Two-part writing insight

Disclaimer: this paper is a personal view on two- part writing way off the academic approach.

 

Two simultaneous notes form an interval while a greater number of simultaneous notes creates either chords or other terms such as Cluster that depend on school and music eras.

In a nutshell, counterpoint uses interval while harmony is based on chords; so Two-part writing is logically the concern of counterpoint.However,counterpoint is prior to tonal music and its rules, justified by Pythagorean intervals, are somehow obsolete with equal temperament. In an other hand, tonal  harmony stems from counterpoint and therefore shares some rules with it but  its at least three voices setting induces inaccuracy in two-part writing. That might be  the reason of the  scattered number of published methods

Hindemith is one of the most prominent contributors to tonal renewal of counterpoint but his sophisticated  method  might be hard to start with.

This paper is an attempt to draw some functional  implications of   intervals from tonal considerations .

1°) Scales

Tonal music consists of two modes: the Major mode and the  minor mode which can appear  under three aspects :

-The natural  scale or descending melodic scale similar to eolian mode with a subtonic instead of leading tone.

-The harmonic minor scale ;a leading tone replace the subtonic.

-The ascending melodic scale with a sharped sixth degree to correct the augmented interval created by the leading tone.

2°) Triads

Stacks of thirds over each scales degrees yield four kinds of triads

  1. Major triad made of a Major third and a minor third (from bottom to top)
  2. Minor triad formed by a minor third and a major third
  3. diminished fifth triad that consist of two minor thirds (to differentiate from consonant harmony)
  4. Augmented fifth triad made of two major thirds (which does not belong to tonal harmony)

3°)Scale degrees

Scale degrees are not equal in importance

The most important are I-IV-V known as primary or tonal  chords which support either a major or a minor triad according to the mode.

others chords are secondary chords that may be of any kind according to the scale.

4°) Chord inversion.

Any triad has two inversions but some are uncommon . As a rule, only primary chords can non-restrictively  be inverted. II and VII can be  inverted under some conditions.Other  chords are normally  not inverted but in sequence

Inversions result in chord structure changes.

5°) Omission of note

When  an  incomplete chord is needed the fifth  is generally omitted. Therefore,  chords  in root position appear under a third form (either Major or minor).

The third  is obviously omitted  in diminished fifth chord.

In tonal harmony the  third can be omitted

-in the Dominant chord and the Tonic chord if the key is well established. Thus, a perfect  fifth means V or I

in sixth  chords so first inverted chords are  under the form of a Sixth interval 

The fourth can be omitted  in 4/6  cadential  chord or the  passing  VII (b) on a weak beat

Removal of the sixth  may occur  in I6 ,V6  and  VII4/6 which occur under a minor third structure

6°)Analysis

3 means either 5/3 or 6/3.  Thus,  CE can CEG or CEA

6 is 6/3 or 6/4. EC can be EGC  or EAC

Primary chords prevails when interpreting  an Interval .Therefore, with CE  in CM we choose CEG=I5  but in minor we’d choose CEA=I6

The precedence is

I >VI>III  so EG  is I6 ,not III5 (In CM)

V>III GE is I4/6,not III5

IV>VI

but IV is equal II

From all those considerations  we can establish  the following guideline

7°) Rhythmic position

is the last consideration  to take into account: Especially  secondary chords should  be on weak beat.

Postlude:

Although the logic  is different from the classical taught  counterpoint, usage shows  a similar  result with  the classical writing rules so  Much ado about nothing but I did try.

Mirrors of the church modes

Mirrors tally ascending scale with descending scale (and vice versa).

For better comprehension few notions has to be kept in mind.

1°) Each scale degree is equivalent to a two fifths skip

with a slight default : F is sharp (#)

To remedy this we have to start our series a fifth below the tonic (F)

Starting on F results in a 7 diatonic notes series bordering the tonality
So C major scale limit are F and B : forming the Triton
2°) A note belongs to 7 tonalities according to an immutable order:
7 3 6 2 5 1 4 . So C is the seventh degree of Db,third degree of Ab and so on….


