Musical intervals

Content

In music, the separation between two musical notes is called interval. The concept of interval is extremely important; in fact, in our experiment in the search for musical notes it was the discovery that notes separated by a fair fifth interval played in unison produced a pleasant harmonic sound which allowed us to obtain the twelve notes of the chromatic scale employed in Western music.

Intervals trainer

To help you in the study of musical intervals, a trainer has been included below that will allow you to listen and become familiar with them. It also allows you to evaluate your ability to recognize these intervals; but keep in mind that refining this ability, what is called relative ear, is something that may take some time. To facilitate the use of this coach, and keep this page simple, the Interval Trainer Manual. has been included separately.

Note that both below the circles corresponding to the notes on the scale and below the square boxes in the interval identification section, three rows have been included; the first corresponds to the position of the notes on the C chromatic scale (also to the hours on the dial of the clock in the clock analogy), the second row to the notes on the scale using sharps, and the third to the notes on the scale using flats. In this page our interest will focus on the first and second rows, the omission of the third row does not prevent to treat all the intervals. When we study the scales it will be necessary to also consider the flat notes in order to adapt what has been learned to the nomenclature used in classical notation.

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Interval characteristics

The procedure for naming intervals normally used in music theory is quite elaborate: the first part of the name constitutes its quantity and is determined by the number of accident-free note names (without sharps or flats) found in its length, and its second part refers to its quality and depends on the scale on which it is measured. For example, in the C scale used in the trainer the interval from C4 to G4 involves the five notes C, D, E, F and G; therefore it is a perfect fifth interval. As these pages do not pretend to make a formal exposition of the theory of music, we are mainly interested in the extension in semitones of each of these intervals, and we will limit ourselves to their names on our fundamental scale: that of C Major. In cases in which it is important to highlight the quality of an interval, we will use the most appropriate denomination in the context of the presentation.

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Familiarization with the intervals

Below we will describe the use of the most important intervals in the approach adopted in these pages.

• The increased first interval corresponds to a semitone and can be considered as the unit of measure of distance between notes. Normally we will refer to it simply as a halftone, and with that name we will use it in the construction of scales.
• The second major interval corresponds to a full tone. Normally we will refer to it simply as a tone,and with that name we will use it in the construction of scales.
• We will use third intervals in the harmonization of scales. The major third interval is also used in the tuning of some frets instruments, including the guitar, ukulele, and cuatro.
• The perfect fourth interval is one of the most used in tuning fretted instrumentss.
• The perfect fifth interval was the first recognized as appropriate in our search for musical notes,and led to their finding. It is used in the tuning of mandolins and violins.

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Consonance of intervals

In order to understand and use the concepts of harmony that we will introduce in these pages it is important that you become familiar with the degrees of harmony or dissonance of each of the possible intervals on the chromatic scale. The following experiment will help you achieve this goal.

The perception of consonance or dissonance is something subjective; however, in our western culture there is a certain consensus in this respect, summarized in the following table:

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Use of intervals

Up to this point we have considered isolated intervals; next we will see that it can be useful to consider sequences of intervals.

You'll probably find the second one; here's why. The first triad is made up of a major third interval and a major second interval (equivalent to a minor third interval), both with a consonant (harmonious) sound, while the second triad is made up of an augmented first interval, which has a sound that implies some distress (and was therefore used and emphasized in the musical theme of the film "Shark") and another augmented sixth interval (diminished fifth), which is not as harmonious as the perfect fifth interval. Together these non-consonant intervals produce a frankly dissonant triad.

In the page corresponding to the study of chords we will use our discovery that a succession of a major third interval and a minor third interval harmonizes with the lowest note, the tonic, to generate triads to harmonize the rest of the notes of the major scale. Note that the colors that we agree to assign to them on the beginning of these pages have been used for notes belonging to the major scale, while the gray color has been used for the notes not belonging to this scale. We will then be using a diatonic harmony.

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