Four models for scale cognition

I've spent a lot of time thinking about scales in this past year. I'm
concerned here with a single bare-bones assumption for which to model
part of the perception of scales, and that's that intervals are easier
to distinguish from one another if they're farther apart.

As an example, 450 cents and 350 cents are easier to tell apart from
one another than 360 cents and 340 cents. And intervals like 351 cents
and 349 cents are almost impossible to tell apart at all and will
likely be confused with one another (or heard as the same interval). I
claim that scales that contain a lot of intervals which are very
similar in size contain more ambiguity and makes it more difficult to
figure out where in the scale you are.

The following are musical phenomena I believe are relevant to this phenomenon:

1) Tracking where you are in a scale, or which mode of the scale's
being played. If the minor thirds and major thirds in your scale are
only 10 cents apart, it's going to be much harder to figure out the
type of third you're playing, and what mode you're playing in general,
than if they're 100 cents apart.
2) Categories. Some people perceive them, and they're apparently based
around scales and not ratios. However they work, for an interval to
activate a category, you definitely need to have some sense of what
interval's being played. This gets harder as intervals get closer
together.
3) Understanding melodic fragments and arpeggiated chords, if you
believe that the ear doesn't inherently analyze these.

I'm going to post four different models that all model the same thing.
These models will give results that closely agree with one another,
showing that the same set of scales typically comes up again and again
at the "top," assuming you choose any decently sensible approach to
modeling this idea.

-Mike

this would imply that the chinese pentatonic is less ambiguous than the japanese one. i think the exact opposite is the case.
compare also the pythagorean major and the 5 limit one.

On 17/03/12 6:25 PM, Mike Battaglia wrote:
> I
> claim that scales that contain a lot of intervals which are very
> similar in size contain more ambiguity and makes it more difficult to
> figure out where in the scale you are.

--

/^_,',',',_ //^/Kraig Grady_^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere:
North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

a momentary antenna as i turn to water
this evaporates - an island once again

On Mon, Mar 19, 2012 at 2:26 AM, kraiggrady <kraiggrady@...>
wrote:
>
> this would imply that the chinese pentatonic is less ambiguous than the
> japanese one. i think the exact opposite is the case.
> compare also the  pythagorean major and the 5 limit one.

I'm not sure what the chinese or japanese pentatonics are.

In the 5-limit major scale, which is LmsLmLs, L and m are fairly close
in size, and can require more training to tell apart. 9/8 and 10/9 are
more "ambiguous" with one another than 9/8 and 16/15.

If you go to 15-EDO, for instance, it's easier to tell these apart.

If you play the pythagorean scale, it's impossible to tell them apart,
because they're the same size.

-Mike

C D E G A chinese like
A B C E F japanese like
I would say in general with all perception, the more differentiation one has the less ambiguous.
if you have a crowd with all the same face, this is very ambiguous and the more different faces the less so even if it might take training for people to adequately define how they are different.
the tuning out of commas is by definition deliberately ambiguous it seems otherwise an interval couldn't stand for two .

On 19/03/12 8:21 PM, Mike Battaglia wrote:
> On Mon, Mar 19, 2012 at 2:26 AM, kraiggrady<kraiggrady@...>
> wrote:
>> this would imply that the chinese pentatonic is less ambiguous than the
>> japanese one. i think the exact opposite is the case.
>> compare also the pythagorean major and the 5 limit one.
> I'm not sure what the chinese or japanese pentatonics are.
>
> In the 5-limit major scale, which is LmsLmLs, L and m are fairly close
> in size, and can require more training to tell apart. 9/8 and 10/9 are
> more "ambiguous" with one another than 9/8 and 16/15.
>
> If you go to 15-EDO, for instance, it's easier to tell these apart.
>
> If you play the pythagorean scale, it's impossible to tell them apart,
> because they're the same size.
>
> -Mike
>
>
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--

/^_,',',',_ //^/Kraig Grady_^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere:
North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

a momentary antenna as i turn to water
this evaporates - an island once again

OK, so sure. That doesn't seem to conflict with anything I'm modeling.

I'm dealing only with scales here, things like LLsLLLs, not with
commas and JI ratios though.

-Mike

On Mon, Mar 19, 2012 at 5:36 AM, kraiggrady <kraiggrady@...>
wrote:
>
> C D E G A chinese like
> A B C E F japanese like
> I would say in general with all perception, the more differentiation one
> has the less ambiguous.
> if you have a crowd with all the same face, this is very ambiguous and the
> more different faces the less so even if it might take training for people
> to adequately define how they are different.
> the tuning out of commas is by definition deliberately ambiguous it seems
> otherwise an interval couldn't stand for two .