Zarlino, the Senario, and Tonality Robert W. Wienpahl

Zarlino, the Senario, and Tonality
Robert W. Wienpahl
Journal of the American Musicological Society, Vol. 12, No. 1. (Spring, 1959), pp. 27-41.
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Zarlino, the Senario, and Tonality
BY ROBERT W . WIENPAHL
HE MOST IMPORTANT advances in
I
harmonic theory
T 6th-century
were made rimarily by one man,
Gioseff o Zar ino (1517-90), and it is
safe to say that probabl no theorist
since Boethius was as indiuential upon
the course of the development of
music theor . He was a man of tremendous ta ents, well versed in the
Greek and Hebrew languages, philosophy, mathematics, astronomy,
and chemistry, to say nothing of
music. While he was a composer and
maestro di cappella at St. Mark's, his
chief claims to fame are his three excellent treatises: L'istitutioni hmnzoniche (first ~ublishedin Venice
in 1558, A d thkn followed by numerous reprints, 1562, 1573, etc.) ;
Dimostrationi hannonicbe (Venice,
I 57 1, etc.) ; and Sopplimenti msicali
(Venice, 1588). The complete set
was republished then in 1589, entitled De tutte ropere del R.M. Giosefio Zarlino da Chi0ggia.l I t is the
complete edition that we have consulted for this study.
It is well to begin the discussion
by setting forth Zarlino's dichotomization of the modal system in his
treatment of consonance and the
common triad.
Thus, Zarlino has the following to
say concerning the use of consonance in composition:
'I
Y
. . . La varieta dell Harmonia in simili accompagnamenti non consiste solamente
nella varieta delle Consonanze che si fa tra
due parti ma nella varieta anco dell' Har1 D e tutte Popere del R. M. Gioseffo Zarlino da Chioggia (Venetia: F. de Senese,
I
589),:
2
L lstitzctioizi harmorziclze, Cap. 3 1 , p.
222.
monie la quale consiste nella positione della
chorda che fh la terza, ouer la Decima
sopra la pane graue del la cantilena. Ande,
ouer che sono minore et l'Harmonia che
nasce e ordinata o s'assimiglia alla proportionalita o mediatione Arithmetica, ouer
sono maggiori et tale Harmonia 2. ordinata
ouer s'assimiglia
alla mediocrita Harmon"
ica. E t da questa varieta dipende tuna la
diversita et la perfettione dell'Hannonie;
conciosiache 2. necessario (come dirb altroue) che nella compositione perfetta si
ritrouino sempre in atto la quinta et la
T e n a ouer le sue Replicate, essendo che
oltra queste due consonanze l'Udito non
pub desiderar suono che caschi nel mezo
ouer fuori de i loro estremi che sia in ~ t t o
differente et variato da quelli .
..
.
. . The variety of harmony in such combinations does not consist solely in the
variety of Consonances which are made
between two parts but also in the variety
of the Harmony which consists of the
types of intervals which make up the
third, or the Tenth above the lowest part
of the song. Either it is minor and the
Harmony which arises is established by or
corresponds to the Arithmetic proportion,
or it is major and such Harmony is established by or corresponds t o the ordinary
Harmonic, and on this variety depends all
the diversity and perfection of Harmony.
For it is necessary (as I have said elsewhere) that in the perfect composition
there always be found in effect the Fifth
and Third or their compounds [i.e., the
10th and ~ z t h lthere being nothing beyond
these two consonances which the ear desires, no sound within or beyond their
limit which may be in any way different
from them. . . .
I t can be seen from this that the
common triad is considered by Zar-
28
JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY
lino as the most important of all consonant combinations. This attitude is
reflected in the increasing inclusion
of the third in the final chord. W e
examined some 5,179 pieces of music
from the period 1500 to 1700 and
found that the period of greatest use
of the final third was from 1580 to
1620; some 93.8% of all final chords
included the third, and it is safe to
say that actual practice exceeded
written practice. Certainly theory
and practice are hand in hand.
Zarlino continues:
Ma perche gli estremi della Quinta sono
invariabili et sempre si pongono contenuti
sott' una istessa proportione (lasciando
certi cosi ne i quali si pone imperfetta),
pero gli estremi della Terze si pongono
differenti tra essa Quinta. Non dico pero
differenti di proportione ma dico differenti
di luogo; percioche (come ho detto altroue) quando si pone la Terza maggiore
nella pane graue l'Harmonia si fh allegra;
et quando si pone nell'acuto si fa mesta.
Di mod0 che dalla positione diversa delle
Terze, che si pongono nel Contrapunto tra
gli estremi della Quinta ouer si pongono
sopra I'Ottava, nasce la varieth dell'Harmonia. . . .
But because the limits of the Fifth are invariable and always are included under the
same proportion (allowing certain types
to be classed as imperfect) yet the limits
of the Thirds are different within the
Fifth. I do not say different in position,
for (as I have said elsewhere) when the
major Third is placed in the lower part
of the Harmony it is happy and when
placed in the upper part it is sad. So that
from the different positions of the Third,
which is placed in counterpoint between
the extremes of the Fifth or placed above
the Octave, is born the variety of the Harmony. . . .
This is one of the earliest discussions of the effect produced by the
major and minor chord and is coms Loc. cit.
pletely in keeping with our own
feeling today. It should be pointed
out, however, that Zarlino does not
speak of the combination as an entity
but rather as a positioning of two
types of thirds. It is evident that he
appreciates the value of happiness or
sadness as one belonging to the third
itself, since he states that it may be
found between the limits of the fifth
or placed above the octave. In clarification of this idea he states:
Se adunque noi uorremo uariar I'Hannonia,
& osseruare pih che si pub la Regola posta
di sopra nel Cap. 29. (ancora che nelle
compositioni di pih voci non sia tanto
necessaria, quanto P in quelle di due) P di
bisogna, che noi poniamo le Terze differenti in questa maniera; c'hauendo prima
posto la Terza maggiore, che faccia la
mediatione Harmonica,. poniamo dapoi la
minore, che farh la divisione Arithmetica.
