Free Organum - Cunctipotens Genitor (1000)
With better notation, a monk's life was enlivened by Free Organa in Cunctipotens Genitor (with Kyrie IV as cantus firmus -- a fixed song) in contrary motion (one part goes up, while another goes down), harmonized mostly in perfect intervals.
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After parallel organum the next development to arise in the practice of organum is postulated to be that of free organum. The earliest examples of this style dating from around 1020-1050 (the Micrologus of Guido d'Arezzo and the Winchester Troper) utilie parallel motion and oblique motion (upper voice moving while the tenor holds one note), but the introduction of contrary motion (voices moving in opposite directions) as well as similar motion (voices moving in the same direction, but to different intervals) led to progressively freer musical lines — a prerequisite element of complex counterpoint.
School of Chartres (b. c. 970) - Alleluia (1000)
There exist a number of manuscript fragments of the later 11th Century and into the 12th Century which document the changing styles, from the works of John Cotton (also referred to as Johannes Cotto or Joannes of Liege) to the so-called Chartres fragments. Although free organum is mostly isochronous meaning that the two voices move in the same pace, there are examples of more than one note of the organal voice against one note in the tenor; another precursor of contrapuntal techniques. Previous techniques may be said to harmonically enhance and reinforce a single melodic line which is why it is essentially heterophony; free organum is a definite break with "harmonically shadowing" chant as it places a new line in contrasting harmony with the chant in the lower voice.
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In music, a cantus firmus ("fixed song") is a pre-existing melody forming the basis of a polyphonic composition.
The plural of this Latin term is cantus firmi, though one occasionally sees canti firmi. The Italian is often used instead: canto fermo (and the plural in Italian is canti fermi).
The earliest polyphonic compositions almost always involved a cantus firmus, typically a Gregorian chant, although the term itself was not used until the 1300's.
The earliest surviving polyphonic compositions, in the Musica enchiriadis (around 900 CE), contain the chant in the top voice, and the newly-composed part underneath; however this usage changed around 1100, after which the cantus firmus typically appeared in the lowest-sounding voice.
German composers in the Baroque, notably Bach, used chorale melodies as cantus firmi. In the opening movement of Bach's St. Matthew Passion, the chorale "O Lamm Gottes, unschuldig" appears in long notes, sung by a separate choir of boys "in ripieno." Many of his chorale preludes include a chorale tune in the pedal part.
Using a cantus firmus as a means of teaching species counterpoint was the basis of Gradus ad Parnassum by Johann Joseph Fux, although the method was first published by Girolamo Diruta in 1610. Counterpoint is still taught routinely using a method adapted from Fux, and based on the cantus firmus.
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P1 = 0 steps
m2 = 1/2 step
M2 = 1 step
m3 = 1 1/2 steps
M3 = 2 steps
P4 = 2 1/2 steps
Tritone (A4 or d5) = 3 steps
P5 = 3 1/2 steps
A sixth that contains 4 steps is called a minor sixth
m6 = 4 steps (m6 is 1/2 step greater than P5)
A sixth that contains 4 1/2 steps is called a major sixth
M6 = 4 1/2 steps (M6 is 1 step greater than P5)
A seventh that contains 5 steps is called a minor seventh
m7 = 5 steps (m7 is 1 step less than P8)
A seventh that contains 5 1/2 steps is called a major seventh
M7 = 5 1/2 steps
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Unisons invert to Octaves 1 / 8
Seconds invert to Sevenths 2 / 7
Thirds invert to Sixths 3 / 6
Fourths invert to Fifths 4 / 5
(in each of the above cases, the two numbers add up to 9
- again, the consequence of no zero in heritage from Roman numerals)
Major intervals invert to Minor intervals M / m
Perfect intervals invert to Perfect intervals P / P
Augmented intervals invert to Diminished invervals A / d
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All intervals formed in a major scale between the tonic and an upper note are either Perfect or Major: i.e. P1 M2 M3 P4 P5 M6 M7 P8.
If the upper note of an interval is in the major scale of the lower note, that interval will be perfect or major, according to the above enumeration.
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Intervals larger than an octave (9ths, 10ths, etc.) may be octave-reduced -- 9ths becoming 2nds, 10ths becoming 3rds, etc.
[7970 Goliard / 7970 Free Organum]
