re : locking in

> >
> > ...when you sing the most 'locked in' major second, is
> > it 9/8, 8/7 or 10/9 or is it something else?
>

> The difference between 9/8 and 8/7 is quite easy to hear. My impression is
> that in an 8/7 second the upper pitch seems to be the "root" and in the 9/8
> second the lower pitch seems to be the root.

>
> In regard to singing a major second over a pedal, it would seem a given that
> the ear would like to hear 9/8--the drone being heard as "root."
> >

This was the answer I expected. There is an ongoing sort of "philosophical
debate" regarding characters of intervals in a tuning system. [This should
be understood to be referring to fixed-pitch instruments/ensembles].

An "odd limit" system is one that expresses rational ratios up to a
certain "odd limit" in either the numerator or denominator. A differrent
viewpoint, held by some, is that prime numbers are the ones that add
"new information", and thus would think more in lines of a "prime limit"
system.

To someone who believed that 'locking in' would have something to do with
the lowest "odd limit", then 8/7 should have more 'gravity' than 9/8. For
someone believing in 'prime limit', then 9/8 would have more gravity than
10/9 (highest prime factor of 3 vs 5) and both more than 8/7 (prime limit
of 7).

However, for dyads, this small selection seem to be pointing to fitting
with the overtone series, where 9/8 expresses the lower note as the root.

Is feeling of locking stronger on 8/7 than 10/9? In 8/7, part of the
dyad will be an 'octave' of the difference tone, whereas neither the
10/9 has that strong of a relation...

> > ...the most natural 'tritone' (for want of a less
> > weighted term), is it 7/5, 11/8, 10/7 or something
> > else?
>
> The term "natural" may be a bit ambiguous here (see, Paul, I am listening),
> but it is quite easy to hear the difference between the 7/5 diminished fifth
> and the 10/7 augmented fourth. Today in my musicianship class I was tuning
> (locking) these randomly and asking my third semester students to identify
> them. They could readily do so by sensing whether the top pitch wanted to
> resolve upward (leading tone to tonic) or downward (chord seventh to third).
>
> The 11/8 "tritone" is not related to the other two, I feel. Its most

This is really interesting to me. I had a good instructor in my 'listenning
analysis' class at Berklee (Tom Plsek(sp), who also did a lot of 'modern
classical' trombone performances). One excercise was him playing a C on the
piano and having us sing an F#. We were all guitar 'flat' relative to the
piano, though our F# was much more pleasing.

I also wrote a song with the same trick. The song was in C major, triadic,
and the bridge ended on an F# major chord with a C in the melody which was
to be held over into the verse, which started again with a C major.
There was a compromise I had to reach in singing the C, wanting to flatten
it to sound good on the F#, but not wanting to have audible retuning when
the C chord sounded.

In both cases, I THOUGHT I was 'locking' on the 11/8 (not the term I used
but thats the feeling). Now I realize that I was probably NOT that far
South! I'll have to go back and see just what that tritone I was singing...

Others mentioned the 45/32, and I think that is probably a strong
candidate.

Ooops, snipped your comments about 11/8. I do believe that this is used
melodically. Before you joined the list we had some discussions with John
Link regarding altered dominant chords or thier logical inverse,
the "lydian dominant" sound 7 9 #11 13. In my experiments I was not
convinced that this was properly tuned in the "lower overtone"
manner, (7:9:11:13) but felt that the "upper structure triad" needed to
be expressed, which would make it more

7/4 9/8 45/32 27/16.

I was somewhat convinced in these discussions that some of the big
jazz chords I like are really coming more from the tempered world than
some other.

> > The idea here is that people who believe in greater
> > importance for "prime limits", "odd limits" and
> > "overtone series significance" would probably see some
> > different sorting.
>
> You left me here, Bob. I'd love to know what these phrases mean in layman's
> English, particularly the first two. Also, how are you using the word
> "sorting."
>

I hope I made it a little more clear what I was looking for. I'm wondering
how deep the pockets are and sorting the intervals according to the depth
of the pocket they fall into when they lock. I'm trying to take that idea
and relate it (somehow) to some of the other discussions we've had regarding
tuning systems. Probably in a very confused manner, luckilly, I'll be
straightened out in no time.

thanks for answerring.

Bob Valentine

> Jerry
>

Robert C Valentine,

>To someone who believed that 'locking in' would have something to do with
>the lowest "odd limit", then 8/7 should have more 'gravity' than 9/8. For
>someone believing in 'prime limit', then 9/8 would have more gravity than
>10/9 (highest prime factor of 3 vs 5) and both more than 8/7 (prime limit
>of 7).

>However, for dyads, this small selection seem to be pointing to fitting
>with the overtone series, where 9/8 expresses the lower note as the root.

Absolutely. It has nothing to do with prime limit.

>Is feeling of locking stronger on 8/7 than 10/9? In 8/7, part of the
>dyad will be an 'octave' of the difference tone, whereas neither the
>10/9 has that strong of a relation...

Gerald noted the former, and I'd say 8/7 does lock a little more strongly
than 9/8, but in a less stable way (if that makes any sense). 10/9 is a
little weaker than either, and the lack of a note equivalent to the
fundamental doesn't help.

>I hope I made it a little more clear what I was looking for. I'm wondering
>how deep the pockets are and sorting the intervals according to the depth
>of the pocket they fall into when they lock. I'm trying to take that idea
>and relate it (somehow) to some of the other discussions we've had
regarding
>tuning systems. Probably in a very confused manner, luckilly, I'll be
>straightened out in no time.

I think the "depth of the pockets" is related to three factors: virtual
fundamental finding (which is a combination of both rootedness and harmonic
entropy); beating/roughness minimization (see Sethares); and combination
tones. These factors interact with one another and are highly dependent on
timbre and amplitude and I don't think a full mathematical model is in our
grasp at the moment. Best to look at the pieces individually for now.