The Tonic Major Chord
Adding a major third and a perfect fifth (5/4 and 3/2) further reinforces the center and starts to carve out some territory on the map.
This is the tonic major chord:
In my view, the tonic major helps the ear grab onto the center, by adding two notes that point directly at it. The ear has more information to work with.
The mind has amazing real time mathematical ability. Maybe a more accurate way to say this is that the mind has an amazing ability to quickly analyze and predict physical phenomena. The physical phenomena can be described by math. I don’t think the mind is working with arithmetic calculations at blinding speed, like a computer. It’s more of a massively parallel, holistic analog processor, that achieves a similar result.
Willie Mays used to catch fly balls with his back to the plate. Here’s a famous one:
Mays watches the ball start its flight, calculates the parabola it will follow (fine tuned by the conditions that day), and sets out at top speed for the spot, 400+ feet deep in center field, where he knows it’s going to land. He doesn’t (can’t!) look at the ball until it’s almost upon him. Marvelous.
So the ear hears a note, another one at 3x the frequency (remember octaves don’t count, 3/2 works like 3/1 in this regard), and another one at 5x. All three notes are direct signposts, pointing exactly at the tonic. Here we are, says the mind.
This may be why the equal-tempered major third gives me that slight queasy feeling. The tonic is the tonic, all right, but that equal-tempered third doesn’t point right at it! It’s close enough that the ear correctly identifies it, but it’s actually pointing at a note about 1% sharp of the tonic, and something sounds subtly off, like day-old sushi.
Here it is again: pure third, ET third, pure third. The middle note, the ET third, has a ratio of about 5.04/4.
Is it slight tonal vertigo? Where is home?