A Practical Supplement to Guido of Arezzo's Pedagogical Method

"His ita perspectis": A Practical Supplement to Guido of Arezzo's Pedagogical Method Author(s): Mark A. Leach Source: The Journal of Musicology, Vol. 8, No. 1 (Winter, 1990), pp. 82-101 Published by: University of California Press Stable URL: http://www.jstor.org/stable/763524 Accessed: 24-04-2016 16:30 UTC Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms

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"His ita perspectis": A Practical Supplement to Guido of Arezzo's

Pedagogical Method MARK A. LEACH

Deinde per singulos sonos brevissimas subposui symphonias, quarum particulas cum diligenter inspexeris, uniuscuiusque vocis omnes

depositiones & elevationes per or-

dinem in principiis ipsarum particularum gaudebis te invenire. Si autem

82 hoc attentare potueris, ut unius & al-

terius symphoniae quaslibet volueris particulas moduleris, omnium neumarum difficiles valde atque multiplices varietates brevissima & facili regula didicisti. Quae omnia cum vix litteris utcumque significemus, facili tantum colloquio denudamus.1

Next I added very short symphoniae (melodies) for the individual sounds, in which, after you have ex-

amined the phrases diligently, you

will be glad to find all the depositions and elevations in turn of each indi-

vidual pitch, at the beginnings of the same phrases. If, moreover, you have been able to attempt this so that you could sing all the phrases you wished of any symphonia, [then] you learned by a very brief and easy rule the quite difficult and manifold types of all the neumae (pitch groups). All which mat-

ters, since we can scarcely indicate

[them] in any way whatever with letters, we disclose just by a simple discourse.

I n this passage from his Epistle to Michael (Epistola ad Michaelem), Guido of Arezzo describes part of a new method for teaching boys, in a novel procedure that allows them to sing an unheard melody without having recourse either to a monochord or to hearing it from anyone else. And in fact, Guido's new system, in many Volume VIII * Number 1 * Winter 1990

The Journal of Musicology ? 1990 by the Regents of the University of California 1 Guido of Arezzo, Epistola Guidonis Michaeli monacho de ignoto cantu directa, in Martin Gerbert, ed., Scriptores ecclesiastici de musica sacra potissimum, 3 vols. (St. Blasien,

1784), II, p. 45.


"HIS ITA PERSPECTIS"

ways the beginning of modern sight-singing technique, was badly needed as a method of learning the chant. One of the major obstacles to becoming a cantor, in the centuries preceding the eleventh, was simply remembering and reproducing the many chants of the liturgy. In the seventh century A.D., for instance, Isidore of Seville had already implied that the assistance of musical notation was not available to help in recording melodies,2 and about A.D. 830 Agobard of Lyons starkly commented: . . . quamplurimi ab ineunte pueritia ... very many, from earliest youth usque ad senectutis canitiem omnes up to the hoariness of old age, exdies vitae suae in parando et confir- pend all the days of their lives in pre-

mando cantu expendunt.3 paring and perfecting song (i.e., chant).

The tremendous time and effort involved in learning the large chant repertory simply by ear, from a master, is reflected again in the tenth-

or early eleventh-century Dialogus de musica, where it is said of singers

that

83

... plures eorum quinquaginta iam ... many of them actually devoted 83

annis in canendi usu & studio inuti- fifty years of their lives in vain to the

liter permanserunt.4 practice and study of singing.

But the Dialogus itself presents a solution to the problem of learn-

ing chants more quickly, by devising a system that does not even require diastematic notation for its implementation. Using the Dialogus' procedure, some boys are said to have learned many antiphons in just three days to a week, without hearing them sung by a master.5 According to the Dialogus, one takes the pitch letters, as marked on a monochord, then writes these pitch letters over the antiphon. At that point the boys use a monochord to pick out the melody, and they are supposed to be able to sing unheard melodies even without the monochord's help after a few months.6 This was the system of pedagogy 2 Isidore of Seville, Etymologiarum, Bk. III, chap. 15, in Gerbert, Scriptores I, p. 20.

See the translation in Oliver Strunk, Source Readings in Music History from Classical

Antiquity through the Romantic Era (New York, 1950), p. 93.

3 Agobard of Lyons, Liber de correctione Antiphonarii, chap. XVIII, in Jacques P. Migne, ed., Patrologiae latinae CIV (Paris, 1864), col. 338. 4 Gerbert, Scriptores I, p. 251. There is an English translation of the Dialogus in Strunk, Source Readings, p. 104, where it is, however, wrongly attributed to Odo of Cluny. On the authorship and date of the Dialogus see Michel Huglo, "L'auteur du

'Dialogue sur la Musique' attribu6e Odon," Revue de musicologie LV, no. 2 (1969), 119-71.

5 Gerbert, Scriptores I, p. 251 (Strunk, Source Readings, p. 103). 6 Gerbert, Scriptores I, pp. 252-53 (Strunk, Source Readings, p. 105).


THE JOURNAL OF MUSICOLOGY that Guido inherited and that he seems to refer to in his Micrologus of about A.D. 1026-28.7 But by the time of his late Prologus in antiphonarium, Guido had invented a very clear diastematic notation using colored C and F lines,8 and to accompany this new notation he then devised a system (reported in his letter to Michael) for teaching boys to sing that did not depend on extended reference to a monochord.

