Expanding on my earlier post regarding Francis Bacon and the Twice 11 Brethren, there’s still a bit more associated with the concept of Twice 11 than was originally addressed.
My book, The Next Octave, approaches such questions from a musical perspective. And while the significance that Francis Bacon applied to numbers tends to fall into the realms of gematria and geometry, the significance I apply to numbers in my book is primarily related to the harmonic series. (For a nice overview of the harmonic series, please check out my video, How is the harmonic series like a spiral?)
Looking at the Twice 11 Brethren musically, we notice that HARMONIC 11 is an F#, the tritone (or, the Devil in Music) off the tonic of C (HARMONIC 1). Its octave, or twice the 11th harmonic is HARMONIC 22, and if you’ve read my book you know that there’s a subtle conspiracy encoded into the text of Francis Bacon’s New Atlantis (as well as the text of King Lear) involving Harmonics 22 and 23:
To recap what’s being covered above in the book, the tritone sits three whole steps above the tonic of any scale. In the harmonic series, the tonic is HARMONIC 1, which is a C note, so the tritone would be three whole steps above C, or F#. Below is a graphic showing that interval of three whole steps (a total of six half steps):
Below we can see that in the harmonic series, the tritone (F#) off the tonic of Middle C produces a frequency of about 360 Hz (it’s actually 359.74 Hz). Note that the Harmonic Octave (below) uses a tonic frequency provided by equal temperament tuning: 261.63 Hz, though the true Middle C frequency calculated within the harmonic series, itself, is actually 256 Hz.
However, the act of equally tempering music (also known as 12-TET, or mis-tuning music) tunes the tritone at 370 Hz (circled in red, below), falling much closer to the note of W, the 23rd harmonic (376 Hz), than to F# or the 22nd harmonic (360 Hz) where the harmonic series naturally places it. The 12-TET tritone is a full 10 Hz away from HARMONIC 22, but only 6 Hz away from HARMONIC 23, aligning it more closely with HARMONIC 23 (W). (For more information on the note of W, please reference my book, The Next Octave.)
[Please note that although our understanding of frequency wasn’t made possible until the work of Heinrich Hertz in the late 1800s, musicians, since the time of Pythagoras, have been measuring intervals and tuning scales via their geometrical understanding of string length on a monochord. Thus, the discrepancy between the notes of HARMONICS
[Please note that although our understanding of frequency wasn’t made possible until the work of Heinrich Hertz in the late 1800s, since the time of Pythagoras, musicians have been measuring intervals and tuning scales via their geometric understanding of string length on a monochord. And so, such a discrepancy between HARMONICS 22 and 23 would have been fully understandable in Elizabethan times.]
The interval between the tonic of C and the true F# is a less dissonant interval than the interval between C and W. (You can hear this for yourself in this video at the 8:44 mark.) So is the equally tempered tritone’s proximity to W, the 23rd harmonic, the reason why the tritone is so dissonant that we call it the Devil in Music?
It’s conceivable that two opposing sides of a tuning debate could have developed as a result of this discrepancy between HARMONICS 22 and 23. Might the Twice 11 Brethren signify a group of men supporting the idea that the tritone of F# off C should be based on HARMONIC 22 (twice HARMONIC 11) rather than Harmonic 23? I attempt to answer this question in the 14th chapter of my book by looking at veiled references to the tritone, harmonic means, and the “usurpation of the mese” made in several Shakespeare plays.