If then we want to vary the harmony, and
observe as far as possible the rule set forth
above in Cap. 29 (although this may not
be as necessary in compositions for several
voices as in those for two) it is merely a
matter of placing the different Thirds in
this fashion; having first employed the
major Third, which constitutes the Harmonic division, we then use the minor,
which arises from the Arithmetic division.
Since he is speaking primarily
about composition in two parts, as he
states in parenthesis, it is clear that
he fully appreciates the shading value
of juxtaposed thirds.
It should be noted in what ways
Zarlino refers to the positioning of
intervals, both in these passages and
those which follow, because there is
a definite change taking place in the
consideration of vertical combinations.
Up to the time of Zarlino the
tenor was held to be the most important voice, the determiner of the
4
Ibid., p.
221.
29
ZARLINO, T H E SENAEIIO, AND TONALITY
mode, and all intervals were figured
in relation to it, both above and below. With Zarlino, however, we can
find many statements which show
directly or indirectly that this is no
longer the case. W e consider the
above quotations as indications of his
desire to construct composite intervals above a bass tone, especially in
the second quotation beginning "Ma
perche. . . ." I t is unfortunate that
Riemann miscopied this particular
k ass age,^ after the parenthesis, where
it continues, ". . . per0 gli estremi
delle Terze. . . ." Instead of the
plural "delle Terze" he used the singular "della Terza." From this mistake he drew the erroneous deduction that Zarlino was speaking of
only one kind of third and its position above and below the keytone,
from whence he decided that Zarlino
was the earliest representative of the
dualistic theorists like Hauptrnann,
dttingen, and himself, who consider
the minor key as an inversion of the
major. W e need not go into this
theory here, but it is well to point
out that the third quotation, beginning "Se adun ue . . . ," continues to
refer to the di erent thirds, proving
that Zarlino did not merit the dubious honor conferred upon him by
Riemann.
Further proof of this may be had
in the following statement by Zarlino, in which he now carries his deductions in harmony into the larger
fields of the modes:
If
La cagione 8, che nelle prime, spesso si
odono le Maggiori consonanze imperfette
sopra le chorde estremi finali, b mezani de
i Modi, b Tuoni, che sono il Primo, il
Secondo, il Settimo, I'Ottauo, il Nono, &
il Decimo; come uederemo altroue; i quali
Modi sono molto allegri & uiui; conciosia
che in essi udimo spesse fiate le Conson6 H. Riernann, Geschichte d m Mzcsiktheorie
(Berlin, 19201, pp. 393ff.
6 L'istitzctioni, Part 111, Cap. 10, p. 192.
anze collocate secondo la natura del Numero sonoro; ci&, la Quinta uamezata, b
diuisa harmonicarnente in una Terza maggiore, & in una minore; il che molto diletta
all'udito. Dico le Consonanze esser poste
in essi secondo la natura del Numero
sonoro, percioche allora le Consonanze
sono poste ne i lor luoghi naturali; . N e
gli altri Modi poi, che sono il Terzo, il
Quarto, il Quinto, il Sesto, l'undecimo, &
il Duodecimo, la Quinta si pone a1 contrario; cio8, mediata arithmeticarnente da una
chorda mezana; di mod0 che molte uolte
udimo le Consonanze poste contra la natura del norninato Numero. Per ilche, si
come ne i prirni la Terza maggiore si sottopone spesse uolte alla minore; cosi ne i
secondi si ode spesse fiate il contrario; &
si ode un non sb che di mesto b languido,
che rende tutta la cantilena molle; . . .
..
The reason is that in the first [case] the
Major imperfect consonances frequently
appear above the final note, as in the case
of the Modes, or Tones, such as the First,
Second, Seventh, Eighth, Ninth, and the
Tenth; [do not forget that these are Zarlino's new numberings71 as we saw elsewhere; such Modes are very cheerful and
lively; because in them we often find the
Consonarlces placed according t o the nature of the Sonorous Number; that is, the
Fifth is divided harmonically into a major
Third and a minor [4:5:61; which is very
delightful to the ears. I say that the Consonances are arranged according to the
nature of the Sonorous Number, for then
the Consonances are put in their natural
. In the other Modes, which are
places;
the Third, Fourth, Fifth, Sixth, Eleventh,
..
De tutte I'opere, Lib. IV, Cap. X, p. 399.
Authentic Modes
I Ionian.
Final C
I11 Dorian.
Final D
V Phrygian.
Final E
V I I Lydian.
Final F
I X Mixolydian.
Final G
X I Aeolian.
Final A
Plagal Modes
I1 Hypoionian.
Final C
I V Hypodorian.
Final D
V I Hypophrygian.
Final E
V I I I Hypolydian.
Final F
X Hypornixolydian.
Final G
X I 1 Hypoaeolian.
Final A
7
3O
JOURNAL OF T H E AMERICAN MUSICOLOGICAL SOCIETY
and the Twelfth, the fifth is placed contrariwise; that is, divided arithmetically
by the middle tone; so that many times we
hear the Consonances arranged contrary
to the nature of the Number in question.
In the first [the Modes first referred to],
the major Third is frequently placed below the minor; while in the second it is
frequently heard otherwise [i.e., the minor
Third below the major]; and there is
heard a sad or languid effect, which makes
the whole melody soft; . . .