Notice the fifth series forms the triton Db -G ( triton of D Maj) which is symmetric to F-B and able to resolve on C

The seven fifths series forming a triton on C can be copied on the seven notes of the scale.With a two fifths shift we obtain the following table.

Notice

  • E corresponds to the tonality of E
  • D corresponds to O accidental.
  • The Tonality of C stretches from Gb to F#

3°) Pivots (common notes) appear only with pair number of accidentals scales
From the C major scale, we can write a scale in opposite direction that respects the tones and semitones position (mirror).Any chromatic note can start the mirror scale but only scale with pair number of accidentals(and 0) has common note (pivot) associated with a tonality

Mirrors adhere to the tones and semitones distribution according two options

  • Share the tonality  but that might make finales dissonant
  • Choose the common note (pivot)

Actually the two options rests on : pivots.
Since modes have no accidentals, D (associated with 0 accidentals) as pivot places the two scale in the same tonality.

The mirror of the ionian scale (C maj) is E min (with no accidentals) ( E phrygien) that’s why Vincent d’Indy considered it as « true minor relative »

The reverse is also true

We’ll use two tables to write mirrors.
The first table states the 12 tonality of C with the seven scale notes according to the normal fifths series order

  • First line give the key signature of the mirror scales
  • second line give the tonality of the mirror scales
  • Bottom line indicates the pivots

The prime scale is always in C whatever the mode since mode is only a different departure of the C scale

Table 2 indicates which degree of the tonality the mirror starts on(bottom line)

Pivot is the junction-point of the two scales but usually neither the tonic nor the starting point(finale) of the mirror (Finale)explaining the table 2 necessity.
The two first lines correspond to the ascending C Maj scale and define modes.
The two next lines are the descending C maj starting on E which is the true mirror (same tonality as the prime scale (given by the D pivot )

The bottom line figures are the interval between C and the tonic of the other tonalities.
This table shows how it is built but practically we need only two columns

We can see that each mode has its only one mirror mode

Summing up table

Example :To write the mirror of a Phrygian (E) scale with G as common note

G tallies with the Bb scale (column G) which starts on the first degree( Line E) (Bb).
A practical trick :The tonic of the mirror always correspond to E of the other scale (whatever the mode)
( E is the only pivot with common tonality;

Some more examples

Both examples having the same pivot share the Bb mirror scale but with a different starting note (tonic) coinciding with E of the prime scale

The pivot being D the mirror has no accidentals


Perfect mirror that share tonic and tonality but contradict the E rule

Modal Cadences

Another difficult and confused topic . Ancient church modes were declamatory melodies, sang in unison, which   phrases  ended with fixed melodic and rhythmic formulas  and therefore had no cadence, as we understand with our tonal mind.
The first real cadences (clausules) appeared with polyphony which caused: the disappearance of modes
We can trace back modal harmonic cadences to the 19th century when composers tried to destruct tonality .However,Tonal culture is so deep-rooted in our mind that we want to make modal music a kind of tonal music transcription ( especially due to functional harmony).
Modal cadences are not conclusive as would be tonal cadences and are generally used to « add an transitory color » to a phrase.
But let’s first remind some tonality elements

 

.

  • Tonality is based upon physical law of resonance with ascending harmonics that explain the Major triad.
  • Minor triad is more difficult to account for since there is not a descending resonance (in normal conditions ). However we saw (in the mirrors of the church modes) that an ascending major scale had its specific descending minor scale .( a major third above the major scale)
  • Tonal music consists of two modes based upon the third (IIIth degree) that determines
    -The Major mode ( III Majeur) which have 3 strong Major degrees (I- IV-V)
    -The minor mode (iii mineur) with 3 strong minor degrees strong (I- IV- V). However the 7th scale degree must be half a tone of the tonic to look like the major scale so the V th degree is altered and became a Major Chord.

Modern harmonic modality can be approach from different point of view.
The most intuitive is the minor mode without leading tone like the Aeolian mode with a minor Vth degre) for both ascending and descending scales resulting in change in degrees numeration . Cadence traces tonal cadence (v-I) for ascending scale or plagal (iv-I) for descending scale

We may consider semi tones as  leading tone : ascending LT B-C and descending LT F-E

According to the slope direction , two possible dominantes and two possible leading tones are available.

