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==Definitions==

==Definitions==

1. Combination or adaptation of parts, elements, or related things, so as to form a consistent and orderly whole; agreement, accord, congruity.

1. Combination or adaptation of parts, elements, or related [[things]], so as to form a consistent and orderly whole; agreement, accord, congruity.

    

    

pre-established harmony, in the philosophy of Leibnitz, a harmony between mind and matter, e.g. between the body and soul, established before their creation, whereby their actions correspond though no communication exists between them.

pre-established harmony, in the [[philosophy]] of Leibnitz, a harmony between [[mind]] and [[matter]], e.g. between the body and [[soul]], established before their creation, whereby their actions correspond though no [[communication]] exists between them.

c1532 G. DU WES Introd. Fr. in Palsgr. 1058 Others have sayd that it [the operation of God] is a maner of armonie. 1597 HOOKER Eccl. Pol. V. xxxviii. §1 The soule it selfe by nature is, or hath in it, harmonie. 1605 BACON Adv. Learn. I. iv. §6 (1873) 32 The harmony of a science, supporting each part the other, is..the true and brief confutation..of all the smaller sort of objections. 1745 De Foe's Eng. Tradesman ii. (1841) I. 18 Here is a harmony of business, and everything exact. 1814 SOUTHEY Roderick XXI. 382 To heavenliest harmony Reduce the seeming chaos. 1847 LEWES Hist. Philos. (1867) II. 273 His [Leibnitz's] favourite hypothesis of a Pre-established Harmony (borrowed from Spinoza). 1860 TYNDALL Glac. II. xxiv. 353 Where other forces mingle with that of crystallization, this harmony of action is destroyed.

c1532 G. DU WES Introd. Fr. in Palsgr. 1058 Others have sayd that it [the operation of God] is a maner of armonie. 1597 HOOKER Eccl. Pol. V. xxxviii. §1 The soule it selfe by nature is, or hath in it, harmonie. 1605 BACON Adv. Learn. I. iv. §6 (1873) 32 The harmony of a science, supporting each part the other, is..the true and brief confutation..of all the smaller sort of objections. 1745 De Foe's Eng. Tradesman ii. (1841) I. 18 Here is a harmony of business, and everything exact. 1814 SOUTHEY Roderick XXI. 382 To heavenliest harmony Reduce the seeming chaos. 1847 LEWES Hist. Philos. (1867) II. 273 His [Leibnitz's] favourite hypothesis of a Pre-established Harmony (borrowed from Spinoza). 1860 TYNDALL Glac. II. xxiv. 353 Where other forces mingle with that of crystallization, this harmony of action is destroyed.

==Historical definition==

==Historical definition==

In Greek [[music]], from which derive both the [[concept]] and the appellation, ‘harmony’ signified the combining or juxtaposing of disparate or contrasted elements – a higher and a lower note. The combining of notes simultaneously was not a part of musical practice in classical antiquity: harmonia was merely a means of codifying the relationship between those notes that constituted the framework of the tonal system. In the course of history it was indeed not the meaning of the term ‘harmony’ that changed but the material to which it applied and the explanations given for its manifestation in music.

In Greek [[music]], from which derive both the [[concepts|concept]] and the appellation, ‘harmony’ signified the combining or juxtaposing of disparate or contrasted elements – a higher and a lower note. The combining of notes simultaneously was not a part of musical practice in classical antiquity: harmonia was merely a means of codifying the relationship between those notes that constituted the framework of the tonal system. In the course of history it was indeed not the meaning of the term ‘harmony’ that changed but the material to which it applied and the explanations given for its manifestation in music.

According to the conception of classical writers, taken over by medieval theorists, harmony was a combining of intervals in an octave scale – a scale understood not as a series but as a structure. Consonances based on simple, ‘harmonic’ numerical proportions – the octave (2:1), the 5th (3:2) and the 4th (4:3 – form the framework of a scale (e′–b–a–e), and in addition to the octave structure resulting from the interlocking of consonances, the consonance itself also qualifies as harmony, as a combining agent (see Consonance, §1).

According to the conception of classical writers, taken over by medieval theorists, harmony was a combining of intervals in an octave scale – a scale understood not as a series but as a structure. Consonances based on simple, ‘harmonic’ numerical proportions – the octave (2:1), the 5th (3:2) and the 4th (4:3 – form the framework of a scale (e′–b–a–e), and in addition to the octave structure resulting from the interlocking of consonances, the consonance itself also qualifies as harmony, as a combining agent (see Consonance, §1).

Carl Dahlhaus

Carl Dahlhaus

==Basic concepts==

==Basic concepts==

===The chord===

===The chord===

The roots of chords (which are no longer their bass notes when the chords are inverted) link together to give the basse fondamentale. The latter is a purely imaginary line, in contrast to the basso continuo, which is the sequence of actual bass notes. It is a construction designed to explain why a progression can become a compelling, intelligible coherence rather than a mere patchwork of separate chords. According to Rameau (whose theories were further developed in the 19th century by Simon Sechter) the cohesive principle is the fundamental progression, from root to root; in fact, the 5th is reckoned a primary, stronger fundamental progression, the 3rd a secondary, weaker one. A fundamental progression or apparent progression of a 2nd (according to Rameau the 2nd, which as a simultaneity is a dissonance, is also not self-sufficient as a bass progression) is reduced to progressions of a 5th: in the chord sequence G–C–D minor, C is indeed a tonic degree (I), related to G as the dominant (V), but it is also a fragment of the 7th on the submediant (VI7), related to the supertonic (II) – the root A being introduced for the sake of the 5th progression A–D: see ex.1 (Rameau, B1722, p.204). For similar reasons, the chord F–A–C–D in C major is considered as a triad of F major with added 6th (sixte ajoutée) provided that it is followed by the C major triad (fundamental 4th progression); on the other hand it is considered an inversion of the 7th on D if it moves on to G major (fundamental 5th progression): F–A–C–D is a chord with two applications (double emploi).

