Harmonic Explorer app

The work of the late Ernest McClain [1918-2014] was based upon a technique in which ever higher numbers appear to have been studied in antiquity as to the harmonic field of intervals possible within that integer limit. Such a single number reference can be mentioned en passant within texts like The Bible, Homer’s Illiad or the Sumerian story of Gilgamesh and be ignored today as a frivolous use of large numbers, such as great ages of the gods, the number of ships, or tithe goods and so on, when in fact the numbers were referring to a musicological field relevant to the narrative and its elements.

McClain’s work was very briefly introduced in  Precessional Time and the Evolution of Consciousness (2011) in its Chapter 3 on the Age of Aries, when such calculational musicology/theology seem to have replaced the megalithic activities in Age of Taurus. After then collaborating with Ernest for a few years, after his death I attempted to make an accessible book on Ernest’ work in my 2018 book Harmonic Origins of the World.

Ernest had a fine sensibility for the Ancient Near East (or A.N.E.), its number science and symbolisms. Through many email exchanges I wanted to be able to generate his tonal diagrams for myself; to both learn more and answer specific questions. I was able to make a web page so that people like myself could more easily enter his world of tonal yantras (that look like mountains) and their corresponding tonal mandalas (the octave circle); without having to learn the method of “limiting the products of powers of three and five and then doubling all numbers to the limiting number”. This Harmonic Explorer app enables ridiculous freedom over the previously required manual calculations, including walking through limiting number space with prime factor buttons, multiplying/dividing by 2, 3, 5, 10 or 12. It can also be very useful for screen grabbing when discussing a given tuning system as in:

TRY IT NOW HERE: Harmonic Explorer

Ernest’s website has study pdf’s of his books and papers plus other resources.