All the notes I’ve discussed so far are found above and to the right of the tonic, in the northeast quadrant of the map. These notes are generated by multiplication alone. What about the notes that are generated by division? These are found to the left and down on the lattice. The closer a note is…
Multiplying the tonic by 2, 3 and 5 creates the octave, fifth and third respectively. The ear hears these intervals very well. We can easily sing them. Each one has a feel, a sort of harmonic flavor, that makes a fifth a fifth and a third a third. It turns out that the ear can…
Notes are pitched sounds. A given note means little by itself. It could be the tonic of a key, or some member of a scale based on a different tonic. By itself, it generates no tension, resolution or sense of place on the harmonic map. So when I name a note in this blog, I’ll…
A note, in music, is a sound with a particular pitch. Pitch is frequency, measured in cycles per second, or Hertz (Hz). The faster the vibration, the higher the pitch. A vibration, at, say, 220 Hz, all by itself is a note by that general definition. But the note doesn’t acquire its distinct personality until it’s…
Pythagoras was a Greek philosopher who lived about a century before Athens’ golden age. Some time before 530 BC, he had an epiphany. He had been investigating vibrating strings, and found that when you cut the length of the string in half, the note it makes is an octave higher. Sound is vibration. When one…