RE: [tuning] constant structure

>I was wondering if anyone could elaborate on the term "constant
>structure" for me. I don't seem to be quite getting it as it appears
>in J. Monaco's "Dictionary of Tuning Terms."

><http://www.ixpres.com/interval/dict/constant.htm>

>Perhaps just seeing it put another way would help.

That's J. Monzo (though he might like being called Mr. Monaco, I don't know
:)!

This term is an invention of Erv Wilson (the other definition, attributed to
Carl Lumma, was simply based on a misunderstanding of Wilson's writings).
The definition reads:

>A tuning system where each interval occurs always subtended by the same
number of steps. >(THAT IS ALL, NO OTHER RESTRICTIONS)

>[from Erv Wilson, via Kriag Grady, " Onlist Tuning Digest # 340, message 15

For example, if the scale contains more than one 5:4, the 5:4 is always
subtended by the same number of steps. In the case of a just or meantone
diatonic scale, that number would always be two (aka a "third").

All strictly proper scales are CS because if a given interval were subtended
by different numbers of steps at different points in the scale, specific
interval size could not be a strictly increasing function of generic step
size. However, not all CS scales are strictly proper or even proper.

Wilson (as far as I know) only used the term to refer to scales in JI and,
as I understand Kraig Grady's remarks, these scales tended to be conceived
of as MOS scales with certain commatic alterations to get more consonant
intervals (e.g., a chain of 3:2s would have one of the 3:2s diminished by a
comma to get a bunch of 6:5 and 5:4 thirds). Perhaps Wilson saw the constant
structures principle as a guiding restriction in the process of making these
alterations.

[Paul H. Erlich:]
>For example, if the scale contains more than one 5:4, the 5:4 is
always subtended by the same number of steps. In the case of a just or
meantone diatonic scale, that number would always be two (aka a
"third").

Right. I got that.

>All strictly proper scales are CS because if a given interval were
subtended by different numbers of steps at different points in the
scale, specific interval size could not be a strictly increasing
function of generic step size. However, not all CS scales are strictly
proper or even proper.

OK, let me see if I've got this... so say a scale like the 7-tone 3L &
4s, this would be strictly proper and a constant structure if it were
constructed from a chain of intervals > 2/7ths of an octave and <
3/10ths of an octave, and an improper scale -- but still a CS -- if it
were constructed from a chain of intervals > 3/10ths of an octave and
< 1/3rd of an octave, and a CS proper scale if it were constructed of
a chain of 360� intervals... is this correct?

> Wilson (as far as I know) only used the term to refer to scales in
JI and, as I understand Kraig Grady's remarks, these scales tended to
be conceived of as MOS scales with certain commatic alterations to get
more consonant intervals (e.g., a chain of 3:2s would have one of the
3:2s diminished by a comma to get a bunch of 6:5 and 5:4 thirds).

Hmm, then maybe what I wrote above isn't right?

Dan

Earlier I wrote,

> OK, let me see if I've got this... so say a scale like the 7-tone 3L
& 4s, this would be strictly proper and a constant structure if it
were constructed from a chain of intervals > 2/7ths of an octave and <
3/10ths of an octave, [etc.]

Just to make sure I'm clear, when I say "if it were constructed from a
chain of intervals" that is some condition, I mean a chain of
intervals of a single size that meets that condition.

Dan

Dan Stearns wrote,

>OK, let me see if I've got this... so say a scale like the 7-tone 3L &
>4s, this would be strictly proper and a constant structure if it were
>constructed from a chain of intervals > 2/7ths of an octave and <
>3/10ths of an octave, and an improper scale -- but still a CS -- if it
>were constructed from a chain of intervals > 3/10ths of an octave and
>< 1/3rd of an octave, and a CS proper scale if it were constructed of
>a chain of 360¢ intervals... is this correct?

I think so -- though Wilson tends to use the specific term "MOS" for a scale
where the generator is always the same size and the resulting scale has two
step sizes, and the more general term "CS" if at least one instance of the
generator is altered.