TromboneChat

First, some links for reference:

http://www.tonalsoft.com/enc/h/harmonic-entropy.aspx

https://en.xen.wiki/w/Harmonic_entropy

From the Tonalsoft source, harmonic entropy "asks the question, 'how confused is my brain when it hears an interval?'", which I think is a pretty good definition.

I brought this up briefly in TTF back in its day but realized that this idea hasn't been discussed here on TromboneChat. Why bother? I think it is a potentially useful tool relevant to understanding playing in tune, even for more than dyads, which is its original context. Anyone who has practiced playing scales with drones (or even better, played with a good strobe tuner) knows how a pitch "slots" in as you get closer and closer to an "in-tune" interval, and how each interval can have it own kind of harmonic "color". Harmonic entropy is a way to translate that perception into a common framework.

Hmmmm, I'm not sure about how to get an image to embed properly. But looking at one of the graphs in the Tonalsoft article, observe the fractions underneath the "low peaks". 3/1 is an octave and a fifth; 2/1 is an octave; 3/2 is a perfect fifth. Basically, that notation follows what we would expect for the overtone series. I think it's instructive to look at 5/4, 9/7, and 4/3, which are (respectively) a major third, another major third, and a perfect fourth. Playing with a drone, if you slowly slide-gliss between 5/4 and 4/3, I think it becomes pretty obvious that the 9/7 major third "slots" in that region that should be "in-between" our two more familiar intervals, although not quite as strongly. FYI 9/7 will be the "third" that you can find via the interval between the dominant 7th and the major 9th of a dominant 9 chord.

<Edit: Added Image -- BG>

Interesting.

I read somewhere that when really skilled musicians are told to tune an interval better, they'll switch to a different one of those three. Wish I could find that reference.

Not all of us play a tone steady enough to stay on one though.