Kite's thoughts on hi-lo notation

Overview

Hi-lo notation is 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 much more accurately than the conventional 1st inversion, 2nd inversion, etc. nomenclature.

Hi-lo notation identifies every chord member by its interval from the chord root as 3rd, 5th, etc., written as 3, 5, etc. It then describes what needs to be done to the root position close voicing (known as the basic voicing) in order to change it into the given voicing.

• C E G = C (the basic voicing is the default voicing)
• C G E = Chi3 (hi3 because relative to the basic voicing, the 3rd is raised by an octave)
• G C E = Clo5 (aka 2nd inversion, the 5th is lowered from basic)
• E G C = ChiR (R stands for root) aka 1st inversion
• E C G = Clo3 (another example of 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 = Cadd8lo5
• 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

"Add" can optionally be written more concisely with a comma: Chi3add8 becomes Chi3,8. This follows the comma usage of ups and downs notation and color notation.

The common open chords of a guitar:

• C major: x32010 = C E G C E = C,8hi3
• D major: x00232 = A D A D F# = Dhi3,8lo5
• E major: 022100 = E B E G# B E = E,8loR5 or possibly Ehi3,8hi58
• G major: 320003 = G B D G B G = G,8hi38 or possibly Glo5,8loR3
• A major: 002220 = E A E A C# E = Ahi3,8hi5lo5

Use addhi8, not add15. No degrees higher than 13 are used, analogous to chord names.

The terms hi and lo and degrees R-8 cover voicings up to a 3-octave range, because every note is in either the lo octave, the central octave or the hi octave. Degrees 9-13 go even higher. To extend the range an extra octave both above and below, use dubhi and dublo, where dub- is short for double. For example, dublo7 is a note a 9th below the root. Dublo is never used for degrees above 7. Dublo9 becomes lo2, dublo11 becomes lo4, and dublo13 becomes lo6.

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 (A7 is a tetrad) - 1 (no 5th) + 1 (add 8ve) = 4 notes.

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 chord roots relative to that tonic as hiC, loF#, loVII, etc. Unlike octave numbers which only increase when going from B up to C, the hi-lo categories only change in the region of the tonic. This has the advantage that transposing to a new key won't change the hi-lo categories.

G major scale in both scientific pitch notation and hi-lo notation

SPN names	D2	E2	F#2	G2	A2	B2	C3	D3	E3	F#3	G3	A3	B3
hi-lo names	loD	loE	loF#	G	A	B	C	D	E	F#	hiG	hiA	hiB

Chord progressions can be written out 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.

Generalized Voicings

Triads

For a triad in 3 voices, the basic, hiR and lo5 voicings (e.g. CEG, EGC and GCE) are all close voicings. The hi3, lo3 and hiRlo5 voicings (e.g. CGE, ECG and GEC) are all open voicings. These two categories of voicings, open and closed, are called generalized voicings. Thinking of the chord as notes in a tritonic (as opposed to pentatonic, heptatonic, etc.) scale, all the notes in the close voicings are 1 scale step above the note below it. And in the open voicing, all notes are 2 scale steps above. Thus the two generalized voicings can be named 1-1 and 2-2, pronounced one-one and two-two. (Open and close are certainly preferable names, but this stepwise terminology is introduced here to pave the way for naming voicings of tetrads and pentads.)

The following table assumes that the interval between any pair of adjacent notes is less than an octave, a very reasonable assumption. Thus there are only 6 possible voicings of a triad, grouped into 2 generalized voicings (assuming only 3 voices). In any 1-1 voicing, the chord spans 2 steps of the tritonic scale. Likewise any 2-2 voicing spans 4 steps. Thus the stepspan of the voicing is simply the sum of the 2 numbers.

Generalized voicings for a triad in 3 voices

stepspan	voicing		root position	1st inversion	2nd inversion
span-2	1-1	close	basic	hiR	lo5
span-4	2-2	open	hi3	lo3	hiRlo5

Generalized voicings are particularly useful when the chord has a homonym. For example, a 12edo augmented chord is simultaneously in 3 different inversions and 3 different voicings, but in only 1 generalized voicing.

