Kite's thoughts on hi-lo notation: Difference between revisions
→Generalized Voicings: added 4-voice voicings of a triad, other changes too |
various small changes |
||
| Line 101: | Line 101: | ||
=== Triads === | === 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'''. | 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'''. We can think of the chord as notes in a '''tritonic''' scale (as opposed to a pentatonic or heptatonic scale). | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
| Line 119: | Line 119: | ||
|10th or 11th | |10th or 11th | ||
|- | |- | ||
|etc. | | colspan="2" |etc. | ||
|} | |} | ||
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.) | In addition, 2nds, 7ths and 9ths might occur with a sus chord. | ||
All the notes in a close voicing are 1 tritonic scale step away from adjacent notes. And in an open voicing, all notes are 2 scale steps away. 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 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. | The following table assumes that the interval between any pair of adjacent notes is less than an octave, a 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. | ||
| Line 306: | Line 307: | ||
|hi38lo7 | |hi38lo7 | ||
|} | |} | ||
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 | 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 lift/drop 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 | To find the stepwise name from the lift/drop 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. | Generalized voicings are particularly useful for dim7 chords. | ||
=== Pentads === | === Pentads === | ||
For a pentad in 5 voices, there are 120 possible voicings grouped into 24 generalized voicings. Above span-9 the drop | For a pentad in 5 voices, there are 120 possible voicings grouped into 24 generalized voicings. Above span-9 the lift/drop terminology becomes rather awkward. Because of the large number of generalized voicings, the stepspan becomes quite useful as a category of categories. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
| Line 322: | Line 323: | ||
!span-4 | !span-4 | ||
|1-1-1-1 = close | |1-1-1-1 = close | ||
! colspan="3" | | |||
| | |||
|- | |- | ||
!span-6 | !span-6 | ||
|2-1-1-2 = drop-2 | |2-1-1-2 = drop-2 | ||
! colspan="3" | | |||
| | |||
|- | |- | ||
!span-7 | !span-7 | ||
|1-2-1-3 = drop-3 | |1-2-1-3 = drop-3 | ||
|3-1-2-1 = lift-3 | |3-1-2-1 = lift-3 | ||
! colspan="2" | | |||
| | |||
|- | |- | ||
!span-8 | !span-8 | ||
| Line 365: | Line 361: | ||
|2-4-3-4 = lift-1-3 drop-4 | |2-4-3-4 = lift-1-3 drop-4 | ||
|4-3-4-2 = lift-2 drop-3-5 | |4-3-4-2 = lift-2 drop-3-5 | ||
! colspan="2" | | |||
| | |||
|- | |- | ||
!span-14 | !span-14 | ||
|3-4-4-3 = lift-1-4 drop-2-5 | |3-4-4-3 = lift-1-4 drop-2-5 | ||
! colspan="3" | | |||
| | |||
|- | |- | ||
!span-16 | !span-16 | ||
|4-4-4-4 = ??? | |4-4-4-4 = ??? | ||
! colspan="3" | | |||
| | |||
|} | |} | ||
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 | 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 basic voicing (GBDFA) is a 2-1-1-2 voicing. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Generalized voicings for a pentad in 5 voices, smallest 3 stepspans only | |+Generalized voicings for a pentad in 5 voices, smallest 3 stepspans only | ||