The harmonic lattice can be divided into four quadrants.
Northeast is pure overtonal energy. All these notes are reached by multiplication alone. Powers of 3 and 5 are in the numerators, and the denominators are all powers of 2.
Southwest is pure reciprocal energy. You get there by dividing. All the 3’s and 5’s are on the bottom of the ratio (or fraction), and the powers of 2 are on the top.
Northwest is mixed reciprocal and overtonal energy. You multiply by fives and divide by threes.
Southeast is also mixed. Multiply by threes and divide by fives.
The major sixth is in the northwest quadrant. First divide the tonic by 3, which gives you a perfect fourth. Then multiply that by 5, and you get the major sixth. Its ratio is 5/3. You can do this in any order, of course — multiplying by 5 gets you to the major third, and dividing by 3 brings you to the sixth again.
A different flavor yet! What do you hear? How does it make you feel?
Musical sensation can be related to other senses and emotions, but really these feelings have their own quality. It’s like a new sense. I had a friend once who had never tasted a peach. She didn’t like the feel of the skin, and she hadn’t dared bite into one. I was saddened, of course, but how to describe the taste of a ripe peach to someone who’s never tasted one? You can draw comparisons forever, but nothing will prepare them for the reality.
That was a long time ago. I hope that some time later, she found herself in the perfect place and went for it. There should be a First Peach ceremony. Yum!
The individual qualities of these notes are easier for me to hear in just intonation than in equal temperament. They are purer flavors, a more direct experience. Later, I’ll present some notes that are very close together in pitch, yet feel different. In just intonation, there are different notes for peach, nectarine and apricot. In equal temperament, a single note, close in pitch, will represent all three. Once you’ve tasted the actual fruits, equal temperament works better than it did before. You know what it is you’re supposed to be tasting.
OK, I’m out on a quivering limb of analogy now, and way ahead of my story. We have enough notes now to start playing with them.
I cannot believe I haven’t come across this website earlier. I love the analogies!