Remark :In tonal music progression B -C, B is leading tone because the semitone leads to a strong degree (The tonic ) while F is not a leading tone because it leads to a weak degree (III).

In the tonal progression F -E, F is not a leading tone because the semitone lead to a weak degree however E,as  descending mirror, is the  tonic and therefore a strong degree : thus F becomes a descending leading tone .

Let’s place a triad on the Vth degree of each scale in ascending and descending forms


Among those V degree chords let’s select those with one of the two possible leading tone F or B which is not at the bass

Besides the ascending Aeolian mode,only two chords appear

  • ii from the original C maj scale(Dm)
  • Dominant 7 chord ( GBD et B D F)

Dominant 7 chord appears under two forms GBD and BDF
BDF can’t be used due to the triton that would resolve to C maj.However, adding the sixth from the descending Aeolian scale enable the BDF chord to form a common dominant chord (DFAB) to Ionian(CM )and Aeolian (am) scale.

Notice that the sixth (B) placed on the( II chord ( dfa) is the leading tone of the ascending scale.
Let’s generalize the method by adding ascending leading tone to descending scale and reversely

  • Ionian Mode GBD ,resolving to CM, is ruled out and FAB as well since it adds a second dissonance to the triton leading to C major). The solution is FAC: creating a plagal cadence
  • Lydian Mode  is particular because we can neither use BDF which lead to C Maj scale nor CEG that would resolve to the F Major scale -The solution is GBDwhich contains the characteristic note and the leading tone altogether
  • Mixolydian Mode : The only possible chord is DFA with added sixth (B) DFAB

    • Aeolian Mode: we keep DFAB for its dominant chord characteristic in a plagal progression IV

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    We can of course use EGB but it’s less characteristic

  • Dorian Mode: Two chord progression are available (ACF) III6– and (GBD)IV-I
  • Phrygian mode The CM titron rules out the BDF chord) so we keep the ACF chord with the so called phrygian cadence II6-I

Another approach

As discussed in old church modes, Octave were divided into two tetrachords. There are different kinds of tetrachord:Four are part of old church modes (3 with perfect fourth and 1 with augmented fourth) and one perfect fourth tetrachord that does’nt belong to church mode:The harmonic tetrachord

The place of the semitones gives the direction of the slope,ascending on the right,descending on the left ,no slope in the middle
Considering Modes as two associated tetrachords

Lydian and Locrian modes do not allow two disjunct tetrachords and therefore those modes are the association of a pentachord and a tetrachord
Notice

    • -The central position of the semitones in minor tetrachord
    • -Ascending slope of the major tetrachord
    • -Descending slope of the phrygian tetrachord .

Association of two opposed sloped tetrachords

Lydian and Locrian modes concentrate semitones in a tetrachord
It should be observed

      • -The Dorian scale is a pivot scale with central position of semitones making this scale ambiguous with no slope
      • – The symmetry of th Ionian,Dorian and Phrygian modes E
      • -The inverted mirror ot Mixolydian and Aeolian modes

Conclusion

This last approach helps to choose progression according of the slope of the scale and a tool for counterpoint which is by essence related to mode

Another  hint

Let’ s write our scale as triads , not as a succession of triads but rather like a three voices counterpoint to take into account the respective location of semitones

The three minor scales share those three chords


The three Major scales share those three chords
However those chords do not necessary content the characteristic tone of the mode.
Adding a 6 th , 7th or 9th make things very interesting provide they don’t create the triton F-B which suggest the C scale.
We also may use medieval cadences discussed in
disappearance of church modes and the Baroque cadences which are similar to the medieval cadences but they may lead to a third interval (instead of octave or fifth)

 

 

Last Hint

We can make a tracing of functional Harmony according to two schools

1-The  Niedermeyer-Ortig’s french school  which uses tonal progression but chords  building abides by the mode (so V can be a minor chord)

2- The Persichetti’s american school which makes a distinction between  three kinds of chords

-The primary chords :The tonic chord and chords that contains the distinctive note of the mode.

