Thursday, January 13, 7820

Anon (b. c. 820) - Musica Enchiriadis (c. 850)

[Harmony and Discord]

Musica enchiriadis is an anonymous musical treatise from about 850. It is the first surviving attempt to establish a system of rules for polyphony in Western music.

The treatise was once attributed to Hucbald, but this is no longer accepted.


Hucbald (Hucbaldus, Hubaldus) (c. 840 – June 20, 930) was a music theorist, composer, teacher, writer, hagiographer, and Benedictine monk. He wrote an early systematic work on western music theory, incorporating the differences between contemporary and ancient practice.

He was born at the monastery of Saint Amand near Tournai, in or about 840. He studied at the monastery, where his uncle Milo occupied an important position. Hucbald made rapid progress in the acquirement of various sciences and arts, including that of music, and at an early age composed a hymn in honour of St Andrew, which met with such success as to excite the jealousy of his uncle. It is said that Hucbald in consequence was compelled to leave St Amand, and started an independent school of music and other arts at Nevers.

In 860, however, he was at St Germain d'Auxerre, bent upon completing his studies, and in 872 he was back again at St Amand as the successor in the headmastership of the convent school of his uncle, to whom he had been reconciled in the meantime. Between 883 and 900 Hucbald went on several missions of reforming and reconstructing various schools of music, including those of St. Bertin and Rheims; but in the latter year he returned to St Amand, where he remained to the day of his death on June 20, 930.

The only work which can positively be ascribed to him is his De harmonica institutione (probably written about 880). The Musica Enchiriadis, published with other writings of minor importance in Gerbert's Scriptores de Musica, and containing a complete system of musical science as well as instructions regarding notation, has now been proved to have been the work of an unknown writer, possibly also bearing the name of Hucbald. This work is celebrated chiefly for an essay on a new form of notation described in the present day as Dasien notation.

The author of the De harmonica institutione wrote numerous lives of the saints and a curious poem on bald men,

[Charles the Bald, in old age, in camouflage]

dedicated to Charles the Bald (823-877).


Musica enchiriadis, along with its companion commentary, Scolica [Scholia] enchiriadis, were widely circulated in medieval manuscripts, typically coupled with Boethius's De Institutione Musica.

It consists of 19 chapters; the first nine are devoted to notation, modes, and monophonic chant.

Chapters 10-18 deal with polyphonic music. The author shows how consonant intervals should be used in order to compose or improvise polyphonic music in early Middle Ages.

The consonant intervals identified by the treatise are the fourth, fifth, and eighth, and sometimes the third and the sixth. A number of examples of organum, an early style of note-against-note polyphony, are included in the treatise.

Musica Enchiriadis also shows rules for performing music and gives some early indications of character for some works, as the Latin words 'morosus' (sadly) or 'cum celeritate' (fast). The last, nineteenth, chapter relates the legend of Orpheus.

The scale used in the work, which is based on a system of tetrachords, appears to have been created solely for use in the work itself, rather than taken from actual musical practice.

The treatise also uses a very rare system of notation, known as Daseian notation. This notation has a number of figures which are rotated 90 degrees to represent different pitches.

The Scolica enchiriadis is written as a tripartite dialogue, and despite being a commentary on the Musica enchiriadis, it is nearly three times as long.

Much of the theory discussed by the treatise is indebted to Augustinian conceptions of music, especially its affirmations of the importance of mathematics to music as kindred disciplines of the quadrivium.

Later sections draw heavily on the music theory of Boethius and Cassiodorus, two early medieval authors whose works on music were widely read and circulated hundreds of years after their death. The treatise makes use of the monochord to explain interval relations. The treatise also discusses singing technique, ornamentation of plainchant, and polyphony in the style of organum.

A critical edition of the treatises was published in 1981, and an English translation in 1995.


Scholia Enchiriadis, contains examples of organa (singular organum -- possibly, but not definitely, related to church pipe organs).

Organum (from Ancient Greek- organon "organ, instrument, tool"; pl. organa) in general is a chant melody with at least one added voice to enhance the harmony, developed in the Middle Ages.

In its earliest stages, organum involved two musical voices: a Gregorian chant melody, and the same melody transposed by a consonant interval, usually a perfect fifth or fourth. In these cases often the composition began and ended on a unison, the added voice keeping to the initial tone until the first part has reached a fifth or fourth, from where both voices proceed in parallel harmony, with the reverse process at the end. Organum was originally improvised; while one singer performed a notated melody (the vox principalis), another singer—singing "by ear" -- provided the unnotated second melody (the vox organalis). Over time, composers began to write added parts that were not just simple transpositions, and thus more ambitious polyphony was born.

The first document to describe organum specifically, and give rules for its performance, was the Musica enchiriadis. The added voice was intended as a reinforcement or harmonic enhancement of the plainchant at occasions of High Feasts of importance to further the splendour of the liturgy.

