7HS Tuning Comments

I suggested that a friend at work, Bill Meadows, who does a lot of multimedia
try out tuning in 7-tone-per-octave octave-repeating harmonic-series-based
tuning. The ratios within each octave for this tuning are 7:7, 8:7, 9:7, 10:7,
11:7, 12:7, 13:7, and 14:7, obvious 7:7 being the unison and 14:7 being the
octave.

This is a tuning I've played with before, and I thought that Bill would very
good at using it in the way that I concluded would be best, after I used it in a
way I concluded to be less than ideal.

Bill tuned it up on his Kurzweil K2500 last night and found it rather
intimidating. He likes to use the phrase "out of tune" because he knows that
that's inadequate to characterize a tuning except at a very high level.

Anyway, here are some suggestions I made to him that perhaps some of you
might want to consider playing with as well:

-------------------------------------------------------------------------------

Yesterday afternoon I wanted to expound further on how to use that 7-step
octave-repeating harmonic-series-based tuning. You said that you weren't sure
how to use it, noting semijokingly that it sounded "pretty out-of-tune".

My responses to that are:
1. Hey, no pain no gain!
2. Is that really any more disconcerting than the microtonal scale-step size
phenomenon you like to tantalyze your audience with? I'm refering to how
you described 19 to Dave E. and me ... oh, probably 9 months back:
Tantalyzingly delaying an expected melodic resolution by approaching it in
small microtonal steps. Is the out-of-tune nature of this tuning really
all that much more disconcerting? And whether it is or not, is that a
problem?
3. One thing you're really good at, and I'm not (yet) is music involving
long, sustained tones with faster stuff, often repeated figures, dancing
on top of the sustained chords. This tuning, I suspect, is well-suited to
that sort of thing:
a. You can build large chords will little chance of a clash in the minor-
second/major seventh sense of the word, because the pitch relationships
are very simple.
b. There exists a semi-standard mixing engineer/artist's analogy of the
sounds they mix to a three-dimensional space: left/right stereo gives
you the left-right dimension with high- vs. low-pitch suggests top-
bottom and quiet- vs. loud-volume suggests far and close. Combine
that with the fact that each tone of the octave has a distinct color to
it, and then play a musical, 3D version of ... Pollock was it? - the
fellow who first painted with squirt-guns).
4. What it's probably not good for is what I used it for on that tape I gave
you early on, with the last three movements of a Symphonietta in that
tuning. In that case I tried to build classical structures - traditional
instrumentation, forms, melodies - with nontraditional harmony. Well, I
concluded that what I did in that regard went reasonably well, but that
that style is not what this tuning is built for.
5. Since when have you been concerned with audiences thinking your music
weird?!


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I have created a list of equal temperaments up to about 650 tones
per octave with their consistency limits as was explained by Paul
Erlich's post of 13 June 1996. However it's not restricted to
integer divisions, all scale step sizes that give a different
consistency limit were calculated. Initially I thought this could
make a nice graph, step size horizontally, limit vertically,
but the function behaves very wildly and there are very many points.
Not included in the file are points where both left and right side
limits are smaller than 5.
This is the filename:
ftp://ella.mills.edu/ccm/tuning/papers/consist_limits.txt

Another larger file
ftp://ella.mills.edu/ccm/tuning/papers/cons_limit_bounds.txt

contains the step size bounds for each consistency limit of 3 to 18,
also up to 650-tET.


The first list looks like this:

Limit at right side (larger step)
Step size in cents
Number of tones per octave
Limit at left side (smaller step)
Uniqueness limits for this temperament

4 589.572 2.03537 5 3 2
5 543.415 2.20825 2 3 2
2 422.656 2.83918 5 4 4
5 413.594 2.90139 6 4 4
6 387.530 3.09653 7 4 4
7 371.508 3.23007 4 4 4
3 320.000 3.75000 7 3 2
7 308.735 3.88682 8 3 2
8 295.424 4.06195 5 3 2
5 293.296 4.09142 4 3 2
4 242.288 4.95278 9 4 4
9 241.594 4.96699 10 4 4
10 233.004 5.15010 6 4 4
6 229.774 5.22251 5 4 4
5 228.571 5.25000 3 4 4
2 200.205 5.99383 5 4 4
5 200.126 5.99622 8 4 4
8 199.770 6.00691 7 4 4
7 199.218 6.02355 3 4 4
3 177.777 6.75000 5 5 4
5 177.254 6.76992 6 5 4
6 168.867 7.10616 4 5 4
4 150.611 7.96752 6 4 4
6 149.050 8.05098 7 4 4
7 145.454 8.25000 3 4 4
4 135.917 8.82887 7 6 6
7 135.843 8.83369 8 6 6
8 132.110 9.08328 6 6 6
6 131.998 9.09104 5 6 6
5 131.169 9.14848 2 6 6
2 122.706 9.77941 5 5 4
5 121.645 9.86475 8 5 4
8 119.717 10.0236 9 5 4
9 118.566 10.1209 4 5 4
3 110.676 10.8423 6 5 4
6 110.375 10.8719 4 5 4
4 101.320 11.8436 6 6 6
6 100.562 11.9329 10 6 6
10 99.2594 12.0895 11 6 6

The second list runs like this:

3 2400.00 0.50000 - 1403.91 0.85475
3 1267.97 0.94639 - 800.000 1.50000
3 760.782 1.57732 - 543.415 2.20825
3 480.000 2.50000 - 467.970 2.56426
3 422.656 2.83918 - 345.810 3.47011
3 342.857 3.50000 - 292.608 4.10104
etc.

Manuel Op de Coul coul@ezh.nl

------------------------------

Topic No. 7

Date: Thu, 11 Jul 96 09:58 EST
From: PAULE
To: tuning
Subject: RE: Another post from McLaren
Message-ID: <73960711145837/0005695065PK2EM@MCIMAIL.COM>


>As I've pointed out in prior posts, the strict
>extreme hard-line Pythagorean viewpoint
>fails when it encounters reality, since
>the 3:5:7 triad demonstrably sounds less
>consonant than the 4:5:6 triad--yet the
>integers of the 3:5:7 triad are obviously
>smaller.

Why are so many things obvious to Brian that are not obvious to the rest of
us?