General musings for those creating scales IE why certain scales sound good...

Note this is a summary of things said before on this list. If you
think this list is "because I haven't listened", on the contrary, it
is gathered from the fact that I have.
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Here are some things I have gathered from this list that appear
crucial to making good scales:

1. Periodicity IE beating is OK so long as it happens at relatively
the same rate between multiple different frequencies (as it does in
the harmonic series).

2. Critical Band: consonance so far as not having two notes (or their
overtone) too close together is an issue, even the harmonic series
around the 20th+ overtone begins to beat too much (even though it beat
periodically) to be tolerable.
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I think it is fair to say BOTH critical band and periodicity need
to be watched...ideally both and not just one or the other need to
work. You can, apparently, make a scale where notes and overtone are
so far apart that periodicity is not an issue, but then it seems you
are talking about things like 4-note chords and not "full" scales.
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3. Just because a scale sounds consonant when you compare any two
notes (dyad)...means a decent % of, but not all the chords formed by
it will be consonant...this is why Sethares' theory is useful but not
by any means perfect.

4. Tunings often sound dissonant (IE all notes in 12TET played "at
once" sound dissonant) while subsets of them (IE 7-note scales built
to approximate JI) sound consonant. IE it is VERY important to
understand the difference between a tuning and a scale. A tuning,
played in free-form, can sound like crap while a scale under it can
sound absolutely fantastic (and ideally, be transpose-able under a
tuning).

5. Not everything HAS to be JI (or something like mean-tone or 12TET,
which approximates JI) to sound good.
Lucy-tuning, Sethares's timbre/scale matching for things like
10TET, MOS scales, tetrad-based scales like 9/8 * 10/9 * 11/12 * 10/9
* 11/10 * 12/11...also sound good. One thing that seems to show
particular promise is spliting the ratios 1 to 1.5 into one JI scale
and 1.5-2 into another JI scale (like the scale I demonstrated above).
IMVHO, taking well-chosen 7-note subsets of the "golden ratio tuning"
can also provide consonant scale.

6. 12TET has some issues. Like 3rds and 6ths off by 10+ cents and
many complex chords that can not be inverted without causing a lot of
dissonance. JI makes some intervals more pure at the expense of
others...only adaptive JI keeps "everything" pure all the time.
Even, for example, simply looking through Carl's 12-tone tuning
section...there are a lot of things around that sound better than
12TET as tunings and I encourage people to make more instead of
"settling" for 12TET.

In my mind...an ideal tuning would have virtually all intervals be
"fairly close to consonant", rather than some almost perfectly close
and others horrendously off (again, thinking of things like the 3rd in
12TET).

7. Repeating proportions seem important; be it the circle of 5ths,
the JI series itself, Equal temperament, repeating difference between
notes in periodicity, rational numbers, repeating interval gaps in
MOS...just something the brain can summarize into a single "function"
easily.
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So, In general I think it's fair to say there is ONE GOLDEN RULE
that dominates what makes a scale under a tuning sound good...and,
rather, it is a combination of factors, such as periodicity, critical
band compliance, and repeating proportions (not just between root
notes but also overtones).

The best scales, IMVHO, are not ones that nail ones single factor
perfectly, but achieve a balance between them all.

--So, In general I think it's fair to say there is ONE GOLDEN RULE
Typo, I meant to say there is NO one golden rule

maybe the golden rule is if it sounds good.

On Wed, Feb 4, 2009 at 12:44 PM, djtrancendance <djtrancendance@...>wrote:

> --So, In general I think it's fair to say there is ONE GOLDEN RULE
> Typo, I meant to say there is NO one golden rule
>
>
>