Hanson guitar chords and scales

Introduction

I play a seven-string 19EDO electric guitar and an acoustic guitar and six-string bass in Hanson temperament, all tuned in minor thirds. This page shows some chord and scale shapes which I've found handy. You can hear and see some of them in action in Grebe dance and an arrangement of Kenny Wheeler's Kind Folk.

Because the strings are tuned in thirds, you can play seventh chords across four strings. Because the octave is four strings up and one fret down, you can also play their inversions across four strings. You can also manageably play the corresponding drop-2 voicings (dropping the second-to-highest voice one octave).

The cents values on the 19EDO fretboard and Hanson fretboard (frets spaced by (9/8)^(1/3) or 68 cents, strings spaced by 3^(1/6) or 317 cents) look like this:

19EDO 
 126'   189'   253'   316'   379'   442'   505'   568'   632'   695'
1011   1074   1137      0'    63'   126'   189'   253'   316'   379'
 695    758    821    884    947   1011   1074   1137      0'    63'
 379    442    505    568    632    695    758    821    884    947
  63    126    189    253    316    379    442    505    568    632
 947,  1011,  1074,  1137,     0     63    126    189    253    316
Hanson 
 113'   181'   249'   317'   385'   453'   521'   589'   657'   725'
 996   1064   1132      0'    68'   136'   204'   272'   340'   408'
 679    747    815    883    951   1019   1087   1155     23'    91'
 362    430    498    566    634    702    770    838    906    974
  45    113    181    249    317    385    453    521    589    657
 928,   996,  1064,  1132,     0     68    136    204    272    340

Here a comma (,) after a cent value means one octave down and an apostrophe (') means one octave up. If you build chords in thirds and invert/revoice using the octave four strings up and one fret down, you can use the same chord shapes on both fretboards - pretty neat!

In all fretboard diagrams below, strings run horizontally, o marks the root of the chord, and x the other notes in the chord. When showing inversions, I move the root up one string (so up by a minor third); this keeps the shape in the same area of the fretboard and so gives smooth voice leading (these progressions with roots moving by minor thirds sound cool too). I've laid out the rows so that going down a column changes chord quality by moving one voice by one fret.

Triads
Inversion
0 1 2
Major 
.  x  .  .
.  x  .  .
o  .  .  .
.  .  .  .

.  x  .  .
o  .  .  .
.  .  .  .
.  .  x  .

o  .  .  .   
.  .  .  .   
.  .  x  .   
.  .  x  .
Minor 
.  x  .  .
x  .  .  .
o  .  .  .
.  .  .  .

x  .  .  .
o  .  .  .
.  .  .  .
.  .  x  .

o  .  .  .   
.  .  .  .   
.  .  x  .   
.  x  .  .

Seventh chords
Inversion
0 1 2 3
Major 7th 
.  .  x  .
.  x  .  .
.  x  .  .
o  .  .  .

.  x  .  .
.  x  .  .
o  .  .  .
.  .  .  x

.  x  .  .
o  .  .  .
.  .  .  x
.  .  x  .

o  .  .  .   
.  .  .  x   
.  .  x  .   
.  .  x  .
Dominant 7th 
.  x  .  .
.  x  .  .
.  x  .  .
o  .  .  .

.  x  .  .
.  x  .  .
o  .  .  .
.  .  x  .

.  x  .  .
o  .  .  .
.  .  x  .
.  .  x  .

o  .  .  .
.  .  x  .
.  .  x  .
.  .  x  .
Minor 7th 
.  x  .  .
.  x  .  .
x  .  .  .
o  .  .  .

.  x  .  .
x  .  .  .
o  .  .  .
.  .  x  .

x  .  .  .
o  .  .  .
.  .  x  .
.  .  x  .

o  .  .  .
.  .  x  .
.  .  x  .
.  x  .  .
Minor 7♭5 
.  x  .  .
x  .  .  .
x  .  .  .
o  .  .  .

x  .  .  .
x  .  .  .
o  .  .  .
.  .  x  .

x  .  .  .
o  .  .  .
.  .  x  .
.  x  .  .

o  .  .  .
.  .  x  .
.  x  .  .
.  x  .  .

