Kite's thoughts on hi-lo notation

Hi-lo notation was invented by Kite Giedraitis for naming chord voicings. It applies to all tunings, even conventional ones like 12-edo or meantone. It allows arrangers, composers and theorists to discuss specific voicings with much more accuracy than the conventional 1st inversion, 2nd inversion, etc. nomenclature.

C E G = C or C close
C G E = Chi3 (because the 3rd is an 8ve higher than in the close voicing)
G C E = Clo5 (aka 2nd inversion)
E G C = ChiR (R stands for root) aka 1st inversion
E C G = Clo3 (also 1st inversion)
G E C = ChiRlo5

When there are multiple high or low notes, the terms "hi" and "lo" are only used once:

C G E B = CM7hi37
G Bb C E = C7lo57

"Add" is used for duplicated notes:

C E G C = Cadd8
G C E G = Caddlo5
G C E G C = Caddhi8lo5
C E G E = Caddhi3 or Cadd10
C C E G = CaddloR or possibly Chi35add8

This doesn't conflict with the usual use of "add" in chord names:

C E G D = Cadd9
C E G C D = Cadd89
C D E G = Caddlo9 or Cadd2
D C E G = Caddlo2

"No" is used as usual to omit notes, as in C9no5. The 4 words are used in this order: no - hi - lo - add - hi - lo. First omit notes, then move notes higher, then move notes lower, then add notes, then add high notes, then add low notes. Following this order removes any ambiguity:

Chi3add8 = C G C E
Cadd8hi3 = C E G C E
Caddhi38 = C E G E C

The common open chords of a guitar:

C major: x32010 = C E G C E = Cadd8hi3
D major: x00232 = A D A D F# = Dhi3add8lo5
E major: 022100 = E B E G# B E = Eadd8loR5 or possibly Ehi3add8hi5hi8
G major: 320003 = G B D G B G = Gadd8hi3hi8 or possibly Glo5add8loR3
A major: 002220 = E A E A C# E = Ahi3add8hi5lo5

To find the number of voices in a chord, start with the obvious: a triad has 3, a tetrad has 4, etc. Then subtract the "no" notes and add the "add" notes. For example, A7no5hi3add8 has 4 (tetrad) - 1 (no 5th) + 1 (add 8ve) = 4.

For more examples, see Kite Guitar Chord Shapes (downmajor tuning).

Notating chord progressions

There are sometimes two possible names for a voicing, depending on what one considers the "home octave" to be. As we saw, C C E G can be either CaddloR or Chi35add8. This ambiguity can be removed by designating one note in a specific octave as "the" tonic, then naming all other notes relative to that tonic. For example, if C2 is the tonic, A1 is loA, A2 is simply A, and A3 is hiA.

This lets us write out chord progressions as e.g. Cadd8 - loAmhi3add8 - Dm7 - loG7hi3. The entire 4-part harmony can be deduced note-for-note from this. Here are the notes, where the lower octave uses underlined letters and the upper octave uses lower-case letters:

C E G c
A E A c
D F A c
G D F B

This works with relative notation as well: Iadd8 - loVImhi3add8 - IIm7 - loV7hi3.

Naming the roots as hi or lo almost allows us to reduce a barbershop tag to a mere succession of chords. However voices sometimes coincide or cross. See Kite Guitar Translations by Kite Giedraitis#Barbershop tags