Sometime around the middle of the ninth century, perhaps in the northern reaches of Lothringia, some singing teachers whose identities remain anonymous organized two basic handbooks to guide instruction in music. These handbooks have been handed down to posterity as the Musica Enchiriadis and the Scolica Enchiriadis. Marginalized with the success of early eleventh-century north Italian theory (Guido of Arezzo its standard bearer), the Musica and Scolica Enchiriadis (henceforth ME and SE respectively) were accorded a place in the canon of European music theoretical texts with their publication in volume one of Martin Gerbert's Scriptores Ecclesiastici de Musica Sacra Potissimum (1784). (That Gerbert misattributed them to Hucbald need not concern us here.)
 The appearance in 1981 of a critical edition
edited by Hans Schmid
paved the way for detailed scrutiny of these and related writings and
set the conditions for a responsible English rendition.
 As Erickson points out in his comprehensive introduction, major
eleventh-century theorists--Guido of Arezzo, Berno and Hermann of
Reichenau, the anonymous author of the Quaestiones in
familiar with the ME/SE. Although they reject the daseian tetrachords
and notation that are the hallmarks of the Enchiriadis group, many of
the concepts they employ and issues they address arise directly from
those treatises. The Enchiriadis theorists insist on the modal
functionality of individual pitches and refer fundamental theoretical
claims to empirical judgment: "when you sing this . . . you will
perceive that . . . " (p. 9). They delve into
reasons for basic
musical phenomena, selectively appropriating from Boethius principles
that have explanatory value and relate directly to ninth-century
practices. They are serious in trying to discover and explain the deep
reasons behind well-formed melody and agreeable sounds (armonia),
the Scolica, with Boethius as guide, pursuing this far into the
numerical realm, the Musica (chapter 19) concluding that the real
profundity of music, its impact upon the soul (anima), can
be expressed in words.
 The Enchiriadis theorists lived in an environment where liturgical chant of the Christian Church (that dialect we call Gregorian) was the prime significant manifestation of sounding music. In trying to understand their realm of musical experience in a rational way, they came to recognize two fundamental realities. One was the four basic pitches or functions that accounted for the four distinct modal qualities familiar to them. Each pitch type was assigned a fixed place in a model tetrachord and received its own distinctive daseian sign. Replication of the daseian tetrachord through various registers generated a scale (two octaves and a tritone) adequate to compass the adult male voice range. (The ME puts it that the pitches may be extended up or down "until the voice gives out" [p. 3].) The other fundamental reality was the agreeable sound of the ymphoniae. These select intervals-- fourth, fifth, and octave--accounted for aurally salient associative relations among pitches and were employed with suave effect in organal singing of chant. The diapason was particularly agreeable, since its two constituent pitches were "not so much consonant as equal-sounding" (p. 53).
 These two realities are not entirely congruent, for the daseian
scale and notational system are periodic at the fifth, ninth, and
thirteenth, while octave equivalence is periodic at the eighth and
fifteenth. In an aural/oral situation, the necessary adjustments can
be slipped in as a simple matter of "sighting," but in a written,
theoretical context, conflict between the two is inescapable. This
incongruence was recognized by the Enchiriadis theorists, and gives
rise to probing questions and expansive answers in the SE (e.g.,
pp. 89-93). The ME theorist invokes a "wondrous change" through which
octaves are made equivalent even though tones a ninth apart are "found
to be the same [daseian symbol and function]" (pp. 18-19). The
discrepancy forces the theorists and the scribes who transmitted their
writings to devise special notational strategies for the examples of
organum involving octave doubling. Although the translation prints
some figures as they appear in the manuscripts (e.g., pp. 8-12), the
reader must refer to the Schmid edition to see how the notational
system was manipulated to represent octave doubling in organum.
 Some acquaintance with the conditions and
ambiance of ninth
century Carolingian culture is essential to an appreciation of how the
Enchiriadis treatises are constituted and what they accomplish. For
this, Raymond Erickson's 46-page introduction provides stellar
guidance. Besides outlining the content of both treatises, the
introduction covers questions of dating, manuscript transmission,
authorship and provenance, literary sources. For much of this
material, Erickson draws on Nancy Phillips's admirable dissertation, a
debt which he scrupulously acknowledges.