Tetrads

For a tetrad in 4 voices, there are 24 possible voicings grouped into 6 generalized voicings. The 2-1-2 voicings are known to guitarists as drop-2 voicings. This drop-N terminology can be extended via "lift" to cover the other generalized voicings, but only if there are no octave doublings.

Generalized voicings for a tetrad in 4 voices

stepspan	voicing		root position	1st inversion	2nd inversion	3rd inversion
span-3	1-1-1	close	basic	hiR	lo57	lo7
span-5	2-1-2	drop-2	hi3	lo37	lo5	hiRlo5
span-6	1-2-3	drop-3	hi35	lo3	hiRlo5	hiRlo37
	3-2-1	lift-2	hi5	lo35	hiRlo57	hi3lo7
span-7	2-3-2	drop-2-4	hi37	hiRlo37	hi3lo5	hiR5lo7
span-9	3-3-3	lift-2 drop-3	hi3loR7	hi5lo3	hiR7lo5	hi38lo7

In the 1-2-3 voicing, the 2nd highest note is 1 tetratonic step below the highest note, the 3rd highest note is 2 steps below the 2nd, and the 4th is 1 step below the 3rd.

The stepwise terminology has the advantage that it directly indicates the stepspan, and hence the "openness" of the voicing. Furthermore, a generalized voicing has only one stepwise name, but possibly more than one drop-N name. Drop-2 could possibly be called lift-3, and drop-2-4 could possibly be called lift-1-3.

To find the stepwise name from the drop-N name: drop-3 changes 1234 to 1243, or more precisely 12(3)4(12)3. From 1 to 2 is 1 step, from 2 to 4 is 2 steps, and from 4 to 3 is 3 steps. Thus the stepwise name is 1-2-3.

Generalized voicings are particularly useful for dim7 chords.

Pentads

For a pentad in 5 voices, there are 120 possible voicings grouped into 24 generalized voicings. Above span-9 the drop-N terminology becomes rather awkward. Because of the large number of generalized voicings, the stepspan becomes quite useful as a category of categories.

Generalized voicings for a pentad in 5 voices

stepspan	voicings
span-4	1-1-1-1 = close
span-6	2-1-1-2 = drop-2
span-7	1-2-1-3 = drop-3	3-1-2-1 = lift-3
span-8	2-2-2-2 = drop-2-4	1-3-3-1 = drop-3-4	1-1-2-4 = drop-4	4-2-1-1 = lift-2
span-9	2-1-3-3 = drop-2-5	3-3-1-2 = lift-1-4	1-2-4-2 = drop-3-5	2-4-2-1 = lift-1-3
span-11	3-1-3-4 = lift-3 drop-4	4-3-1-3 = lift-2 drop-3	2-2-4-3 = lift-2-4 drop-3	3-4-2-2 = lift-3 drop-2-4
span-12	4-2-2-4 = lift-2 drop-4	3-3-3-3 = lift-3 drop-2-5	1-3-4-4 = lift-2-3 drop-4	4-4-3-1 = lift-2 drop-3-4
span-13	2-4-3-4 = lift-1-3 drop-4	4-3-4-2 = lift-2 drop-3-5
span-14	3-4-4-3 = lift-1-4 drop-2-5
span-16	4-4-4-4 = ???

The 9th of a pentad is treated as a 2nd in a pentatonic scale. Thus for G9 in root position, the 1-1-1-1 voicing is GABDF, the lo9 voicing. The more consonant GBDFA voicing is a 2-1-1-2 voicing.

Generalized voicings for a pentad in 5 voices, smallest 3 stepspans only

stepspan	voicing		root position	1st inversion	2nd inversion	3rd inversion	4th inversion
span-4	1-1-1-1	close	lo9	hiR	hiR3	lo79	hiRlo9
span-6	2-1-1-2	drop-2	basic	hiR5	lo59	hiRlo79	hiR3lo9
span-7	1-2-1-3	drop-3	hi3	lo39	hiRlo59	hiRlo7	lo27
	3-1-2-1	lift-3	hi3lo9	hiR7	hi38	lo7	lo237

Hexads, heptads, etc.

For an N-ad in N voices, there are N! possible voicings, which are grouped into (N-1)! generalized voicings, which are grouped into (N-2)² + 1 stepspans.