Topic: Beep-9 and Pelog

3 scales

Thread (3 messages)

From: Herman Miller (2004-01-10)
Subject: 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).

-- 
see my music page --->   ---<http://www.io.com/~hmiller/music/index.html>--
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@io.com  email password: thing till they were sure it would offend no body,
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From: wallyesterpaulrus (2004-01-12)
Subject: Re: Beep-9 and Pelog

--- In [email protected], 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".

From: Herman Miller (2004-01-12)
Subject: Re: [tuning] Re: Beep-9 and Pelog

On Mon, 12 Jan 2004 00:59:01 -0000, "wallyesterpaulrus"
<[email protected]> 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.

-- 
see my music page --->   ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller)   "If all Printers were determin'd not to print any
@io.com  email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" /  there would be very little printed." -Ben Franklin