THE AMAZING, OPTIMAL DIATONIC GUITAR OR HARMONICA-GUITAR OF 6-STRING OR 12-STRING , TUNING.
See also post 164 and 407.
ABOUT ISOMPORPHIC 2-DIMENSIONAL LAYOUTS FOR KEYBARDS STRING INSTRUMENTS TUNINGS AND SOFTWARE PADS FOR ARRANGING THE MUSICAL NOTESAND THEIR IPORTANCE IN IMPROVISING SEE POST 310.
THE MAIN IDEA OF THIS TUNING OF THE 6-STRING GUITAR IS TO APPLY THE DIATONIC TUNING OF AN HARP ON EVEN OR ODD STRINGS OR AN HARMONICA, VERTICALLY AMONG THE STRINGS, WHILE LETTING THE FRETBOARD ENHANCE IT CHROMATICALLY IN THE USUAL WAY.
Here is a diatonic rather than chromatic version of the isomorphic layout based on alternating major-minor 3rds:
https://www.youtube.com/watch?v=OwiF_ATumKM
Normally a guitar with the standard tuning is a chromatic instrument e.g. compared to diatonic wind instruments like a recorder or a diatonic tuned Celtic harp. But there is a natural harmonic diatonic tuning of the guitar.
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
ABOUT ISOMPORPHIC 2-DIMENSIONAL LAYOUTS FOR KEYBARDS STRING INSTRUMENTS TUNINGS AND SOFTWARE PADS FOR ARRANGING THE MUSICAL NOTESAND THEIR IPORTANCE IN IMPROVISING SEE POST 310.
THE TERM ISOMORPHIC REFERS TO THE CHORD-SHAPES THAT REMAIN THE SAME (ARE ISOMORPHIC) WHEN CHANGING THE ROOT NOTE AS LONG AS THE TYPE OF THE CHORD REMAINS THE SAME.
Isomorphic layouts: What they are and why they are awesome for your music
THE MAIN IDEA OF THIS TUNING OF THE 6-STRING GUITAR IS TO APPLY THE DIATONIC TUNING OF AN HARP ON EVEN OR ODD STRINGS OR AN HARMONICA, VERTICALLY AMONG THE STRINGS, WHILE LETTING THE FRETBOARD ENHANCE IT CHROMATICALLY IN THE USUAL WAY.
Here is a diatonic rather than chromatic version of the isomorphic layout based on alternating major-minor 3rds:
https://www.youtube.com/watch?v=OwiF_ATumKM
Normally a guitar with the standard tuning is a chromatic instrument e.g. compared to diatonic wind instruments like a recorder or a diatonic tuned Celtic harp. But there is a natural harmonic diatonic tuning of the guitar.
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 ( default scale Bb) or F2-A2-C3-E3-G3-B3 (default scale F major) or A2-C3-E4-G4-B4-D4 (default scale C major) or G2-B2-D3-F#3-A3-C4 (default scale G major) or B2-D3-F#4-A4-C#4-E4 (default scale D major) or G2-Bb2-D3-F3-A3-C4 (default scale Bb major)
Notice also the tuning of alternate minor and major thirds seem to occur for a 5-string Mexican instrument the Jarana huasteca https://en.wikipedia.org/wiki/Jarana_huasteca)
As notes ,
The 1st string , counting from lower to higher defines the Aeolian 6th mode, the 2nd string the Ionian 1st mode, the 3rd string the Phrygian 3rd mode , the 4th string the Myxolydian 5th mode , the 5th string the Locrian 7nth mode, and the 6th string the Dorian 2nd mode.
As triad-chords,
1) the first 3 strings , starting from the lower to the higher (e.g. in the last tuning, the G2-Bb2-D3) create the Aeolian mode of the default diatonicscale (here Bb).
2) The next 3 strings (e.g. in the last tuning, the Bb2-D3-F3 ) create the Ionian mode of the default diatonic scale (here Bb).
3) The next 3 strings (e.g. in the last tuning, the D3-F3-A3 ) create the Prygian mode of the default diatonic scale (here Bb).
4) Finally the last 3 strings (e.g. in the last tuning, the F3-A3-C4 ) create the Myxolydian mode of the default diatonic scale (here Bb).