 Erickson's translation itself is excellent and renders the Latin sense intelligibly without being stiffly literal. The numerous technical terms offer a major challenge. In clarification, Erickson often provides the Latin term or phrase in parentheses after an English word or supplies copious notes explaining the range of a term or referring to other passages in the treatises where it is employed. Cues throughout the translation to pages in the Schmid edition facilitate reference to the original language. Besides dealing with terms, the notes also identify quotations or borrowings from source writings and refer to manuscript glosses when these shed light on contemporary interpretations. In the case of an intriguing phrase by the master of SE "things outside [the discipline] to which the science of singing aptly conforms" (extrinsecus occurrentibus disciplina canendi sese apte conformat) (p. 34), Erickson reports one gloss that refers to "a good voice" and another that invokes the character (joyful or sad) of a text and its appropriate delivery. He ventures that if the locution "refers to matters discussed in the treatise, the phrase probably refers to organum, which is not necessary to the performance of chant and thus is extrinsic to it" (p. 34, note 3). Given the full context, I tend to give more credit to the glosses and to understand the master here as alluding to the many facets of expert singing, such as vocal quality, delivery in performance, attention to the character of a text, that cannot be subsumed under written or rational principles. Organum itself can be explicated within the discipline, as the subsequent section of the SE shows.
 Erickson has produced an English version that reads smoothly, respects the theoretical issues addressed, and preserves the straightforward tone of the theorists's discourse. In very few passages would I quibble about the sense conveyed in the translation. Although relatively minor in import, I cite three examples to give some notion of the care it takes to render these ninth-century treatises in modern English. About the middle of Part I in SE, the master has the student sing the opening of the standard protus formula from each of the four daseian degrees so that he can experience for himself the resulting modal transformations. Then the master has him sing the protus version once again and remarks:
For present purposes, use whichever type of the protus you want, and you will note that all melodies sung according to the protus mode end on the protus tone. (p. 46-7).
Huc adhibe proti quos volueris modos, et videbis omnia, quae ad protum modum canuntur, sono proto finiri. (Schmid, p. 80.)
 Although Erickson's rendition is defensible grammatically, I find it difficult to grasp what might be meant by "use whichever type of the protus you want," as though there were more than one category of protus. What I take the theorist as conveying is:
Match this [the protus formula just sung] to any melody whatever in protus, and you will see that all melodies sung according to the protus mode end on the protus tone.
The subsequent illustrations for the other three modal categories confirm the methodology of singing the characteristic modal fragment (a descending pentachord) and comparing to it melodies known to be in that mode. The basic thrust is toward aural perception that the pentachord above the final traversed in melodies of a particular modal class will align with the standard pentachord unique to that mode.
 Another slight hitch occurs when the master is explaining how one sings at the diapason. After describing such singing with the help of a diagram, he says:
For whether one pitch is taken after the other an octave apart or is sung simultaneously with two equal-sounding pitches, the song of a simple diapason is made by this method. (p. 54)
Sive enim alia post aliam per octava loca sumatur, sive in unum binis aequisonis vocibus canatur, fit hac ratione cantio diapason simplicis. (Schmid, p. 91)
The provision of "pitch" as referential noun for "alia" suggests an odd manner of singing a melody in which successive tones seem to be sung alternately at the lower and upper octaves. Nor does "pitch" work well as subject of "canatur." It makes more sense to take "cantio" as the implied noun, and to understand the first procedure as involving alternation between phrases in different registers (the initial one being repeated at the octave above), the second as involving concurrent performance in parallel octaves. I would render the passage:
For whether one melody [see figure 27] is taken up after the other at the octave or whether [the melody] is sung simultaneously with two equal-sounding [i.e., octave] pitches, a song of the simple diapason is made by this method. (p. 54)
Although the diapason has yet to be defined in the treatise as a 2:1 proportion, it may be noted that "ratio," rendered appropriately here as "method," also has overtones of "ratio," a mathematical relationship, a meaning made explicit in the third part of the SE.
