The Book: Untempered Music
In March of 2011, I had a powerful epiphany, in which I deeply and directly felt the connection between music and mathematics, two of my great loves. Over the next two years, I explored further, encountered the astonishing work of W.A. Mathieu, and wrote a blog attempting to describe my epiphany and my journey into harmonic space, the lattice of fifths and thirds. I hope you will come along.
Here is the blog, in chronological order.
- Untempered Music
- Flying Dream on YouTube
- Back Story
- Pythagoras’ Epiphany
- Beauty is Truth
- Notes and Intervals
- The Tonic
- Harmonic Experience
- Between the Keys
- The Chord of Nature
- Notes As Ratios
- Octave Reduction
- The Major Third
- Harmonic Space
- The Lattice
- The Tonic Major Chord
- Compound Notes
- The Major Seventh
- A Reciprocal Note: The Fourth
- Mixed Messages
- Names
- The Major Scale
- Reciprocal Thirds
- The Minor Third
- The Minor Seventh
- Untempered Vs. Tempered
- The Minor Second
- The Augmented Fourth
- Prime Numbers and the Big Bang
- Seven
- Summary (So Far)
- Mozart on the Lattice
- Melodic Space, Harmonic Space
- Cents
- “Untempered” vs. “Just Intonation”
- The Untempered Major Scale
- The Major Scale in Cents
- The Untempered Chromatic Scale (Part 1)
- The Untempered Chromatic Scale (Part 2)
- An Easy Experiment To Try
- More Experimenting
- Entrainment
- Resonance
- Saturn’s Rings
- Extending the lattice
- Another Major Second: The 10/9
- Commas
- Another Comma
- The Infinite Lattice
- Why Equal Temperament?
- Rosetta Stone
- Tonal Gravity
- Cadences
- Intervals
- Be Love
- Home
- The Compass Points
- Leading the Ear
- The Power of the Seventh Chord
- To the Far Northwest
- The Septimal Minor Third
- Mixolydian Mode
- Mixolydian Matchsticks
- Consonance and Dissonance
- Consonance Experiment
- Polarity Experiment
- Harmonic Distance
- Mirror Twins
- Polarity
- More Mirror Twins
- Why Can We Hear Harmony?
- A Mirror Quad
- One More Mirror Pair
- Real Girl, Animated
- 100 Girlfriends
- 100 Girlfriends, Part 2
- The Blue Tritone
- More Blue Tritones
- Chords on the Lattice
- Three Flavors of Seventh Chord
- Straight Line Chords: Aug, Dim, Sus2, Sus4
- Putting Some Numbers on Tonal Gravity
- Tonal Gravity and the Major Scale
- A Theory of Everything
- A Harmonic Journey: ET and JI Compared