This is the first recognition of the
fact that there were actually only
two types of modes, those which had
a tonic major third and were cheerful, and those which had a minor
third and were sad. H e then affirms
the identity of each group of modes
with the major and minor triad respectively, although they are identified by the placement of the thirds
rather than by the term "chord." It
is remarkable that Zarlino did not go
one step further and call them major
and minor modes, but it was more
than one hundred years before these
labels were applied.
We
like to
attention'
before proceeding, to the
use of the terms "harmonic" and
"arithmetic."
"Harmonic" applies t o the division
of the monochord according to the
various string length ratios, expressed
by the series: 1, '/z, %, 1/4, 5, %,
which produces the first six partials;
thus, fundamental, octave, fifth, double octave, major third, and minor
third (i.e., C , c, g, c ' , e ' , g ' ) . T h e
major harmony, therefore, corresponds to this series, due to the position of the major third below the
minor.
"Arithmetic" refers to the arithmetical division: thus, I :2 :3:4: 5 : 6, in
which the denominator, 6, remains
i'e'>6/6, 5/6, 4/6, 3/6, 2/6,
1/6. This produces respectively the
fundamental, minor third, fifth, octave, fifth, fifth (ice., C, Eb, G,c, g,
hi^ is, of course, the minor barmOny.
Thus, the example (omitted above)
in the first quotation, which he labels
Harmonica and Arithmetica, is derived from these two series. Below,
he places the superparticular ratios,s
Sesquiquarta (5/4 or major third)
and Sesquiquinta (6/5 or minor
third).
Zarlino's whole theory of consonance, then, is related to a series of
six numbers, from one t o six, or the
arithmetical series I :2 :3 :4: 5:6. This
is not used, however, as was described above with the constant denominator of six. But rather, it is the
source for all possible ratios involving these six numbers. This is really
an extension of the Pythagorean system, which stated that all the perfect
consonances were derived f r o m
the first four numbers; thus, I : t is
the octave, 2 : 3 the fifth, and 3:4 the
fourth. Zarlino calls his series the
Senario. T h e r e f ~ r e , ~
Delle propried del numero Senario er delle
sue pani et come tra loro si ritroua la
fo,
dsogni consonanze musicale.
TRANSLATION
From the propositions of the number Six
and from its pans and the relation between them is found the form of every
consonance.
T h e perfection of consonances, as
derived from the Senayio, is related
to the simplicity of the numbers
making up the ratio: l o
Et k in tal maniera semplice la Diapason,
che se ben 2 contenuta da sue Suoni diversi per il sito, dirb cosi; paiono nondiy u p e r p a r t i c u l a r l refers to a ratio in
which the antecedent exceeds the consequent
b y Q ~ ~ ~ t i t q , L t iCap,
o l ? i r5,
, Chapter heading
l o Ibid., Cap. 3, p. 1 8 4
ZARLINO, THE SENA.RIO, A N D TONALITY
meno a1 senso un solo, percioche sono
molto simili; & cib aviene per la viciniti
del Binario all'Unita. . .
.
TRANSLATION
And it is in such a simple fashion that the
Octave derives its sound from its position,
thus let me say, however, that it seems to
be a single sound; for they [the two tones
of the octave] are much alike and are a
result of the proximity of T w o to One.
T h e octave, therefore, is the most
perfect because of the proximity of
two to one.
By carrying out the various ratios
the following consonances are obtained: 2: I equals the octave, 3 :2 the
perfect fifth, 4: 3 the fourth, 5:4 the
major third, and 6: 5 the minor third.
I t will be noted that these are superparticular ratios and that they form
the basic consonances because of this
close relationship; i.e., their component numbers do not differ b y
greater than unity ( Unitd), for, as he
says: l1
. . . Ma la Vniti, benche non sia Numero,
tuttauia i. principio del Numero; & da essa
ogni cosa, b semplice, b composta, b corporale, b spirituale che sia, uien detta Vna.
TRANSLATION
Unity, although not itself a
Number, nevertheless is the source of
Numbers; & everything, whether it be
simple, compound, corporal, or spiritual,
comes from this Unity. .
. . . But
. .
From this it can be seen that the
major and minor sixth are not considered by Zarlino to be basic consonances, since their ratios are respectively 5: 3 and 8: 5.
Of the major sixth he speaks as
follows: l2
L'hexachordo maggiore i. Consonanza
composta, percioche i minimi termini della
sua proportione, che sono 5 & 3, sono
capaci d'un mezano termine, che 6 il 4.
The major sixth is a composite Consonance, for the minimum limits of its proportions, which are 5 & 3 , have a middle
term which is 4.
It is unfortunate, perhaps, that Zarlino, as well as others both ancient
and modern, became enamored of
t h e Senario system, because i t
blinded him to certain fundamental
principles of inversion which otherwise might have been obvious. T h e
minute that he considered sixths as
composite intervals, he banished the
idea that they were also inversions of
thirds. A t any rate, he continues: l3
Vedsi oltra di questo I'hexachordo maggiore, contenuto in tale ordine tra questi
termini 5 & 3, il quale dico esser Consonanza composta della Diatessaron & del
Ditono: percioche 6 contenuto tra termini,
che sono mediati dal 4.
There may be seen in this major sixth
contained within its limits 5 & 3, what I
call a Consonance composed of the Fourth
and the Major Third: for it is contained
between its boundaries by means of the
number 4.
Thus, the perfect fourth equals
3:4 and the major third 4:s. It has a
neatness which could easily appeal
to the orderly mind.
Figure 114 shows one of the numerous graphic demonstrations of
ratios; in this case, for the Senario. A
comparison of this with a figure of
similar function by Salinas, which
follows shortly, will show why the
latter made a clearer statement of interval compliments.