Drop-2 seventh chords
Inversion
0 1 2 3
Major 7th 
.  .  x  .
.  .  .  .
.  x  .  .
o  .  .  .
.  .  .  .
.  .  x  .

.  x  .  .
.  .  .  .
o  .  .  .
.  .  .  x
.  .  .  .
.  .  x  .

.  x  .  .
.  .  .  .
.  .  .  x
.  .  x  .
.  .  .  .
.  o  .  .

o  .  .  .  .
.  .  .  .  .
.  .  x  .  .
.  .  x  .  .
.  .  .  .  .
.  .  .  .  x
Dominant 7th 
.  x  .  .
.  .  .  .
.  x  .  .
o  .  .  .
.  .  .  .
.  .  x  .

.  x  .  .
.  .  .  .
o  .  .  .
.  .  x  .
.  .  .  .
.  .  x  .

.  x  .  .
.  .  .  .
.  .  x  .
.  .  x  .
.  .  .  .
.  o  .  .

o  .  .  .
.  .  .  .
.  .  x  .
.  .  x  .
.  .  .  .
.  .  .  x
Minor 7th 
.  x  .  .
.  .  .  .
x  .  .  .
o  .  .  .
.  .  .  .
.  .  x  .

.  x  .  .
.  .  .  .
o  .  .  .
.  .  x  .
.  .  .  .
.  x  .  .

x  .  .  .
.  .  .  .
.  .  x  .
.  .  x  .
.  .  .  .
.  o  .  .

o  .  .  .
.  .  .  .
.  .  x  .
.  x  .  .
.  .  .  .
.  .  .  x
Minor 7♭5 
.  x  .  .
.  .  .  .
x  .  .  .
o  .  .  .
.  .  .  .
.  x  .  .

x  .  .  .
.  .  .  .
o  .  .  .
.  .  x  .
.  .  .  .
.  x  .  .

x  .  .  .
.  .  .  .
.  .  x  .
.  x  .  .
.  .  .  .
.  o  .  .

o  .  .  .
.  .  .  .
.  x  .  .
.  x  .  .
.  .  .  .
.  .  .  x

Useful shapes
Shape Cents Description 
.   .   .   o   .   .   .   .   .   .
.   .   .   .   .   .   .   .   .   .
.   .   x   .   .   x   .   .   .   .
.   .   .   .   .   .   .   .   .   .
.   .   .   .   o   .   .   .   .   .

 .   .   . 1200  .   .   .   .   .   .
 .   .   .   .   .   .   .   .   .   .
 .   .  498  .   .  702  .   .   .   .
 .   .   .   .   .   .   .   .   .   .
 .   .   .   .   0   .   .   .   .   .
Basic form (skeleton for tetrachordal scales) 
.   .   .   o   .   .   .   .   .   .
.   .   .   .   .   .   .   .   .   .
.   .   .   x   .   x   .   x   .   x
.   .   .   .   .   x   .   .   .   .
.   .   .   .   o   .   .   .   .   .

 .   .   . 1200  .   .   .   .   .   .
 .   .   .   .   .   .   .   .   .   .
 .   .   .  566  .  702  .  838  .  974
 .   .   .   .   .  385  .   .   .   .
 .   .   .   .   0   .   .   .   .   .
Harmonics 
.   .   .   .   .   .   .   .   .   .
.   .   .   .   .   .   .   .   .   .
.   .   x   .   .   .   .   .   .   .
.   .   .   x   .   .   .   .   .   .
.   .   .   .   o   .   .   .   .   .

 .   .   .   .   .   .   .   .   .   .
 .   .   .   .   .   .   .   .   .   .
 .   .  498  .   .   .   .   .   .   .
 .   .   .  249  .   .   .   .   .   .
 .   .   .   .   0   .   .   .   .   .
Split fourth cluster 
.   .   .   o   .   .   .   .   .   .
.   .   .   .   x   .   .   .   .   .
.   .   x   .   .   x   .   .   .   .
.   .   .   x   .   .   .   .   .   .
.   .   .   .   o   .   .   .   .   .