In fact, Guido now disapproved the use of a monochord after the most elementary stage of instruction: Ad inveniendum igitur ignotum cantum, beatissime Frater! prima & vulgaris regula haec est, si litteras,

quas quaelibet neuma habuerit, in

monochordo sonaveris, atque ab ipso audiens tamquam ab homine magistro discere poteris. Sed puerulis ista est regula, & bona quidem incipientibus, pessima autem perseve-

rantibus.9

Therefore, in order to find out an

unknown song, most blessed brother, the first and common rule is this: you sound on a monochord the letters

that are placed over every neuma, and hearing from it just as from a living teacher, you can learn. But that rule is childish, and good indeed for beginners, but bad for those more ad-

vanced.

84 Using his technique, Guido says, it now takes much less time to produce an accomplished singer. Nam si illi pro suis apud Deum de-

For if those, who thus far were able

votissime intercedunt magistris, qui

to obtain from their teachers scarcely

imperfectam scientiam consequi potuerunt, quid putas pro nobis nostrisque adiutoribus fiet, qui annali spa-

an imperfect knowledge in ten years of singing, intercede before God for them, what do you think will be done for us and our assistants, who can

hactenus ab eis vix decennio cantandi

tio, aut si multum, biennio perfectum

cantorem efficimus?10

produce a finished singer in the space of a year, or at most, in two years?

The first key to Guido's new procedure lies in teaching beginners the differences and properties (diversitates proprietatesque) of pitches: 7 See Joseph Smits van Waesberghe, ed., Guidonis Aretini Micrologus (Rome, 1955),

p. 92 (monochord), and p. 151 (use of letter notation). There is a translation of the

Micrologus in Hucbald, Guido, and John on Music, trans. by Warren Babb, edited, with

Introductions, by Claude V. Palisca (New York, 1978).

The date is Palisca's, from Hucbald, Guido, and John, p. 51. 8 See the Prologue in Joseph Smits van Waesberghe, ed., Guidonis "Prologus in Antiphonarium" (Tres Tractatuli Guidonis Aretini) (Amsterdam, 1975). The chronology of Guido's works is Palisca's in Hucbald, Guido, and John, p. 51. Guido too, in the Prologus, comments on the inordinate time that it took to learn the chant: see the Smits van Waesberghe edition p. 61, and translation in Strunk, Source Readings, p. 177. 9 Gerbert, Scriptores II, p. 44. o1 Ibid, p. 43.



for this purpose Guido himself used the now-famous hymn "Ut queant laxis," although this hymn is not essential to the process, and other melodies could be used instead.ll The second key, and the point of the opening quotation, consists in teaching a pupil to sing, from diastematic notation, the intervals that may follow any diatonic pitch

either ascending (in elevation) or descending (in deposition). One learns this second matter by memorizing specially constructed melodies that Guido says he has written, and indeed, many manuscripts containing the Epistle include melodies directly after this passage, examples that might possibly be Guido's own (Example i).12 Certainly one cannot teach according to Guido's method without these or similar melodies. And whether it was from lack of these examples in a

copy of the letter to Michael (several manuscripts do not contain them, and they might have been later insertions into the context),'3 or

whether it was from another circumstance where Guido's methods

but not these melodies were available, still other examples were writ-

ten for the same purpose. Thus it happens that different melodies appear in the eleventh-century tractate beginning "His ita perspectis": this is an instructional letter that describes to its recipient the eleva-

tions and depositions possible from each pitch. 4 85

"His ita perspectis" survives in three sources.l5 The first of these, MS Conventi soppressi F III 565 of the Biblioteca Nazionale in Florence (hereafter F), is a collection of treatises formerly owned by the

Dominicans of Santa Maria Novella in Florence, and was probably 1 Ibid, p. 45. The main point of "Ut queant laxis" or other melodies used for the same purpose is to teach the position of half-steps. 12 The melodies have been transcribed from MS F, excepting "Deus iudex," which is missing in F and is here supplied from MS R. See below for explanation of manuscript sigla. 13 A study of the Epistle's manuscript tradition might suggest whether lack of these

melodies represents an omission from the letter or not. In his study of Guido's theory and pedagogy, Joseph Smits van Waesberghe leaves the question of the authenticity of the melodies open, although he thinks that they have some claim to be Guido's (De Musico-Paedagogica et Theoretico Guidone Aretino eiusque Vita et Moribus [Florence, 1953], p. 91). Manuscripts containing the Epistle are catalogued in Smits van Waesberghe, ed., Guidonis "Prologus," but there is usually no indication if the melodies of Example 1 are present or not.

These melodies were omitted from the Epistola editions of Michael Hermesdorff (Epistola Guidonis Michaeli Monacho de ignoto cantu directa, d.i. Brief Guidos an den Monch Michael iiber einen unbekannten Gesang [Trier, 1884]), Antonio Brandi (in Guido Aretino [Florence, 1882]), and Gerbert, Scriptores II, and from Strunk's partial translation of the Epistle in Source Readings (in which he states, p. 125, that the melodies seem to have been lost). 14 More precisely, it seems to be part of a letter, the full contents of which are lost.

