Yahoo Tuning Groups Ultimate Backup tuning Beep-9 and Pelog

The "beep" temperament (based on tempering the large limma 27/25) turns out
to have a good approximation of the Indonesian 7-note pelog scale!

In Paul Erlich's "top" (Tenney-optimal) version of this temperament, the
generator is 260.26 cents. This has a 9-note scale of the sort that used to
be called MOS, but I gather is now being called DE (distributionally even).
Two modes of this scale have a good 7-note pelog subset.

If we name the notes of beep-9 after the number of iterations of the 260.26
cent generator, the basic scale is 0 5 1 6 2 7 3 8 4. The sizes of the
steps are s-L-s-L-s-L-s-L-L, where s is 101.3 cents and L is 158.96 cents.
Then the two pelog modes of beep-9 are:

2 7 3 4 0 5 1
3 8 4 5 1 6 2

So if you want to compose in pelog, while allowing the possibility of
modulating into different keys, this temperament looks like a good choice.
Beep has larger DE scales of 14 and 23 notes that would be useful for this.
Here's the basic 7-note pelog:

! beep9-pelog.scl
!
Beep-9 approximation of pelog scale
7
!
101.30000
260.26000
520.52000
679.48000
780.78000
939.74000
2/1

A Scala search finds a close match to this scale as pelog_pb.scl:

! pelog_pb.scl
!
"Primitive" Pelog, step of blown semi-fourths, von Hornbostel, type b.
7
!
105.000 cents
261.000 cents
522.000 cents
678.000 cents
783.000 cents
939.000 cents
2/1

This is essentially "beep" temperament. If you add steps at 366.0 cents and
1044.0 cents, you have a version of beep-9 with a 261.0 cent generator. So
it seems reasonable to call this the "von Hornbostel" temperament (or
"horn" for short).

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🔗wallyesterpaulrus <paul@stretch-music.com>

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

> The "beep" temperament (based on tempering the large limma 27/25)
turns out
> to have a good approximation of the Indonesian 7-note pelog scale!

Kraig's pointed out that a generator of this size, extended to 9
tones, gives 'pelog' as a subset. Different than the 'pelogic' pelog,
of course -- where you only need 7 tones from the chain and no extras.

> In Paul Erlich's "top" (Tenney-optimal) version of this
temperament, the
> generator is 260.26 cents. This has a 9-note scale of the sort that
used to
> be called MOS, but I gather is now being called DE
(distributionally even).

It's both -- when the period is a fraction of an octave, though, it's
DE but seemingly not considered MOS anymore.

> Two modes of this scale have a good 7-note pelog subset.
>
> If we name the notes of beep-9 after the number of iterations of
the 260.26
> cent generator, the basic scale is 0 5 1 6 2 7 3 8 4. The sizes of
the
> steps are s-L-s-L-s-L-s-L-L, where s is 101.3 cents and L is 158.96
cents.
> Then the two pelog modes of beep-9 are:
>
> 2 7 3 4 0 5 1
> 3 8 4 5 1 6 2
>
> So if you want to compose in pelog, while allowing the possibility
of
> modulating into different keys, this temperament looks like a good
choice.
> Beep has larger DE scales of 14 and 23 notes that would be useful
for this.
> Here's the basic 7-note pelog:
>
> ! beep9-pelog.scl
> !
> Beep-9 approximation of pelog scale
> 7
> !
> 101.30000
> 260.26000
> 520.52000
> 679.48000
> 780.78000
> 939.74000
> 2/1

Three step sizes, as I expected.

>
> A Scala search finds a close match to this scale as pelog_pb.scl:
>
> ! pelog_pb.scl
> !
> "Primitive" Pelog, step of blown semi-fourths, von Hornbostel, type
b.
> 7
> !
> 105.000 cents
> 261.000 cents
> 522.000 cents
> 678.000 cents
> 783.000 cents
> 939.000 cents
> 2/1
>
> This is essentially "beep" temperament.

von Hornbostel's version of "pelogic", I would assume, is also to be
found in the Scala archives, yes?

> If you add steps at 366.0 cents and
> 1044.0 cents, you have a version of beep-9 with a 261.0 cent
generator. So
> it seems reasonable to call this the "von Hornbostel" temperament
(or
> "horn" for short).

I think you'll find that some other pelog variant, not "primitive",
and based on "blown fifths", is also due to von Hornbostel but
corresponds to "pelogic" instead of "beep".

🔗Herman Miller <hmiller@IO.COM>

On Mon, 12 Jan 2004 00:59:01 -0000, "wallyesterpaulrus"
<paul@stretch-music.com> wrote:

>> A Scala search finds a close match to this scale as pelog_pb.scl:
>>
>> ! pelog_pb.scl
>> !
>> "Primitive" Pelog, step of blown semi-fourths, von Hornbostel, type
>b.
>
>von Hornbostel's version of "pelogic", I would assume, is also to be
>found in the Scala archives, yes?

Yes, that'd be pelog_pa.scl.

! pelog_pa.scl
!
"Blown fifth" pelog, von Hornbostel, type a.
7
!
156.000 cents
312.000 cents
468.000 cents
678.000 cents
834.000 cents
990.000 cents
2/1

And, as I noted in one of the other threads, you'll also get "pelogic" if
you carry out von Hornbostel's "type b" tuning to 14 steps.