-The secondary chords :chords that don’t contains the distinctive note of the mode.

-The Chords to avoid because of tritone  that lead to major mode.(It can be a primary chord with an added  7th  or 9th

PERSEC

 

to summarize

Modal music is mostly melodic based on intervals and two functions Teneur (kind of dominant) and Final (Tonic). Its harmony is rather static and baffle functional harmony

The old church modes

Their theoretical constitution is very simple : With C Maj scale for reference (old Ionian mode ) we play one octave starting on each degree of the scale

Table 1:
Names are objectionable due to confusion in their origins.

Thus the mode phrygian (E) mode in the middle age was called  Dorian under Platon .

Futhermore Greek names do not refer to ancient Greek scales which were descending but to ascending scales from probable byzantine origin.
Another difficulty stems from Gregorian songs, from which church mode were born,that are under two forms

  • -The authentic form that begins by the finale (our tonic); but the scale may start on one degree below ; so Dorian mode (from D to D) may extend from C to D
  • -The plagal form that starts a lower fourth below the authentic one. The name is then preceded by the prefix Hypo so Dorian is the authentic and Hypo Dorian the Plagal form( from A to A)  of the same mode

 

It is simpler to consider octave either as the association of

a pentachord and tetrachord that share a common note (authentic mode )

    • or an tetrachord and a pentachord ( plagal mode)

. The finale is the first note of the pentachord in both forms

Table 2 Mode Authente et Mode Plagal

Table 3:Shows ambiguous span

Some modes share their range :The authentic phrygian mode (E ) is   similar to  plagal  Aeolian mode   (hypoéolien) , or authentic mixolydian mode similar to the plagal ionian mode.

The  difference between authente and  plagal rests upon the  teneur (our dominant); but here again things are not so simple:
In  authentic mode , the  teneur   is normally  a fifth  above THE  FINALE  but if  the teneur  is B it becomes C
In the  plagal form, the teneur is  normally a fourth above the finale but it might be a third or a sixth above the finale .

Table 4: Finales and teneurs

To crown it up accidentals (especially F# and Bb)was gradually introduced to set up the semitone tone of leading tones .

Others accidentals might appear in the descending forms . All those changes led to the reduction of the number of modes  to the only major and minor modes of the tonal system.

Remark

The 14 modes previously listed are pure theory and don’t reflect the confused historical reality.
Classically there are only 8 byzantine modes ( D E F G ) under the 2 forms.

 

For simplicity we’ll  keep the nomenclature of scales without   accidentals of table 1, currently used especially in jazz music.

Characteristic Notes and key signature

Each mode has a characteristic note except the Locrian mode that has two characteristic notes
This note is said characteristic because it makes the difference between the tonal scale and the parent C Major scale.

For example the Lydian mode starts on F and runs on one octave without  alteration  so it is different from F major which has a Flat (Bb) . The characteristic note is therefore B=4th degree of the F maj scale.

For the minor modes (dorian, phrygian et locrian) one must reason from the major relative
For example the phrygian mode (mode of E) is a minor scale without alteration  while, E minor is the relative G major scale with a sharp(F#) ),the characteristic note is therefore F: second degree of the E scale

Remark Aeolian mode has not a characteristic note since it is the relative of C major (no accidentals)

Let’s draw a table to enable characteristic note finding and transposition .
1°)From tonal notes CFG and their minor relative ADE, plus B by assimilation to minor mode,our table looks like this

2°) Key signature adaptation
F major scale is a fifth below C Maj To transpose the F major scale to C major one must add a fifth.
The trick is to count the number of degree from the tonic (N1) to C . Reporting the number of degree from C give the new key signature

In minor modes the goal is not C but A

 

We can now complete our table

    • Mode of Fa :Key signature of G major 1#
    • Mode of Sol:Key signature of F major 1b
    • Mode of Ré: Key signature of E Minor=G major 1#
    • Mode of Mi: Key signature of D Minor=F Major 1b


