FOOTNOTES 

1 The principal arguments of Mr. Collins's dissertation may be consulted in two articles: 
"The performance of sesquialtera and hemiolia in the 16th century" , JAMS 17: 5-28 (Spring 
1964), and "The performance of triplets in the 17th and 18th centuries", JAMS 19:281-328 
(Fall 1966). 

2 These theorists incelude Finck, 1556; Quitschreiber, 1607; Vulpius, 1608; Beringer, 1610; 
Elsmann, 1619; Gengenbach, 1626; Hase, 1657; and TrUmper, 1668. 

REPLY TO ARTHUR HILLS 

Michael Collins 

Mr. Hills's main criticism of my work is aimed at my "failure to fashion an 
adequate method". It seems to me that there is a great deal of talk about 
method lately; but certainly no matter how airtight the researcher's method, 
it is no substitute for his having investigated all sources, finally choosing those 
relevant to the subject. This has been my "method", and the virtually com-
plete list of l6th-, 17th-, and 18th-century theorists consulted can really not 
be listed. I chose those who seemed to be talking about real practice rather 
than abstract mathematical theory. Mr. Hills has turned up no new sources, 
to contradict my theory; instead, he has attacked it on the rather dubious 
grounds of national styles. 

We shall for the moment leave 'aside the 17th-century German theorists of 
the conservative camp who so clearly call for resolutions of three black 
minims <l!!) into binary figures (ll !). In the 16th century there were, 
no national styles in the sense that Mr. Hills claims. There were different .. 
genres, such as madrigal, mass, motet, and chanson, and there was an interna-
tional style-that of the Netherlanders. They developed the polyphonic 
style about which the Italians discourse; they brought it to Italy and they' 
were employed there to write and perform this music in the great churches' 
and courts of Italy. The Italian theorists I quote are speaking of the notation 
and the music of these Netherlanders. Aron cites Obrecht, Josquin, and 
Isaac as his masters and acquaintances in Florence; Zarlino cites Willaert, 
his teacher, Ockeghem, Josquin, de Rore, and Mouton. Tigrini is beholden, 
as, are they all, to Gafurio, whose treatise is not about Italian music, and to 
Tinctoris, Aron, and Lusitano (a Portuguese theorist); he cites Josquin as 
well as Palestrina. Zacconi cites the theorists Zarlino and Heyden among 
others, and most of his examples are drawn from Ockeghem, Obrecht, Isaac, " 
Josquin, and Mouton. ' 

Now the first theorists to write out resolutions ofsesquialtera and hemiolia 
were Agricola (1532) and Bourgeois (1550), both of them perhaps somewhat 
removed from the center of musical culture. The former, however, quotes 
Gafurio, the latter Heyden, Frosch, and Listenius. They do not make ref- ' 
erence to tactus in regard to their resolutions. The later 17th-century Ger-
man theorists, perhaps stemming from the great influence of the Netherlander 

128 



Lassus, do refer to tactus. They all say the same thing. Beringer (1610), who 
is perhaps the clearest, says: " ... in this case [three black minims against 
two white ones] the notes are counted as three-part, but measured off as only 
two-part. Thus the first two are worth a half tactus, and the third by itself 
is also worth a half tactus" . 

I maintain that this is exactly what the Italians were saying since 1553. It is 
futile to argue that ZarIino distinguished between "della" and "nella"; he 
might also have used "alIa", as we shall see in the following quotations 
describing the relation of the three notes of sesquialtera (or hemiolia) to an 
equal tactus: 

Lusitano (1553): 
Zarlino (1558): 
Tigrini (1588) : 

Pisa (1611): 

"Ie due si metterano nella prima testa, & una nella seconda" 
"due si pongono della Positione & uno nella Levatione" 
"due si metteranno nella positione, & una nella levatione" 
"due si metteranno nel descendere & una nell'ascendere" 
"due vanno nell'abbassare della mano, & una nellevare" 

Picerli (1630): "dando similmente due note alIa prima, un'altr'alla seconda 
parte della battuta" 

Lorente (1672): "dos Semibreves al dar del compas y uno al als:ar" 

While none of these writers illustrates a resolution as do Agricola (1532), 
Quitschreiber (1607), Vulpius (1608), Beringer (1610), Elsmann (1619), 
Gengenbach (1626), Hase (1657), and Triimper (1668), it is quite obvious 
that the Italians agree with the Germans. Had one of the Italians written 
"la terza nel mezzo della seconda" or something similar, then there would be 
something to argue about. When we add to these theorists Bourgeois (1550) 
and the Portuguese Lorente (1672), whose examples and explanations are 
all about 16th-century prima prattica, then the practice of resolving sesquial-
tera and hemiolia appears to be international. Therefore, I conclude that I 

. am not dealing with a well-defined national school, and I would further say 
that the mainstream is not Italian but rather Netherlandish. 