To clarify at the outset a potentially confusing point, the seven pitches are ABCDEFG and their octaves. Pitch A is named the "first," even though Gamma-Ut is

added below it.

15 These sources are cross-indexed in Pieter Fischer, ed., The Theory of Music from

the Carolingian Era up to 1400. Volume II: Italy (RISM B 111/2) (Munich and Duisburg, 1968).


THE JOURNAL OF MUSICOLOGY EXAMPLE 1. The Epistola melodies

Al- me rector mo- res nobis da sacra- tos.

Sum- me pa- ter ser- uis tu- is mi- sere- re.

Sa- lus nostra ho- nor noster es- to deus.

[MS: G] [MS: A B B

De- us iudex iu- stus for- tis & pa- ti- ens

86

t_e0 0 r C , -* w c ? , e ' C Ti- bi o- mnis seruit mundus u- ne deus.

Sta- bunt iu- sti ante deum semper lae- ti.

Do- mi- no laudes o- mni[s] crea- tura dicat.

written around A.D. 1loo in a Tuscan monastery;'6 "His ita" appears

on ff. 68r-69r. The second manuscript-Rome, Biblioteca Vallicelliana B 81 (R)-comprises two manuscripts, one eleventh- and one twelfth-century, that were probably written at Norcia;l7 the present treatise, on ff. 137v-139r, forms part of the earlier segment. Finally, the extensive Ars musica compilation of Montecassino, Archivio della

Badia MS Q 318 (Mc) includes "His ita perspectis" on pp. 206-207;

this source was written at Montecassino in the second half of the

eleventh century, according to the usage of Santa Maria de Albaneto.18 Judging from the extant copies, then, "His ita" seems part i6 Michel Huglo, Les Tonaires (Paris, 1971), p. 188.

17 Ibid, p. 200.

s8 Ibid, p. 193. The heading "De eleuatione et depositione omnium sonorum,

xxvj" has been affixed in MS Mc immediately preceding our treatise.



of a central and southern Italian theoretical tradition. It may not have been composed much later than the Epistola (ca. A.D. 1030-32),'9 the last of Guido's writings and the only one to announce special pedagogical melodies. The Tuscan manuscript F furnishes the best reading, subject to a few copyist's errors, or mistakes that occurred in transmission.20 Hence the following edition and translation of "His ita perspectis" come from F.21 The melodies in MSS R and Mc, however, differ from

Fs in some respects, and have been reproduced in an appendix. '9 The dates are those given in Joseph Smits van Waesberghe, Musikerziehung.

Lehre und Theorie der Musik im Mittelalter (Musikgeschichte in Bildern, ed. H. Besseler &

W. Bachmann, Bd. III, Lfg. 3) (Leipzig, 1969), p. 112. 20 MSS R and Mc-in related versions-misplace most of the musical examples, displace one sentence ("In hac autem notabis .. ," placed before "In hac simphonia inuenies ..." in these two sources), and omit another ("Ad hunc modem ... A.E.); the

reading of the text itself is corrupt in MS Mc, and there is music for only three of the six melodies in this source.

21 Abbreviations have been expanded, and "-q" (or as appropriate "-e") has been

filled out to "-ae," but the orthography is otherwise that of this source.

87 EDITION

(Notes to the edition follow the text directly.) His ita perspectis paucissimas tibi set ualde utiles: subdidi antiphonas. per quas breuiter et lucide omnes eleuationes et lucide omnes eleuationes et

depositiones omnium sonorum po-

teris scire. Si tantum eas summo stu-

dio discas. et perfecte memoriae tradas. Notandum enim quia nulla2 uox habet ultra quattuor eleuationes uel

depositiones. quia nulla uox potest

eleuari uel deponi. nisi ad secundam

uel tertiam. aut quartam uel quintam. Omnes quoque uoces has quattuor eleuationes uel depositiones

habere non possunt. quam quare ita sit alias si requiras inuenies. Habebis

itaque quattuor eleuationes uel de-

positiones in uoce prima. tertia. uel quarta. [septima.]3 In secunda eleua-

tiones tres depositiones duas. In quinta eleuationes tres. et deposi-

tiones quattuor.4 In sexta eleuationes duas. depositiones tres. Ecce ad hunc

Therefore, since these [matters] have

been examined, I appended a very few but extremely useful antiphons for you, by means of which you will

be able to understand briefly and

clearly all the elevations and depositions of all the sounds, if only you learn them [i.e., the antiphons] with the greatest assiduity, and memorize

them perfectly. For it should be noted that no pitch has more than four elevations or depositions, because no pitch can be raised or low-

ered unless to the second or third, or fourth or fifth [pitch above or below]. In addition, all pitches cannot have these four elevations or depositions; why it may be so you will find elsewhere if you should require. And so you will have four elevations or depositions on the first, third, fourth, or seventh pitch. On the second [pitch there are] three elevations, two dep-


THE JOURNAL OF MUSICOLOGY exemplum eleuatur omnis neuma uocis primae uel quartae. A.D.

ositions. On the fifth [pitch there are]

three elevations and four deposi-

tions. On the sixth [pitch there are] two elevations, three depositions. Behold: every neuma (i.e., every pitch group) of the first or fourth pitch is elevated in this example. A.D. --

4

A

I

b 4 J d J /4\ J 4 9 J t Be- a- tus uir qui non hati-it in con-

o.~0 '; -S 3

si-

li-

o

im-

pi-

o-

rum.

r X r

r # # ^- ^X .. m

88

.1 t J - < t , 1

J Jm J J

/C ,- - . - , .'1.r , 1/

-

_

-

.

