Full gallery here
Okay folks, this week the pictures are more colourful, and we can see all of pianospace. The left side is A_0, the bottom of a typical piano, and the right goes past the piano’s range and on to the upper limit of human hearing. Now that the overtone bands are properly smearing out, I should point out that they decrease in volume the higher up they are from the root. So to be totally accurate, we might need to lower the brightness toward the right, but the images are easier to read this way, and anyway, the particular way that a given series fades out depends on the timbre of the instrument producing it.
For these 3-note images, the top half shows all the harmonics while the bottom half shows just the parts that overlap with one another. Here’s another:
If you want to take a really good look you’ll have to open the image in a new tab. Now, musicians sometimes say that chords built from notes lower down get “muddy.” We’re seeing that just a little bit already, but let’s take a look at lower versions of C major.
Woah! Now the notes are clearly interfering with one another.
It’s a rainbow! Down here the notes are so “muddy” they completely smear together.
I said previously that I wanted to look at 4-note chord. I did find a way to do that.
These pictures are more complicated. Root note’s series is shown in white at the top, the other three notes are given in R, G, and B in the bottom-middle quarter and you can see them mixing there. In between are their overlaps with the root note, such as those first two thin bands of red and blue. And at the bottom are the overlaps of the coloured notes (non-root). Here’s one I especially like the sound of:
And here is a highly dissonant and also commonly used one:
One more interesting direction to go with this: adding more space between notes. You may remember from near the beginning of this inquiry I talked about a drop-2 minor chord, and that it should have a clear harmonic overlap early on, and that it sounds very consonant. Well here it is:
It seems at this point that we can state some patterns about these visualizations and how they relate to consonance and dissonance. The thin overlaps don’t seem to matter much; they’re probably not very perceptible. In highly consonant chords, the first significant overlap is a complete one. Whereas in highly dissonant chords, the first significant overlap is muddy. The above is an example where it’s kind of hard to say if those first two are significant, but then there is a very strong complete one. For another example of a clearly muddy one:
I’m excited to see if I can apply this technology to music composition.