Re: mistuning of octave considered good

> Subject: What *is* an "Octave"?
>
> > I'm very behind reading the TL. Scala uses the
> > Blackwood/Rapoport/Regener limits. The lower bound is
> > 2^4/7 = 685.71 cents and the upper bound 2^3/5 = 720 cents.
> > Outside this range, a 12-tone Pythagorean scale becomes
> > nonmonotonic, i.e. some pitch classes will get higher tones
> > than their successors.
> >
> > Manuel
>
> Manuel and other scholars,
>
> In a private dialog with another list member, the very fascinating
> question came up about: "What exactly is an octave?". In other words,
> how do we define the boundaries of the octave (if we dare)?

In the hacked psuedo harmonic entropy calculation I'm using in my scale
'tool', I've tuned the 'bucket' where 3/2 falls into to the
Blackwood/Rapoport/Regener limits. This results in a bucket for the
2/1 something in the region of 1200+-30c.

Paul said :

> According to my harmonic entropy model (with "typical" resolution of
> 1% assumed), any interval in the range
>
> 667.1_ to 736.7_
>
> is more likely to be heard as a 3:2 ratio than to be heard as any
> other ratio.
>
> Similarly, any interval in the range
>
> 1158.0_ to 1242.0_
>
> is more likely to be heard as a 2:1 ratio than to be heard as any
> other ratio.
>

Basically, I gave my tool sharper ears than 'typical resolution'.

Bob Valentine

Robert C Valentine wrote:

> > Subject: What *is* an "Octave"?
> >
> Paul said :
>
> > According to my harmonic entropy model (with "typical" resolution of
> > 1% assumed), any interval in the range
> >
> > 667.1_ to 736.7_
> >
> > is more likely to be heard as a 3:2 ratio than to be heard as any
> > other ratio.
> >
> > Similarly, any interval in the range
> >
> > 1158.0_ to 1242.0_
> >
> > is more likely to be heard as a 2:1 ratio than to be heard as any
> > other ratio.
> >

I've been thinking about this a lot lately. As I stated in my earlier post the octaves in Uganda
are purposely out, just as they are in Bali. I'm staring at Danielou's Universal Scale
approximated in 72-tET and a little surprised to see so many versions clustered around 1/1 and
3/2. On my keyboards 1/1 would have a +17� version at 81/80; -17� at 160/81; -33� @ 125/64; -50�
@ 31/16 and a -67� version at 48/25.

Then 3/2 has a -17� version at 40/27; -33� @ 25/18; and -50� @ 62/45.

A tentative analysis of Barbara Lewis' "Hello Stranger"shows the backup singers coming in flat to
the organ. But with Danielou's scale hitting me over the head there is a way to think of these
octaves as higher harmonies.

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

> In the hacked psuedo harmonic entropy calculation I'm using in my scale
> 'tool', I've tuned the 'bucket' where 3/2 falls into to the
> Blackwood/Rapoport/Regener limits. This results in a bucket for the
> 2/1 something in the region of 1200+-30c.
>
> Paul said :
>
> > According to my harmonic entropy model (with "typical" resolution of
> > 1% assumed), any interval in the range
> >
> > 667.1_ to 736.7_
> >
> > is more likely to be heard as a 3:2 ratio than to be heard as any
> > other ratio.
> >
> > Similarly, any interval in the range
> >
> > 1158.0_ to 1242.0_
> >
> > is more likely to be heard as a 2:1 ratio than to be heard as any
> > other ratio.
> >
>
> Basically, I gave my tool sharper ears than 'typical resolution'.

Not necessarily! The range I gave doesn't correspond to the "width
of the bucket" -- would that be the distance between the two
nearest local maxima?