The Tone and Semitone

Returning to the keyboard we introduced in the previous lesson, we now consider the difference in pitch between one key and its neighbour.

If we count the number of keys between the key C with the asterix * (we call this middle C) and the key marked with a B that lies just below the C above (i.e. to the right of) middle C we find that there are twelve keys (five black and seven white) that match the twelve different notes on the stave below.

The difference in pitch (the pitch 'interval' or just interval), between a key and its immediate neighbour is called a semitone, meaning 'half' a tone. Two semitones are equivalent to a 'whole' tone. Where there is no black key between them (for example, between B and C) neighbouring white keys are a semitone interval apart. If there is a black key between them (for example, between F and G) neighbouring white keys are a tone interval apart. In this case the black key (F sharp / G flat) is the white key's immediate neighbour and the interval between the white key F and the black key, F sharp/ G flat, is a semitone.

This is shown clearly in the diagram below.

The Octave

Sharpening or flattening the pitch of a note changes the pitch by a semitone, in the former case sharpening, increasing or raising the pitch by a semitone and in the latter case flattening, reducing or lowering the pitch by a semitone. Raising the pitch of a note by twelve semitones raises the pitch by one 'octave'. If the original note was C, the new note one octave higher will also be called C. In a similar way, lowering the pitch by twelve semitones lowers the pitch by an 'octave'. You might wonder why the word 'octave' which seems to have something to do with the Greek word for 'eight' (e.g. octagon - a shape with eight sides) is used in this situation. If you count the number of white keys that lie across an octave - as, for example, C, D, E, F, G, A, B and C again - you will see that there are eight, hence the word 'octave'.

Notice that the interval between each successive pair of notes on the two staves above is a semitone.

The pitch of a note can be raised by two semitones, in which case a double sharp sign is employed, while the equivalent for lowering the pitch by two semitones is the double flat sign. The double sharp and double flat signs are illustrated in the table below.

notation	English	French	German	Italian	Spanish	Catalan
	double sharp	double dièse	Doppelkreuz	doppio diesis	doble sostenido, elevación de dos semitonos	doble diesi, elevació de dos semitons
	sharp	dièse	Kreuz	diesis	sostenido, elevación de un semitono	diesi, sostingut
	natural, natural sign	bécarre, naturel	Auflösungszeichen, Quadrat	bequadro	becuadro	becaire
	flat	bémol	B, Be	bemolle	bemol, bajada de un semitono	bemoll, disminució d’un semitò
	double flat	double bémol	Doppel-B, Doppel-Be	doppio bemolle	doble bemol, bajada de dos semitonos	doble bemoll, disminució de dos semitons

The Chromatic Scale

The succession of all twelve semitones in ascending or descending order is the chromatic scale.

The standard 'convention', which we have mentioned before, is that sharp signs are using for rising chromatic scales and flat signs are used for falling chromatic scales.

We will return to this matter again in lesson 11.

Microtones

The Boston Microtonal Society Website discusses the problem of what a microtone is.

The quarter-tone is defined as that pitch which exists midway (48-50 cents or 2 Pythagorean commas) between any two semitones (half-tones), with neither semitone predominating. A semitone is equal to 100 cents. The quarter-tone may be considered a universal interval, like the tone and semitone, as it exists in numerous Eastern and Western musical cultures. Irish folk tunes, for example, sometimes feature the inclusion of 'half-sharp' notes, quarter tones mid-way between natural and sharp. [ref: Peter Cooper, Mel Bay's Complete Irish Fiddle Player, Mel Bay Publications, 1995]

Other divisions of the tone have their place in Eastern and Western musical cultures. The eighth-tone is measured at 24-25 cents (or, for example in Turkish music, a Pythagorean comma).

Quartertone Accidental Signs (there are other sign conventions)
	3/4 tone flat sesquiflat trois-demi de bémol (French) double bémol barré (French) bemol y medio (Spanish)
	1/4 tone flat semiflat semi-bemolle (Italian) bémol barré (French) demi bémol(French) bémol inversé (French) semibemol (Spanish)
	1/4 tone sharp semisharp semi-diesis (Italian) dièse barré (French) demi dièse avec une seule barre verticale (French) semisostenido (Spanish)
	3/4 tone sharp sesquisharp trois-demi de dièse (French) dièse avec trois barres verticales (French) sostenido y medio (Spanish)

We include below a quarter-tone/semitone or half-step interval chart.

While experimenting with his violin in 1895, Julian Carrillo discovered sixteenths of a tone, i.e., sixteen clearly different sounds between the pitches of G and A emitted by the fourth violin string. Because there are six whole tones in conventional tuning to the next octave, a musical scale made with sixteenths of each tone has 96 different notes or pitches. In contrast to this, the scale made with half-tones has only 12 different pitches.

References: (many taken from the Boston Microtonal Society Links Page)