Plainspeak:
How the “white notes on a piano” are structured and interact is to be considered the template upon which all other musical structures are based upon. A solid understanding of the structure and expectations of the Major Scale is thus crucial as a starting point to any musical exploration. By casting modes as a category in category theory, we open up music to analogy and comparison with many other categories in a natural way. As such, we see that through the major mode, music is universal.
Visuals supporting this axiom:
How the Major Scale is universal
- The majority of musical frameworks throughout the globe and throughout history rely on the heptatonic or pentatonic major scale.
- The Tritone present in the Major Scale is present in all heptatonic scales and defines being “in key” for all heptatonic scales
- The 6 accidentals required to move from mode to mode in the major scale define an irreducible representation for movement between modes, which connects all heptatonic scales.
- The tonal dynamics (Ton, Dom, Sub) set up by the Tritone in a 13th chord, as seen in a jump skip diagram, replicate themselves in all other heptatonic scales and are modified by the extra Tritone(s) present in all heptatonic scales.
- The major, minor, and diminished chord qualities of the major scale are a template for all other chord qualities: full-diminished, augmented, and minor-major.
- Given that the major scale has all the above properties and the entire major scale can be expressed as permuations off of the Ionian Mode, we can also extend the universality and say that the Ionian Mode is universal.
The major mode in western music theory
There is no doubt that the major mode is central to western music theory.
The major mode in KCM
z12 –> z7
Z7 key
z7 chord
z7 mode
talk about transition between the threeShow how jumps skips and steps are exemplified in th Z12 magic circle (ie the major mode teaches us how to use and what the different spaces are)
Talk about step scales as first generatlization to the major mode (melodic minor and neapolitan major)
The major mode in Category Theory
Define “natural” in CT and how the major mode qualifies
Talk about naturalness and universality in CT.
Define how the major scale defines this for accidental space and music
Position it within conventional western MT (wwhwwwh) and show how permutations make it automorphic
Plainspeak: “all scales are isomorphic to the major scale“
proof: all share a six set element of accidentals plus a key
Plainspeak: “modes within a scale are automorphic with respect to each other“.
proof: permuation of WWHWWWH
proof: internal six-d accdiental representation of mode, |234567>
proof: accidental abacus