Ca- licem sa-lu-ta- ris accipi- am

& no- men do-mi-ni in- uo- ca-bo



Ad hunc modum deponitur omnis neuma uocis primae. uel quintae.

A.E.

t- / 1 I -_ A a

-S

In this manner every neuma of the first or fifth pitch is lowered. A.E.

;r - 1 J -.,-

e e- e- t gentes & - 'pu- i me' f Quare fre-mu-e-runt gen-tes & po- pu- li meditati

sunt

in-

a-

ni-a.

A

J 1 - /1 t- , .f.r ,- T^lffi

In hac simphonia inuenies tres ele-

In this simphonia you will find the

uationes uocis secundae5 uel quintae.

three elevations of the second or fifth

quartam eleuationem habere potest.

pitch, of which [elevations] the fifth [pitch] can have the fourth elevation to the upper fifth, but from love of

quarum quinta ad superquintam.

set amore secundae sororis non uti-

tur. Deponuntur enim secunda6 et quinta7 ad similitudinem primae. Set secunda duabus tantum depositioni-

bus utitur. et quinta raro habet [alias]8 nisi duas similiter. B.E.

the second sister it is not used. In-

deed, the second and fifth [pitches]

are lowered like the first. But the sec-

ond is only used with two depositions, and the fifth rarely has other-

wise unless two as well. B.E.

s - - -f , -j ^ J J 1f _ }I -I^ ^ # ; t 94 4

Do-mi-ne quid multi-pli cati sunt qui tribulant me.

z-

~~1

?

*

'

?

sN

;b^7w

?v

_

-.

N

#\~'

In hac armonia deprehendes9 quat-

In this armonia you will discover the

tuor eleuationes uocis tertiae uel se-

four elevations of the third or sev-

ptimae. C[.]G[.]

enth pitch. C.G.

A4

-_4 --i7x

.9-,-


89

THE JOURNAL OF MUSICOLOGY In hoc melo uidebis quattuor depo-

sitiones uocis tertiae. uel sextae. set

sexta. quartam depositionem non

pitch, but the sixth [pitch] does not admit the fourth deposition. C.F.

recipit.'? C.F[.] c

In this melos you will see the four depositions of the third or sixth

...I. 1.1 ' )1'

,

h '-"---q

Do-mi-ne ne in i-ra ti-a ar- gu- as me neque

i

'

1

A

in fu-ro-re tu-o cor- ri- . pi- a; me

.. ._^ ,-, . ,. ,-_ J In hac autem'1 notabis quattuor depositiones uocis quartae uel septimae.

D.G.

In this [example], moreover, you will

note the four depositions of the

fourth or seventh pitch. D.G.

90

_V. +

1. 1, 1 J 1 3 '1

Do- mi-ne de-us meus in te spe- ra- ui li-

be- ra me 4 |

CA ^ / ? Vox quinta eleuatur ad similitudinem secundae. deponitur uero ad similitudinem primae ut iam di-

ctum est. Vox sexta eleuatur ut tertia.

set duabus tantum eleuationibus uti-

tur. Deponitur quoque ut eadem tertia. Vox tandem septima eleuatur ut tertia. deponitur autem2vt quarta.

The fifth pitch is elevated like the

second, however it is lowered like the

first, as was already said. The sixth pitch is elevated like the third, but makes use of just two elevations; it is lowered, too, like the same third [pitch]. Finally, the seventh pitch is elevated like the third, lowered

moreover like the fourth.

'MS:utilis 2MS:nula

3MS omits "septima," but the word is found in R ("prima. tercia. quarta. septima.")

4MS:quarta



5MS:primae (1me) 6MS:quintae (scde) 7MS:quintae (qnte)

8MS omits "alias," but it is found in both R and Mc.

9MS:deprehendens

'MS:fecipit

""autem" abbreviated" ."

"autem" superscripta as" ."

COMMENTARY

In his letter to Michael, Guido's own analysis of the similarities between different pitches includes a description of the specific intervals that occur in their elevations and depositions: Moreover, the seventh pitch

Praeterea septima vox cum tertia

in elevatione concordat; utraque

enim duobus tonis & semitonio, & item duobus tonis elevantur. Eadem

quoque septima cum quarta concor-

agrees with the third in elevation; for

each is elevated by two tones and a semitone, and likewise by two [more] tones. Also, the same seventh [pitch]

dat uno tono in elevatione, & in de-

agrees with the fourth by one tone in

positione tono & semitonio, et duobus tonis in utroque cantatur similiter.

elevation, and in both it is sung similarly in deposition by a tone and a semitone and by two tones.

