page_title: Perfect fourth
section_title: Renaissance and Baroque
hierarchical_section_title: Perfect fourth / History / Renaissance and Baroque
caption_attribution_description: English: Cadences and the ending of the piece from Palestrina and Orlando di Lasso
context_page_description: A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth is the fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, because the note F is the fifth semitone above C, and there are four staff positions between C and F. Diminished and augmented fourths span the same number of staff positions, but consist of a different number of semitones.
  The perfect fourth may be derived from the harmonic series as the interval between the third and fourth harmonics. The term perfect identifies this interval as belonging to the group of perfect intervals, so called because they are neither major nor minor but perfect.
  A perfect fourth in just intonation corresponds to a pitch ratio of 4:3, or about 498 cents, while in equal temperament a perfect fourth is equal to five semitones, or 500 cents.
  Until the late 19th century, the perfect fourth was often called by its Greek name, diatessaron. Its most common occurrence is between the fifth and upper root of all major and minor triads and their extensions.
context_section_description: The development of tonality continued through the Renaissance until it was fully realized by composers of the Baroque era.
  As time progressed through the late Renaissance and early Baroque, the fourth became more understood as an interval that needed resolution. Increasingly the harmonies of fifths and fourths yielded to uses of thirds and sixths. In the example, cadence forms from works by Orlando di Lasso and Palestrina show the fourth being resolved as a suspension. (Listen)
  In the early Baroque music of Claudio Monteverdi and Girolamo Frescobaldi triadic harmony was thoroughly utilized. Diatonic and chromatic passages strongly outlining the interval of a fourth appear in the lamento genre, and often in passus duriusculus passages of chromatic descent. In the madrigals of Claudio Monteverdi and Carlo Gesualdo the intensive interpretation of the text (word painting) frequently highlights the shape of a fourth as an extremely delayed resolution of a fourth suspension. Also, in Frescobaldi's Chromatic Toccata of 1635 the outlined fourths overlap, bisecting various church modes.
  In the first third of the 18th century, ground-laying theoretical treatises on composition and harmony were written. Jean-Philippe Rameau completed his treatise Le Traité de l'harmonie réduite à ses principes naturels (the theory of harmony reduced to its natural principles) in 1722 which supplemented his work of four years earlier, Nouveau Système de musique theoretique (new system of music theory); these together may be considered the cornerstone of modern music theory relating to consonance and harmony. The Austrian composer Johann Fux published in 1725 his powerful treatise on the composition of counterpoint in the style of Palestrina under the title Gradus ad Parnassum (The Steps to Parnassus). He outlined various types of counterpoint (e.g., note against note), and suggested a careful application of the fourth so as to avoid dissonance.
caption: Conventional closing cadences
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