The Tone and Semitone
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.
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.
elevación de dos semitonos
elevació de dos semitons
elevación de un semitono
bajada de un semitono
disminució d’un semitò
bajada de dos semitonos
disminució de dos semitons
The Chromatic Scale
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.
The Boston Microtonal Society Website discusses the problem of what a microtone is.
Interpretations of the term microtonal vary widely, and for our purposes it is useful to note the following two basic types of usage:
1) The most literal and narrow definition of the word microtone has as its reference point the Western tone (or whole tone). If a semitone is half of a tone (in terms of cents*), then anything smaller is classified as a microtone, or microinterval, according to this definition. (More specific names are "quarter-tone," "fifth-tone," "eighth-tone," "sixth-tone," etc.)
* Alexander J. Ellis' system for measurement of musical intervals, in which the equal-tempered semitone equals 100 cents, the whole tone 200 cents, the octave 1200 cents, and so on.
2) The most general, inclusive—and most common—usage of the term microtonal is its application to any music made using intervals other than the traditional intervals of 12-note equal temperament (with its multiples of 100-cent semitones and 200-cent whole tones), which has been the standard tuning for Western music since the mid-nineteenth century.
If we consider this second, more general application, we can easily see that there are a variety of artistic, theoretical and philosophical channels through which musicians may be drawn to those 'other intervals'. As a result there are a few different disciplines, only loosely inter-related, all of which may fall into the category 'microtonality'. These include:
- the practice of simply adding pitches to 12-note equal temperament (most often through microtonal equal temperaments such as 24-note (quarter-tones), 36-note (sixth-tones), 48-note (eighth-tones), 72-note (twelfth-tones), 96-note (sixteenth-tones), etc.)
- contemporary pure tuning methods such as the various modern forms of just intonation, Pythagorean and mean-tone tunings
- historically accurate tunings of Medieval, Renaissance, Baroque and Classical pieces
- the study of non-Western tuning systems
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
trois-demi de bémol (French)
double bémol barré (French)
bemol y medio (Spanish)
||1/4 tone flat
bémol barré (French)
bémol inversé (French)
||1/4 tone sharp
dièse barré (French)
demi dièse avec une seule barre verticale (French)
||3/4 tone sharp
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.
no. of quarter tones from unison||
no. of semitones or half steps from unison||interval description||
|1|| ||quarter-sharp unison||+u|
|quarter-flat minor second||-m2|
|3|| ||quarter-sharp minor second||+m2|
|quarter-flat major second||-M2|
|5|| ||quarter-sharp major second||+M2|
|quarter-flat minor third||-m3|
|7|| ||quarter-sharp minor third||+m3|
|quarter-flat major third||-M3|
|9|| ||quarter-sharp major third||+M3|
|quarter-flat perfect fourth||-P4|
|11|| ||quarter-sharp perfect fourth||+P4|
|quarter-flat augmented fourth||-A4|
|12||6||augmented fourth = diminish fifth||A4|
|13|| ||quarter-sharp augmented fourth||+A4|
|quarter-flat perfect fifth||-P5|
|15|| ||quarter-sharp perfect fifth||+P5|
|quarter-flat minor sixth||-m6|
|17|| ||quarter-sharp minor sixth||+m6|
|quarter-flat major sixth||-M6|
|19|| ||quarter-sharp major sixth||+M6|
|quarter-flat minor seventh||-m7|
|21|| ||quarter-sharp minor seventh||+m7|
|quarter-flat major seventh||-M7|
|23|| ||quarter-sharp major seventh||+M7|
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)What is Microtonality?
Centre for Microtonal Music
John Starrett's Microtonal Music Page
Graham's Microtonal Website
NewMusicBox.org - Issue on Microtonality
Where Are the Microtones? by Julia Werntz
Legacy of Microtonal Music in the 20th Century by Anton Rovner
World Scale Depository
Graphic Representation of Some Gamelan Tunings by Bill Alves
Mande Jeli Balafon Tuning
Xian Shi Yue Tuningby Mercedes DuJunco
A Gentle Introduction to South Indian Classical (Karnatic) Music by Mahadevan Ramesh
Hear Various Bagpipe Chanter Tunings by Ewan Macpherson
This whole field is considered in greater depth in Pitch, Temperament and Timbre.
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