improved definitions?

I could use some improvements to the definitions
for the following terms:

- roughness
- critical band
- MOS (isn't even in there yet)
- tonalness
- matrix
- determinant

Joseph L. Monzo....................monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html

|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |

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JOE!
This is the best I can do for now!

MOS- A term coined by Erv Wilson in 1975. The process of producing a
scale of melodic integrity by the superposition of a single interval
(generator). Those points where there is only 2 different size intervals
are called MOMENTS OF SYMMETRY. This cycle has the property that any
occurrence of an interval will always be subtended by the same number of
steps. When a harmonic system is used instead of a single interval and
all the melodic gaps are filled the scale is referred to as a CONSTANT
STRUCTURE. It is also been found fruitful to utilized the Moments of
Symmetry within a preexisting Moment of Symmetry.

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

Joe Monzo wrote,

>I could use some improvements to the definitions
>for the following terms:

>- roughness
>- critical band
>- MOS (isn't even in there yet)
>- tonalness
>- matrix
>- determinant

roughness

A quantity measuring the sonance of a tone, interval, or chord, based the
critical band interactions of proximate partials. This conception of sonance
is associated with the harmonic theories in the tradition of Helmholtz, and
finds a modern advocate in Sethares.

partial

One of the pure tones that makes up a complex tone.

complex tone

A sound produced by a musical instrument that evokes the sensation of a
single pitch. It is composed of pure tones whose frequencies are taken from
an exact (as in sustained instrument) or slightly altered (as in the piano)
harmonic series over the perceived pitch.

(I noticed that harmonic series has an entry but is not listed)

critical band

A range of frequency-ratios which is less than a minor third across much of
the audible spectrum, but considerably wider in the lower registers. If the
interval between two pure tones is greater than a critical band, there will
be no roughness in the sensation; as the interval is further decreased the
roughness will at first increase, then the notes will sound like they are
fusing into one rough sound; then the sensation will be of one tone of
varying amplitute (beating); then the roughness will decrease as the rate of
beating decreases, slowing down to zero as the interval approaches unison.

tonalness

A quantity measuring the sonance of an interval or chord, based on the
degree to which the notes approximate a harmonic series over a single
fundamental and thereby blend into a single sensation. The perceived pitch
of that single sensation corresponds to the root of the chord. This
conception of sonance is associated with the harmonic theories in the
tradition of Rameau, and finds a modern advocate in Parncutt.

matrix: the representation of ratios in terms of the exponents of the prime
factors is really a vector, not a matrix; vector addition is what you mean
instead of matrix addition. A matrix is not a mathematical model so much as
a mathematical construct, a generalization of the concept of number. Also,
only prime factors, not odd factors, should be used in calculations with
matrices; I noticed the same problem with the "unison vector" definition.
Another problem in the latter: the 225/224 is not a septimal schisma (which
is 33554432/33480783) but I think it's a kleisma.

determinant

A calculation made on a matrix. When the matrix is square and the rows
represent independent unison vectors, the determinant indicates the number
of pitches contained within the corresponding periodicity block. This was
documented by Fokker.

Interestingly, the same numbers which delimit ETs with good rational
implication often also specify the number of pitch-classes in
just-intonation systems which incorporate bridging to delineate the finity
of the system.