Oakeley, Sir Herbert (Stanley)

2. 9th-century theory.

In the organum of the early Middle Ages the vox organalis generally lies beneath the vox principalis (ex.1; see also Score, fig.1). The latter, as the melody pre-existing in its own right, placed as it is in the prominent register, is still heard as the primary voice. Organum theory begins with performance in either parallel 5ths or parallel 4ths. Free interchange between these two intervals was not expressly permitted until about 1100. In even the earliest sources the 4th was favoured. This must have been partly because it was the concordant interval which would most perceptibly have the effect of ‘sounding apart’, and partly because the two voices were then closer together and could most easily converge on to a unison. The Daseian notation used in Musica enchiriadis was, as will be seen later, obviously designed with organum at the 4th in mind.

In the discussion of organum in Musica enchiriadis a crucial role is played by the tritone. It is the tritone’s inconsonantia or absonia which makes deviation from strict parallel movement necessary. It is that also which brings about a change in texture to one in which the vox organalis often clings to a particular note and produces a drone-like effect. Since the writer of Musica enchiriadis was clearly very concerned with such deviations, he found that a system of disjunct tetrachords offered the means whereby the occurrence of tritone intervals in organum at the 4th – and the need for avoidance – could by comparison with the normal octave system be doubled. This system was built of identical tetrachords grouping themselves around the tetrachord of the finals D, E, F and G (ex.2: note the brackets under the letter names; the four degrees of the main tetrachord appear with their Greek number names archoos, deuteros, tritos and tetrardos). Adjacent tetrachords were always separated by a whole tone – hence they were disjunct. Because of this they cut across the octave structure of the normal tonal system; the pattern of intervals repeats at the 5th rather than at the octave. Thus it is possible to sing in parallel 5ths in this system without disturbance. A critical factor was, however, that when singing in 4ths a tritone now occurred on every fourth degree of the scale, between the tritos of one tetrachord and deuteros of the next tetrachord up: B–e, f–b, c'–f', g'–c'' (see ex.2, the brackets above the letter names). By contrast, the tritone in the octave system arises only between B and e, and between f and b. Each of the four degrees of the tetrachord has its own sign, and this sign is modified with its reappearance in each higher tetrachord by being reversed, inverted and reverted respectively – the sign for the tritos being slightly modified in shape also. The practice of changing a sign by turning it round is reminiscent of Greek instrumental notation and is possibly directly influenced by that. The signs themselves were named Daseia signs after their basic sign, which was the Greek for the prosodia daseia (cf Schmid, pp.5–7).

If the teaching of Musica enchiriadis is followed, organum takes shape as a result of the joint operation of the tetrachord system and the law prohibiting the tritone. In order to avoid each tritone the vox organalis must constantly avoid the sonus tritus. To cope with this there is one prime rule: the vox organalis must not, in the course of a phrase, descend beyond the sonus tetrardus; nor, where the vox principalis begins a melodic ascent, must the vox organalis approach the tetrardus from below (cf Schmid, p.49: ‘ut in quolibet tetrachordo in qualibet particula nec infra tetrardum sonum descendat positione nec inchoatione levetur obstante triti soni inconsonantia, qui tetrardo est subsecundus’). The vox organalis is only allowed to ‘stray’ into the register of a neighbouring tetrachord if the vox principalis changes its register correspondingly (ed. Schmid, pp.51–2; cf ex.1: from the syllable -lis onwards the vox organalis shifts into the next tetrachord down). In practice each sonus tetrardus (c, g, d', a') functions as a lower limit of pitch to which the vox organalis clings like a drone. The vox organalis quits this limit in the upward direction only if the vox principalis itself moves beyond a 4th above it, or if the vox organalis moves to a unison with the vox principalis at the end of a section (the latter, as the pre-existing and hence unchangeable melody, thus drawing the vox organalis towards it, as it were). The second of these situations arises in ex.1 at the syllables pi-is; the first does not occur until after the dip down into the tetrachord below at the syllable -lis, the vox organalis therefore having to cling to the same tetrardus for the first nine syllables.