zarlino, the senario, and tonality

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Zarlino, the Senario, and Tonality Author(s): Robert W. Wienpahl Source: Journal of the American Musicological Society, Vol. 12, No. 1 (Spring, 1959), pp. 27-41Published by: on behalf of the University of California Press American Musicological SocietyStable URL: http://www.jstor.org/stable/829515Accessed: 21-05-2015 15:09 UTC

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Zarlino, the Senario, and Tonality BY ROBERT W. WIENPAHL

T HE MOST IMPORTANT advances in I6th-century harmonic theory

were made primarily by one man, Gioseffo Zarlino (1517-90), and it is safe to say that probably no theorist since Boethius was as influential upon the course of the development of music theory. He was a man of tre- mendous talents, well versed in the Greek and Hebrew languages, phi- losophy, 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 harmoniche (first published in Venice in 1558, and then followed by nu- merous reprints, I562, 1573, etc.); Dimostrationi harmoniche (Venice, 1571, etc.); and Sopplimenti musicali (Venice, 1588). The complete set was republished then in 1589, en- titled De tutte l'opere del R.M. Gio- seffo Zarlino da Chioggia.' It is the complete edition that we have con- sulted 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:2 . . La varieta dell Harmonia in simili ac- compagnamenti non consiste solamente nella varieta delle Consonanze che si fa tra due parti ma nella varieta anco dell' Har-

monie la quale consiste nella positione della chorda che f! la terza, ouer la Decima sopra la parte graue del la cantilena. Ande, ouer che sono minore et l'Harmonia che nasce e ordinata o s'assimiglia alla propor- tionalita o mediatione Arithmetica, ouer sono maggiori et tale Harmonia e ordinata ouer s'assimiglia alla mediocrita Harmon- ica. Et da questa varieta dipende tutta la diversita et la perfettione dell'Harmonie; conciosiache e necessario (come dir6 altroue) che nella compositione perfetta si ritrouino sempre in atto la quinta et la Terza 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 tutto differente et variato da quelli ..

TRANSLATION ... 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 to 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 ioth and I2th] there being nothing beyond these two consonances which the ear de- sires, no sound within or beyond their limit which may be in any way different from them. ...

It can be seen from this that the common triad is considered by Zar-

1 De tutte l'opere del R. M. Gioseffo Zar- lino da Chioggia (Venetia: F. de Senese, 1589).

2 L'istitutioni harmoniche, Cap. 31, P. 222.

27


28 JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY

lino as the most important of all con- sonant combinations. This attitude is reflected in the increasing inclusion of the third in the final chord. We examined some 5,179 pieces of music from the period 5oo00 to i7oo and found that the period of greatest use of the final third was from I580 to I620; some 93.8%o 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:3 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 parte graue l'Harmonia si fa allegra; et quando si pone nell'acuto si fa mesta. Di modo che dalla positione diversa delle Terze, che si pongono nel Contrapunto tra gli estremi della Quinta ouer si pongono sopra l'Ottava, nasce la varieta dell'Har- monia. ...

TRANSLATION But because the limits of the Fifth are in- variable 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 Har- mony. ....

This is one of the earliest discus- sions of the effect produced by the major and minor chord and is com-

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 clari- fication of this idea he states: 4 Se adunque noi uorremo uariar l'Harmonia, & osseruare pi'I che si pub la Regola posta di sopra nel Cap. 29. (ancora che nelle compositioni di pidi voci non sia tanto necessaria, quanto C in quelle di due) e 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 fard la divisione Arithmetica.

TRANsLATION 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 Har- monic 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

3 Loc. cit. 4 Ibid., p. 221.


ZARLINO, THE SENARIO, AND TONALITY 29

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. We 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. . . ." It is unfortunate that Riemann miscopied this particular passage,5 after the parenthesis, where it continues, ". . . pero gli estremi delle Terze. . ." Instead of the plural "delle Terze" he used the sin- gular "della Terza." From this mis- take he drew the erroneous deduc- tion 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 Hauptmann, Ottingen, and himself, who consider the minor key as an inversion of the major. We need not go into this theory here, but it is well to point out that the third quotation, beginning "Se adunque .. . ," continues to refer to the different thirds, proving that Zarlino did not merit the du- bious honor conferred upon him by Riemann.

