an end to Confusing Structures

>>......C E F G B
>>2nds 4 1 2 4 1
>>3rds 5 3 6 5 5
>>4ths 7 7 7 9 6
>>5ths 11 8 11 10 8
>>6ths 12 12 12 12 12
>>
>>The interval 11 appears only twice in the scale, both times as a 5th. If
>>it appeared as a 5th and anything else, it would remove strict propriety.
>
>That's all fine, but still has nothing to do with modes. All 25 intervals in
>your table appear in all modes. Intervals are not always contructed up from
>the tonic!!!

As you point out, there is no point in considering "all the modes" if
you're not measuring up from their tonics! I've always called the columns
in the above chart modes, and I can't see myself stopping anytime soon. I
have even taken the trouble never to call a subset of a scale a mode, as is
often done.

>>"A list of integers representing the cardinalities of nested MOS's is a
>>Constant Structure of all scales that can support the entire nest. The
>>larger the numbers, and the more of them, the fewer the number of scales in
>>the Constant Structure (tho the number of scales is always infinite if you
>>assume infinite tuning precision)."
>
>Whoa, that's far out! Clearly not related to what we're arguing strict
>propriety may or may not be implied by, right?

Right. This was my stab at Lumma-CS, which we now know is not CS. It is a
concept I got from Erv, tho; I wonder if he has a name for it?

>The word from our favorite goat herder (hearder!) is that a Constant
>Structure is one where each interval occurs always subtended by the same
>number of steps. THAT IS ALL NO OTHER RESTRICTIONS this allows such scales
>as the enharmonic which rothenberg does not!

Bingo! John Chalmers had also confirmed this in a message sent to me off
the list last night. Here's the scale...

1/1 28/27 16/15 4/3 3/2 14/9 8/5

...probably Paul's example works too, when tuned in JI: CS does not require
any kind of propriety, even with the restriction that an interval appears
in more than one mode!

When I first made my statement to the contrary, I was reading from a chart
I posted here a while back...

>Every a has only one s.
>(g) strict propriety

..."a" stands for "acoustic interval", "s" for "scalar interval", and "g"
for "guaranteed by". The chart also had "r", for "requires", which does
not appear above. Just now I went to take strict propriety out of this
section of my chart, and found that it was correct all along- strict
propriety does guarantee CS!

-C.

Carl wrote,

>strict
>propriety does guarantee CS!

Yes it does. You just had it backwards before. OK, on to better things.