The harmonic series contains 16 usable notes (notes with large enough intervals that we can distinguish them) in its chromatic scale. Of those 16 notes, each one generates its own scale. This graphic shows the list of frequencies that each note generates within its own scale for A4. Note that nowhere in the harmonic series…
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Dissonance in Kubrick’s last film
In Stanley Kubrick’s Eyes Wide Shut, Bill Harford is unmasked before the secret society while three notes are ominously struck on the piano. First we hear an oscillation between F and F#, followed by a dissonant and repeated high G. In The Next Octave, we track these notes in the harmonic series and uncover some startling…
“We were in all, (sick and whole,) one and fifty persons, whereof our sick were seventeen.“
In Chapter 13 of The Next Octave, we delve into the coded messages of Francis Bacon. This chapter, entitled “An alchemical wedding of tones” is a fascinating look at Bacon’s hints regarding the harmonic series.
The Next Octave is now available!
Click here to visit the Amazon ordering page. Music and money share an immutable connection. Both systems, encoded with mathematical ratios of creative tension, have the power to produce both harmony and dissonance. Over the centuries, governing philosophies tempering both music and money have created two systems of fiat notes, the values of which have…
Rosencrantz and Guildenstern are Danish
My partner, Allan, is Danish and we toured Denmark in 2019. The highlight of the trip was Kronborg Slot, the real-life setting of Shakespeare’s tragedy, Hamlet. Kronborg often hosts performances of the play on the castle grounds; the first production here was in 1816 when amateurs performed it at the garrison. Another production took place in 1916, and…
Intro to 3-6-9
Marko Rodin’s Mobius Circuit illustrates the movement of energy: flow is driven by the power of two through the doubling of 1-2-4-8-7-5 and flow is governed by the power of three, generated by the oscillating 3 and 6 ascending to 9. This is just the first toe into a pond of complex water… my new…
Exploring 2:3 :: 6:9
This ratio is all about the perfect fifth interval in music, which can be expressed as 2:3 or 3:2. The ratio 3:2 can be expressed as 3/2 = 1.5, the generator used to build a scale by stacking fifths. But the ratio also suggests a tension between two concepts: duality and trinity, a dichotomy and…
Chartalism before it was cool
Plato wasn’t the big promoter of democracy and equality that he’s praised for being. In fact, economist Joseph Schumpeter described Plato’s views as just shy of fascism.
The ratio of three deciduous forests to one ship’s peanut
The term “inflation” causes glazed eyes. Call it a “leaf problem,” instead, and more people might sit up and take notice.
The secret to economic sustainability
The act of sharing is energized by the HEART chakra. But we can’t share without ascending through the first three matter-based chakras. That’s because you can’t share without first producing something, then consuming some of it (so you have energy to move) and then saving some of it. The secret to economic sustainability is in…