7:4 versus...

On Aug. 26 Kami Rousseau asked:
>>What is your opinion on sevenths? What is the difference between 16/9 and
9/5? (I you tell me that the difference is a comma, I will have to kill you.
What I want to know is when to use the two different intervals.)

I haven't dealt with 16/9, but I'm a great believer in 7/4, 7/5, 7/6, and
their consonant, or at least relatively consonant, nature.

I really enjoy contrasting the 9/5 and 7/4 in seventh chords (tetrads)
built on the same root. In 12-ET, these two intervals are represented by
the 10th chromatic pitch, and our ears bend the pitch to best fit the
harmonic context.

As proof of my previous sentence, and to silence any sceptics about the
importance of 7/4:

--create a pure 4:5:6:7 chord on your synth
--create a 4:5:6 triad, but add a 9/5 on top (9/5 * 4/4)
--create a 10:12:15:18 chord on the same root as each of the previous chords

After you are convinced thatchord #1 is smoother than chord #2, play
chord #1 and #3 one after another, and enjoy the perfectly consonant
harmonies with their thoroughly microtonal soprano line.

In ET contexts, 22 provides a good 7/4 (better than 19), and 27 and 31
are each progressively better yet.

Another ear-shock: 22 also has a very good 11/8. Try playing a
4:5:6:7:9:11 chord in 22, and you'll see what I mean. We all know that
in 12, we must omit the major third of this chord (5/4), but notice
how smooth this chord is with good 7/4 and 11/8 approximations!

--Harold

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I would think that it would be fairly easy to cut the tubes that valve tubes,
and easy to lengthen them (since you have a slide anyway).

I would imagine that you'd want to think about having a larger number of
valves as well. You might, for example, want to have separate second valves for
1/19 down and 2/19 down (second valve is half-step down, right? Sorry, I'm more
of a woodwinder).

Four methods of managing this sort of thing pop into mind:
1. A second second-finger valve next to the existing one (i.e., closer vs.
farther from the palm of the hand, not closer vs. farther from the other
valves). That's probably not a good idea from the perspective of changing
fingerings in that it would be very difficult to switch from one valve on
the same finger to the other.
2. Increasing the tuning differences of alternate fingerings (e.g., making
first and second play 4/19 down and third play 5/19), and not necessarily
increasing the number of valves.
3. Add a second set of left-hand valves for similar 1/19-separated pitch
relationships. Obviously this wouldn't work too great for the horn.
4. Give the valves two or more levels (e.g., press second valve down until you
bottom-out onto the relaxed setting of a second spring to go down 1/19, and
then depress that second spring down 2/19). Or if the springs can be made
light enough, it may be possible to make a valve that can be pulled up or
pushed down.


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