Concerning the minor sixth, Zarlino has this to say: l5
Ibid., Cap. 15, p. 33. Ibid., Cap. 15, p. 32. 1 5 Ibid., C a p 16, p. 34. 13
Ibid., Part I , Cap. 12, p. 29. 12 Ibid., Cap. 16, p. 34. 11
3'
14
Prima
32
pcllr
~ o p r i e i idrf nymrro Srnrrio fl dellrjiic parti ;0 comc tra
loyo l; ritrow la forma d'ogni [o$nan<d (aujicale,
cap. X V .
N
c H o a c H r moltcfianole propricti dcl,numero Scnario; nondimcno,
pernon andar troppo in lungo, racconteri, folamentc qucllc chc fauno a1 pro
pofito ;& la prilnafari ,che cgli 2 tra i Numcri pcrfctti il Primo ; & conticncin fe Parti, chcfono proportionate trzloro in tal modo ; chc pigliandonc
Due qua1 fi uagliono ,hnnno tal rclatione, chc ne danno la ragionc ,b for~nadi unit
deUe Proportioni dellc muficali confonanze j o femplicc , 6 compoff ;I ch' clk fia ; come fi pud uederc nclla fottopoita figura
.
Sonoancoralc fueParti in tal no do collocatcPcordinatc, chelc Formc di cinfcuna
delle Ducrnaggiori femplici confonanzc, Ic qunli da i Mufici urngon chianlntc IJcrKbttc ;efindo c6tcnutc tralc parti dclTcrnario,fono in ducparti diuifc in Hnr~nonicnpro
jmrtionaliti,dn un tcrminc mcrmo: conciofin cllc ritroamdoliprimn la Dinparon nrla forma& proportionc,chc 2 trn s S( I. fcnz'alc~lnmczo, 6 tiopoi dnl Tcr~larinlioflo tl.;~
i14.&il 2 . in duc parti diuic~;c1o2, in duc conihnatlt.~,nclla DintcKiron pri~nn~noit ~ ~ c h c f i r i t r otra
u a 4.& 3.hnclln I)inpc11tccollocrtatrnil3. &il 2. Q c R n poi liritroua tra 6.& 4, diuifa dnl 9 , in duc particonionanti; cio6,in 1111Ditono contcnuto tra 7.
& 4. &in un Scmiditonocontcnuto tra 6. Sr j. H o dctto, chc hnodiuik in Duc parti
in
Figure
I
33
ZARLINO, THE SENARIO, AND TONALITY
Alquale aggiungeremo il minor Hexachordo, che nasce dalla congiuntione della
Diatessaron col Semiditono, . . . Imperoche
ritrouandosi tal proportione tra 8 & 5. tai
termini sono capace 8 u n mezano termine
h-onico,
ch'b il 6; il quale la divide in
questa maniera 8.6.5. in due proportioni
minori; c i d , in una Sesquiterza & in una
Sesquiquinta.
TRANSUTION
similarly we shall figure the minor Sixrh,
which is born of the union of the Fourth
with the ~i~~~ Third, . . For such proportions are found between 8 & 5 whose
limits contain a middle harmonic number
which is 6; which divides it in this way
8:6:5, in two minor proportions; that is, in
a Fourth & in a Minor Third.
Here he seemingly goes outside of
the Senario but manages to excuse it
in this way: le
Et benche la sua fonna non si troui in atto
tra le parti del Senario; si troua nondimeno
in potenza; conciosiache ueramente la
piglia dalle parti contenute tra esso; c i d ,
dalla Diatessaron & dal Semiditono; perche
di questa due consonanze si compone: la
onde tra'l primo numero Cubo, il quale 6
8 uiene ad hauerla in atto.
And although its ratio is not found in
actuality within the parts of the Senario,
they are nevertheless found potentially;
because indeed the elements of the parts
are contained within; that is, in the Fourth
& in the Minor Third: wherefore it is
composed of two consonances: so that
actually this 8 is a Cube of the first number.
And further on: l7
. . . PerB dico .. . che nel Senario; ciob, tra
le sue Parti, si ritroua in atto ogni Semplice
musical consonanza, & anco le Composte
in potenza. . . .
TRANSLATION
I say . . that as every
. . . However
10 bid. 17 Ibid., p.
35. .
Simple musical consonance is found in
actuality in the Senario, so the composite
are found potentially. . . .
And elsewhere, he
seals the union which Cut him off
from the invertibility of sixths and
thirds.ls
. . . L'hexachordo mapeiore,
""
. & anco il minore, nascono dalla congiuntione della Diatesaron col Ditono, b Semiditono; come
diligentemente habbiamo dimostrato nel
second0 Ragionamento delle Dimostrazioni
harmoniche'
TRANSLATION
. . . T h e major sixth, and also the minor,
are a product of the union of the Fourth
with the Major Third, or Minor Third; as
we have carefully demonstrated in the
second Rule of the Dimostrazioni harmoniche.
However, in spite of this statement
and his reference to the Dimostrazioni hamzonichse, it is in the latter
work that he gives some hint that he
may have understood the invertibility of intervals; for, in the Ragionmento Terzo, he gives the following rules: l9
Delle Consonanza e ordinate in cotal guisa,
dal fine del Semiditono A quello del Ditono
ui b la dxerenza del Semituono minore; &
dal fine del Ditono A quello della Diatessaron ui B quella del Semituono maggiore.
I1 fine della Diatessaron da quello della
Diapente si troua differente per il Tuono
maggiore; & il fine della Diapente da
quello dell'Hexachordo minore i: differente per il Semituono maggiore. Dal fine
di questo Hexachordo al fine del maggiore
ui cade la differenza del minor Semituono.
Et dal fine della Diapente A quello dell'Hexachordo maggiore ui b la differenza
del Tuono minore. Dal fine dell'Hexachordo minore a1 fine della Diapason si
troua la differenza del Ditona. E t dal fine
dell'Hexachordo maggiore A quello dell
istessa Diapason ui b quella del Semiditono.
