Yahoo Tuning Groups Ultimate Backup tuning Why e?

This is a belated post, so my apologies.

You've been wondering why in the world anybody would devise an equal
temperament scale based not on the 2/1 ratio we know as the octave but on
the constant e which is not only a non-integer but a non-rational number.
Well, here's my apologia.

First, equal temperament is about compromising the intonation of intervals
for the sake of the convenience of playing in any key, as well as not having
to discriminate between two kinds of major second and other intervals that
change according to major/minor environments. The fifth is not exact. The
thirds aren't exact. But the octave is. If the ET scale repeats itself
every multiple of 2, then the octaves are just. That doesn't apply to
non-traditional ET scales based on, say, the natural twelfth (3/1) or other
intervals.

And I thought that was kinda unfair. So to be egalitarian in regards to all
the intervals, I decided to compromise all intervals including octaves. Now
there is "pain" even in octaves. And I chose the natural logarithm base
because it's called "natural", and is a feature in natural processes. I
could've used pi, I guess, but I think that's been done already anyway.
(Circle of fifths?)

Also, maybe I'm warped, but I like a little "pain" in intonation. Just
intonation sounds sterile and flat to me. When notes are slightly detuned,
I hear more richness in tone, like a slight chorus effect that a rock
guitarist might use. I took a piano solo MIDI and applied the 52-NET scale,
skipping every third note in the scale, which approximates 12-tone ET very
reliably. With the octaves a little "off", the piano sound took on a new
characteristic. Then I applied what I call the "ugly tuning": 17-tone NET,
which results in a 12-tone ET where each chromatic step is 11 cents sharp --
cumulatively. Go up a few octaves and you're WAY out of tune. It sounded
like an old piano that hasn't been tuned in ages.

49-tone NET is a good substitute for 17-tone ET (skip every second note),
and 153-tone NET emulates 53-tone ET (again, skip every second note). If
you use only every fourth note in 127-tone NET, you get 22-tone ET, and if
you use every fifth note in 137-tone NET, you get 19-tone ET.

Finally, my rationale for using 2.7183 as a basis for equal temperament is
something of a cultural statement. Back when Western "civilization"
abandoned just intonation for equal temperament, music underwent a radical
change which many of the old school railed against. All the old perfect
intervals were gone (but hey, at least we had slain that "wolf fifth"!). So
my satirical response was to destroy the last perfect interval in modern
music -- the octave. I have consummated the revolution.

And I'm afraid I'm going to have to unsub from the group in order to save
time; I'm getting way too much e-mail as it is and can't even read a
fraction of what I get. I got so much going on in the "real world", but
I'll keep working on new ideas. When I come up with something grand -- or
at least something grandiostically eccentric -- I'll let y'all know.

So catch my six everybody....

Danny

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--- In tuning@y..., "Danny Wier" <dawier@y...> wrote:

/tuning/topicId_30711.html#30711

> And I'm afraid I'm going to have to unsub from the group in order
to save time; I'm getting way too much e-mail as it is and can't even
read a fraction of what I get. I got so much going on in the "real
world", but I'll keep working on new ideas. When I come up with
something grand -- or at least something grandiostically eccentric --
I'll let y'all know.
>
> So catch my six everybody....
>
> Danny
>

This is funny... or am I just getting "cynical.?" It looks rather as
though Danny unsubscribed just at the moment that he might be getting
some "feedback" on his proposal... :)

Why e?

🔗Danny Wier <dawier@yahoo.com>

🔗jpehrson@rcn.com

🔗Jon Szanto <JSZANTO@ADNC.COM>