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The Systems Of Hucbald And Guido D'arezzo--the Beginningof Counterpoint Post by :morpheoz Category :Essays Author :Edward Macdowell Date :November 2011 Read :3794

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The Systems Of Hucbald And Guido D'arezzo--the Beginningof Counterpoint

We have seen that by order of Charlemagne, Ambrosian chant was superseded by that of Gregory, and from any history of music we may learn how he caused the Gregorian chant to be taught to the exclusion of all other music. Although Notker, in the monastery of St. Gall, in Switzerland, and others developed the Gregorian chant, until the time of Hucbald this music remained mere wandering melody, without harmonic support of any kind.

Hucbald (840-930) was a monk of the monastery of St. Armand in Flanders. As we know from our studies in notation, he was the first to improve the notation by introducing a system of lines and spaces, of which, however, the spaces only were utilized for indicating the notes, viz.:


His attempt to reconstruct the musical scale was afterwards overshadowed by the system invented by Guido d'Arezzo, and it is therefore unnecessary to describe it in detail. His great contribution to progress was the discovery that more than one sound could be played or sung simultaneously, thus creating a composite sound, the effect which we call a chord. However, in deciding which sounds should be allowed to be played or sung together, he was influenced partly by the mysticism of his age, and partly by a blind adherence to the remnants of musical theory which had been handed down from the Greeks. As Franco of Cologne, later (1200), in systematizing rhythm into measure, was influenced by the idea of the Trinity in making his (3/8) or (9/8) time tempus perfectum, and adopting for its symbol the Pythagorean circle (O.) or (O), so Hucbald, in choosing his series of concords or sounds that harmonize well together, took the first three notes of the overtones of every sonorous fundamental, or, to express it differently, of the series of natural harmonics, that is to say, he admitted the octave and fifth: (F: g, d g). But from the fifth to the octave gives the interval of the fourth, therefore he permitted this combination also.

From the works of Boethius (circa 400) and others, he had derived and accepted the Pythagorean division of the scale, making thirds and sixths dissonant intervals; and so his perfect chord (from which our later triad gets its name of perfect) was composed of a root, fifth or fourth, and octave.

Hucbald, as I have already explained, changed the Greek tone system somewhat by arranging it in four regular disjunct tetrachords, namely:

(F: (g, a, b-, c) (d e f g) G: (a b c' d') (e' f+' g' a'))

This system permitted the addition of a fifth to each note indiscriminately, and the fifths would always be perfect; but in regard to the octaves it was faulty, for obvious reasons. As his system of notation consisted of merely writing T for tone and S for semitone between the lines of his staff, it was only necessary to change the order of these letters for the octave at the beginning of each line. With the fourth, however, this device was impossible, and therefore he laid down the rule that when the voices proceeded in fourths, and a discord (or augmented fourth) was unavoidable, the lower voice was to remain on the same note until it could jump to another fourth forming a perfect interval:

(F: {g b} {g b} {g a} {g b} {d a} {d g} {c f} {c e} {a, d} {g, c})

This at least brought into the harmony an occasional third, which gradually became a recognized factor in music.

We probably know that the year 1000 was generally accepted as the time when the world was to come to an end. In the Bibliothèque Nationale in Paris there is a manuscript containing the prophecy which had been handed down for many centuries; also the signs for the notes to which it was to be sung, viz.:

(Figure 07)

The text is:

The Judge will speak and the earth shall tremble
with awe. The stars shall be destroyed and the glory
of the moon shall die, the mountains shall be crushed
and the world with all in it shall utterly perish.

With the opening of the eleventh century, such was the relief from this fear which had been oppressing Christendom, that even the church reflected it in such strange rites as the Feast of Asses (January 14th), which was a burlesque of the Mass.

In this travesty of the Mass a young girl, dressed to represent the Virgin, riding on an ass and carrying a child in her arms, was conducted to the church door. Upon being admitted and riding up the aisle to the altar, the girl tethered the ass to the railing and sat on the steps until the service was finished. The Credo, Gloria, etc., all ended with a "hee-haw," and at the conclusion of the service the officiating priest brayed three times, and was answered by the congregation. The mixing of the vernacular with Latin in this service is the first instance of the use of any language but Latin in church music.

This quasi-symbolical pantomime gave rise in time to the mediaeval Passion Plays, or Mysteries, as they were called. That these travesties of the Mass took different forms in various countries is very evident when we remember the description of the "Abbot of Unreason," in Scott's "Abbot." In England, among other absurdities such as the "Pope of Fools," the "Ball Dance," etc., they also had the festival of the "Boy Bishop," in which, between the sixth and twenty-eighth of December, a boy was made to perform all the functions of a bishop.