As notes ,
The 1st string , counting from lower to higher defines the Aeolian 6th mode, the 2nd string the Ionian 1st mode, the 3rd string the Phrygian 3rd mode , the 4th string the Myxolydian 5th mode , the 5th string the Locrian 7nth mode, and the 6th string the Dorian 2nd mode.
As triad-chords,
1) the first 3 strings , starting from the lower to the higher (e.g. in the last tuning, the G2-Bb2-D3) create the Aeolian mode of the default diatonicscale (here Bb).
2) The next 3 strings (e.g. in the last tuning, the Bb2-D3-F3 ) create the Ionian mode of the default diatonic scale (here Bb).
3) The next 3 strings (e.g. in the last tuning, the D3-F3-A3 ) create the Prygian mode of the default diatonic scale (here Bb).
4) Finally the last 3 strings (e.g. in the last tuning, the F3-A3-C4 ) create the Myxolydian mode of the default diatonic scale (here Bb).
THIS MAY BE CALLED THE HARMONIC TUNING OF THE GUITAR AS IT IS BASED ON THE HARMONIC 2-OCTAVES 7-NOTES SCALE (see also post 79)
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 (as in strumming) 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 unsurpassed.
At the same time , the easiness with which one can make 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!
The main advantages are
1) Greater number of major or minor triads per number of frets, thus easier chord playing
2) Less number of chord-shapes, thus easier guitar to learn
3) The shapes of chords require less number of frets
4) 1st inversion chords require only 1 or 2 frets, thus have easier shapes and are easier to play
5) In the melodies the notes are closer in total thus easier to find by the fingers
The main advantages are
1) Greater number of major or minor triads per number of frets, thus easier chord playing
2) Less number of chord-shapes, thus easier guitar to learn
3) The shapes of chords require less number of frets
4) 1st inversion chords require only 1 or 2 frets, thus have easier shapes and are easier to play
5) In the melodies the notes are closer in total thus easier to find by the fingers
6) Because the chords are in one or 2 only frets, their arpeggios also and neighboring melodies are in fewer frets thus easier to play as finger picking style.
7) The odd number of strings or the even number of strings are in intervals of 5 (7 semitones) thus as in the tuning of Cello, Octave mandolin , Viola, Violin , mandolin , Irish bouzouki, mandocello etc therefore any one trained to play solos in the previous instruments can keep his knowledge and play the same solos in such an harmonic tuned guitar (on odds or even strings).
Also the isokratic technique in the 3-courses instruments tuned so as to contain a 5th like bouzouki, boulgari, tampour , saz where two string a 5th apart accompany the melody on another string still applies in the harmonic guitar as all odd and even number strings are tuned a 5th apart. Nevertheless compared to the previous instruments (violon , mandolin etc) in the harmonic guitar the 3-notes or 4-notes major or minor chords , or diminished and augmented chords are played radically easier with one or two rarely 3 frets and is the densest such placement on the fretboard among all tunings of the guitar . At the same time any guitar jazz player one trained to play 3-notes chords (triads) in the standard guitar and especially on the 4 highest strings can keeps his knowledge and with slight modifications apply it to the harmonically tuned guitar. Furthermore any one playing the panduri (a russian or georgian folk 3-courses instrument coming from ancient Geek panduris, which is tuned in open major or minor 3-notes chord) will pass his knowledge to this harmonic tuned guitar in the upper 3 or middle 3 and lower 3 strings!
7) The odd number of strings or the even number of strings are in intervals of 5 (7 semitones) thus as in the tuning of Cello, Octave mandolin , Viola, Violin , mandolin , Irish bouzouki, mandocello etc therefore any one trained to play solos in the previous instruments can keep his knowledge and play the same solos in such an harmonic tuned guitar (on odds or even strings).
