Professional preparatory music theory: Basic elements of music theory.

Chapter 4 of the Basic elements of music theory – by Oscar van Dillen ©2014-16

 

The advanced learning book can be found at Outline of basic music theory.

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Building blocks of harmony – part 2: Intervals

Pages and chapters:

Chapter 1: Introduction
Chapter 2: Musical notation
Chapter 3: Building blocks of harmony – Scales
Chapter 4: Building blocks of harmony – Intervals
Chapter 5: Building blocks of harmony – Chords
Chapter 6: Keys and key signatures
Chapter 7: Further study

Intervals

• An interval is the harmonic relationship between 2 tones.

A more simple description runs: an interval describes the distance between two tones. This distance is then measured by a scale in the background.

Names of intervals

The names are partly counting numbers (some derived from Italian music theory), starting with the lower tone as 1, so for example upwards from d to a counts as d, e, f, g, e = 1, 2, 3, 4, 5 = basic tones with a as 5th, meaning d–a is called a fifth. This counting part of the interval name is always counted against a background of the 7 basic tones c, d, e, f, g, a and b.

This leads to the following basic names of intervals:

But, as we know from our study of scales: there are whole tone and semitone steps between tones. This means there are two types of seconds. And therefore also of thirds and others. So to give an exact name to an interval a double indication is needed: the qualitative and the quantitative naming:

• the quantitative naming describes the distance, this can be unison 1, second 2, third 3, fourth 4, fifth 5, sixth 6, seventh 7 or octave 8;
• the qualitative naming describes the sound quality, this can be major M, minor m, perfect P, augmented A or diminished d.

Music theory distinguishes further between harmonic and melodic intervals:

• in an harmonic interval, the two tones sound at the same time (simultaneity);
• in a melodic interval, the two tones sound one at a time, either ascending or descending.

Seconds

Following are the harmonic whole- and semitone distances, and these are the seconds:

In this and the following examples, only basic tones without accidentals are used, so you can see the intervals in their simplest form, with their names in abbreviations below. M2 = major second, m2 = minor second.

• of the seven basic tone seconds, only 2 are minor and 5 are major (2:5 ratio)

The seconds are here presented harmonically (sounding simultaneously) but are normally used in melody as well. Seconds in harmony are also relatively full of tension in sound, which is why they are classified among the dissonants. The intervals which are commonly used as the basis of most harmony are the consonant thirds.

Thirds

Here are the basic tone thirds:

The difference in sound between a major third M3 and a minor third m3 is essential in harmony, and often used as a means for expression of emotions. Thirds are called imperfect consonants.

• of the seven basic tone thirds, 3 are major and 4 are minor (3:4 ratio)

Fourths

With the fourths and the fifths, we come into another sound quality, called: perfect consonance. This can be recognized by a stronger sounding-together, with also one of the two tones being more prominent, taking on a function of a root, a fundamental tone. In perfect fourths, the root is the top tone; this can be checked by adding one by one each of the tones in a bass register, evaluating the sound.

Although fourths, which are also used to tune the open strings of a (bass) guitar, are counted among the perfect consonances, they retain an element of perceived tension, especially in a lower register. This is why they are treated with special care in chord progressions when they occur relative to the bass.

• of the seven basic tone fourths, 6 are perfect and only 1 is augmented (6:1 ratio)

Tritone

The augmented fourth A4 deserves a special passage. The distance here is f–g–a–b, 3 whole tone steps (6 semitones together). In the reverse order, called inversion, this would be b–c–d–e–f, 2 whole- and 2 semitone steps (also 6 semitones together). The two are the same size, which is a unique phenomenon: it means they cannot be distinguished by acoustic hearing! For this reason, these intervals have a special common name:

• the common name for the acoustic sound of both an augmented fourth and a diminished fifth is the tritone;
• the inversion of a tritone is a tritone, it is the only interval acoustically identical to its inversion.

Fifths

All the larger intervals are inversions of the smaller ones treated before, as is demonstrated in the examples following, starting with the fifths:

The exact same two tones making up a fourth make up a fifth as well, depending on their position.

• An inversion is an alternative vertical order of the same tones, with another tone as lowest (bass);
• Any interval plus its inversion adds up to a perfect octave.

Fifths are even stronger prefect consonances than fourths; they are traditionally used for tuning the open strings of violins, violas and cellos.

Sixths

As can be heard in these examples, the sound of inversions resembles that of the original intervals. But it is not the same as well! Careful study and training is needed to not confuse these pairs of related sounds, especially the consonants may sound very much alike at first.

Nevertheless, the sixths are the intervals used to check the tuning of a piano, just because of their imperfect consonance, their inner vibrations, called the beating, a rather subtle aspect of sound.

Sevenths

The sevenths are all dissonances, the major by far the more sharply dissonant of the two, resembling its inversion the minor second, but a very different and open sound at the same time.

Octaves and unisons

To complete the set of intervals, and their inversions, the octaves and their inversions, the unisons, are listed below, and all of these are are perfect, a 7:0 ratio:

Consonance to dissonance in intervals

Below, an order of intervals is shown, by acoustic sound quality, from most consonant to most dissonant:

To better appreciate the sound, and the relative acoustic dissonance evolving from left to right, this example notates all the intervals in a lower register, and uses also one and the same lower tone of each interval, low c. The place of the tritone is remarkable, but its tension is really somewhere between the minor and major seventh, and it is sometimes confused with the former.

• the perfect unison, octave, fifth and fourth are perfect consonances;
• the major and minor thirds and sixths are imperfect consonances;
• major and minor seconds and sevenths are dissonances;
• the tritone (and all other augmented and diminished intervals) are dissonances.

EXERCISES 8

• Read intervals of a melody: what is the interval to the next tone;
• Read intervals of a harmony: what are the intervals in a chord;
• Sing each and all the intervals to any given tone, upward at first;
• Sing each and all the intervals to any given tone, downward next;
• Write out all the intervals to all chromatic tones in both treble and bass clefs, both upwards and downwards.

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goto chapter 5 ► Building blocks of harmony – Chords

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Oscar van Dillen ©2014-16