Notice : characteristic notes are either F or B (the triton of CM)
Locrian mode is  particular since its tonic  fifth is diminished . It’s origin is not a relative major scale like other minor mode but its third being minor it can be assimilated to a minor scale to used our trick ( from B to A = 7 degrees: A +7= G Minor= 2b )

Transposition

1°) Write a mode in another tonality
Our table give the direction to the key signature modification.(Toward more  flats/less sharps or More sharps/less flats)
Examples :
1-to write an A lydian scale ( F mode)
– Lydian=Major mode so we have to adapt A major scale(3#)
-our table reads 1 # to add to to scale
So A lydian is a scale with 4# (starting on A)

2-To write a Eb lydian scale (F Mode )
– Lydien =Major Mode so we have to adapt Eb Major scale(3b)
-Our table indicates +1 # so flats go opposite (-1b)
Eb lydian is a scale with 2 b (begins on Eb)

3-To write a G phrygienne scale (E Mode )
– Phrygien =Minor Mode Mineur – we have to adapt G minor scale –Major relative Bb= 2b
-our table read+1 b
G phrygian is a scale with 3b flats and start on G

Caution the reference minor scale have no accidentals(but the stuctural one of the major relative) and therefore no leading tone

Building a kind of sliding rule will make things easier especially for minor modes.

1°) Writing a mode in another tonality (Key center)
The fixed part( règle fixe) is a fifths series from 6b to 6 # on the upper part and the corresponding tonalities on the lower part
The movable part( règle mobile) is the same fifths series with a colored part indicating the seven modes .

By coinciding the note of Mode from the movable part with 0 accidentals ( C) ,key signature are given for tonalities on the fixed part .

With our former example A Lydian scale ;from the movable part align F= Lydian mode with O on the fixed part;  from A on the movable part A we reads 4# on the fixed part

Same thing for minor mode : D ( Dorian mode ) facing 0 accidentals (CM),  A Dorian is a scale with 1#

2°) Identifying a mode from a tonality
We use the same fixed part of our sliding rule and reverse the fifths series on the movable part,using only the 7 modes (from F to B).

The tonality is on the movable part facing 0 of the fixed part. The movable part lists the 7 modes coinciding with key signature on lower fixed part
Example A scale with 1#.What is the mode?
Align A from the movable part with 0 on the fixed part, the 1# column reads D on the movable part
So A scale with 1# is a A Dorian scale

Key signature

Tonal system is based upon Major and minor scales but the reference scale is C maj that

  • Begins with C
  • Has neither flat nor sharp
  • forms the following tone-semitone succession:A more comprehensive approach is to consider major scale as two disjointed tetracordsThis presentation displays two symetrical patterns T-T-S

Reproduction of Tetrachord in either directions requires some adaptation to keep the pattern of tone and semitone

← Each tetrachord adds a flat                                  Each tetrachord adds a sharp →
Two scales with a fifth apart have a common tetrachord and one with an adding alteration (sharp in ascending progression,flat in descending progression

Begining a scale on each degree of the C Maj scale requires mainly additionnal sharps to keep the maj scale pattern

Scales sorted by increasing number of sharp produce an ascending progression of fifths

Scales sorted by increasing number of flat produce an ascendig progression of fourths

put together

In equal temperament Gb and F# are enharmonic (sound the same) and close up the progression

Since the scale is made of 7 notes,7 possible flats and sharps are available.

However we saw in the previous page that 6 flats and sharps yield the same note
Gb/F# said enharmonic (in our modern tempered system) so the progression closes up forming the so called Fifths cycle

Combination of the 7 flats and sharps would produce ,including C maj, 15 theorical scales ,but due to enharmony only 12 scales are available.

0 and 6 are common,7 are excluded (6 closes up the circle)

Tonalities with sharps.

The order of the sharps is a fifth series:F C G D A E B:
The Last sharp of the key signature is the seventh degree(leading tone ) of the scale so the tonality is half a tone higher

For example Key signature = 3# tonality=A maj

Conversely what is the key signature of B maj?

