named for some reason or
other; most in fact are ragas in at least one mode, often more.
There's also the Liszt Prometheus scale, which is an interesting
example as it has the same number of triads as the diatonic
scale--six--using only six notes, *and* is proper. Even so, it hasn't
taken over the world of music.

I did find one scale without a name, so I named it Majorminor, as it
has both a major and a minor triad on the same degree. All these are
available for examination in the files section.

Gene Ward Smith wrote:
> This note has less to do about tuning that I hoped it would. This is
> because I had hoped to get 19-et strictly proper scales corresponding
> to 12-et proper scales in the same way as works for 7-note scales, and
> they just aren't talking to each other.
> > The 6-note proper scales in 12-et are mostly named for some reason or
> other; most in fact are ragas in at least one mode, often more.
> There's also the Liszt Prometheus scale, which is an interesting
> example as it has the same number of triads as the diatonic
> scale--six--using only six notes, *and* is proper. Even so, it hasn't
> taken over the world of music.
> > I did find one scale without a name, so I named it Majorminor, as it
> has both a major and a minor triad on the same degree. All these are
> available for examination in the files section.

Another thing that would help when looking at these is to add a comment for each note, showing the number of degrees of the ET for each note (to save the trouble of dividing by 1200 and multiplying by the size of the ET). If there's a standard notation, as in the case of 12-et and 19-et, that would also be useful to add (example:)

! prop19_8a.scl
Sensi[8] = Mandelbaum 8/19 = Oljare Octatonic
8
!
126.315789 ! 2 Db 9
315.789474 ! 5 Eb 14
442.105263 ! 7 E# Fb 0
568.421053 ! 9 F# 5 16
757.894737 ! 12 G# 2
884.210526 ! 14 A 7
1010.526316 ! 16 Bb 12
1200.000000 ! 19 C

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> Another thing that would help when looking at these is to add a comment
> for each note, showing the number of degrees of the ET for each note
(to
> save the trouble of dividing by 1200 and multiplying by the size of the
> ET). If there's a standard notation, as in the case of 12-et and 19-et,
> that would also be useful to add (example:)

Doing that creates a kind of format I don't like, since it makes it
harder to convert the file into another form, such as a Maple file.
What do you think of sticking that kind of information on the bottom?

I wish Scala allowed more data types for scales.

>> Another thing that would help when looking at these is to add a comment
>> for each note, showing the number of degrees of the ET for each note
>> (to save the trouble of dividing by 1200 and multiplying by the size of
>> the ET). If there's a standard notation, as in the case of 12-et and
>> 19-et, that would also be useful to add (example:)
>
>Doing that creates a kind of format I don't like, since it makes it
>harder to convert the file into another form, such as a Maple file.
>What do you think of sticking that kind of information on the bottom?
>
>I wish Scala allowed more data types for scales.

Why not just write a bit to bail after !, like Scala itself does?

-Carl

Gene Ward Smith wrote:
> --- In tuning-math@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> >> Another thing that would help when looking at these is to add a comment >> for each note, showing the number of degrees of the ET for each note
> (to >> save the trouble of dividing by 1200 and multiplying by the size of the >> ET). If there's a standard notation, as in the case of 12-et and 19-et, >> that would also be useful to add (example:)
> > Doing that creates a kind of format I don't like, since it makes it
> harder to convert the file into another form, such as a Maple file. > What do you think of sticking that kind of information on the bottom?
> > I wish Scala allowed more data types for scales.

It might be just as good to show the steps of the scale on the comment line as in the format used in Scala's modenam.par (e.g.)

! prop22_10a.scl
prop22_10a = Erlich symmetrical major = Pajara[10] 2 2 3 2 2 2 2 3 2 2
10
!
.....

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> It might be just as good to show the steps of the scale on the comment
> line as in the format used in Scala's modenam.par (e.g.)

I might put up new versions. However, until then, Scala will "fit to
mode of et" for you, and also will tell you when you run "show data"
what the scale is in n-et, if it is an n-et scale.

>It might be just as good to show the steps of the scale on the comment
>line as in the format used in Scala's modenam.par (e.g.)
>
>! prop22_10a.scl
>prop22_10a = Erlich symmetrical major = Pajara[10] 2 2 3 2 2 2 2 3 2 2
>10
>!
>.....
>

Can make the comment lines too long.
The bottom is fine with me (it's how I usually do it).

-Carl