It can be proved mathematically that the tuning with the highest number of chords per fret is the harmonic Guitar Tuning :
An optimal but unknown tuning for the 6-string guitar when chord-playing is the main target and not so much solo playing is by alternating minor and major 3rds. In semitones for the 6 strings 4-3-4-3-4 or 3-4-3-4-3
E.g. Bb2- D3-F3-A3-C4-E4 or F2-A2-C3-E3-G3-B3 or A2-C3-E4-G4-B4-D4 I tried the last one in the artiphon.
THIS MAY BE CALLED THE HARMONIC TUNING OF THE GUITAR AS IT IS BASED ON THE HARMONIC 2-CTAVES 7-NOTES SCALE (see also post 79 in my blog http://simplerguitarlearning.blogspot.gr/2018/04/88-remarkable-harmonically-tuned-6.html 3 )
The latter is the most natural open tuning. There the same shape for major and minor chords and only 3 of them and in only one or frets compared to the 6 in the standard tuning guitar. If we want also dominant and major 7nth chords we use again only 2 frets. The same with the aug chords Only the dim7 chords require 3 frets. Because of the symmetry of the tuning among the strings, the relations of relative chords and also chords in the wheel of 4ths is immediate to grasp also geometrically. Of course when we say shape of chords as it is standard in jazz, we do not play all 6-strings but only 3 or 4 strings.
The easiness with which one can improvise melodies within a diatonic scale (all notes within 3 frets and in a very symmetric zig-zag pattern) together with 3-notes chords of the scale (gain all chord patterns within 3-frets) is unsuprassed.
At the same time , the easiness with which one can me diatonic scale modulations, chromatic (1 semitone apart) or by changing a minor to a major chord and vice versa and continuing in a relevant diatonic scale is unsurpassed again!
This harmonic tuning by alternating minor-major 3rds, allows, for all 4-notes chords of e.g. the D major scale in the 3rd octave (c3,d3,e3,f3,g3,a3,b3), Cmaj7->Em7->G7->Bm6->Dm7->Fmaj7->Am7 in 1st normal position across the fretboard, something not possible with the standard tuning of the guitar. In the standard guitar it is possible only by 2nd or 3rd inversion, or by shifting to the 4th octave or 2nd octave. Therefore there are important very natural voicing of the 4-notes chords of the 3rd octave that we miss with the standard tuning and it is in a single octave!
THERE ARE 4 VERY SYMMETRIC WAYS THAT THE CHORDS IN A WHEEL BY 4THS CAN BE REPRESENTED AND PLAYED IN THE FRETBOARD WITH THIS TUNING.
WE ENLARGE IN THE NEXT WITH MAPS OF THE CHORDS AND THEIR SHAPES IN THE THREE WHEELS, THE ONE BY 4THS, THE ONE BY 3RDS AND THE CHROMATIC.
I do not have much space to write the 4-shapes and the 4 ways to represent the wheel of chords by 4ths in one only post, but maybe I will do it in the future in more posts.
Now talking about grids here is an idea that I call
THE MAGIC OF THE MELODIC CORRIDOR
An interesting question when designing settings for grid use of the fretboard in the Artiphon is "What is a geometric arrangement of notes of the 12-notes scale, that allows fast and easy “In the flow” playing and improvisation of melodies , especially tonal melodies with many intervals of 3rd 4th and 5th? (that is within the harmony of one scale) ?
The answer seems to have been given by the design of the next instruments
The Handpan and Hang
The thump piano
The double series of pipes zampona Pan-flutes.
And it is the natural sequence of notes of successive relative chords in a diatonic scale. It is the next scale:
The sequence of notes C3-E3-G3-B3-D4-F4-A4_C5 is 2-octaves 7-note scale by alternating minor and major 3rds (Small wheel of 3rds).
This scale is also the Harmonic tuning of the guitar (see a relevant topic by me in thsi forum ) which is optimal when chord playing is mainly the target and not soloing so much
THE MELODIC CORRIDOR
Constructing therapeutic harps, or similar instruments (e.g. thump pianos https://en.wikipedia.org/wiki/Mbira or hang and handpans or zamponas diatonic double row pipes, pan-flutes ) or such keyboards with this scale, has the property that almost what ever we play sounds harmonic as 3 or 4 notes in sequence are well known cords, and overlapping such triads , are relative chords. In fact we may design such an harmonic diatonic double row keyboard
Similarly this can be a beautiful , practical and harmonic tuning for harmonicas.
The blue is blowing and the red is draw. Then with the key we may have the sharps too thus in total
-D3- F3- A3- C3- E4- G4- B4-
-C4- E3- G3- B3 -D4 -F4- A4- C5-
-D3- F3- A3- C3- E4- G4- B4-
-C4- E3- G3- B3 -D4 -F4- A4- C5-
This type of tuning can be applied also as setting to 4 strings frets of the fretboard of the artiphon the midi-controller, and give it sound of adouble diatonic harp or flute etc.
Here is the image of the grid setting in artiphon
Melodic_CorridorMelodic_Corridor.jpg1366x768 278 KB
THIS KIND OF KEYBOARD OR TUNING OF INSTRUMENTS (FLUTES, HARMONICA, ARTIPHON , KEYBOARD ETC) ALLOWS FOR MELODIES IMPROVISATION IN A FAST WAY EASILY WITHOUT COMPLICATED FINGERINGS OBSTRUCTIONS AS LONG AS THE MELODY IS A DIATONIC SCALE. IT IS A BIT BETTER THAN PIANO KEYBOARD AS IT FOLLOWS THE SHAPING OF CHORDS BY INTERVALS OF 3RDS. IT IS EVEN EASIER THAN SINGING OR WHISTLING FROM THE HARMONY POINT OF VIEW!
The advantages are
The steps of the melody by intervals of 3rds are successive frets
The steps of the melody by intervals of 2nd (one semitone or one tone) are zig-zag frets among the two central strings
Steps of the melody by intervals of 4th or 5th are frets in the two central strings that have distance two only frets
The 1) 2) 3) are particular usefull when one wnat to improvise melodies with steps mainly intervals of 3rds ths and 5ths and less by intervals of 2nds (As e.g. in the Folk Irish and Celtic music).
The melodic corridor can be also be spotted on the fretboard of the standard tuning 6-string guitar. It will also define an unusual unique shape of the diatonic scale with 2 only notes per string.
I encourage to define the above grid settings on the artiphon and experiment by playing and improvising melodies (with flute sound or organ or vibraphone , or guitar etc)
A simpler uniform version of the Melodic Corridor is the Lippens Keybord, which is considered to be at least 20 times easier than the usual pinao keybord. It is based on the whole tones scale .
A pan-flute tuned to whole tones instead of a diatonic scale is already a simple Lippens Keybord
Here are two relevant videos
And here are the settings in the editor of the Artiphone for a simplest Lippens Keyboard
Try it and enjoy melodies