 .   .   . 1200  .   .   .   .   .   .
 .   .   .   .  951  .   .   .   .   .
 .   .  498  .   .  702  .   .   .   .
 .   .   .  249  .   .   .   .   .   .
 .   .   .   .   0   .   .   .   .   .
Split fourth pentatonic 
.   .   .   .   .   .   .   .   .   .
.   .   .   .   .   .   .   .   .   .
x   .   .   .   .   .   .   .   .   .
.   .   x   .   .   .   .   .   .   .
.   .   .   .   o   .   .   .   .   .

 .   .   .   .   .   .   .   .   .   .
 .   .   .   .   .   .   .   .   .   .
362  .   .   .   .   .   .   .   .   .
 .   .  181  .   .   .   .   .   .   .
 .   .   .   .   0   .   .   .   .   .
Split neutral third cluster 
.   x   .   o   .   .   .   .   .   .
.   .   .   x   .   .   .   .   .   .
x   .   x   .   .   x   .   .   .   .
.   .   x   .   .   .   .   .   .   .
.   .   .   .   o   .   .   .   .   .

 . 1064  . 1200  .   .   .   .   .   .
 .   .   .  883  .   .   .   .   .   .
362  .  498  .   .  702  .   .   .   .
 .   .  181  .   .   .   .   .   .   .
 .   .   .   .   0   .   .   .   .   .
Split neutral third tetrachordal scale 
.   .   .   o   .   .   .   .   .   .
.   .   .   .   .   .   .   .   .   .
.   .   x   .   .   x   .   x   .   x
.   .   .   .   .   .   .   .   .   .
.   .   .   .   o   .   x   .   x   .

 .   .   . 1200  .   .   .   .   .   .
 .   .   .   .   .   .   .   .   .   .
 .   .  498  .   .  702  .  838  .  974
 .   .   .   .   .   .   .   .   .   .
 .   .   .   .   0   .  136  .  272  .
Split subminor third tetrachordal scale 
.   .   .   o   .   .   .   .   .   .
.   .   .   .   .   .   .   .   .   .
.   .   x   .   .   x   x   .   .   x
.   .   .   .   .   .   .   .   .   .
.   .   .   .   o   .   .   x   x   .

 .   .   . 1200  .   .   .   .   .   .
 .   .   .   .   .   .   .   .   .   .
 .   .  498  .   .  702 770  .   .  974
 .   .   .   .   .   .   .   .   .   .
 .   .   .   .   0   .   .  204 272  .
Marwa permutation based on Archytas' diatonic tetrachord 
.   .   .   o   .   .   .   .   .   .
.   .   .   x   .   .   x   .   .   .
.   .   x   .   .   x   .   .   .   .
.   .   .   .   .   x   .   .   .   .
.   .   .   .   o   .   .   x   .   .

 .   .   . 1200  .   .   .   .   .   .
 .   .   .  883  .   . 1087  .   .   .
 .   .  498  .   .  702  .   .   .   .
 .   .   .   .   .  385  .   .   .   .
 .   .   .   .   0   .   .  204  .   .
Major scale 
.   .   .   o   .   .   .   .   .   .
.   .   .   x   .   .   x   .   .   .
.   .   x   .   .   x   .   .   .   .
.   .   x   .   .   x   .   .   .   .
.   .   .   .   o   .   .   .   .   .

 .   .   . 1200  .   .   .   .   .   .
 .   .   .  883  .   . 1087  .   .   .
 .   .  498  .   .  702  .   .   .   .
 .   .  181  .   .  385  .   .   .   .
 .   .   .   .   0   .   .   .   .   .
Major scale (repeated tetrachord) 
.   .   .   o   .   .   .   .   .   .
.   .   .   x   .   x   .   .   .   .
.   .   x   .   .   x   .   .   .   .
.   .   x   .   x   .   .   .   .   .
.   .   .   .   o   .   .   .   .   .

 .   .   . 1200  .   .   .   .   .   .
 .   .   .  883  . 1019  .   .   .   .
 .   .  498  .   .  702  .   .   .   .
 .   .  181  .  317  .   .   .   .   .
 .   .   .   .   0   .   .   .   .   .
Dorian scale (repeated tetrachord)

Naren Ratan, 2026