1s Ibid., Cap. 16,p. 30.
19 Dimostrazioni harmoniche,
p. 184.
Proposta 40,
34
JOURNAL OF T H E AMERICAN MCTSICOLOGICAL SOCIETY
Simigliantemente il fine della Diapason da
quella della Diapason diatessaron c5 differente per la Diatessaron, & da quell0
della Diapason diatessaron 1 quello della
Diapason diapente casca la differenza del
Tuono maggiore. Vltimamente dal fine
dalla Diapason diapente vi 1: la differenza
della Diapente; & da quello della Diapason
diapente a1 fine della Disdiapason si troua
la differenza della Diatessaron.
TRAMLATION
Concerning consonances and how they are
arranged. From the end of the minor third
to that of the major third there is a difference of a minor half step; and from the
end of the major third to that of the
fourth it is a major half step. From the
end of the fourth t o that of the fifth is
found a major whole step; and from the
end of the fifth to that of the minor sixth
there is a difference of a major half step.
From the end of this sixth to that of the
major sixth there is a difference of a minor
half step. And from the end of the fifth to
that of the major sixth there is a difference
of a minor whole step. From the end of
the minor sixth to that of the octave there
is a difference of a major third. And from
the end of the major sixth to that of the
same octave is a minor third. Similarly
from the end of the octave to that of the
octave and a fourth there is a difference of
a fourth, and from that of the octave and
a fourth to that of the octave and a fifth
there is a difference of a major whole step.
And finally from the end of the octave to
that of the octave and a fifth there is a
difference of a fifth, and from that of the
octave and a fifth to the end of the double
octave there is a difference of a fourth.
This is as close as Zarlino comes to
the realization of invertibility. Riemann thought that he clearly understood the principle, in justification of which Riemann points to the
word "Replicate" (which will be
found in the first quotation shortly
after the parenthesis). This he translates as "Oktavversetzungen" or "inversion."20 However, we believe that
20
Riemann, lor. cit., p. 3 7 I.
the following statement by Zarlino
clearly shows that by "replicate" he
meant compound intervals in contradistinction to simple intervalS.21
La onde dico, che gli Elementi del Contrapunto sono di due soni; Semplici &
Replicati. I Semplici sono tutti quelli Intervalli che sono minori della Diapason;
com'1: l'Vnisono, la Seconda, la Terza, la
Quana, la Quinta, la Sesta, la Settima, &
l'ottaua; ciok, essa Diapason. Et li Replicati sono tutti quelli che sono maggior di
lei; come sono la Nona, la Decima, la
Vndecima, la Duodecima, & gli altri per
ordine.
TRANSLATION
Therefore I say that the Elements of
Counterpoint are of two types: Simple &
Compound. The Simple are all those intervals which are smaller than the Octave;
such as the Unison, the Second, the Third,
the Fourth, the Fifth, the Sixth, the Seventh,
& the Octave; that is, the Diapason. And
the Compound are all those which are
larger than the Octave: as are the Ninth,
the Tenth, the Eleventh, the Twelfth, &
the others in order.
again like
At this point we
to digress briefly in order t o discuss
similar views held by Zarlino's
contemporary, Francisco de Salinas
(15 13-90). W e do not know whether
the two men ever met, but it seems
highly probable in view of the fact
salinas came to R~~~ in 1538
and remained in Italy until I 56 I . At
least, if they did not meet, the similarity of their basic theories indicates
that Salinas was acquainted with Zarlino's writings.
Salinas's treatment of consonance
is also based upon the Senario and is
clear and concise. T h e accompanying figure (Figure 2 ) is of considerable interest since it helps to clarify
the explanation. Thus, concerning
the Senmio, Salinas saysz2
21 L'istitutiolti, Part 111, Cap. 3, p. 183.
22 De nzusica libri V I I (Salamanticae :
M.
ZARLINO, T H E SENA,RIO, AND TONALITY
Et quo clarius Senarii virtus elucescat non
solum in eo omnes formae consonantiarum
simplicium inveniuntur singulis ejus partibus ad proximas et ad quamcunque ejus
partem comparata consonantiam facit simplicem aut compositam, ut non tantum in
sex primis simplicibus sed etiam in sex
primis (cum aequa) multiplicibus inveniantur, in tripla sicut in sesquialtera, in
quadrupla sicut in dupla, in quintupla sicut
in sesquiquarta et in sextupla sicut in tripla
et sesquialtera. Neque Jtrn sextuplam in
proportione septupla consonantiam inveniri, sicut neque in sesquisexta ultra sesquiquintam. . . . Sciendum est, intervalla
nunc secundum Arithmeticam divisionem
disponi nunc secundum Harmonicam. Divisione Arithmetica aequales esse differentias ac spacia, inaequales vero proportiones . . . talem autem divisionem in primo
Senario reperiri satis et praecedenti figura
liquet.
And to what extent the real value of the
Six begins to shine forth not only in all
forms of simple consonances t o be met
with in their single parts in the closest and
most immediate comparison . . . but in all
parts in relation to the whole and in each
part united in consonance, simple or composite, where it is met with not only in six
simple ratios, but also six multiple ratios,
in 1:3 just as in 2:3, in 1:4just as in 1:2,
in I: j just as in 4:j and in 1:6 just as in
I : 3 and 2:3. And neither beyond I :6 in
the ratio 1:7is a consonance to be found,
just as not in 7:6 beyond 6:j . . . It is understood, intervals are distributed now according to the Arithmetic division and
now according to the Harmonic. Arithmetic divisions may be equal in difference
and also in space, unequal indeed in proportion. . . . for such a division moreover
right from the first the Six is found to be
Gastius, I 577), Lib. 11, Cap. 12, pp. 61-62. The
Senario concept continued to be quoted in
later years, as by Descartes, Compendium Musices, written in 1618, published in 1650;
English trans. Renatus Des-Cartes Excellent
Compendium o f Musick (London : T . Harper,
1 6 5 3 ) ~pp. 9-10. And Kircher, Musurgia universalis (Romae : F. Corbelletti, 1 6 5 0 ) ~Lib.