The analogue evolution of sacred architecture and music is evident: during previous centuries monophonic Mass was celebrated in Abbatial churches (i.e. churches connected with abbeys), in the course of 1100's and 1200's the newly consecrated cathedrals resounded with ever more complex forms of polyphony. Exactly what developments took place where and when in the evolution of polyphony is not always clear, though some landmarks remain visible in the treatises. As in these instances, it is hard to evaluate the relative importance of treatises, whether they describe the 'actual' practice or a deviation of it. As key-concept behind the creative outburst that manifested in the 1000's and 1100's is the vertical and harmonic expansion of dimension, as the strongly resonant harmony of organum magnified the splendour of the celebration and heightened its solemnity.

The first embarkations in to organum are hidden in obscurity but most probably involve forms of parallel singing not unlike practice in Eastern liturgies. Considering that the trained singers were imbibed in an oral tradition that was several centuries old, singing a small part of the chant repertory in parallel harmony or other ways of 'singing by the ear' would come naturally. It is made clear in the Musica enchiriadis that octave doubling was acceptable, since such doubling was inevitable when men and boys sang together. The 800's treatise Scolica enchiriadis treats the subject in greater detail. For parallel singing, the original chant would be the upper voice, vox principalis; the vox organalis was at a parallel perfect interval below, usually a fourth. Thus the melody would be heard as the principal voice, the vox organalis as an accompaniment or harmonic reinforcement. This kind of organum is now usually called parallel organum, although terms such as sinfonia or diaphonia were used in early treatises.

The Musica enchiriadis documented a practice which obviously had been in use for some time, although it has not been possible to establish even an approximate dating for the commencement of the practice, which may go back hundreds of years. Both of the Enchiriadis treatises are primarily works on the concept of a mathematical derivation of the gamut and the modes based on theories of conjunct and disjunct tetrachords (series of four pitches involving fixed tone and semitone relationships within them). To some extent it is probable that the treatment given to organum was a treatment designed to explain it in the terms of the evolving theory of the gamut (not least by the observation that parallel fourths outline tetrachords), and was not a descriptive or prescriptive manual of practical organum.


Scholia Enchiriadis (c. 850)

Nos Qui Vivimus

In Nos Qui Vivimus, a pre-existent chant is harmonized in parallel octaves, fifths, and fourths below the original chant. It is the kind of "accidental" harmony that occurs when men and boys/women (octaves) or the "tone-deaf" (4ths and 5ths) attempt to "match pitch" (see Meredith Willson's The Music Man)! Occasionally accidentals crop up to avoid the tritone (3 steps) which was called Diabolis in Musica (The Devil in Music). Tritones sound a bit devilishly odd even in recent times (Jimi Hendrix's Purple Haze)!


Sit Gloria Domini

Sit Gloria thickens the texture over two octaves, resulting in 4ths and 5ths.


Rex Coeli (King of Heaven)

Rex Coeli is a bit more harmonically radical, starting with a unison, moving to a major second and third in oblique motion (one part moves, the other part holds), and then continuing in perfect parallel fourths.


Harmony is the use of different pitches simultaneously, and chords, actual or implied, in music.


A chord (from Greek: gut, string) is two or more different notes that sound simultaneously. Two-note combinations can also be referred to as dyads or intervals.


Harmony often refers to the "vertical" aspects of music, distinguished from ideas of melodic line, or the "horizontal" aspect.

For this reason, considerations of counterpoint or polyphony are often distinguished from those of harmony, though contrapuntal writing of the common practice period of western music is often conceived and defined in terms of underlying harmonic motion.

The term harmony originates in the Greek ἁρμονία (harmonía), meaning "joint, agreement, concord."

In Ancient Greek music, the term was used to define the combination of contrasted elements: a higher and lower note.

In the Middle Ages the term was used to describe two pitches sounding in combination, and in the Renaissance the concept was expanded to denote three pitches sounding together.


A consonance (Latin consonare, "sounding together") is a harmony, chord, or interval considered stable, as opposed to a dissonance considered unstable (or temporary, transitional). A stereotypical definition of consonance is that of a combination of pitches which sound "pleasant" together -- a notion which has varied over time and space.

Consonance has been defined variously through:

Frequency ratios: with ratios of lower simple numbers being more consonant than those which are higher (Pythagoras). Many of these definitions do not require exact integer tunings, only approximation.

Coincidence of harmonics: with consonance being a greater coincidence of harmonics or partials (collectively overtones) (Helmholtz, 1877/1954). By this definition consonance is dependent not only on the quality of the interval between two notes, but on the combined spectral distribution and thus sound quality (timbre) of the harmonic interval (see the entry under critical band).