It would seem that all this has but little bearing upon the development of music. As a matter of fact it was a most potent factor in it, for music was essentially and exclusively a church property. By permitting the people to secularize the church rites at certain seasons, it was inevitable that church music would also become common property for a time, with this difference, however, that the common people could carry the tunes away with them, and the music would be the only thing remaining as a recollection of the carnival. Indeed, the prevalence of popular songs soon became such that writers of church music began to use them instead of their being derived from church music, as was originally the case. This continued to such an extent that almost up to 1550 a mass was known by the name of the popular song it was based upon, as, for instance, the mass of the "Man in Armour," by Josquin dés Pres, and those entitled "Je prends conge" and "Je veult cent mille ecus."

Now we know that the tempus perfectum was par excellence (9/8) and (3/4) time. It was natural therefore that these first church tunes should have been changed to dances in the hands of the common people. Even in these dances it is interesting to note that the same symbolic significance appears to be present, for the earliest form of these dances was the "round song," or roundelay, and it was danced in a circle.

Duple time did not come into general use until the beginning of the fourteenth century. About the same time, the organum (as it was called) or system of harmonization of Hucbald was discarded, and Johannes de Muris and Philippe de Vitry championed the consonant quality of the third and sixth, both major and minor. The fifth was retained as a consonant, but the fourth was passed over in silence by the French school of writers, or classed with the dissonants. Successive fifths were prohibited as being too harshly dissonant, but successive fourths were necessarily permitted, as it would be an impossibility to do without them. Nevertheless, the fourth was still considered a dissonance, and was permitted only between the upper parts of the music. Thus the harsh consecutive passages in fifths and fourths of the organum of Hucbald disappeared in favour of the softer progressions of thirds and sixths.

In order to make clear how the new science of counterpoint came into existence, I must again revert to Hucbald.(09)

Before his time, all "recognized" music was a more or less melodious succession of tones, generally of the same length, one syllable being sometimes used for many notes. He discovered that a melody might be sung by several singers, each commencing at a different pitch instead of all singing the same notes at the same time. He also laid down rules as to how this was to be done to produce the best effect. We remember why he chose the fourth, fifth, and octave in preference to the third and sixth. He called his system an "organum" or "diaphony," and to sing according to his rules was called to "organize" or "organate." We must remember that at that time fourths and fifths were not always indicated in the written music; only the melody, which was called the principal or subject. By studying the rules prescribed for the organum, the singers could add the proper intervals to the melody. We must keep in mind, however, that later fourths were preferred to fifths (being considered less harsh), and that the musical scale of the period compelled the different voices to vary slightly, that is to say, two voices could not sing exactly the same melody at the interval of a fourth without the use of sharps or flats; therefore one voice continued on the same note until the awkward place was passed, and then proceeded in fourths again with the other voice as before:

(G: {e' a'} {d' g'} {d' f+'} {d' e'})

On account of the augmented fourth that would occur by a strict adherence to the melodic structure of the subject, the following would have been impossible: (G: {e' a'} {d' g'} ({c' f+'})) Thus we find the first instance of the use of thirds, and also of oblique motion as opposed to the earlier inevitable parallel motion of the voices. This necessary freedom in singing the organum or diaphony led to the attempt to sing two different melodies, one against the other--"note against note," or "point counter point,"(10) point or punct being the name for the written note. There being now two distinct melodies, both had to be noted instead of leaving it to the singers to add their parts extemporaneously, according to the rules of the organum, as they had done previously. Already earlier than this (in 1100), owing to the tendency to discard consecutive fourths and fifths, the intermovement of the voices, from being parallel and oblique, became contrary, thus avoiding the parallel succession of intervals. The name "organum" was dropped and the new system became known as tenor and descant, the tenor being the principal or foundation melody, and the descant or descants (for there could be as many as there were parts or voices to the music) taking the place of the organum. The difference between discantus and diaphony was that the latter consisted of several parts or voices, which, however, were more or less exact reproductions, at different pitch, of the principal or given melody, while the former was composed of entirely different melodic and rhythmic material. This gave rise to the science of counterpoint, which, as I have said, consists of the trick of making a number of voices sing different melodies at the same time without violating certain given rules. The given melody or "principal" soon acquired the name of cantus firmus, and the other parts were each called contrapunctus,(11) as before they had been called tenor and descant. These names were first used by Gerson, Chancellor of Notre Dame, Paris, about 1400.

In the meantime (about 1300-1375), the occasional use of thirds and sixths in the diaphonies previously explained led to an entirely different kind of singing, called falso bordone or faux bourdon (bordonizare, "to drone," comes from a kind of pedal in organum that first brought the third into use). This system, contrary to the old organum, consisted of using only thirds and sixths together, excluding the fourth and fifth entirely, except in the first and last bars. This innovation has been ascribed to the Flemish singers attached to the Papal Choir (about 1377), when Pope Gregory XI returned from Avignon to Rome. In the British Museum, however, there are manuscripts dating from the previous century, showing that the faux bourdon had already commenced to make its way against the old systems of Hucbald and Guido. The combination of the faux bourdon and the remnant of the organum gives us the foundation for our modern tone system. The old rules, making plagal motion of the different voices preferable to parallel motion, and contrary motion preferable to either, still hold good in our works on theory; so also in regard to the rules forbidding consecutive fifths and octaves, leaving the question of the fourth in doubt.

