Intonation exercices

This  page  is an illustration of  What does means play in tune on violin

  • Harmonics 
     Harmonics technique yields eight notes out of the twelve chromatic scale notes.The four missing notes are in yellow
  •  Those four missing notes appear  as  Tartini’s third sound technique
  • tar
    int-tartarenc

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Public Domain Mark

Cette œuvre (Intonation exercices on violin, de Alain lefébure) est libre de restrictions de droits d’auteur connues

Harmonics on violin and its family

1: Background

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


Exemple On the G string :We can see that

      • 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 :

        1. 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.

Using a artificial harmonics on the next string for seventh  of the chord  is safer with a better intonation     7art

 

 


        1. 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.

Double harmonics

Artificial and natural harmonics can be combined on two adjacent strings

  1. 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
allows to fill the chromatic space between open string

is possible up to the following limits
    • 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

Recapitulation:

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)

Recapitulation cont…

Compositions using harmonics
The Inner voice
Irish theme

La Felicita (Second Mouvement)

Aires iIbericos (Cello)

Czardas for violin solo (With careless notation)

Tartini’s third tones

  • During the Baroque era ,theoreticians tried to link up music to  acoustics.  Nevertheless ,natural origin of the minor chord were difficult to explain. Rameau suggested the lower harmonics (the  Fm chord resulting  from the mirror of C Maj) that would be in sympathy with upper harmonics according to the  theory of resonance but he failed since in rejected the  7th division and mixed up the origin of  the  string division :

« The major third appears between the fourth and  the fifth  division of a string. Since the minor third appears between the fifth and sixth division of the string, the minor third is of the same kind of the Major third. »  

The issue is  the fundamental sound which is different:

Fourth division yields C

Fifth division     «  »    E

Sixth  division «  »         G

so  CE =major third  root=C

EG=minor third  root=E
Tartini evolved another  theory from the differential or resultant tones:Two notes played in pure intonation yield a faint note lower .

 

Those terzo suoni (third tones) or ghost tones are useful for intonation in double stops but unfortunately failed to explain the natural origin of minor chord since the minor third produces a major third (17 th) below.
Remark: interval from the bottom note of the double stops are similar to harmonics

 


Beware: for both Rameau and Tartini. »Natural » sometimes means  « physical »  based on resonance  and sometimes   purely mathematical .

 

 

I am a bit doubtful about the   Tartini’ s third tone, because nobody  seems talking about the same thing.

The physical phenomena used  for lower sound in organ or in otoacoustic emission study requires pure sounds which don’t fit with a violin (futhermore a Stradivarius )

The issue is that some bearings of the resultant tone,additive tone for example, are   posterior to Tartini,so we don’t know any longer what Tartini’s third tone is exactly.

I have read some excerpt of his treatise on  (differential) resultant tones that was obviously based upon  a mathematics view. I think this topics was only  supposed to prove the origin of the minor third  while his description of intonation technique,although related to resultant tone, was  from another  point of view.

Two simultaneous near frequencies yield beats which slow down then disappear  when frequencies fuse but speed up and swell when they stray until another pure tone appears (the third tone) when both sounds frequencies tally  with the  harmonics of a fundamental sound.

Later on  otoacoustic emission  was discovered: inner ear cells produce a rather loud sound in respond to two pure sounds with a similar intensity. This compound  sound consists of manifold sounds called « Distortion products » which frequencies are multiple of both injected sounds frequencies. D.P intensity is changeable  accord to their frequency the loudest intensity appears  when the ratio  F2/F1=1,22 (near the fifth value)

Neglecting his mathematical approach, we have a better understanding of intonation  Tartini’s  technique: a tuning with a inferior limit through beats disappearance  and a superior limit through a sound reinforcement .