Overtonal energy is stable, restful, it belongs where it is and wouldn’t mind staying there.<\/p>\n
If I divide by 3, 5 or 7, I get a completely different kind of note. I call this division energy “reciprocal,” after\u00a0W.A. Mathieu’s<\/a> suggestion in his amazing book Harmonic Experience<\/a>.<\/p>\n Reciprocal<\/a> energy is restless, unstable. The note wants to move, or for the music to come to it, until it is overtonal.<\/p>\n On the lattice of fifths and thirds, there are two axes, fifths and thirds, and two directions, overtonal and reciprocal.<\/p>\n This makes four total directions one can move on this lattice. Each direction has\u00a0own characteristic flavor, or energy. I use the following names for these energies, mostly after Mathieu.<\/p>\n Every interval<\/a> has its own unique recipe of moves in these four directions. The perfect fifth has pure dominant energy, the major third<\/a> pure major. The minor third, b3 on the lattice, is a compound note<\/a> — dominant and minor.<\/p>\n It’s interesting to look at the minor third<\/a> (b3) from the viewpoint of tonal gravity<\/a>. On the horizontal axis, dominant\/subdominant, the b3 is overtonal, stable, restful. On the vertical axis, major\/minor, the note is reciprocal, unstable, restless.<\/p>\n Tonal gravity is stronger the closer you are to the center. To make a minor third, you multiply by 3 (an overtonal jump of a fifth), and divide by 5 (a reciprocal jump of a third). I know, 3 generates fifths and 5 generates thirds, a confusing coincidence<\/a>.<\/p>\n Fifths are closer to the center, harmonically, than thirds are, so the overtonal energy is stronger than the reciprocal.<\/p>\n This makes the minor third a stable note, although less stable than the major third. Songs can end on a tonic minor chord and they will still sound finished.<\/p>\n\n
![\"Compass](\"http:\/\/www.garygarrett.me\/wp-content\/uploads\/2013\/06\/Compass-Points-1024x768.png\")
<\/a><\/p>\n