To sum up, we may say, therefore, that up to the sixteenth century, all music was composed of the slender material of thirds, sixths, fifths, and octaves, fourths being permitted only between the voices; consecutive successions of fourths, however, were permitted, a license not allowed in the use of fifths or octaves. This leads us directly to a consideration of the laws of counterpoint and fugue, laws that have remained practically unchanged up to the present, with the one difference that, instead of being restricted to the meagre material of the so-called consonants, the growing use of what were once called dissonant chords, such as the dominant seventh, ninth, diminished seventh, and latterly the so-called altered chords, has brought new riches to the art.

Instead of going at once into a consideration of the laws of counterpoint, it will be well to take up the development of the instrumental resources of the time. There were three distinct types of music: the ecclesiastical type (which of course predominated) found its expression in melodies sung by church choirs, four or more melodies being sometimes sung simultaneously, in accordance with certain fixed rules, as I have already explained. These melodies or chants were often accompanied by the organ, of which we will speak later. The second type was purely instrumental, and served as an accompaniment for the dance, or consisted of fanfares (ceremonial horn signals), or hunting signals. The third type was that of the so-called trouvères or troubadours, with their jongleurs, and the minnesingers, and, later, the mastersingers. All these "minstrels," as we may call them, accompanied their singing by some instrument, generally one of the lute type or the psaltery.


(09) There is much question as to Hucbald's organum. That
actually these dissonances were used even up to 1500 is
proved by Franco Gafurius of Milan, who mentions a Litany
for the Dead (De Profundis) much used at that time:

(G: {f' g'} {f' g'} {g' a'} {g' a'} {g' c''} {e' a'} {f' g'})
(W: De profundis, etc.)

(10) Counterpoint is first mentioned by Muris (1300).

(11) Only principal (tenor or cantus firmus) was sung to words.


All other text enclosed between square brackets represents or
describes the illustrations:

Pitches: (c, ... c ... a b c' (middle-C) d' e' ... c'' ... c''')

Round brackets: when around a single note these represent a note
in the extract which was bracketed or otherwise highlighted.
When around two or more notes, they represent a slur or beam.

Braces: surround simultaneous notes in a chord {a c' e'}


(f++) = F double-sharp
(a+) = A sharp
(c=) = C natural
(e-) = E flat
(d--) = D double-flat

In the main text, accidentals are written out in full, as (natural), A(flat), G(sharp). One table uses (#) for (sharp).

Accents and marcato: denoted by > and ^ before a note.

Time signatures: (4/4), (6/8), etc.

(C) or (C/4) = C-shaped (4/4) time.
(C|) or (C/2) = C-shaped (2/2) time.
(O) = A circle
(O.) = A circle with a dot in the center
(C.) = A broken circle (C-shaped) with a dot in the center

(G:) = Treble clef ((G8:) = Treble clef 8va bassa)
(F:) = Bass clef ((F8:) = Bass clef 8va bassa)

Rhythms (A trailing . represents a dotted note):
(L) = Longa
(B) = Brevis
(S) = Semibrevis
(1) = Whole-note (Semibreve)
(2) = Half-note (Minim)
(4) = Quarter-note (Crotchet)
(8) = Eighth-note (Quaver)
(16) = Sixteenth-note (Semiquaver)

Lyrics and Labels: words aligned with the notes begin (W: ...)

Breves and macrons, used to denote short and long stresses in poetry are denoted ' and '-' respectively.

(| = Bar (Bar line)
(< = Crescendo hairpin
(x = small cross
( = 45 degree downstroke
(/ = 45 degree upstroke
(/ = large circumflex shape
(O| = a circle bisected by a vertical line protruding both ways
(Gamma) = The Greek capital gamma
(mid-dot) = a dot at the height of a hyphen
(over-dot) = a single dot over the following letter
(Over-slur) = a frown-shaped curved line
(Under-slur) = a smile-shaped curved line (breve)
(reverse-apostrophe) = the mirror image of a closing quote
(Upper Mordent) = an upper mordent: /// with thick downstrokes
(Crenellation) = horizontals, low, high, low, connected by verticals
(Podium) = (Crenellation) with the third horizontal at half-height
(Step) = horizontal, vertical, horizontal, vertical, ascending
(Turn) = a turn (~)

(Figure 01) = extract available as a MIDI file (figure01.mid).
(Illustration) = all other illustrations.

For example, here's a D minor scale set to words:

(G: d' e' (f' g') a' b-' (c+'' d''))
(W: One, two, three, four, five, six. )

And a simple rhythmic example:

(3/4: 4 4 8 8 | 8. 16 2) = (- - ' ' - ' -)

(The end)
Edward MacDowell's essay: Systems Of Hucbald And Guido D'arezzo--The Beginningof Counterpoint

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