Prima quoque cum quinta omnes depositivas neumas communiter facit; deponitur enim duobus tonis & semitonio. Itaque hae voces

similes faciunt neumas, prima cum

quarta; secunda cum quinta; tertia cum sexta; septima cum prima vel

In addition, the first [pitch]

makes all lowered neumae in common

with the fifth; for it is lowered by two

tones and a semitone. And so these

pitches make similar neumae, the first with the fourth; the second with the

cum tertia. Nulla autem vox ultra

fifth; the third with the sixth; the sev-

quatuor elevationes vel depositiones

enth with the first or with the third.

habet, quia non potest gravari vel

acui, nisi ad secundam vel tertiam,

Moreover, no pitch has more than four elevations or depositions, be-

vel quartam vel quintam, secundum

cause it cannot be lowered or raised, unless to the second or third, or

tono, semitonio, ditono, semiditono,

fourth or fifth [pitch], according to

sex species, quas supra dixi, id est,

diatesseron & diapente.22

the six species, which I mentioned

above, that is, by a tone, semitone, major third, minor third, fourth and

fifth.

Here one notices a resemblance between part of Guido's text and an opening sentence of "His ita perspectis," a similarity which might suggest that the author is recalling Guido's words: 22 Guido of Arezzo, Epistola, in Gerbert, Scriptores II, p. 49.


91

THE JOURNAL OF MUSICOLOGY

"His ita perspectis": Notandum enim quia nulla uox "Epistola" : Nulla autem vox habet ultra quattuor eleuationes uel depositiones. quia

ultra quatuor elevationes vel depositiones habet, quia

nulla uox potest eleuari uel deponi. nisi ad secundam non potest gravari vel acui , nisi ad secundam uel tertiam . aut quartam uel quintam.

vel tertiam, vel quartam vel quintam...

In any event, the position of "His ita perspectis" in its sources points to the intended conceptual setting: in all three manuscripts it has been appended to a collection of Guido's writings. In MS F, for instance, our treatise closely follows some additions to the Epistle to Michael.23 In

MSS R and Mc, on the other hand, "His ita" occurs immediately after the Regulae rhythmicae, a writing of Guido's which, like the Epistle, includes a description of the elevations and depositions as an introduction to reading diastematic notation. Its manuscript position, then,

92 as well as its content, show that "His ita" was incorporated as a supplement to Guidonian theory and pedagogy. The treatise supplies,

with simple explanations, systematically-arranged pedagogical melodies by which a pupil may learn to sing and recognize the elevations and depositions of each pitch, according to Guido's program. In turn, some of Guido's writings, or perhaps even those of his disciples, can be used to expand matters not covered in the present tractate; these issues are noted in the phrases "His ita perspectis" and ".quam quare ita sit alias si requiras inuenies," but unfortunately the precise referents of these phrases are not clear.

The initial first-person verb ("subdidi") and singular dative

("tibi") of the first sentence quickly disclose that this is a letter. Appearing as it does at the conclusion of Guido's collected writings, then, might this letter too stem from Guido's hand? Yet if the idea is tempting, it cannot be substantiated, since no source ascribes it to Guido. Moreover, if the melodies of Example 1 are Guido's, there would be 23 This short series of textual additions with charts has been directly appended to Guido's Epistle in three sources, which are: i) Brussels, Bibliotheque Royale de Belgique, II 4141 (Germany, 14th century), 2) Milan, Biblioteca Ambrosiana, D.5. inf. (beginning of the 14th century), and MS F, which is much the earliest source. See Fischer, ed., The Theory of Music II (RISM BIII/2), pp. 28 and 53, and Joseph Smits van Waesberghe, ed., The Theory of Music from the Carolingian Era up to 1400. Volume I (RISM B III/i) (Munich

and Duisburg, 1961), p. 64.



no point in using different examples here. All we can say is that "His ita perspectis" seems to have been composed by someone familiar with the Epistle or its pedagogical program who did not have at hand, or who had perhaps never seen, the "Guidonian" melodies.24 Whoever wrote the letter, the choice of texts for musical examples is perhaps even better than in the melodies of Example i: these texts are, in order, the beginnings of Psalms 1 through 7, which would be familiar texts very easy to remember.25 But, curiously, there is no

example using Ps. 4 ("Cum invocarem exaudivit me"). Is this an accident of scribal transmission or not? Examining the letter's constructional pattern, it can be seen that each melodic example except Ps. 3, "Domine quid multiplicati," directly follows an introductory sentence, such as "In hoc melo . .," or something similar. Now if the melody on

Ps. 3, illustrating B's and E's elevations, were moved up slightly to follow its introductory statement immediately-instead of appearing

after a corresponding description of B's and E's depositions-then there would be a slot into which Ps. 4 would fit. The absent melody could then have illustrated B's and E's depositions, as described in the text. On the other hand, no unattached introductory statement re-

mains to indicate that an example for these depositions is missing. 93 Neither is there actually any need to illustrate them, since both B and E are lowered to some extent in the same manner as the first pitch A,

as the author does not fail to point out. No reason exists, then, to suspect that this specific example existed and was deleted, either accidentally or on purpose. The Epistola melodies suggest another approach to the problem of the Ps. 4 omission. Since the seventh Epistola melody, demonstrating F's elevations, lacks an equivalent among "His ita" 's six examples, perhaps this was the Ps. 4 tune eliminated. "His ita" does, however, point out characteristics of F's elevation pattern, so there is no practical reason to state that something is wanting. If the Epistola melodies 24 While it is initially striking that the corresponding melodies illustrating the

depositions of A and of C both begin syllabically, the tunes showing E's elevation

