Division of string by whole numbers produces an higher gentle sound named harmonics or flageolet
Division by whole number from 2 to 6 produces intervals and harmonics that yield a major triad (neglecting octaves)
Fundamental sound (or open string) is notated 1
The intervals are from the fundamental sound
Division of the string yields a shorter part and a longer part and therefore harmonics share only half the length of the string .
The starting point can be either the nut or the bridge . So,the fifth (1/3 of the string ) appears as well at the 2/3 of the string.
From the middle as axis, harmonics are mirrored symetrically
- only one way produces the octave(sound number 2) because it corresponds to the half of the string(2 equal parts)
- two possibilities for others harmonics (sounds number 3,4 and 6)
- third (sound Number 5)is the exception that can be played according 4 different theorical places (but only one is really satisfactory ,two are difficult because very close to the fifth) and one is practically unusable .
2:-Production of harmonics
There are two kinds of harmonics :
- The natural harmonics that produce the major triad (The root beeing the open string) Natural harmonics are played by slightly touching the string (notated ◊) at the exact place of the note (except for minor third played a bit higher) For clarity, the desired sound written in standard but smaller headed note may be added up. When the slightly touched note is similar to the desired sound (real harmonics) ,the note,in standard notation, is simply topped by °
This particularly occurs on the upper half of the neck.
Fifths can be produced on two adjacent strings.If a change in timbre is required, the string is specified
If you are a bit clever and very obstinate, the Seventh-harmonics can be emitted but only in first position and preferably in a arpegiated dominant seventh chord due to the proximity of the already difficult fifth and the possible unsuitable octave;those three intervals been located in the small interval between Bb(slightly higher) and A (on the G string) ; The notation is as insure as intonation.
I suggest to contact the performer.
The artifical harmonics that allow to emit any tons.
The index finger normally stops the string while the third or fourth finger slightly touches the string at distance of fourth,fifth,major third, minor third, or octave
that produce a major triad which root is the stopped note accordingly to the interval
The interval are therefore similar to the natural harmonics ones.
However those interval are not equally available.
The fourth (that yields the octave of the root )is the commonest along with the fifth(producing the 12th 5th+octave)
The thirds are very difficult
Octave are mostly theoretical .They are only available on the upper part of the neck where intervals between fingers are smaller but very difficult and somewhat useless.
- Octave is a combination of fifth on the lower string and fourth on the higher string.The upper note of the first interval is the lower note of the other interval creating a unisson.Unisson requires an extension of fingers making scales in simultaneous octaves difficult. Furthermore ,the two lower notes,forming a fifth, require a simultaneous stopping with the index finger
Broken octaves are a bit easier to play: a motion of translation of the fingering
- Unisson:The fingers combination is reversed The common fifth is stopped with the pinky .
this combination can be extended to an octave span
- SixthsIt very difficult to make 2 harmonics ring simultaneously. The fingering is uneasy
- Thirds: Fingering for chromatic succession of third tierces is easier than for the sixths because the progression between open strings is parallel in all parts but the difficulty to make them ring is the same.Natural scale adds difficulty with it major-minor interval succession
Natural harmonics is marked either
- ◊ =Note slightly touchedwith optionnal addition of the result in smaller headed note
- by a standart note topped with ° that means either
Real harmonics (that sounds as played ) or « desired « note whatever the mean of production
Artificial harmonics The only difference is the fundamental (stopped note) marked at the bottom
Some careless composers only add ° to the desired note and let the choice of technique to the performer( sometimes in perplexity)
Czardas for violin solo (With careless notation)