Fusion or pattern matching: fundamentals may be perceived through pattern-matching of the separately analyzed partials to a best-fit exact-harmonic template (Gerson & Goldstein, 1978) or the best-fit subharmonic (Terhardt, 1974). Or harmonics may be perceptually fused into one entity, with consonances being those intervals which are more likely to be mistaken for unisons, the perfect intervals, because of the multiple estimates of fundamentals, at perfect intervals, for one harmonic tone (Terhardt, 1974). By these definitions inharmonic partials of otherwise harmonic spectra are usually processed separately (Hartmann et al., 1990), unless frequency or amplitude modulated coherently with the harmonic partials (McAdams, 1983).

In what is now called the common practice period in Western music, consonant intervals include:

Perfect consonances:
unisons and octaves
perfect fourths (see below*) and perfect fifths
Imperfect consonances:
major thirds and minor sixths
minor thirds and major sixths

*The perfect fourth is considered a dissonance in most classical music when its function is contrapuntal.


The common practice period, in the history of Western art music encompasses those periods identified as Baroque, Classical, and Romantic. It lasted from about 1600 until about 1900, and is most often contrasted with much earlier and later musics.


Dissonance is the quality of sounds which seems "unstable," and in certain styles seem to imply a tendency to "resolve" to a "stable" consonance. Both consonance and dissonance are words applied to harmony, chords, and intervals and by extension to melody, tonality, and even rhythm and meter. Although there are important physical and neurological facts important to understanding the idea of dissonance, the precise definition of dissonance is culturally conditioned -- definitions of and conventions of usage related to dissonance vary greatly among different musical styles, traditions, and cultures. Nevertheless, the basic ideas of dissonance, consonance, and resolution exist in some form in all musical traditions that have a concept of melody, harmony, or tonality.

Additional confusion about the idea of dissonance is created by the fact that musicians and writers sometimes use the word dissonance and related terms in a precise and carefully defined way, more often in an informal way, and very often in a metaphorical sense ("rhythmic dissonance"). For many musicians and composers, the essential ideas of dissonance and resolution are vitally important ones that deeply inform their musical thinking on a number of levels.

Despite the fact that words like "unpleasant" and "grating" are often used to explain the sound of dissonance, in fact all music with a harmonic or tonal basis -- even music which is perceived as generally harmonious -- incorporates some degree of dissonance. The buildup and release of tension (dissonance and resolution), which can occur on every level from the subtle to the crass, is to a great degree responsible for what many listeners perceive as beauty, emotion, and expressiveness in music.


In music, polyphony is a texture consisting of two or more independent melodic voices, as opposed to music with just one voice (monophony) or music with one dominant melodic voice accompanied by chords (homophony).

Within the context of Western music tradition the term is usually used in reference to music of the Middle Ages and Renaissance.

Two treatises, both dating from ca. 850, are usually considered the oldest surviving part-music though they are note-against-note, voices move mostly in parallel octaves, fifths, and fourths, and they were not intended to be performed. The 'Winchester Tropers', from c. 1000, are the oldest surviving example of practical rather than pedagogical polyphony, though intervals, pitch levels, and durations are often not indicated. (van der Werf, 1997)

Incipient polyphony includes antiphony and Call-and-response, drones, and parallel intervals.


In music, counterpoint is the relationship between two or more voices that are independent in contour and rhythm, and interdependent in harmony. It has been most commonly identified in Western music, developing strongly in the Renaissance, and also dominant in much of the common practice period, especially in Baroque music. The term comes from the Latin punctus contra punctum ("note against note").


[P5 from E to B in Bass Clef]

A perfect fifth is a musical interval that involves 5 letter names on the staff (counting from bottom to top) and a distance of 3 1/2 steps on a piano keyboard.

All white-note fourths and fifths are perfect, with the exception of the dreaded F-B combination (this latter tritone [3 steps] is described as an augmented fourth when involving four letter names [F-B] or diminished fifth as five [B-F] -- in these particular cases the intervals can be turned into perfect ones by lowering the B to Bb or raising the F to F#).

The term perfect identifies it as belonging to the group of perfect intervals (perfect fourth, perfect octave) so called because of their simple pitch relationships and their high degree of consonance.[1] There are two other kinds of fifths: the diminished fifth, which is one chromatic semitone smaller, and the augmented fifth, which is one chromatic semitone larger.

The perfect fifth is occasionally referred to as the diapente, and abbreviated P5. Its inversion is the perfect fourth.

The perfect fifth is an important interval in music. It is more consonant, or stable, than any other interval except the unison and the octave. It is a valuable interval in chord structure, song development, and western tuning systems. It occurs on the root of all major and minor chords (triads) and their extensions. It was the first accepted harmony (besides the octave) tropes evolving from Gregorian chant.