pattern differ in this respect. Then too, "Beatus uir" from "His ita" and the Epistle's "Alme rector"-both showing the elevations of D-contain a nearly identical phrase at the end of each text ("impiorum" and "da sacratos"), but the types of melodic motion one is likely to find in such examples is limited, and this may be simple coincidence. "Verba mea" and the Epistle's "Salus nostra" (elevations of C) have in common the first three notes, but no more. It is interesting, however, that the examples in the Epistle and

those of "His ita" demonstrate elevation and deposition patterns on the same pitches, i.e., D's and A's elevations on D, E's and A's depositions on A, and so on. 25 Learning the Psalms was part of the education of a "puer." The age of the boys in question may have been about 6-13 years old: see Smits van Waesberghe, Musikerziehung, pp. 17-18.


THE JOURNAL OF MUSICOLOGY

are seven, just as there are seven pitches, and "His ita" contains only six examples, this is a numerical but not an empirical fault. Nevertheless, the absence of Ps. 4 is glaring, and that pitch F's special case

is mentioned in the closing sentences does not preclude its having originally had an example earlier: all of the remaining information in the text following the final example is just a restatement of previous material. Assuming then that Ps. 4 carried an example of F's elevations, it would have fitted between Ps. 3: "Domine quid," demonstrating B's and E's elevations, and Ps. 5: "Verba mea," showing the dep-

ositions of C and F. Unfortunately, inserting a melody here would interrupt the consecutive sequence of pitches established for the examples, from 1) the first (A) and fourth pitches to 2) the first (A) and fifth pitches to 3) the second (B) and fifth pitches to 4) the third (C) and

seventh pitches, and so on. This sequence could be maintained if F were to be paired with C in elevation, as the last section of the treatise in fact suggests (since through two elevations C and F are alike), but "His ita" has already paired the identical elevation patterns of C and

G in an example on Ps. 5 ("Verba mea"). So we are left with the

distasteful situation that in terms of the examples' texts something is 94 obviously missing, that in terms of musical illustration something could be missing, but that in terms of the treatise's logical progression and

illustration of its intended points all the information necessary is present, and that inserting a hypothetical missing example on F into the treatise's framework disturbs that progression. Could "His ita" have been written around a group of pre-existing melodies, of which the author possessed or used just six of an original seven? In any case, "His ita perspectis" provides a coherent means for

learning the intervals that can directly follow any of the seven

pitches-thus demonstrating qualities of musical space-by the means of memorizing sample antiphons supplied with the text: these antiphons demonstrate the intervals in order, from lesser to greater. We are told ("Notandum autem .. . quartam uel quintam.") that no pitch is directly connected to another either in ascent or descent by any greater interval than a fifth.26 Yet all pitches cannot have this maximal leap of the diapente, and the author gives a preliminary summary of the elevation and deposition patterns to be learned ("Habebis itaque

... depositiones tres.").

26 Guido did not allow the sixth as a direct interval between any two pitches. For a comparison of Guido's opinion with the views of other earlier medieval theorists on this matter, see Hans Oesch, Guido von Arezzo (Bern, 1954), p. 85.



The initial example (Ps. 1: "Beatus uir") exhibits the four possible elevations of the first or fourth pitch, i.e., of A or D. Since both of

these contain the same pattern of tones and semitones in ascent

(TsTT), "Beatus uir" serves for both pitches, although written on D. Each example in MS F is extended by a considerable melisma which gives additional sequences of the intervals needed. "Beatus uir," for instance, shows A's or D's elevations during the Psalm text as labeled

in Example 2 below, then proceeds in the melisma to present two more sequences of the same in ascending order, one in descending order, then a further group of intervallic exercises within the fifth D-a. The melismas in F are not present in either R or Mc (see appendix), and it seems likely that they were not original, but added by an overzealous instructor: not only do the Psalm texts contain within their bounds all that the musical examples are supposed to demonstrate, but the melismas negate the easily-memorized quality of the examples in their shorter non-melismatic form. As with the examples in the Epistola, the original length of these antiphons must have been moderate, in their capacity as elementary instruction. Nor do either MSS R or Mc contain the antiphon "Calicem salutaris" (for the Ves-

pers of Maundy Thursday) appended to "Beatus uir." Presumably 95

"Calicem salutaris" was meant to take the student from the pedagogical melody to a genuine chant on the same pitch, although none of the remaining examples provide such additions.27 The depositions possible from the first or fifth pitch, A or E, are unproblematic (see "Quare fremuerunt"), since both have the succession TTsT to the lower fifth, yet, as becomes apparent, E is a special

EXAMPLE 2. Elevations of D in the texted portion of "Beatus uir" n

z

1

-.

-

Be-

a-

-

2

.^

tus

:

uir

3

'

-

qui

r

non

9.

-

ha-

bi-

it

4

" in

con-

_ si-

-O-W

li-

o

im-

I"

pi-

v

o-

.

..

rum.

27 The Psalm for "Calicem salutaris" in the Antiphonale sacrosanctae Romanae Ecclesiae pro diurnis horis (Paris, Tournai, Rome, 1949), p. 436, is no. 1 15, "Credidi propter

quod locutus sum"; "Calicem salutaris" as a text is itself the fourth verse of Ps. 115.