Last sharp is A# Key signature=5 sharps

As seen previously, the last sharp of the key signature is the seventh degree(leading tone ) of the scale then comes the third degree,the sixth etc

the complete serie is

Tonalities with Flats

The order of flats is a fourths series: Bb Eb Ab Db Gb Cb Fb

Tonality is given by the flat before last

for example : Key signature= 4 flats
tonality=Ab maj

The trick is one flat. The tonality is F Maj to be learn by heart

Key signature is the flat after tonality

For example : key signature of Db maj ps 5b

The last flat is the Fourth degree of the scale then comes the first, the fifth and so on…. in the reverse order of the sharps one

Tonalities of minor scales

As previously mentionned Tonal system is composed of major and minor scales. So a key signature shares two scales:

    • a major scale
    • a minor scale called « relative » whose tonic is a minor third below

So C Major → A minor

In transposition we don’t need to bother to know if the scale is major or minor in the first instance, just decide how many sharps or flats to add or to remove.

The difficulty is then to adapt the accidentals of the two minor scales

  • The Harmonic scale with its sharped Seventh degree in ascending and descending scale as well
  • The two Melodic scales with their 6th anf 7th degree altered in going up and both degree natural in going down
    Those two melodic scales are independant
    but under this presentation melodic scale it’s sometimes called Rameau’scale

Key signature of Major and minor scales

Key signature of Church modal scales

Church modes are based on C Major scale. Each degree of the C Maj scale becomes the tonique of a scale with neither flat nor sharp.

A practical method to find the key signature of those transposed modes is to build a sort of sliding rule.

  • The fixed part reads key signature
  • the moveable part indicates the fifths circle

By coinciding the tonic of the mode with 0
Key signature is given by the corresponding tonality

Example:Key signature of F on Dorian scale

Dorian = D mode so D=0
Tonality= F so 3b

As a whole

 

A  new tool indicates the key signature of a given tonality in the different church modes.

It is specially useful to know which mode you’re in


What mode is it?

By coinciding the given tonality (here D) with 0

Key signature is given for each mode: Here 2b reads E=Phrygian mode

Disappearance of church modes

Because church modes still prevails in numerous cultures, « Desertion » could be a proper word.

Actually the reducing evolution of mode that give birth to tonal music,based upon only two modes, is a very slow process that makes difficult to find a proper word to describe it.

There are many reasons that lead to the disappearance of modal scales.

    • One of the main reasons results from the way to avoid the triton F-B in polyphonies by lowering B, so it becomes Bb, or altering F into F#.
    • the second reason is a rule of counterpoint: an imperfect consonance(thirds and sixths) followed by a perfect  consonance is better approached by a semi-tone in one part and one tone in the other part
      A or B are better than C

      In three part this rule yields the double leading tones cadence which is of two kinds

      1-Machaut cadence:The two upper parts contain an half tone, opposed to the Bass:

      Adding a cambiata produces a Landini cadence


      2-Phrygian cadence:The two upper parts contain a tone, opposed to the bass

The third factor is the movement to a fifth lower at the cadence which created a forbidden dissonance seventh with the double leading tones cadence. So the authentic cadence is born: a major third resolving into an octave and a movement of fifth but leading to the disappearance of double leading tones cadence the F mode and G mode at the advantage of the C mode due to the necessary adaptation to avoid the dissonance seventh

To summarize we can say the main cause of the change is the growth of polyphony

* X th century with melody accompanied with parallel fifths or fourths.
* XI th century the melody starts and ends with the same note (named final, now tonic) and is accompanied with oblique motion which begins and ends in unison preceded by major second.
* XI-XIIth century introduction of the contrary motion with a major second as pre-cadential dissonance and a fifth added to the tonic
* The third is henceforth a imperfect consonance (formerly a dissonance) XIII th century cadence with double leading tone according to the rule of counterpoint edicted by Jean De Murs) The final chord has no third.
Consonance (8-5-4) evenly appear at the beginning of each « perfection » (group of 3 breves); there are non harmonic tones in short values between groups
* Ars Nova give up the rhythmic modes so consonances may appear on weak beat (XIVth century); the third is included into the fifth chord except in final position. Appearance of the movement V-I at the bass and the movement VII-I at the soprano {G-D-G}-{CGC}
* XVth Century: Instrumental music spread over the sonorous space with non modulating sequences on each degree. The third appears on the final chord so the authentic cadence is completed
*
* XVI-XVIIth centuries is period of great change:alteration to approach consonance by half step resulting in 12 divisions of the octave and the polyphonies that jut out the octave impeded to distinguish the authentic and plagal forms-another cause of disappearance of modes Adoption of the Zarlino’s system with pure third and false fifths will yield new rules of counterpoint such as to forbid direct fifth and change the rule of third and sixth which become perfect consonance.

