Pitch reference in Scala

Hi tuners,

Recently I calculated the frequencies for a standard quarter comma
meantone scale with Scala. Scala shows 437.3989 Hz for the tone A. I
expected it to give 440 Hz. Until now, I thought that A was always
440 Hz nowadays, independent of the tuning. But since my Scala
experiment I am not sure about that.

Part of params.par looks like:

[-------------------------------------
! Default frequency of middle C in Hz:
261.625565301
-------------------------------------]

so, according to Scala, it is middle C that always has the same
frequency. And A is only equal to 440 Hz in 12 EDO.

I find this very strange. Does anyone know whether this is right ?

I used the following coomands to calculate the frequencies:

[-------------------------------------
calculate 3/2-$k^1/4
pythagorean
12
2/1
7
$0
3
show /frequency
-------------------------------------]

I use Scala version 1.41 for DOS. Maybe that's an old one ?

Bart Pauwels

Beste Bart,

This is indeed how it's intended to be. The pitch
reference is tied to scale degree 0 or 1/1. When your
A is scale degree 9, it will indeed vary with the
scale. This can't be changed, because Scala was not
built for 12-tone scales only.
However, you can set your A to be scale degree 0
and see the right frequencies for concert pitch by
doing

set freq 440.0
key 9
show/freq

This doesn't apply to tuning a synthesizer or retuning
a MIDI file, they use the frequency setting of the
keyboard mapping.
But 440 Hz. is not really a universal standard. Some
orchestras use 442 Hz, and other baroque ensembles a
lower pitch.

>I use Scala version 1.41 for DOS. Maybe that's an old one ?

Yes, quite. I recommend you get a newer version, for Windows
there are 2.05 (graphic) and 1.8 (console).

Manuel

I don't doubt that Scala can be configured to do anything you want.
The question remains whether A or C should be taken as reference
pitch for alternate tunings. When a contemporary organ builder has to
build an organ in 1/4 comma meantone, and the customer wants standard
pitch, does it have to be A=440 or 437.3989 Hz ?
Even if the 440 Hz standard is not always used by anyone, the
necessity for a standard remains.
Maybe the people who raised A=440 Hz to a standard didn't think about
alternate tunings at all. I suppose the standard was established
sometime in the first half of the 20th century. And I suppose that
were bad times for anything else but 12EDO ?

Bart Pauwels

--- In tuning@y..., manuel.op.de.coul@e... wrote:
> Beste Bart,
>
> This is indeed how it's intended to be. The pitch
> reference is tied to scale degree 0 or 1/1. When your
> A is scale degree 9, it will indeed vary with the
> scale. This can't be changed, because Scala was not
> built for 12-tone scales only.
> However, you can set your A to be scale degree 0
> and see the right frequencies for concert pitch by
> doing
>
> set freq 440.0
> key 9
> show/freq
>
> This doesn't apply to tuning a synthesizer or retuning
> a MIDI file, they use the frequency setting of the
> keyboard mapping.
> But 440 Hz. is not really a universal standard. Some
> orchestras use 442 Hz, and other baroque ensembles a
> lower pitch.
>
> >I use Scala version 1.41 for DOS. Maybe that's an old one ?
>
> Yes, quite. I recommend you get a newer version, for Windows
> there are 2.05 (graphic) and 1.8 (console).
>
> Manuel

--- In tuning@y..., "bps1572ya" <bps1572@m...> wrote:

/tuning/topicId_36454.html#36535

> I don't doubt that Scala can be configured to do anything you want.
> The question remains whether A or C should be taken as reference
> pitch for alternate tunings.

*** I believe this question is somewhat open. Several years ago,
when I was "studying" piano tuning, there were two "competing"
systems, a German "A" method and a Smith "C" method. I believe they
both ended up with A-440, but the beginning "reference note" was
obviously different in the different systems... And that was just
for 12-tET systems.

J. Pehrson