What is the correct name for this kind of scale generation?

Dear Tuning Terminology Pundits,

What do you generally call a scale which has any
number of tones and is created using 2 generators,
one of which is 2/1 and the other of which is an
interval of any arbitrary size?

Thanks,
Aaron Hunt
H-Pi Instruments

Aaron Andrew Hunt wrote:
> Dear Tuning Terminology Pundits,
> > What do you generally call a scale which has any > number of tones and is created using 2 generators, > one of which is 2/1 and the other of which is an > interval of any arbitrary size?

"Generated scale." To be precise, "generated scale with an octave period".

Graham

Hi Aaron,

It would still be a scale (you say so yourself).
But it may be an instance of a *linear temperament*.
Provided there is an (implicit or explicit) mapping.

When one of the two generators is not required to
be 2/1, then you have a *rank 2 temperament* (all
linear temperaments are rank 2 temperaments).

Hope that's useful,

-Carl

--- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@...> wrote:
>
> Dear Tuning Terminology Pundits,
>
> What do you generally call a scale which has any
> number of tones and is created using 2 generators,
> one of which is 2/1 and the other of which is an
> interval of any arbitrary size?
>
> Thanks,
> Aaron Hunt
> H-Pi Instruments

Graham's answer is more precise, since it tells you what
to call it if there isn't a mapping.
Though we do say the diatonic scale is an instance of the
meantone linear temperament, despite there is no official
body making the mapping explicit. In fact, 12-ET also
supports the schismatic mapping (-8 instead of +4), as
Erv Wilson points out in his famous paper ('On Extended
Linear Mapping'...).

Also, my "instance of" isn't 100% accurate. "Scale that
supports" or "scale generated from" may be better.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Aaron,
>
> It would still be a scale (you say so yourself).
> But it may be an instance of a *linear temperament*.
> Provided there is an (implicit or explicit) mapping.
>
> When one of the two generators is not required to
> be 2/1, then you have a *rank 2 temperament* (all
> linear temperaments are rank 2 temperaments).
>
> Hope that's useful,
>
> -Carl
>
> --- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@> wrote:
> >
> > Dear Tuning Terminology Pundits,
> >
> > What do you generally call a scale which has any
> > number of tones and is created using 2 generators,
> > one of which is 2/1 and the other of which is an
> > interval of any arbitrary size?
> >
> > Thanks,
> > Aaron Hunt
> > H-Pi Instruments
>

Graham and Carl,

Thanks for the answers. I had been calling such a thing
a Linear Temperament, but I had misgivings about this
that I could quite put my finger on. Carl put it succinctly
pointing to the mapping. I was bothered by the name
Temperament when the resulting scale did not have
clear connections to 5-limit harmony. So, I'm going to go
with Graham's terminology of Generated Scale.

I asked this question because the next H-Pi software
updates are going to include user programmable tuning
functions and algorithms, and I have programmed default
functions and algorithms dealing with (among other things)
what I will now refer to as Generated Scales.

Yours,
Aaron Hunt
H-Pi Instruments

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Graham's answer is more precise, since it tells you what
> to call it if there isn't a mapping.
> Though we do say the diatonic scale is an instance of the
> meantone linear temperament, despite there is no official
> body making the mapping explicit. In fact, 12-ET also
> supports the schismatic mapping (-8 instead of +4), as
> Erv Wilson points out in his famous paper ('On Extended
> Linear Mapping'...).
>
> Also, my "instance of" isn't 100% accurate. "Scale that
> supports" or "scale generated from" may be better.
>
> -Carl
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > Hi Aaron,
> >
> > It would still be a scale (you say so yourself).
> > But it may be an instance of a *linear temperament*.
> > Provided there is an (implicit or explicit) mapping.
> >
> > When one of the two generators is not required to
> > be 2/1, then you have a *rank 2 temperament* (all
> > linear temperaments are rank 2 temperaments).
> >
> > Hope that's useful,
> >
> > -Carl
> >
> > --- In tuning@yahoogroups.com, "Aaron Andrew Hunt" <aahunt@> wrote:
> > >
> > > Dear Tuning Terminology Pundits,
> > >
> > > What do you generally call a scale which has any
> > > number of tones and is created using 2 generators,
> > > one of which is 2/1 and the other of which is an
> > > interval of any arbitrary size?
> > >
> > > Thanks,
> > > Aaron Hunt
> > > H-Pi Instruments
> >
>