Topic: Music theory

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Math and structure in music: the Circle of Fifths

Music theory Tunings, Temperaments, and Scales

In music theory, the circle of fifths (or circle of fourths) is the relationship among the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys. More specifically, it is a geometrical representation of relationships among the 12 pitch classes of the chromatic scale in pitch class space.

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Parsons code

Music theory

The Parsons code, formally named the Parsons code for melodic contours, is a simple notation used to identify a piece of music through melodic motion — movements of the pitch up and down. Denys Parsons developed this system for his 1975 book The Directory of Tunes and Musical Themes. Representing a melody in this manner makes it easier to index or search for pieces, particularly when the notes values are unknown.

The book was also published in Germany in 2002 and reprinted by Piatkus as The Directory of Classical Themes in 2008.

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Picardy Third

Music theory

A Picardy third () (French: tierce picarde), also known as a Picardy cadence, is a major chord of the tonic at the end of a musical section that is either modal or in a minor key. This is achieved by raising the third of the expected minor triad by a semitone to create a major triad, as a form of resolution.

For example, instead of a cadence ending on an A minor chord containing the notes A, C, and E, a Picardy third ending would consist of an A major chord containing the notes A, C, and E. Note that the minor third between the A and C of the A minor chord has become a major third in the Picardy third chord.

Musicologist Peter Kivy writes:

Even in instrumental music, the picardy third retains its expressive quality: it is the "happy third". ... Since at least the beginning of the seventeenth century, it is no longer enough to describe it as a resolution to the more consonant triad; it is a resolution to the happier triad as well. ... The picardy third is absolute music's happy ending. Furthermore, I hypothesize that in gaining this expressive property of happiness or contentment, the picardy third augmented its power as the perfect, most stable cadential chord, being both the most emotionally consonant chord, so to speak, as well as the most musically consonant.

According to Deryck Cooke, "Western composers, expressing the 'rightness' of happiness by means of a major third, expressed the 'wrongness' of grief by means of the minor third, and for centuries, pieces in a minor key had to have a 'happy ending' – a final major chord (the 'tierce de Picardie') or a bare fifth."

The Picardy third does not necessarily occur at the end of a section: it can be found at any perfect cadence or plagal cadence where the prevailing key is minor. As a harmonic device, the Picardy third originated in Western music in the Renaissance era.

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