There are various ways to train the ear to recognize a perfect fifth. One is to sing the first five notes of the major scale in solfege: do re mi fa sol; the first and last notes form a perfect fifth.

Another is to sing the first four notes of the familiar tune Twinkle, Twinkle, Little Star, which likewise outline a perfect fifth. On a piano keyboard, a perfect fifth can be approximated by holding down two notes, one of which is the seventh note higher than the base note.

Additionally, the opening of Richard Strauss's Also Sprach Zarathustra (used in Stanley Kubrick's 2001: A Space Odyssey) and the Wicked Witch of the West's Soldiers' March (Oh-Ee-Oh-Yo-Oh-Yo!) in Harold Arlen's The Wizard of Oz prominently feature the interval.

The idealized pitch ratio of a perfect fifth is 3:2, meaning that the upper note makes three vibrations in the same amount of time that the lower note makes two. In the cent system of pitch measurement, the 3:2 ratio corresponds to approximately 702 cents. Something close to the idealized perfect fifth can be heard when a violin is tuned: if adjacent strings are adjusted to the exact ratio of 3:2, the result is a smooth and consonant sound, and the violin is felt to be "in tune". Idealized perfect fifths are employed in just intonation.

In keyboard instruments such as the piano, a slightly different version of the perfect fifth is normally used: in accordance with the principle of equal temperament, the perfect fifth must be slightly narrowed: seven semitones, or 700 cents. (The narrowing is necessary to enable the instrument to play in all keys.) Many people can hear the slight deviation from the idealized perfect fifth when they play the interval on a piano.

The open fifth, bare fifth, empty fifth, or power chord contains only a perfect fifth. The closing chords many Renaissance compositions as well as those of the Kyrie in W.A. Mozart's Requiem and the first movement of Anton Bruckner's Ninth Symphony, plus much of the harmony of Medieval music and Claude Debussy's Piano Preludes: The Sunken Cathedral are all examples of open fifths. These chords are common in Sacred Harp singing and throughout rock music, especially hard rock, metal, and punk music, where overdriven or distorted guitar can make thirds sound muddy, and fast chord-based passages are made easier to play by combining the four most common guitar hand shapes into one. Power chords often include octave and fifth doublings.

Open fifths are often used in various world music, e.g. in some Andean music genres of pre-Columbian origin, such as k'antu, tarqueada and sikuri. The same melody is being led by parallel fifths and octaves during all the piece. Hear examples: K'antu, Pacha Siku.
[edit]Use in tuning and tonal systems

A perfect fifth in just intonation, a just fifth, corresponds to a frequency ratio of 3:2, while in 12-tone equal temperament, a perfect fifth is equal to seven semitones, or 700 cents, about two cents smaller than the just fifth.

The just perfect fifth, together with the octave, forms the basis of Pythagorean tuning. A flattened perfect fifth is likewise the basis for meantone tuning.

The circle of fifths is a model of pitch space for the chromatic scale (chromatic circle) which considers nearness not as adjacency but as the number of perfect fifths required to get from one note to another.


A perfect fourth is a musical interval which spans four scale degrees (letter names) and contains 2 1/2 steps, for example, the interval between a C and the next F above it (or G and the next C, etc.)

The term perfect identifies this interval as belonging to the group of perfect intervals, so called because of their extremely simple pitch relationships resulting in a high degree of consonance.

The perfect fourth is occasionally called the diatessaron. It is abbreviated P4. The perfect fourth's inversion is the perfect fifth.

Its most common occurrence is between sol and do above it.

A perfect fourth in just intonation corresponds to a pitch ratio of 4:3, or approximately 498 cents, while in equal temperament a perfect fourth is equal to five semitones, or 500 cents.

A helpful way to recognize a perfect fourth is to hum the starting of the "Bridal Chorus" from Wagner's Lohengrin ("Treulich gefuehrt," the colloquially titled Here Comes the Bride), which is a familiar perfect fourth.

An ascending P4 from Sol to Do seems to be the most common opening melodic interval, across cultures and history. Other popular melodies which include this beginning are Giuseppe Verdi's Aida: Triumphal Entry and the folksong La Cucaracha.

The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, and it is a sensory consonance. In common practice harmony, however, it is considered a stylistic dissonance in certain contexts, namely in two-voice textures and whenever it appears above the bass.

Conventionally, the strings of a double bass and a bass guitar are tuned by intervals of perfect fourths, as well as all but one of the strings of a guitar. It is also a very common musical interval to which timpani and tom-toms are tuned.

The ends of many compositions, including the consequent phrases of Strauss's Also Sprach (mentioned above) and finale to Dmitri Shostakovich's Symphony No. 5 feature prominent ascending P4 Sol Do strokes on timpani.

[7854 Notker / 7820 Musica Enchiriadis / 7800 Gambia]