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)

Clef and transposition

Introduction

Human voice full range would require an eleven lines staff to be represented

A readable survival of this fictitious staff lies in the grand staff

It clearly appears that the fictitious staff had to be reduced to a five lines staff to become readable.
Actually three staves were extracted from this imaginary eleven lines staff with an assigned letter,namely FCG, called « clef » to keep them distinct

    • The five bottom lines gave birth to the staff labelled F, the clef beeing placed on the fourth line from the bottom
    • The middle (sixth)line along with two lines on each side resulted in the C staff with the clef resting on the middle line (the sixth line)
    • The five top lines yield the staff labelled G with the clef on the second line from the bottom

  • The C staff is the medium register enclosed by the F and G clef
  • F staff is the low register
  • G staff is the high register

Clefs are always placed on a line and give their name to the note F,C or G

There are Seven clefs in usage (like the number of scale notes)

  • One G key
  • Four C keys
  • Two F keys

so a given note may received seven name

Clefs aim to limit to two ledger lines above staff so all clefs but treble key have the same range

Clefs are always placed on a line and give their name to the note F,C or G

Succession of clefs rely on the alignment of the reference pitch A which is or would be in a space

Summary: Clefs have Three functions

  • Name a sound
  • Give the pitch compared to the reference
  • limit the ledger lines above the staff and therefore enhance legibility

Clefs in transposition

Use of clef is especially valuable in transposition
For example: Play a violin /oboe /flute melody with a clarinet Bb .

Clarinet Bbmeans that C play with a clarinet sounds Bb (a tone lower) than violin or oboe C

therefore clarinetist Bb must play a tone higher than written
using the alto clef


Conversely if the oboeist wants to play the clarinet part ,he must play a tone lower using the tenor clefFrom the two preceding examples we notice agreement between clefs<

A complication may occur when transposing from bass clef .The reasoning is the same but the clefs are different

  • Reasoning with treble clefClarinet Bb : I say Bb=C and I write the Bb with treble clef and search the fitting  clef (remember clefs are always on one of the first four lines from the bottom)
  • Reasoning with bass clef
    Clarinet Bb : I say Bb=C and I write the Bb with bass clef and search the fitting clef

Transposition with two different transposing instruments

For example Playing the Clarinet in A part with a clarinet in Bb

The reasoning is the same provide the part to transpose is taken into account.
Clarinet Bb : I say Bb=A   I write the Bb with treble clef and search the fitting clef


Conversely ,Playing Clarinet in Bb part with a clarinet in A

Clarinet A : I say A=B  I write the A with treble clef and search the fitting clef

Important remark Neither accidentals nor register is taken into account by Clef transposition
so B is the same as Bb and E4 is similar to E2

Clef transposition in counterpoint

1°) Voce piena

Clefs in transposition was a common usage in old time.

In renaissance music a common texture named Voce piena was used . It consists of two groups made of two voices an octave apart (ST and AB)
The 2 groups form either a fourth or a fifth

Thank to clefs each voice had the same range notation

Two sets of clefs were used :


    • The Chiavi Naturali set
      that use the Soprano,alto,baritone and bass clefs

    • Tthe Chiavettes set that consists of treble,mezzo soprano,alto and baritone ot tenor clefs

Clef transposition in counterpoint:(cont..)

1°)Voce piena (cont..)

Switching from

    • naturali to chiavette causes a higher third transposition of plagal mode
    • chiavette to naturali yields a lower third transposition of Authente mode

  • other inversions are not valid

2°)Fugue

Subject and answer are similar in notation but the assigned proper clef makes answer  sounds a fifth higher or a fourth lower

Clef transposition in counterpoint:(cont..)