111, Cap. V, p. 100.
35
sufficient and this is evident from the foregoing figure. [See Figure z below.]
T h e example happens to be for the
arithmetic division, but the principle
would be the same for the harmonic,
concerning which he states: 23
Et mirum est quanto suaviorem efficiant
auribus concentum hae consonantiae, sic
Harmonica medietate divisae, quam Arithmetica ut in priori chorda dispositae sunt.
T~kvsLAnox
And it is wonderful how smooth these
combinations are to the ear, whether divided in the Harmonic manner, or the
Arithmetic, as the intervals are distributed
above.
It scarcely seems possible that
Salinas could have looked at the
graphic representation without realizing the principle of inversion, especially when, in a later chapter, he
continues as follows: 24
. . . Inter duo Diapason extrema ita dispositae sunt consonantiae, ut quae ad alterum eorum sit Semiditonum, ad alterum
Hexachordum maius esse reperiatur; &
quae Ditonum Hexachordum minus; &
quae Diatessaron, Diapente . . . unde props
similem concentum auribus effeciunt. Et
multb manifestius experimur Diapente, &
Diatessaron esse tamquam germanas gemellas eodem partu editas d Diapason; & solhm
quantitate differre, quoniam altera minor,
altera maior sit.
. . . Between the two extremes of an Octave are distributed the consonances, where
on the one hand may be found the Minor
Third, and on the other the !Major Sixth;
and the Fourth and Fifth . . . whence they
produce an almost similar effect on the
ears. And many effects are experienced in
the Fifth and Fourth being like twin
brothers within the parts of the Octave;
and only differing in size, because it may
be either minor or major.
23
24
Salinas, op. cit., p. 63. Ibid., Cap. 25, p. go. JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY
.
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~leli
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~i
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T h i s is actually considerably
clearer than Zarlino's statement.
In either case, while the final conclusion is never reached, it is symptomatic of the new harmonic thinking and shows a definite break from
the past.
2
In the foregoing stud of consonance it is interesting t at, for the
most part, the treatment is intervallic
rather than chordal. Yet, in the first
two quotations at the beginning of
this study Zarlino is dealing with the
chordal combination of the third and
b
37
ZARLINO, T H E SENARIO, AND TONALITY
fifth. It should be noted that at this
time the term chord (Italian: la
chorda) refers usually to interval,
but also occasionally to a single tone,
rather than a chord in our sense.
Nevertheless, he is chord-conscious
as the following passage will demonstrate: 25
Oltra di questo B da auertire, che quella
Compositione si puo chiamar Perfetta, nella
quale in ogni mutatione di chorda, tanto
ueno '1 grave, quanto uerso I'acuto, sempre
si odono tutte quelle Consonanze, che
fanno uarieth di suono ne i loro estremi.
E t quella 6 ueramente Hmmonia perfetta;
ch' in essa si ode tal consonanze; ma i
Suoni b Consonanze che possono far diversith al sentimento sono due, la Quinta &
la T e n a , ouer le Replicate dell' una &
dell' altra; percioche loro estremi non
hanno tra loro alcuna simiglianza, come
hanno quelli dell' Ottava; essendo che gli
estremi delle Quinta non mouono l'Vdito
nella maniera, che fanno quelli della T e n a ,
ne per il contrario; . . dobbiamo per ogni
mod0 (accioche habbiamo perfetta cotale
hannonia) cercare con ogni mostro potere,
di fare udir nelle mostre Compositione
questa due consonanze pih che sia possibile, ouer le loro Replicate.
.
Another thing which you should heed is
that that composition is called Perfect in
which every change of harmony, whether
u p or down, always includes a variety of
sounds within its limits. And such is indeed truly the Perfect Harmony which
includes in itself such Consonances; but
the Tones or Consonances which can produce this diversity of feeling are two, the
Fifth and the Third, or the compound of
2 5 I,'istitutioni, Part 111, Cap. 59, pp. 299300. The Harmonia fierfetta had many followers. Lippius, Synofisis musicae novae (Argentorati: Ledertz, 1612), p. 16, states: "In
practica observa Triadem harmonicam." G.
Doni, Compendia del trattato dB'generi, e
de'modi (Rome: Fei, 1635)~p. 387, says "In
quanti modi si possa practicare l'accordo perfetto nelle Viole." And Mersenne, Harmonie
universelle (Paris : Cramoisy, 1636-37), First
que I'on appeile
Book of Consonance,
ordinairement Harmonie parfaite."
". . .
each; for their limits do not have any
similarity to each other, as do those of the
Octave; since the limits of the Fifth do
not incite the ear in the way which those
of the Third do, nor contrariwise;
we ought in any case (in order that we
have such a perfect harmony) t o find out
how each of us can use in our Compositions those two consonances as much as
possible, o r their Compounds.
...
The Harmonia perfetta, or the
combination of the third and fifth, or
their compounds, is indeed a chord,
and this is the first reference to such
a vertical structure.
