Re: [tuning] Rothenberg question

Jason!
I am not going to answer your question at all but in the context of the material you are
looking at you might be interested In Walter O'Connell's All interval sets. These are sets of
four tones that each contain all 12 intervals ( by inversion). These are C D F Gb, C Db E F#,
C Db Eb G, C E F# G. These would be of use if you were looking for efficient material. A form
of defining scales you might find interesting is Moments of Symmetry .
http://www.anaphoria.com/mos.html

Jason_Yust wrote:

> I'm using David Rothenberg's pitch perception calculus in a thesis I'm
> working on and am having a little difficulty with exactly what property of
> scales the efficiency quantity is meant to capture. Since some of you seem
> to be pretty familiar with the system, I thought you might have an answer
> to this question. He introduces the idea of efficiency by saying that an
> efficient musical language is one which can form the greatest number of
> distinct words (ordered sequences of tones) given the number of notes in
> the scale. The way I interpret this comment is that, for instance, two
> augmented triads, C E G# and D F# A# (both 444), are not distinct words.
> The calculation succeeds at what it is clearly meant to do: distinguish
> asymmetrical proper scales with high stability such as the diatonic scale,
> from symmetrical scales with higher efficiency (although much less common
> in practice) such as the whole tone and octatonic scales. However, it
> gives the highest efficiency rating to scales which seem intuitively closer
> to symmetrical scales, such as C E F# G# A#. This scale contains
> indistinct 4 note subsets E F# G# c and G# A# c E (2244), indistinct 3 note
> subsets C E A#, E F# A# and F# G# c (246), subsets E F# c, G# A# e, and A#
> c f#, (264) and so on. But it is because of this property of the scale
> that it recieves a high efficiency rating (it always takes 5 notes to
> distinguish the scale from one of its transpositions), relative to the
> anhemitonic pentonic, which contains more distinct 2, 3 and 4 note subsets.
> I must be interpreting "distinct words" incorrectly, in which case the
> question becomes, how should we think of the distinctness of pitch
> sequences as Rothenberg defines it, and what is the value of that way of
> looking at it?
>
> jason
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com