2°)Fugue

The reasononing is always the same
1°) Write a sound in given clef
2°)assigned the name of the desired transposed sound
3°) search the fitting clef

3°) Correspondance of clefs

Stage 1:Assign a name to the lower Note
Stage 2: Assign the transposed name to the upper(same note on the score)

Stage 3: Find the clef that names the note

The scale is given by the following sequence of clefs

C3 (Alto clef) F4 (Bass Clef)C2(Mezzo soprano clef) F3(Baritone clef) C1 (Soprano)C4 (tenor clef) G(treble clef) assigned to a given note

Transposition is a mere shifting of this sequence of clefs
Transposed C2 F3 C1 C4 G C3 F4
ROOT C3 F4 C2 F3 C1 C4 G
Interval 1 2 3 4 5 6 7

Pizzicati on violin

1-Background. A finger,usually ,the index finger ,plucks the string creating a kind of percussive note called pizzicato plural= pizzicati.
This mode of playing has two limitations compared to bow playing

  • 1. The speed of execution:
    Benjamin Britten cautiously notes » Presto possibile » in Simple Symphony. (104 to the quaver-note(crotchet) seems the limit for a sixteenth notes passage provide it is short.
  • 2.The register

There is no exact limit but it’s safer to adhere to the following for orchestra.

Extension of range has two indications

  • Arpeggiated chord in solo
  • Arpeggiated chord in orchestra when doubled with wind instruments.

2-Notation: The expression Pizz over the score starts the passage. The term Arco cancels Pizz

Other kinds of Pizzicati:

  1. Left hand pizzicato :marked Pizz Lh or + above the note :A finger stops the note while the next finger plucks the string. Other notes are arco
  2. Bartok : Bartok introduced to kinds of pizz
    The actual  Pizz Bartok orSnap Pizz    noted  :The string is pulled vertically and strikes the neck: Most effective on lower strings.           pizz glissando writtengliss pizz.  The normaly plucked note slides downwards or preferably upwards.
  3. Other :
    • Pizz used by Ligeti markedThe finger is placed between strings and touch the side of the string on the desired note spot .The right finger plucks the string
      It must not be mixed up with the Nail pizz
      which is a regular pizz  but using the nail rather than the flesh of the finger.It rings more clearly but it is not advisable since violonists have usually shortly cutted nails
    • Chords in pizz : writtenQuasi Guitare
      are played « Presto » and slightly arpeggiated from lower to upper strings. Chords have to be simple.
      Only cello is able to easily play arpeggio downwards.
    • pizz tremolo :

      very exhausting -Avoid lengths
    • Related Sound The note is produced by tapping the finger against the neck of the violin
      This ambiguous notation has many significances such as regular note played with high bow pressure producing a scratching sound or played with the bow behind the bridge but in this case only open strings are concerned See special effects

4-Switch Arco-Pizz:

Quick change requires to play at the frog of the bow

Special effects on violin

Special effects

  • Behind the bridge
    Notes are bowed or plucked(pizz)
    (Not to be confused with percussion
  • Sul tasto ou flautando (play over the neck)
  • Sul ponticello (play on or near the bridge) The expression Ord (ordinario)cancel those two expressions
  • Col legno Play with the wood of the bow
      1. Tratto (rub the string (as the hair would do)
      2. Battuto strike the string (kind of spiccato) Ord (ordinario)indicates to switch to normal bowing

     

  • Percussion Beside stopped notes related to pizz ,fingers, palm of the hand, or screw of the bow can execute rythme on different parts of the instruments. Notation depend upon each composer
  • Subharmonics or George Crumb’sPedal tones. Require an electric violin,high bow pressure and electrocoustic devices. The notation is in actual tone (bass clef added to the treble clef staffcrumbMore recently the violinist Mari Kimura evolved a bowing technique allowing the production of subharmonics on G string on a real violin. The interesting point is the technical mirror :the bow pressure must increase when straying from the bridge.