Zarlino then continues: 26
E ben vero, che molte volte i Prattici
pongono la Sesta in luogo della Quinta, &
1: ben fatto. Ma si de auertire, che quando
si porrh in una delle parti la detta Sesta
sopra'l Basso, di non porre alcun' altra
pane; che sia distante per una Quinta
sopra di esso; percioche queste due parti
uerrbono ad esser distanti tra loro per un
Tuono, ouer per un Semituono; di maniera che si udirebbe la dissonanza . . Osseruarh adunque il Compositore questo,
c'hb detto nelle sue compositione; cioh, di
far pih ch'ello potra, che si ritroui la
Terza, & la Quinta, & qualche siate la Sesta
in luogo di questa, b le Replicate; accioche
la sua Cantilena uenghi ad esser sonora &
piena. .
.
. .
It is indeed true that many times Composers use the Sixth in place of the Fifth,
& this well done. But be forewarned that
when one uses in one of the parts the said
Sixth above the Bass, not to allow any
other part to be a Fifth above this; for
these two p a m should not have the space
between them of a Tone, or a Semitone;
so that the dissonance can be heard. .
The Composer will then observe this that
I have said in composition; that is, as much
as possible, let the Third be met with, &
the Fifth, & sometimes the Sixth in place
of this, or the compounds; so that the
Song may be sonorous & full.
..
This statement is interesting- for
zel'istitutioni, Cap. 59, pp. 300-301.
38
JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY
two reasons: ( I ) he is dealing with a
first inversion chord but makes no
attempt to explain it as a harmony
different from the same
with
a fifth-thus, agdnindicating that he
did
grasp the invenibility , of
chords; and (') he 'peaks of
a "Sixth above the Bass."
T h e idea of building intervals
above the bass is a new one, at least
as far as theory is concerned. It
would seem that it had been done in
practice for some considerable time,
since practice usually precedes
theory. At any rate, in the chapter
just before the above statement, Zarlino speaks in the following manner: 27
.
. . 1 Musici neUe lor cantilene sogliono il
pih dklle uolte porre Quanro pani, nelle
quali dicono contenersi mas la perfettione
dell'harmonia. Et perche si compongono
per- le
principalmente de cotalai
chiamarono Elementali dells compositione,
guisa de i quactro Elementi la onde si
come F~~~~
et cagione di far
lontani pih de quelli, che si pongono nell'
altre parti; accioche le pane mezani possin0 prwedere con movimenti eleganti, Ec
congiunti, & massima mente il Soprano;
percioche questo 2 1' suo proprio. Debbe
adunque esser' il basso non molto diminuito; ma procedere per la maggior pane con
nell' altre parti; & debbe esser' ordinat0 di
maniera, che faccia buoni effetti, & che
non sia difficil da cantare; & cosi l'altre
Parti si potranno collocare onimamente ne
i propij luoghi nella cantilena. I1 Tenore
segue immediatamente 1'Basso uerso l'acuto,
ilqual' 6 quells pane, che regge, & governa
la cantilena, & & quella, che mantiene '1
Mode, 0 Tuono, nelquale 6 composto; . . .
osseruando di far le Cadenze A i luoghi
proprij, Pr con proposito~
TRANSLATION
.
The Musicians in their
Of the time put them in four parts*
in which
are 'Ontained
the Perfections of the harmony. And because it is
c O m ~ s e dOf such pans,
that reason
the
Of the
after the manner of the four Elements
whence as the Fire is fed and is the cause
producing every
thing which is
produrre ogni cosa naturale the si troua
found
in
the
ornamentation
and conservaad omamento et a conservatione del Mondo
tion of the world so the Composer strives
cosi il ~~~~~~i~~~~si sforzara di far
make the upper part Of the
more
la parte piu acuta della sua cantilena habOrnate, and
in a way
bia hello, ornato ed elegante procedere di
maniera
nutrisca et pasta
which feeds and maintains the listening
is
to be the
ascoltano. E t si come la Terra e posts per 'pirit. And as the
fundament
of
all
the
other
elements;
so
fondamento de gli altri Elementi; cosi
16Bassoh i tal proprieti, the sostiene, stabi- the Bass has such a propriety$ which
lisce, fortifica, & da accrescimento all' altre tains, stabilizes, fortifies, and gives support
pd; conciosiache
posto per Bass & to all the other pans; because it is the Base
fondamento dell'Harmonia; onde & detto and fundament Of the
whence
the Bass, as a Base and
Basso quasi, Basa, & sostenimento dell' altre it is
of the other parts. But as when an Element
panis M~ si come auerebbe, quando
the Earth is missing (and this may be
mento dells Terra mancasse (se cib fusse
possible)
which
Illin the good Order
possible) the tanto bell' ordine di case
things and 'poi' the
and the
ruinarebbe, & si guastarebbe la mondana, &
human
Harmony,
so
when
the
Bass
is lackla humans ~
~cosi quando
~ 61 Basso~
~
i
~
;
mancasse, tuna la cantilena si emperebbe di ing, the whole song is filled with confusion
confusione, & di dissonanza, & ogni cosa and dissonance and e v e ~ h i n ggoes
andarebbe in ruins. Quando dunque il ruin' When then the
~~~~~~i~~~~ componer~l~Basso della sua the Bass of his composition, he will promore 'low,
compositione, procederA per mouimenti al- ceed in a manner 'Ornewhat
and
different
as
far
as
possible,
from the
quanta tardi, & separad alquanto, ouer
other parts; so that the middle parts can
proceed with elegant and united animation,
27 Ibid., Cap. 58, pp. 293-94.
ZARLINO, THE SENA.RIO, AND TONALITY
and particularly the Soprano; since this is
its right. The .bass then ought not to be
diminished much; but proceed for the
most part with notes of somewhat greater
value than those which are used in the
other parts; and ought to be ordered in
such a fashion that it may produce a good
effect, and that it be not too difficult to
sing, and all the other Parts should be well
arranged in their proper places in the
song. The Tenor follows immediately the
Bass in the upper part and is that part
which rules and governs the Song and is
that which maintains the Mode or Tone
in which it is written . . . observing when
to make the Cadence in its proper place
and position.