 A particularly thorny passage in the SE is where the pupil inquires of the master how the first two types of composite organum at the diapente differ from the first two types of composite organum at the diatessaron. The answer hinges on the delicate issue of modal identity, which holds at the fifth, but not at the fourth:
Indeed, as long as the tropes or modes always recur at the fifth and at the octave, and as long as the lower voice corresponds with the upper voice at the diapente in the same category of trope, it is necessary that there be at the octave a correspondence again with each voice in the same trope. This is done so that, when the organal voice is doubled at the diapason and the principal voice is the middle voice, the lower organal voice is separated from the middle voice by a fifth and from the upper voice by a fourth, which is the first composite form of the diapente. (pp. 61-2)
Siquidem dum quintis et octavis locis semper sit troporum vel tonorum reversio, necesse est, ut, dum vox inferior ad superiorem vocem eodem tropi modo diapente respondet, utrique rursus voci ab octava sua eodem tropo espondeatur. Fitque, ut organali voce per diapason geminata et principali voce media vox organalis inferior quintis locis a media separetur et superior quartis, quod est compositum diapente primum. (Schmid, p. 103).
The translation introduces a distinct impression of agency--fitque, "this is done so that . . ."--and encourages the notion that the modal correspondence is carried out in order to produce a certain disposition of intervals between the voices. But the modal relationships at octave and fifth are systematic and in no way depend upon the particularities of a specific type of composite organal singing. I take "fitque" to be simply descriptive here, "hence it happens [from the modal relationships] that...," or as a gloss puts it, "the resulting disposition is." A clause has somehow escaped in the translation also, so that the lower organal voice is said to be separated from the upper by a fourth, whereas the theorist knows they stand an octave apart. I would revise the passage thus:
Indeed, since the recurrence of tropes or modes always takes place at the fifth and at the octave, it follows necessarily that just as the lower voice responds at the diapente to the upper voice in the same category of trope, so in turn their octave doublings respond to each one of them in the same trope. Hence it happens that when the organal voice is doubled at the diapason and the principal voice is in the middle, the lower organal voice is separated from the middle voice by a fifth and the upper [organal voice] from the middle one by a fourth [above], which is the first composite form of the diapente.
Subsequent passages with parallel language on the second composite type of diapente organum and on organum at the diatessaron should be similarly emended.
 The book is well produced, with clear musical examples and nicely proportioned daseian symbols. I am puzzled, however, why Yale University Press chose to set the Scolica Enchiriadis in a smaller font than the Musica Enchiriadis. As a result, quotations in SE do not stand out typographically as they do in ME, the musical examples and their texts are magnified in relation to the surrounding dialogue, and the treatise itself seems diminished relative to the larger font of ME and the Introduction. Presumably economic factors entered into this decision, but the volume would have been handsomer, and SE more justly served, at least symbolically, had the size of the main font remained consistent throughout.
 The publication of clear and trustworthy English translations of the Musica and the Scolica Enchiriadis should be celebrated among those who concern themselves with the early stages of European music theory. This volume should encourage thoughtful study of these seminal treatises and should stimulate inquiry into the theoretical problems they engage.
2. Erickson points out (pp. xxvi-vii) that scholars have
this final chapter of ME because it differs so sharply in character
from the rest of the treatise and comes after a paragraph in chapter
18 that resembles a closing statement. It has been suggested that the
passage could be allied with SE, but all the manuscripts consistently
transmit it in ME.
Return to text
3. The representations in one manuscript are readily
Paris, Bibliothque nationale, fonds latin 7211: Analysis, Inventory
and Text, ed. Alma Colk Santosuosso (Ottawa: Institute of Mediaeval
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4. Nancy Phillips, "Musica and Scolica
Enchiriadis: The Literary,
Theoretical, and Musical Sources," Ph.D. Dissertation, New York
Return to text
5. Adjacent to "protus tone" is the daseian symbol for
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