Posts Tagged ‘Counterpoint’

Two-part writing insight

dimanche, janvier 6th, 2013

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


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


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.


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.

Disappearance of church modes

lundi, novembre 26th, 2012

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.

Tonal Transposition

mercredi, février 16th, 2011

Transposition means playing a tune in another key
Transposition arises mainly in two situations

  • Put the music in a more suitable range: Especially for vocalist .Or for an easier fingering as seen in Schubert’ unfinished symphonyinachWith the Bb  clarinet this example is very difficult to play and the phrasé and intonation are  foolhardy. In some case, it allows to to extend the range of a timbre. The A clarinet can reach the C# (in pitch tone) insted of D with the Bb clarinet.
  • Write for transposing instruments ie that sound differently from written note

In the case of transposing instrument the aim is to keep the same fingering so that one can interchange instrument

For example alto sax Eb and tenor sax Bb would play C D E with the same fingering but it sounds Eb F G for alto sax and Bb C D for tenor sax

Technique (Especially for transposition at sight)

    1. Determine the interval of transposition

The interval is measured from the key of the transposing instrument to C (no sharp, no flat)

    1. Change notes name with help of clef

To determine the transposing clef

      • write the transposing note in treble clef (Bb for a clarinet in Bb for example)
      • Call this note C
      • Search the corresponding clef which is C,F or G
      • Use de correct key signature

The new tonality is given by C written in treble clef ,read in the new clef

    1. Adapt accidentals

This is the real difficulty that occurs frequently in minor mode.

Flats and sharps are not taken into consideration to find the clef

Practical method

From the previous page it brings out that there are only three reversible steps in transposition that will add or substract flat or sharp to initial tonalities

Direction is given by clef

Here is a practical table that indicates the reading clef and change in key signature

To change  transposed part into real sound take the alternative with same step

example: to play piano part with clarinet in Bb :Use alto clef and add 2 #

To play Clarinet Bb part with Piano :Use Tenor clef and add 2 flats

Transposing instruments
More about clef

More about Key signature