This lesson is showing us how the tempered frequencies, or the Equal Temperament that we use today,came into existence. The pure natural 5th between 220 Hz and 440 Hz - is exactly 330 Hz, (you can play iton the 5th open string, second harmonic, 7th fret). But the cyclic nature of the Equal Temperament demandsthat we make some adjustments, and slightly detune the geometrically perfectly aligned natural intervals, so the tempered note E is 329,63 Hz. When we superimpose 12 fifths over the 55 Hz note A, to get to the note A that is exactly seven octaves higher (7040 Hz), we must detune and lower each pure natural 5th - by 2 cents.

The value for each harmonic note (expressed in cents, 1 semitone = 100 cents), is refering to the diThe value for each harmonic note (expressed in cents, 1 semitone = 100 cents), is refering to the difference between the natural pitch, and the tempered equivalent we use today in our equally tempered musical system. Of course that every harmonic background has to be well tempered, but if the soloist’s notes lean away from tempered, and towards natural pitches, (in relation to a tonal center, of course), that solo simply - souns better. It is no secret why, since the melody notes are more prominent, if they also geometrically align with the bass notes - the harmonics of the bass notes will superimpose much better with oscillations of the solo. Precisely, as the bass note is sounding, with itas the bass note is sounding, with it’s harmonic content it sets zero crossings at a certain rate (zero crossingsare marked with vertical lines). So, if we produce vibrations with the exact zero crossings - matching the bass frequencies zero crossings - the bass note’s harmonics will in fact, boost our melody notes. It is because our notes are now perfectly geometrically aligned with bass frequencies. Their amplitudes augment each other, and mix much better, superimposing so that they push each other to vibrate stronger, which unfortunately - never happens among tempered frequencies...

HARMONY

The Sequence of Harmonics

for root note A = 55 Hz