The roots of chords (which are no longer their bass notes when the chords are inverted) link together to give the basse fondamentale. The latter is a purely imaginary line, in contrast to the basso continuo, which is the sequence of actual bass notes. It is a construction designed to explain why a progression can become a compelling, intelligible coherence rather than a mere patchwork of separate chords. According to Rameau (whose theories were further developed in the 19th century by Simon Sechter) the cohesive principle is the fundamental progression, from root to root; in fact, the 5th is reckoned a primary, stronger fundamental progression, the 3rd a secondary, weaker one. A fundamental progression or apparent progression of a 2nd (according to Rameau the 2nd, which as a simultaneity is a dissonance, is also not self-sufficient as a bass progression) is reduced to progressions of a 5th: in the chord sequence G–C–D minor, C is indeed a tonic degree (I), related to G as the dominant (V), but it is also a fragment of the 7th on the submediant (VI7), related to the supertonic (II) – the root A being introduced for the sake of the 5th progression A–D: see ex.1 (Rameau, B1722, p.204). For similar reasons, the chord F–A–C–D in C major is considered as a triad of F major with added 6th (sixte ajoutée) provided that it is followed by the C major triad (fundamental 4th progression); on the other hand it is considered an inversion of the 7th on D if it moves on to G major (fundamental 5th progression): F–A–C–D is a chord with two applications (double emploi).

===Dissonance===

===Dissonance===

The idea that a chord presented not a mere combination of intervals but a unit, primary and indivisible, was associated with a far-reaching change in the concepts regarding the nature and the functions of dissonances. In counterpoint before 1600, a dissonance in strict writing was a relation between two voices; and the dissonant note was regarded as being the one that had to advance to the resolution of the dissonance, hence in ex.2a the lower note, in ex.2b the upper. (The second, or ‘reference’, voice could either remain on the same note or move to a new one at the resolution.) A suspension on the strong beat is produced by a step in the ‘reference’ voice (ex.2a), and a dissonant passing note on a weak beat by a step in the voice making the dissonance (ex.2b).

The idea that a chord presented not a mere combination of intervals but a unit, primary and indivisible, was associated with a far-reaching change in the concepts regarding the nature and the functions of dissonances. In counterpoint before 1600, a dissonance in strict writing was a relation between two voices; and the dissonant note was regarded as being the one that had to advance to the resolution of the dissonance, hence in ex.2a the lower note, in ex.2b the upper. (The second, or ‘reference’, voice could either remain on the same note or move to a new one at the resolution.) A suspension on the strong beat is produced by a step in the ‘reference’ voice (ex.2a), and a dissonant passing note on a weak beat by a step in the voice making the dissonance (ex.2b).

From the 17th century the formation of dissonances in strict counterpoint was complemented by new approaches that extended the system of contrapuntal writing without violating any of its fundamental characteristics. But at the same time it was confronted with phenomena grounded in basic principles of a different kind, relating to other categories of musical listening. Among the new approaches to dissonance that merely extended the system were some that characterized the modern counterpoint of the 17th century, the seconda pratica: for example, changing note quitted by downward leap (ex.3a), the suspension resolved by downward leap (ex.3b), and the accented passing note (ex.3c), which in Palestrina’s style was permitted only in a rudimentary form as a weakly accented passing note of the duration of a semiminima (ex.3d).

From the 17th century the formation of dissonances in strict counterpoint was complemented by new approaches that extended the system of contrapuntal writing without violating any of its fundamental characteristics. But at the same time it was confronted with phenomena grounded in basic principles of a different kind, relating to other categories of musical listening. Among the new approaches to dissonance that merely extended the system were some that characterized the modern counterpoint of the 17th century, the seconda pratica: for example, changing note quitted by downward leap (ex.3a), the suspension resolved by downward leap (ex.3b), and the accented passing note (ex.3c), which in Palestrina’s style was permitted only in a rudimentary form as a weakly accented passing note of the duration of a semiminima (ex.3d).

These dissonances, which are to be found in contrapuntal practice, in no way invalidate the strict rules of counterpoint. They require, if their intended effect is to be understood, an awareness of the norms with which they conflict. It is precisely as exceptions to the conventional rule, which they infringe and in so doing confirm as valid, that they gain their expressive or symbolic meaning: the downward-leaping suspension (ex.3b) owes its character of pathos to its very deviation from the normal resolution by step.

These dissonances, which are to be found in contrapuntal practice, in no way invalidate the strict rules of counterpoint. They require, if their intended effect is to be understood, an awareness of the norms with which they conflict. It is precisely as exceptions to the conventional rule, which they infringe and in so doing confirm as valid, that they gain their expressive or symbolic meaning: the downward-leaping suspension (ex.3b) owes its character of pathos to its very deviation from the normal resolution by step.