Now, with reference to 17th- and 18th-century instrumental music, I do 
not conclude on the basis of quotations from Mattheson and Printz that 
resolutions also apply in the Baroque period. I merely add them to the afore-
mentioned theorists in order to construct a hypothesis for Baroque practice. 
Since no theorists before 1750 actually mention dotted figures or pairs of 
eighth-notes in conjunction with eighth-note triplets, I have examined the 
music in the light of my hypothesis. Briefly, the hypothesis is that the l6th-
century rules for the resolution of sesquialtera, hemiolia, and coloration are 
to be applied to lower note levels in the 17th and 18th centuries. I was greatly 
encouraged by the fact that the subtraction of one-fourth and one-half 
respectively in the resolution of the trochaic figure (. = l.l), advocated by 
virtually all 16th-century theorists, exactly conforms to the difference be-
tween the trochaic triplet and the dotted figure (f.F=ny Variants found 
even in one and the same autograph further supported the hypothesis that 
triplets were occasionally resolved into binary figures. 

Mr. Hills has given us a completely unsupported hypothesis as a statement 
of fact when he asserts that the" 'Italian style' is real triplets against dup-
lets". In the light of common sense and Marpurg, would anyone claim this 
for the gigues of Corelli ? To this I must add that the only writer I know ever 

129 



to have expressly forbidden the use in composition of triplets against duplets 
was the Italian Giannantonio Banner, Maestro di Cappella in Padova, in his 
Compendia musico of 1745. 

The real reason for rewriting the piece by Zannetti seems to have been 
overlooked by Mr. Hills. It has nothing to do with Brossard or Walther, but 
with the nature of the piece itself. It is labelled a Corrente, and one might 
expect it would be in triplet meter like other correntes, but it is duple on 
every level. Yet it bears in every part the sign 3 of triple meter. I conclude, 
therefore, that the sign is an indication that the piece is actually ternary. 

I heartily agree with Mr. Hills that the definitive work on performing 
17th-century triplets is still to be written. I submit that it is not a refinement 
of method that is needed, but more information, from treatises or from the 
music itself. Should anyone be able to supply me with such evidence, I shall 
be more than happy to refine my present conclusions. 

University of Rochester 

Donald M. Mintz-The sketches and drofts oj three oj 
Felix Mendelssohn's major works 

Ann Arbor; University Microfilms (UM order no. 61-16), 
1960. (Vol. I, 497 pp. text; Vol. II, 151 pp. music, Cornell 
University diss.) 

Arnold Salop . 

As the title indicates, this dissertation consists of a study of early drafts of 
three well-known works by Felix Mendelssohn: Elijah, the D Minor Trio, 
Op. 49, and the A Major Symphony, Op. 90. Thanks to a Fulbright, Dr. 
Mintz was given the opportunity. to visit the Deutsche Staatsbibliothek in 
Berlin 'and examine the volumes of the Mendelssohn Nachlass containing 
these drafts. His findings are reported here. 

Dr. Mintz goes about his task by first discussing any matters of background 
that seem relevant to the work or movement in question, then describing in 
more or less detail the published versions of the various movements-i.e. 
those of the Breitkopf & Hartel Gesamtausgabe (GA), and finally drawing 
comparisons with the versions found in draft form (MS). In doing this, Pro-
fessor Mintz demonstrates complete familiarity with the pertinent literature, 
with the versions of these works contained in the GA, and also presumably 
with those of the MS-I say presumably because only isolated passages of the 
early drafts are presented as musical examples. Indeed, he has demonstrated 
something more than mere familiarity; he has gone into these works in their 
various versions with a fine-toothed comb. He has studied what makes them 
tick motivically, thematically, harmonically, and dramatically, and has 
applied this knowledge, and that gained from comparing the versions, to the 

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