T h e latter part is very interesting,
for he still refers to the tenor as the
"part which rules and governs the
Song" and "maintains the Mode or
Tone;" which is the view generally
held UD until this time.28
~ev'ertheless,four pages later Zarlino qualifies this view, since it is not
really in keeping with the rest of the
~taternent.~~
Ma si debbe anco ouertire, che quantunque
il basso possa alle uolte tenere il luogo del
Tenore, & Cosi l'una dell' altre parti, quel
dell'altra; nondimeno si d& fare, che '1
Basso finisca sempre sopra la Chorda regolare & finale del Modo, sopra '1 quale i.
composta la cantilena, & cosi 1' altre parti
B i lor luoghi proprii; .percioche da tal
chorda haueremo B giulcare il Modo. E t
se bene il Tenore uenisse B finire in altra
chorda, che nella finale, questo non sarebbe
di molto importanza; pur che si habbia
proceduto nella sua modulatione secundo
la natura del Modo del Cantilena. . . .
But also one should be warned, that although the bass may be able in turn to
take the place of the Tenor, and thus the
one take the part of the other, and vice
2 8 E.g., Pietro Aaron, Trattato della natura
e cognizione di tutti gli toni di canto figurato;
in Oliver Strunk, Source Readings i n Music
History (New York, 1950), p. 209.
29 L'istitutioni, Cap. 59, p. 298.
39
versa; nevertheless if this is done, the Bass
always will finish so as to govern the
Tone and final of the Mode upon which
the piece is composed, and thus the other
parts in their proper places; since by such
tone we can judge the Mode. And if indeed the Tenor comes to finish on another
note than on the final, this will not be of
much importance; although it may have
proceeded in its modulation according to
the Mode of the Song. . . .
This certainly seems to complete
the final reduction of the importance
of the tenor.
Before proceeding to the last part
of Zarlino's harmonic theory, as respects the needs of this study, we
should like to digress briefly and enlarge somewhat on the above topic
of maintaining the mode or tone of
a composition.
In the middle of the 16th century
there was a growing desire for the
expressive treatment of the text in
what Adrian Coclico described as
mzlsica reservata, a style of treatment
which could scarcely fail to disrupt
the character of the modes, which is
precisely what happened. I t is interesting to read what another contemporary of Zarlino's had to say
concerning this problem. W e are
referring to Nicolo Vicentino (ca.
1511-7z), who was one of the first
theorists to experiment with the restoration of the Greek modes and
genera which he considered as more
expressive, since the Greek philosophers had ascribed great powers t o
their music. A t any rate, he was well
aware of the need for digression
from modal restrictions in order to
better express the affections of the
text. Thus, he says: 30
Quando comporra cose Ecclesiastiche, &
che quelle aspetteranno le risposte dal
Choro, ?I dal'organo, come saranno alcune
30 N. Vicentino, L'antica musica ridotta alla
moderna prattica (Roma : A. Barre, 1 5 5 5 ) ~
Lib. 111, Cap. 15, p. 48.
ZARLINO, THE SENARIO, AND TONALITY
of harmony which indicate the
changes whlch will lead to a concept
of tonality.
The importance of consonance as
the basis of composition was, of
course, emphasized by all theorists
and made abundantly clear by Zarlino, who says: 32
Le Compositione si debbono comporre
prirnieramente di Consonanze & dopoi per
accidente di Dissonanze.
TRANSLATION
Compositions ought to be made up primarily of Consonance & thereafter perchance by Dissonance.
He then continues: 3a
.
. . La Dissonanza fa parer la Consonanza,
la quale immediatemente la seque, pih
diletteuole.
TRANSLATION
. Dissonance prepares Consonance, &
what follows is therefore more delightful.
. .
The principle of this statement is
that dissonance enhances the value of
consonance and exists for this purpose. Furthermore, it prepares the
consonance, and here, we feel, is an
implication of considerable importance for the further development of
tonality. It suggests that Zarlino understood the basic principle of functional harmony. ( W e have already
indicated that he was the first theorist to begin a serious consideration
of chordal structure with his Harmonia perfetta, or common chord.)
The increasin use of both the V7
and the I in t e final cadence shows
that Zarbno's opinion was pretty
\
88
33
L'istitutioni, Part 111, Cap. 27, p.
Ibid.
212.
4'
generally held. It is also indicative of
the growing awareness of the vertical concept. In analyzing the music
of the period 1500 to 1700 we
pointed earlier to the almost universal use of the third in the final
chord during Zarlino's time. In addition to its significance as the Harnzonia perfetta is the added importance of the inclusion of the final
third for the use of the passing penultimate dominant seventh. Zarhno's
feeling for functional harmony is
clearly supported by the practice of
the times, as exemplified by the increasing use of the V7 and the 1: in
the final cadence. During the forty
years from 1580 to 1620 the music
examined shows a total use of the V7
in almost ten per cent of all closes,
and of the I ;in eleven per cent. In
both cases this represents a five fold
increase over the preceding forty
years. T h e greatest use of the V, in
the period around I 600 is to be found
with the English composers, who
used it in some 2 2 . 2 % of all final
cadences. If I may quote from my
article referred to above: "The importance of the V7 in delineating the
tonic triad can scarcely be overestimated and, coupled with England's
over-all tonal feeling, is of the greatest significance in the mutual interrelationship of tonality and the authentic dominant-seventh ~adence."~'
In summation, Zarlino's Senario
forced a dichotomization of modal
theory which closely paralleled actual
practice and pointed the way toward
the major and minor tonalities.
San Fernando Valley State College
34 OP. cit., p. 382.