Have you ever wondered where the notes on the guitar originated? Why are the frets located where they are? Our tuning system evolved from a set of notes used as far back as ancient Mesopotamia in 650 B.C.
No theory of music is truly complete without an understanding of the nature of the notes themselves. Other methods may choose not to approach this subject for two reasons. First, the arithmetic involved may scare away some students. Second, this understanding is not strictly speaking essential to being able to learn and play music. We include the discussion here to satisfy the curiosity of all brave souls who wish to possess this secret knowledge.
The set of videos below will explain the journey of musical notes in terms of natural harmonics, pitch frequencies, and arithmetic ratios.
Part One: Harmonics
The journey begins in nature. Every note contains within itself all the multiples of its natural frequency. By harmonizing these frequencies and making scale melodies from them, we can take advantage of the music that already exists in the universe.
Part Two: The Harmonic Scale
See how the ratios between the harmonics create a mathematical scale that can be used to compose music. Construct scales of seven and eleven notes using the lower level harmonics.
Part Three: The Pythagorean Scale
The harmonic scale is limited by the diversity of intervals that it creates. A melody that works in one key may sound completely different in a different key, due to these differences. The Pythagoreans in ancient Greece, (and the Mesopotamians and Babylonians before them), stacked consonant intervals of a perfect 5th in order to create a scale with much more consistency in its intervals. We will construct twelve and seven note scales using the method of stacked perfect 5ths.
Part Four: The Equal Temperament Scale
Constructing seven and twelve note scales using stacked perfect 5ths results in more consistent intervals than the harmonic series, but there are still some discrepancies, most notably the “Pythagorean Comma” that results in what some refer to as a “wolf tone” in certain intervals in certain keys. The ancients avoided these intervals because of the harshness of the sound. In order to build a scale that has no wolf tones, a further compromise must be made. By making every half step equal, we can build a scale where all keys are equal. Other than the octave, there are no intervals which can be considered “pure” according to the harmonic series. But the amounts by which they vary are so familiar to our ears by now, that anything else sounds at least slightly strange or out of tune. See how the equal temperament scale is created by adding identical half steps.
Part Five: Summary and Bonus
After quickly reviewing the preceding material, finish by building the popular major and natural minor scales using notes from the equal temperament scale.
I hope you have enjoyed this lesson. Knowing where the musical notes come from can enhance your understanding and enjoyment of playing music.
Demonstration Piece
I wrote the following piece to demonstrate how music can be made using only the first six harmonics on each guitar string. The guitars are tuned in perfect fourths — E A D G C F.
- You can download the supplemental material that went into the making of these videos.
- Transcript of the videos.
- Notes
- Harmonic 1 Tone
- Harmonic Octave
- Harmonic Series 3
- Harmonic 5th
- V-I Resolution
- Harmonic 2 Tone
- Harmonic 4 Tone
- V7-I Resolution
- Harmonic 8 Tone
- Harmonic 16 Tone
- Harmonic Diatonic
- Harmonic 11 Tone
- Pythagorean Comma
- Pythagorean Comma Harmony
- Stacked 5ths 12 Tones
- Pythagorean 12 Tone
- Pythagorean Diatonic
- Equal Temperament 12 Tone
- Equal Temperament Major
- Equal Temperament Minor