Re: [tuning] Digest Number 1807

> From: "genewardsmith" <genewardsmith@juno.com>
> Subject: A diatonic scale
>
> Is anyone familiar with the scale MmMmMss, where M is a major
> tone, m is a minor tone, and s is a semitone? In both the 46 and
> 72 ets, it turns out to be quite a good scale; particularly in the 72-et.
>

I'm more familiar of it from basic diatonics applicable in 12. The only
possible seven tone diatonics of 5L and 2s are

LLsLLLs : traditional 'major' system
LsLLLLs : melodic minor system (ascending form for classical weenies)
sLLLLLs : what I think of as 'whole tone with pasing tone'.

If I look at your particular rotation of this last scale, and assuming
that tunings are chosen such that 'Mm' or 'LL' are chosen to approximate
a major third, (as yours are) then the tonic chord is a maj7#5 in jazz
terminology, meaning an augmented triad with a major senventh on it.
A wonderful chord and a wonderful scale and its got wonderful stuff
in its other rotations as well.

I'm not much of a latticeistician, but I think the following
5-(prime)-limit lattice represents the scale in a tileable format. The
'xxx' denotes a hole in the

25/16-----xxx------225/128
5/4------15/8-------45/32
1/1-------xxx--------9/8

Of course, in an et there are puns going on and the 225/128 is
much more likely a 16/9 and the 45/32 is also a 64/45. If you want to
go into higher prime interpretations, the 25/16 is more accurately an
11/7 in 46 (I didn't look at 72), but that sort of thing could go on
forever and since there are so few other 11 and and 7 identities
present, would probably not be heard as such.

Cool, makes me want to play.

Bob Valentine

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>
> > From: "genewardsmith" <genewardsmith@j...>
> > Subject: A diatonic scale
> >
> > Is anyone familiar with the scale MmMmMss, where M is a major
> > tone, m is a minor tone, and s is a semitone? In both the 46 and
> > 72 ets, it turns out to be quite a good scale; particularly in
the 72-et.
> >
>
> I'm more familiar of it from basic diatonics applicable in 12. The
only
> possible seven tone diatonics of 5L and 2s are
>
> LLsLLLs : traditional 'major' system
> LsLLLLs : melodic minor system (ascending form for classical
weenies)
> sLLLLLs : what I think of as 'whole tone with pasing tone'.

This last scale is associated in classical music with augmented sixth
and Neapolitan chords, and in fact Manuel's list of modes
(http://www.xs4all.nl/~huygensf/doc/modename.html), now with 1000
modes!, names this as "Neapolitan Major".

> Of course, in an et there are puns going on and the 225/128 is
> much more likely a 16/9

In 12-tET, yes, but . . . the puns going on in the ETs that Gene
specifically mentioned, 46 and 72, are different from this, and
different from one another. For example, in 72, 225/128 puns for 7/4.
Perhaps Gene could catalogue, for Bob V.'s interest, the puns in the
two tunings he proposed for this scale.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:
> --- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>
> This last scale is associated in classical music with augmented
sixth
> and Neapolitan chords, and in fact Manuel's list of modes
> (http://www.xs4all.nl/~huygensf/doc/modename.html), now with 1000
> modes!, names this as "Neapolitan Major".
>
> > Of course, in an et there are puns going on and the 225/128 is
> > much more likely a 16/9
>
> In 12-tET, yes, but . . . the puns going on in the ETs that Gene
> specifically mentioned, 46 and 72, are different from this, and
> different from one another. For example, in 72, 225/128 puns
> for 7/4.
> Perhaps Gene could catalogue, for Bob V.'s interest, the puns
> in the two tunings he proposed for this scale.

That would be nice, I do seem to get 16/9 as the likely target
for 2^38/46. You are right that others pun to 7/4. In particular,
this looks like a great scale in 31 since the the puns line up
very nicely in the 5 and 7 space there and are very much in
tune. (Thats going to a meantone version of course, 5555533).

(25/16,14/9)------xxx---(225/128,7/4)
5/4--------------15/8----(45/32,7/5)
1/1---------------xxx---------9/8

34 and 46 look like 225/128 AKA 16/9.
22, 31, 41 look like 225/128 AKA 7/4.

Bob Valentine

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

/tuning/topicId_32497.html#32514

>
> > Of course, in an et there are puns going on and the 225/128 is
> > much more likely a 16/9
>
> In 12-tET, yes, but . . . the puns going on in the ETs that Gene
> specifically mentioned, 46 and 72, are different from this, and
> different from one another. For example, in 72, 225/128 puns for
7/4.
> Perhaps Gene could catalogue, for Bob V.'s interest, the puns in
the two tunings he proposed for this scale.

Hi Paul...

I'm sorry to say that I forgot what the term "pun" means in
tuning... I looked in Monz' Dictionary and it's not there either.

I'm assuming it's a pitch that's a close "substitute" for another
pitch?? But how close does one pitch have to be to another to
constitute a "pun..?" This is somewhat involved with harmonic
entropy, yes?? since, if I have the definition right, these are
various pitches that could be "eliminated" in closing a periodicity
block, yes? Or something like that...

Yes, no, maybe? Maybe no?? Yes?

MONZ WE NEED an entry for "pun" when you get a chance...

Thanks

JP

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

> Hi Paul...
>
> I'm sorry to say that I forgot what the term "pun" means in
> tuning... I looked in Monz' Dictionary and it's not there either.
>
> I'm assuming it's a pitch that's a close "substitute" for another
> pitch?? But how close does one pitch have to be to another to
> constitute a "pun..?"

In this context, they have to be exactly the same. Remember, we're
talking about ETs such as 72-tET . . . since 225 = 5*5*3*3, the
statement "225/128 is a pun for 7/4" means "stacking two of the
approximation to the 5/4 in the ET, atop two of the approximation to
the 3/2 in the ET (and descending an octave), gives you the
approximation of the 7/4 in the ET."

Saying that 225/128 and 7/4 are a pun in a certain tuning system is
the same thing as saying their difference (actually, quotient),
225:224, _vanishes_ or is _tempered out_ in that tuning system.

> since, if I have the definition right, these are
> various pitches that could be "eliminated" in closing a periodicity
> block, yes?

Yes.

In fact, the closest term we have for "pun", especially for a case
such as this one, is Monz's term "bridge".

--- In tuning@y..., "bval_bobvalentine" <BVAL@I...> wrote:

> That would be nice, I do seem to get 16/9 as the likely target
> for 2^38/46. You are right that others pun to 7/4. In particular,
> this looks like a great scale in 31 since the the puns line up
> very nicely in the 5 and 7 space there and are very much in
> tune. (Thats going to a meantone version of course, 5555533).

I mentioned 46 and 72 because those were the only ones I checked. Any of the 225/224 ets, which includes 22, 31, 41, 53, 84 and 94 as well as 72, will have the same 7/4 pun.