THE JOURNAL OF MUSICOLOGY case because of its modal partner B. This second pitch B, says "His ita perspectis," may have only three elevations (to E), but does not state the reason, namely, the tritone from B to f. Correspondingly, B has only two depositions (to G), again as a result of the tritone, now below at the fourth. But since B and E together form the second (i.e., deuterus) mode, E should behave much like B. Therefore, "His ita" says that E is rarely used with more than two depositions-the point to which it resembles B-and that, although E may in the abstract have four elevations to the upper fifth, it is used with only three elevations (to a) "from love of the second sister [B]"; and indeed, the third

example ("Domine quid"), on E, illustrates just three elevations, so that the melody can serve equally well as an exemplar for B. Neither does the Epistle's melody on E ("Tibi omnis") ascend higher than

a (see Example 1 above).28 The elevations of the third and seventh pitches, C and G, are identical, although MS Fs melody is in need of slight emendation, since the scribe has miscopied the fourth elevation as D-G rather than C-G. The depositions of the third and sixth pitches, C and F, are also equivalent, although F may not make the fourth deposition because of 96 the tritone below. Why not add b-flat to solve the problem?29 Possibly because b-flat, according to Guido's final opinion in the Epistle, leads to the undesirable consequence that F-sharp should be admitted to the gamut as well: Quod si quis dicat, hanc vocem ideo

esse addendam, ut gravis F. sexta

usque ad superquartam supra lineam

ad a. per diapente possit ascendere, aut eadem sexta ad subquintam descendere, illud quoque debebit recipere, ut inter sextam F. & septimam G. alia vox addatur, ut naturalis se-

cunda gravis B. elevetur ad quintam,

& eadem acuta deponatur ad quar-

tam. Quod quia a nemine est factum,

hoc quoque a nemine est

faciendum.30

Now if someone should say, therefore this pitch [i.e., b-flat] ought to be

added, so that F gravis, the sixth

pitch, can ascend all the way to the upper fourth, beyond the line at a, through the fifth, or the same sixth [pitch] can descend to the fifth below, he will also have to assent, that between the sixth [pitch] F and the seventh G, another pitch may be placed, so that the natural second [pitch] B

gravis may be raised to the fifth

[pitch], and the same [b ] acuta may

be lowered to the fourth. Because

that is done by no-one, this also

ought to be done by no-one. 28 See below for a discussion of the modal affinities.

29 This b-flat, Guido says below, might even occur in the gravis register, although there is no low b-flat in the Micrologus. 30 Guido of Arezzo, Epistola, in Gerbert, Scriptores II, p. 49. In the earlier Micrologus Guido still admitted b-flat in limited contexts.



The final example-the four depositions of the fourth or seventh pitch, D or G-is again unproblematic, and the remainder of "His ita perspectis" simply reiterates previous material. However, we do finally learn that pitch F is limited to two elevations since, implicitly, we must avoid the tritone at the upper fourth just as at the lower fifth. In

summary, then, for each of the seven pitches:

A-may have either four elevations, maximally A to E, or four depositions, maximally a to D. B-may have three elevations, maximally B to E, or two depositions, maximally B to G. C-may have four elevations, maximally C to G, or four depositions, maximally c to F. D-may have four elevations, maximally D to a, or four depositions, maximally D to G. E-may have four elevations, maximally E to b (i.e., b-natural), but is used with only three-E to a-because of its affinity with the second sound B, which can itself have only three elevations. E may also have four depositions, E to A, but, again from its affinity with B, is rarely used with more than two (E to C). F-may have just two elevations, maximally F to a, or three depositions, maximally F to C. To know these elevation and deposition patterns is not important to the student for sight-singing alone, since it is the overall similarities

between pitches in this respect that establishes the modes and the pitches on which the modes may begin. As Guido says in his letter, ... prima vox A. & quarta D. similes & unius modi dicuntur, quia utraque in depositione tonum, in elevatione

vero habent tonum & semitonium &

duos tonos. Atque haec est prima similitudo in vocibus, hoc est, primus

modus.

. . . the first pitch A. and fourth D. are called similar and of one mode, because both have one tone in deposition, in elevation truly they have a tone and semitone and two tones.

And this is the first resemblance in

pitches, that is, the first mode.

Secundus modus est in secunda

The second mode is on the sec-

B. & in quinta E. Habent enim

ond [pitch] B. and on the fifth [pitch]

utraque in depositione duos tonos, in

elevatione semitonium & duos tonos.

Tertius modus est in tertia C. & in

sexta F. ambae enim semitonio &

duobus tonis descendunt, duobus

vero tonis ascendunt. Sola vero septima G. quartum modum facit, quae in depositione unum tonum & semi-

E. For they both have two tones in deposition, and a semitone and two

tones in elevation. The third mode is

on the third [pitch] C and on the sixth F, for both descend by a semitone and two tones, truly they ascend by two tones. Indeed, only G makes the fourth mode, which has in depo-


97

THE JOURNAL OF MUSICOLOGY tonium & duos tonos, in elevatione vero duos habet tonos & semitonium.31

sition one tone and a semitone and

two tones, in elevation truly two

tones and a semitone.