Also the isokratic technique in the 3-courses instruments tuned so as to contain a 5th like bouzouki, boulgari, tampour , saz where two string a 5th apart accompany the melody on another string still applies in the harmonic guitar as all odd and even number strings are tuned a 5th apart. Nevertheless compared to the previous instruments (violon , mandolin etc) in the harmonic guitar the 3-notes or 4-notes major or minor chords , or diminished and augmented chords are played radically easier with one or two rarely 3 frets and is the densest such placement on the fretboard among all tunings of the guitar . At the same time any guitar jazz player one trained to play 3-notes chords (triads) in the standard guitar and especially on the 4 highest strings can keeps his knowledge and with slight modifications apply it to the harmonically tuned guitar. Furthermore any one playing the panduri (a russian or georgian folk 3-courses instrument coming from ancient Geek panduris, which is tuned in open major or minor 3-notes chord) will pass his knowledge to this harmonic tuned guitar in the upper 3 or middle 3 and lower 3 strings!
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 in the harmonically tuned guitar, 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 HARMONIC 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.
In post 67 are also described harmonically tuned 4-course (Greek 4-courses bouzouki, ukulele, mando-lele etc) or 3-courses (Balalaika, Greek 3-course Bouzouki) instruments that are easier to play but have the same remarkable advantages due to the harmonic tuning.
E.g. for 4-course , the tuning D3D4-F3F4-A4A4-C4C4 abd for 3-courses the F3F4-A4A4-C4C4 or
G3G4-Bb4Bb4-D4D4.
THE DIATONIC-GUITAR OR HARMONICA-GUITAR HAS A DIRECT ADVANTAGE OF APPLYING THE CLASSICAL GROUP OF VARIATIONS OF MELODIC THEMES AS IN POST 279 (TONAL TRANSLATIONS BY 3RDS AND 5THS OR 4THS IN AT LEAST 2/3 OF THE CASES AND CHROMATICALL IN AT MOST 1/3 OF THE CASES). THE MELODIC THEME SUCH TONAL TRANSLATION BY 3RDS OR 5THS/4THS IS SIMPLY SHIFTING THE MELODIC THEME FROM ONE STRING ON THE SAME FRET VERTICALLY TO THE ADJACENT STRING ( A 3RD) OR NEXT TO ADJACENT STRING (5TH OR 4TH).
THERE ARE 3 MAIN WAYS THAT TWO TRIAD-CHORDS HAVE HARMONIC RELATION ON THE FRETBOARD OF A 6-STRING SUCH GUITAR
1) By inversting the interval of 5th that each fret has with the samE fret but two strings higher
2) By and interval of 4th that each fret has 2 frets lower and 2 strings higher (as created by the same interval of 5th as before but one tone lower onthe higher string)
3) By an interval of 4th as created on two succcesive strings that have always an intervalof 3rd and an additional interval of 2nd twoards higher.
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.
In post 67 are also described harmonically tuned 4-course (Greek 4-courses bouzouki, ukulele, mando-lele etc) or 3-courses (Balalaika, Greek 3-course Bouzouki) instruments that are easier to play but have the same remarkable advantages due to the harmonic tuning.
E.g. for 4-course , the tuning D3D4-F3F4-A4A4-C4C4 abd for 3-courses the F3F4-A4A4-C4C4 or
G3G4-Bb4Bb4-D4D4.
THE DIATONIC-GUITAR OR HARMONICA-GUITAR HAS A DIRECT ADVANTAGE OF APPLYING THE CLASSICAL GROUP OF VARIATIONS OF MELODIC THEMES AS IN POST 279 (TONAL TRANSLATIONS BY 3RDS AND 5THS OR 4THS IN AT LEAST 2/3 OF THE CASES AND CHROMATICALL IN AT MOST 1/3 OF THE CASES). THE MELODIC THEME SUCH TONAL TRANSLATION BY 3RDS OR 5THS/4THS IS SIMPLY SHIFTING THE MELODIC THEME FROM ONE STRING ON THE SAME FRET VERTICALLY TO THE ADJACENT STRING ( A 3RD) OR NEXT TO ADJACENT STRING (5TH OR 4TH).
THERE ARE 3 MAIN WAYS THAT TWO TRIAD-CHORDS HAVE HARMONIC RELATION ON THE FRETBOARD OF A 6-STRING SUCH GUITAR
1) By inversting the interval of 5th that each fret has with the samE fret but two strings higher
2) By and interval of 4th that each fret has 2 frets lower and 2 strings higher (as created by the same interval of 5th as before but one tone lower onthe higher string)
3) By an interval of 4th as created on two succcesive strings that have always an intervalof 3rd and an additional interval of 2nd twoards higher.
