This document is for strictly personal use only. No public use may be made, including in the course of teaching, without the prior consent of the author.

½
½

Tones and semitones

The tones and semitones constitute the unit of measurement of the intervals between the notes.

Principles

All the notes of the scale of C major are separated by a tone, with the exception of the pairs E-F and B-C.

FIGURE 1 - The tones and semitones on C major scale
1 tone 1 tone 1 tone 1 tone 1 tone ½ tone ½ tone

C major scale

Played on the piano.

Tones and semitones are easily visualizable on keyboard instruments. A tone is the interval between two white keys separated by a black key. A semitone corresponds to the interval between two white keys without being separated by a black key.

KEYBOARD 1  - The tones and semitones on the white keys of a keyboard (hover or click on the keys to view)
C B D D C E E D F F E G G F A A G B B A C C D D E F G G A A B C B D

Semitones

There are two types of semitones: the diatonic semitone and the chromatic semitone. It takes a diatonic semitone and a chromatic semitone to form a tone.

The chromatic semitone

The chromatic semitone is the interval separating a note with the same note raised by a sharp or lowered by a flat. A chromatic semitone has 5 commas.

FIGURE 2 - Examples of chromatic semitones
Ascendingchromatic ½ tone Ascendingchromatic ½ tone Descendingchromatic ½ tone Descendingchromatic ½ tone

To know more about the notion of comma, cf. Equal Temperament

The diatonic semitone

The diatonic semitone is the smallest interval separating two conjunct notes. It measures only 4 commas. The diatonic semitone always involves two notes with different and contiguous names (hence its qualification of dia-tonic, "of separate tones")

FIGURE 3 - Examples of diatonic semitones
Ascendingdiatonic ½ tone Ascendingdiatonic ½ tone Descendingdiatonic ½ tone Descendingdiatonic ½ tone

On a tempered keyboard (see below), the two previous examples will be executed in the same way, using the same keys.

To remember. A chromatic semitone is always formed by 2 notes with the same name. For example, G-G or E-E. Conversely, a diatonic semitone is always formed by 2 notes whose names are different. For example, G-A, or E-D.

The tone

A tone is formed of a chromatic semitone and a diatonic semitone. It therefore has a total of 9 commas.

FIGURE 4 - Examples of decompositions of a tone in two semitones
Chromatic ½ tone +Diatonic ½ tone = 1 tone Diatonic ½ tone +Chromatic ½ tone = 1 tone Chromatic ½ tone +Diatonic ½ tone = 1 tone

FIGURE 5 - Counterexample
Diatonic ½ tone +Diatonic ½ tone < 1 tone Chromatic ½ tone +Chromatic ½ tone > 1 tone Diatonic ½ tone +Diatonic ½ tone < 1 tone

To remember. A tone is always formed by two conjunct notes. For example, C-D or E-F. If the two notes are not conjunct (that is, if you can insert another note between the two), it is not a tone. For example, C-E: between C and E, there is D, so C-E is not a tone.

The octave

The octave is the smallest interval that separates two notes with the same name. For example, between two Cs, there is an octave.

An octave is thus formed by 5 tones and 2 diatonic semitones (see Figure 1 at the beginning of the course). Since a tone itself consists of a chromatic semitone and a diatonic semitone, the octave is thus formed of 12 semitones, of which 5 chromatic semitones and 7 diatonic semitones.

Equal temperament

Since the XVIIth century, Western music has adopted the system of equal temperament. The octave is divided into twelve equal semitones. These semitones, whether diatonic or chromatic have the same pitch difference in the ear. A tone is no longer divided into 4 + 5 commas but 4.5 + 4.5 commas. This technique allows, with a small concession to accuracy, to greatly simplify the tuning of keyboard instruments, which previously were tuned according to the key signature of the work that was to be interpreted. Since the appearance of the equal temperament, it is possible to play in any key on a keyboard instrument.         

        However, some contexts (eg for string instruments) need to take into account the difference between chromatic and diatonic semitones. Moreover, at the theoretical level, their differentiation is essential because it allows to understand many concepts such as the construction of scales or the qualification of the intervals, which is why, whatever the temperament used, it is important to be familiar with the concepts mentioned in this chapter.

Last update on 2018/12/03

Printing for premium user only !

Print this course with a high quality layout by subscribing at www.musiclever.com

Do you master the concepts discussed in this lesson?

Report a bug or an issue