Music Theory Concepts
HARMONY - 2
  • What is Harmony?
  • Chord
  • Types of Chords
  • Versatility of Triads
  • Labeling the Chord Functions
The word harmony is a very common one. It is not surprising – since its meaning is congruency, accordance, which are the qualities we are so often striving for in our lives. Harmony has a very special place in music also, where it presents a vertical component of the music texture. In a narrower sense, it can present also a theoretical discipline dealing with composing and connecting of the chords. Sometimes the word harmony is used also as a synonym for a chord itself.

A chord is a common sound of at least three different notes played (or sung) together.

Chords consisting from three notes are triads, chords of four, five and six notes are ninth, eleventh and thirteenth chords.

Click the picture for sound.
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Chords can consist from different intervals. The basis for a traditional harmony is a triad chord in thirds (derived from the row of overtones).
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Some other intervals – fourths, fifths, seconds can also be a material for chord building. Chords built of adjectant (diatonic or chromatic) scale degrees are described as tone-clusters.
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There are many other ways and possibilities of building chords – either with combining the possibilities named above or completely different. In the following example you can see a triad with added second, a bichord and a mirror chord.
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  • Chords by thirds
  • Cords by fourths
  • Chords by fifths
  • Chords by seconds
Basic chord of common-practice harmony is the triad. Diatonic triads (built on major and minor scales degrees) in root position are consisting with combining the intervals of major and minor third. These are major, minor, diminished and augmented triad. A major third (M3) and a minor third (m3) with an enclosing perfect fifth (P5) make a major triad. m3 and M3 with an enclosing P5 make a minor triad, two m3 with an enclosing dim5 make a diminished triad and two M3 with a enclosing aug5 make an augmented triad:
The basis on which all the mentioned triads are built is called a root which is a fundament and acustically the most important note (combination tones). The other two tones of the triad are a third and a fifth. A third of a major and a minor triad is sometimes called also a characteristic tone (since it determines a »tone gender«), a fifth – if perfect can be named also an »empty« fifth.
A triad can be constructed on any of the tones mentioned. A triad with its root as its lowest tone is in a root position. If built on a third (root is moved an octave higher) – a triad becomes a sixth chord or first inversion. Functions of the chord tones remain the same. Major sixth chord consists of m3 and P4 with an enclosure of m6.
A triad with its fifth as its lowest tone is a six-fourth chord or second inversion. Functions of the tones in triad remain the same again. A major six-fourth chord is built from P4 and M3.
Inversions of the minor, diminished and augmented triads can be constructed in the same way. A minor sixth chord consists of M3 and P4 with enclosing M6 and six-fourth chord of P4 and m3 with an enclosing m6.
Diminished sixth chord consists of m3 and aug4 with an enclosure of M6. Diminished sixth-fourth chord is bult from aug4 and m3 vith enclosing M6.
Augmented sixth chord consists of M3 and dim4 with an enclosure of m6. Augmented sixth-fourth chord is bult from dim4 and M3 vith enclosing m6.

 

TRIADS ON DEGREES OF MAJOR AND MINOR SCALE

Triads can be built on all of the scale degrees. In major scale and natural minor scale three major, three minor and a diminshed triad can be found. Harmonic and melodic minor scales give two major, two minor, two diminished and an augmented chord:
  1. chords on a major scale degrees:
      
2. chords on a natural minor scale degrees:

3. chords on a harmonic minor scale degrees:

4. chords on a melodic minor scale degrees:

How wolud a resume of these chords/scales look like? Let us classify the resuts from above into a table::

 

durov trozvok
major triad

molov trozvok
minor triad

zmajšani trozvok
diminished triad

zvečani trozvok
augmented triad

(naravni) dur
(natural) major

I, IV, V

II, III, VI

VII

/

naravni mol
natural minor

III, VI, VII

I, IV, V

II

/

harmonični mol
harmonic minor

V, VI

I, IV

II, VII

III

melodični mol
melodic minor

IV, V

I, II

VI, VII

III

Triad of fourths with its inversions:

Triad of fifths with its inversions
Comparing both the above examples it can be stated that only the two root position chords are different and their inversions are identical. Triad of seconds brings a different picture:

VERSATILITY OF TRIADS

From the previous chapter it could be stated that in major and all the forms of minor scale all of kinds of diatonic triads can be found. If we compare different tonalities, we can notice that the same triad can be found not only in one but in more of them. A human with many different ocupations is called versatile and the same term is used for chords as well. Let us take a closer look on the triads on  scale degrees of C-major and d-minor:

Chords are mostly different but d-minor triad is presented in both scales. In C-major it is placed on the second degree and in d-minor on the first degree. Is this everything or can we find d-minor chord somewhere else also? A table we constructed before will be helpful by answering this question. The triad which versatility we are examining is a minor chord and the table shows that minor chord can be found at IIIrd, VIth and VIIth degree in three different major scales. Which are these scales? If we take into consideration that the triad is lying on the II. degree of a certain major scale and if we know that in major scale IInd degree is a M2 above the Ist one, we can conclude a major scale with the tonics which is a M2 below the root of the d/minor chord is to be found… d –>c:

We just proved again the conclusion from the beginning of this chapter. But in similar way we can find another two major scales that contain d-minor chord – Bb-major (d-minor triad on the IIIrd degree) and F-major (d-minor chord on the VIth degree. Let us find with the help of the table also the minor scales containing the d-minor triad:

d-minor scale has been found – where d-minor triad is on the Ist degree of all three forms of this scale. The same triad can also be found on the IVth degree of natural and harmonic a-minor scale, on the Vth degree of natural g-minor and on the IInd degree of natural and harmonic c-minor. Following this procedure it is not difficult to find a versatility of all the diatonic triads – we only need to remember the table and we need to know the interval structure of the major and minor scales.This explanation is too brief to expect from one who read it to be skilful vith the versatility of triads immediately. For a good knowledge of it some practice is necessary, off course (a special trainer will be dedicated to this issue).It is important to know however, that the multiple apperance of triads is bringing some certain »bridges« among tonalities. »A switch, a transition« of the musical flow using such a »bridge« from one to another tonality, is called a diatonic modulation or a modulation with a common chord.

LABELING CHORDS' FUNCTIONS

Sound space, formed by chords of a certain scale and some characteristic connections among them (e.g cadences) is called a tonality. The most important chord of the tonality, a center of a tonal gravity and sort of a tonal »home« (since it is a point of departure and a final chord) is a tonic chord (T). With a sensible, musical use of the scale chords, with awareness of their mutual relations and tensions among them and towards tonic chord the basics for shaping of whole the tonal music is set. Placement of the chords in the music flow is not accidental – the chords are fulfilling their characteristic »roles«, usually called – functions. Triads of the Ist, IVth and Vth degrees of scale are so called primary chords – pillars of tonality and a skeleton of the tonal music. Other, side chorda are functionally subordinated but in their sound not less important as the primary ones.There are different ways of labeling the chords' functions. Let us take a look of them:
a) labeling the primary triads and their parallels is based on the functions of major and its parallel minor scale (m3 lower) degrees. The side triads, parallel to the primary ones sre lying in major scale a minor third below and in minor scale a minor third above the primary triads. Their names are Tp – tonic parallel, Sp – subdominant parallel and Dp – dominant parallel. A common picture of the parallel major and minor scales shows that the primary triads in major scale make parallel triads in minor scale and vice versa:
In harmony the relations among chords are of a great importance. In this text let it be mentioned only that two chords are related with each other when they contain at least one common note. More of the common notes they have - stronger the relationship is (closer together are the chords in a sense of their function and their sound). The tertial relationship is a strong one, since such chords have two common notes. It means that a primary chord and its parallel side chord (that are in tertial relationship) are importantly connected and close in function. This way of labeling chords has a weakness, however: it is functionally exposing only one of the primary triad tertial related chords  (a. e. T-Tp etc.) but not also the second one (which in major is lying a third above and in minor a third below the primary triad). Futhermore e.g. the VIth degree triad is in minor labeled as subdominant parallel although in praxis it usually acts as a chord with predominate tonic function.
b) Labeling of the side triads with both the tertial related primary triads has its origin in russian harmony and is succesfully solving the problem mentioned above:
Side degree triad includes the characters/functions of the tertial related primary chords indeed, but in fact usually only one of the primary tertial related chords function is really dominating. E.g. the IIIrd degree triad is acting in most cases either as tonic or as dominant chord but it can not present both T and D together.Thus many authors are using simple
c) neutral labeling of the scale triads with the roman numerals:
Such labeling was used already by establishing versatility of triads. The weakness of this method is that the primary triads are visually completely equalized with the side ones what differs from the factic state. It is not good in a harmonic analysis if the primary triads are not emphasised as more important chords,  pillars of the tonality.  Well tested and succesful solution is
d) labeling of the scale triads with the combination of letters and roman numbers:

We can present even more pieces of information with usage of capital letters for major chords and capital letters with added + for augmented ones and on the other hand lower letters for minor chords and the same ones with added ° for diminished triads. With this method the difference between primary and side triads, functional character of the side chords is opened and the quality of the chord is clearly defined.

© Dušan Bavdek
Contact: leon.stefanija@ff.uni-lj.si