so, what are seconds?

I guess this is just the nature of melody vs harmony,
but... seconds (major and minor) are the most common
melodic interval, yet most limit-based systems don't
get into seconds except as a side effect "well, theres
this note here, and this one over here, and melodies
mosy from one to another". This is referring to actual
attempts to map melodies to lattices and noticing that
it is non-intuitive.

Any thoughts? (Take your time, I won't see them till
after Thanksgiving. A happy one to all the celebrating
USians...)

Bob Valentine

Robert C Valentine wrote,

>I guess this is just the nature of melody vs harmony,
>but... seconds (major and minor) are the most common
>melodic interval, yet most limit-based systems don't
>get into seconds except as a side effect "well, theres
>this note here, and this one over here, and melodies
>mosy from one to another". This is referring to actual
>attempts to map melodies to lattices and noticing that
>it is non-intuitive.

You're absolutely right, it's "just the nature of melody vs harmony". To me
a scale must be analyzed in four ways. (1) its harmonic lattice
configuration, including any possible "bridges"; (2) its melodic structure,
putting the notes in order of pitch; (3) how the relations in (1) are
expressed as a function of the structure in (2); (4) whether all these
elements can conspire to create the conditions for a stable tonic and hence
tonality. In (2), I enjoy noting similarities in the arrangement of steps at
fourths or fifths. The most common scales in the world have 5 or 7 notes,
and usually have some similarity within a lower fourth and an upper fourth
in the octave (sometimes you find non-octave repeating scales with three or
more similar fourths or fifths in a row). My decatonic theories hinge on the
ability to increase the number of steps per octave from 5 or 7 to 10 while
preserving the important "diatonic" characteristics according to (1), (2),
(3), and (4).

P.S. Don't discount the importance of the whole range of sizes of "seconds"
in the world's melodies. Major and minor seconds are just the two we're most
familiar with.