Of course, no two of the seven pitches have exactly the same elevation and deposition pattern beyond certain limits, so Guido comments that while two chants may be of the same mode, they are not necessarily

"of the same sound" ("Ideoque multi cantus eiusdem sunt modi, sed non eiusdem soni"),32 since they may appear on different pitches. Therefore, as he explains in the Micrologus, In .D. vero & .a. quae unius sunt modi, saepissime possumus eundem cantum incipere vel finire. Saepissime autem dixi & non semper, quia similitudo nisi in diapason perfecta

non est.33

To be sure, on D and a, which are of one mode, we can very often begin or end the same chant. I said however

most often, and not always, because the similitude is not perfect except at the diapason.

Guido's disapproval of b-flat (and the apparent reflection of this

98 in "His ita perspectis") also limits available positions for any mode to a maximum of two places. Using b-flat, one could transpose D-mode pieces to G, or E-mode chants to a, but even in the Micrologus Guido was uneasy about its use, and, as noted earlier, he does not permit it

at all in the Epistle.34 Modally speaking, the use of b-flat at any position

in the gamut alters the propriety of the individual pitches, and invites

chaos:

... si autem duorum vel plurimorum modorum unam vocem esse liceat, videbitur haec ars nullo fine con-

cludi, nullis certis terminis coarctari.

Quod quam sit absurdum, nullus ignorat, cum semper sapientia con-

fusa quaeque & infinita sponte

repudiet.35

... if however one pitch is permitted to be of two or of several modes, this art will seem to have no end, to be shortened by no terminus. That this

is quite absurd, no one does not

know, since wisdom always repudiates all disorderly and endless things

of its own accord.

But "His ita perspectis" takes us no further than the similitude of pitches. The treatise barely hints at modal theory, merely warning us that we would need to look elsewhere for the reasons that all seven

pitches may not have four elevations or depositions. Yet these reasons 3' Guido of Arezzo, Epistola, in Gerbert, Scriptores II, p. 47. 32 Ibid, p. 49. 33 Guido of Arezzo, Micrologus (ed. Smits van Waesberghe), pp. 131-32. 34 See the Micrologus opinion on pp. 124-26 of Smits van Waesberghe's edition. 35 Guido of Arezzo, Epistola, in Gerbert, Scriptores II, p. 49.



are not obscure. The first limitation, the tritone, restricts the elevations and depositions of both B and F, while, second, it is desirable to maintain behavioral similarity between the deuterus pitches B and E. At this stage of instruction reasons are not as important as the ped-

agogical melodies themselves, which are designed to make sightsinging possible once they have been memorized and assimilated. Indeed, these melodies would need to be learned with assistance from

a monochord or from a teacher, aids that will not be required for additional tunes once these specimens are known by heart. When the student has worked through illustrations of the elevations and depositions possible from every pitch, he will know "the quite difficult and manifold types of all the neumae,"36 and can begin to reproduce unheard melodies on his own.

Indiana University-Purdue University at Fort Wayne 36 See the opening quotation of this article.

APPENDIX

The Melodies of R and Mc "Beatus uir"

- 4, J -v 4 J 1 J R 4 JI -v J .. J . . -. J 1 J I I I I I i I I I i _-1

itw 7\., I \. I I,V I - \ 1 - `-

McBe- tus - Be- atus uir uir

J,:

qu non habi in consiqui non ha-biit in consi-

|1

M li- o im- pi- o- rum


99

THE JOURNAL OF MUSICOLOGY "Quare fremuerunt"

~ '"?'./"-O ,n 7 .- r-1 \ . Imp. | ? !f7l I 1-7 W/ If I I

" w ' l "? !w-- -** '* 1'!1 r !;m" I i" lf l" | r' j

R

j I;.|? .1. ,,,_S_, l |.,l |.ji|,l.l.|.

Mc Qua-re fremu-e- runt gentes & po- pu- li medita-ti sunt

R

in-

a-

100 ;in-aMc

ni-a

ni-

a

"Domine quid multiplicati" (No music in Mc)

R Domi- -ne quid

M -3TT

I 0*, ._

APAP- it _ ) lant me


"HIS ITA PERSPECTIS" "Uerba mea"

*'i

A4

- "" 'i ' 11 V

AA __ - m> - Jr YI 1 J JJr" - p e

t

J

c,-,. Mc Ue - ba me- a au- ri-bus per-

A . 1 /1 '1. 4 /

R

w

cl

a-

mo-

ci -pe

It

rem

me-

um

~A, I Ij | | | rj [No Music]

Mc mi- ne in-tel- le-ge clamorem meum

101

"Domine ne in ira tua" (No music in Me)

4,~ -t -9A41 R- -"I' dpn__ 0 i? ' a dp- ar/l gc I - * r.

'

_-.

'

'

R Do- mi-ne ne in i- ra tua ar-~ gu -as s me -

A

,

*

-r

.-

~~~~~~~~~~~~~~~~~~~~4

neque in fu-rore tv- o

cor-ri- pi- as me

"Domine deus meus" (No music in Mc) , -A-

R Do- mi-ne deus me-us in te spe-ra- ui li-

4 , 1 _ J ) 11 L t

be- ra me-a'[sic] pe se- quen-tibu- me ,bu-" - I bus

me


A Practical Supplement to Guido of Arezzo's Pedagogical Method

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