Comma pumps as a second type of categorical perception, generalizing Rothenberg

On Fri, Apr 22, 2011 at 1:19 PM, Mike Battaglia <battaglia01@gmail.com> wrote:
>
> This would be tremendously useful to me as a type of Rosetta stone,
> enabling one to easily figure out how another temperament lays out in
> relation to chromatic hearing.

As a last note, I think what this demonstrates is an opportunity to
bridge between certain principles of Rothenberg and those of regular
temperament. One way of looking at Petr's comma pumps is that they
define and then violate a generalized type of categorical perception,
expanding on Rothenberg's stuff with melody.

Rothenberg is all about how we fit melodic patterns to learned scalar
structures; e.g. how you can transpose a melody and still have it be
recognizable. If you play a melody in an unfamiliar scale, such as
porcupine, you'll get a minor third where a major third should be, and
you end up violating your internalized map. Some retraining can teach
you to overcome this. However, Petr's work demonstrates a
generalization of this form of categorical perception, which is much
more embryonic: an internalized rank-2 logic for meantone temperament
in general. This breaks when you play a comma pump from a different
temperament than you're used to, where things just lay out
differently.

To be even more precise, one needs not to have the full negri[9]
melodic template internalized to understand that, in the negri pump
Petr posted, moving down by a bunch of diatonic semitones lands you a
5/4 below where you started. You only need to understand this small
chunk of negri logic to exploit it in a larger chord progression.
Likewise, you don't actually have to utilize all aspects of your
"diatonic" melody map to understand that the chord progression from
Hey Joe will land you back where you started - a single diatonic scale
doesn't even work over the whole progression.

I think that regular temperament can predict when this will happen by
finding inconsistencies between temperaments as suggested in my
previous post. So, what I'm proposing in my last post would be a good
way to see how porcupine "logic" matches up against meantone "logic"
in general, one aspect of which will be how porcupine[7] matches up
against meantone[7]. I think this would be extremely useful in
learning new systems, since who cares about sticking to one scale
anyway?

You can perhaps think of all of this as embryonic Rothenberg
mini-mappings that tell you how different intervals relate to one
another, and which can then unfold either in a larger Rothenberg
proper scale or within chord progressions in general. Working out the
differences in the logic above will tell you when your expectations
will get violated.

-Mike

Mike wrote:

>You can perhaps think of all of this as embryonic Rothenberg
>mini-mappings that tell you how different intervals relate to one
>another, and which can then unfold either in a larger Rothenberg
>proper scale or within chord progressions in general. Working out
>the differences in the logic above will tell you when your
>expectations will get violated.

On the Rothenberg angle, I suggest you need a realtime algorithm
that builds ROMs in response to music (MusicXML, say). It might
have an inventory of known ROMs, to which it tries to fit incoming
stimuli. When it encounters a contradiction, it switches to
building a new ROM instead. These should be the moments when
listeners' expectations are violated. Rothenberg sketched out how
a realtime algorithm might build a ROM upon listening, but there
are many details to fill in. An exceptional project for the
aspiring theorist.

But all that is for melody only. I would suggest that for chord
progressions like you're talking about here, recognition of
common dyads, recognition of specific harmonic identities and
intervals, overrides melodic considerations for most listeners
most of the time. The general paradigm would be the same, but
instead of a realtime ROM algorithm, you need a realtime
automatic JI algorithm.

You can imagine incoming notes shown on a lattice while the
music plays
http://www.musanim.com/mam/v19.htm
http://www.musanim.com/player/
Now the "contradictions" occur whenever a pitch class is assigned
to a new point on the lattice. When this occurs for a given music
input will depend on the particular automatic JI rules you choose.
But that's almost certainly true for different human listeners too.

Again, the system could be loaded with a learned temperament, so
that "contradiction" signals are only triggered when a pitch class
moves between lattice points related by a comma that is NOT in the
kernel of the learned temperament. And again, automatic JI
algorithms are fantastic projects for the aspiring theorist.
David L Code published the one he used for the Groven Piano
http://www.wmich.edu/mus-theo/groven/
in CMJ in 2005 or something. Make that 2002
http://muse.jhu.edu/journals/cmj/summary/v026/26.2code.html
But this has the additional feature of modeling categorical
perception.

-Carl

On Fri, Apr 22, 2011 at 8:06 PM, Carl Lumma <carl@lumma.org> wrote:
>
> On the Rothenberg angle, I suggest you need a realtime algorithm
> that builds ROMs in response to music (MusicXML, say).

What's a ROM??

-Mike

At 05:12 PM 4/22/2011, you wrote:
>>
>> On the Rothenberg angle, I suggest you need a realtime algorithm
>> that builds ROMs in response to music (MusicXML, say).
>
>What's a ROM??
>

Rank Order Matrix -C.