Further proof of this may be had in the following statement by Zar- lino, in which he now carries his de- ductions in harmony into the larger fields of the modes: 6 La cagione ', che nelle prime, spesso si odono le Maggiori consonanze imperfette sopra le chorde estremi finali, 6 mezani de i Modi, 6 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 Conson-

anze collocate secondo la natura del Nu- mero sonoro; cioe, la Quinta tramezata, 6 diuisa harmonicamente 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; .. . Ne gli altri Modi poi, che sono il Terzo, il Quarto, il Quinto, il Sesto, l'Undecimo, & il Duodecimo, la Quinta si pone al contrario; cioe, mediata arithmeticamente da una chorda mezana; di modo che molte uolte udimo le Consonanze poste contra la natura del nominato Numero. Per ilche, si come ne i primi la Terza maggiore si sot- topone spesse uolte alla minore; cosi ne i secondi si ode spesse fiate il contrario; & si ode un non s6 che di mesto 6 languido, che rende tutta la cantilena molle; ...

TRANSLATION 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 Zar- lino's new numberings7] as we saw elsewhere; such Modes are very cheerful and lively; because in them we often find the Consonances placed according to the nature of the Sonorous Number; that is, the Fifth is divided harmonically into a major Third and a minor [4:5:6]; which is very delightful to the ears. I say that the Con- sonances are arranged according to the nature of the Sonorous Number, for then the Consonances are put in their natural places;... In the other Modes, which are the Third, Fourth, Fifth, Sixth, Eleventh,

5 H. Riemann, Geschichte der Musiktheorie (Berlin, 1920), pp. 393ff.

6 L'istitutioni, Part III, Cap. Io, p. 192.

7 De tutte l'opere, Lib. IV, Cap. X, p. 399. Authentic Modes

I Ionian. Final C III Dorian. Final D

V Phrygian. Final E VII Lydian. Final F

IX Mixolydian. Final G XI Aeolian. Final A

Plagal Modes II Hypoionian. Final C

IV Hypodorian. Final D VI Hypophrygian. Final E

VIII Hypolydian. Final F X Hypomixolydian. Final G

XII Hypoaeolian. Final A



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. He then affirms the identity of each group of modes with the major and minor triad respectively, although they are identi- fied 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 should like to call attention, before proceeding, to the repeated use of the terms "harmonic" and "arithmetic."

"Harmonic" applies to the division of the monochord according to the various string length ratios, expressed by the series: i, V, 1/3, ?, V, V, 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'). The 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, 1:2:3:4: 5:6, in which the denominator, 6, remains constant; i.e., 6/6, 5/6, 4/6, 3/6, 2/6, i/6. This produces respectively the

fundamental, minor third, fifth, octave, fifth, fifth (i.e., C, El, G, c, g, g'). This is, of course, the minor harmony.

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,8 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 to six, or the arithmetical series 1: 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 involv- ing these six numbers. This is really an extension of the Pythagorean system, which stated that all the perfect consonances were derived from the first four numbers; thus, I: z is the octave, 2:3 the fifth, and 3:4 the fourth. Zarlino calls his series the Senario. Therefore,9 Delle proprieta del numero Senario et delle sue parti et come tra loro si ritroua la forma d'ogni consonanze musicale.

TRANSLATION

From the propositions of the number Six and from its parts and the relation between them is found the form of every consonance.

The perfection of consonances, as derived from the Senario, is related to the simplicity of the numbers making up the ratio:'" Et C in tal maniera semplice la Diapason, che se ben e contenuta da sue Suoni di- versi per il sito, dir6 cosi; paiono nondi-

s "Superparticular" refers to a ratio in which the antecedent exceeds the consequent by one.

9 L'istitutioni, Cap. I5, Chapter heading. o10 Ibid., Cap. 3, p. 184.


ZARLINO, THE SENARIO, AND TONALITY 31 meno al senso un solo, percioche sono molto simili; & ci6 aviene per la vicinita 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 Two to One.

The octave, therefore, is the most perfect because of the proximity of two to one.

By carrying out the various ratios the following consonances are ob- tained: 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. It will be noted that these are superparticular ratios and that they form the basic consonances because of this close relationship; i.e., their com- ponent numbers do not differ by greater than unity (Unita), for, as he says: 11

... Ma la Vnita, benche non sia Numero, tuttauia e principio del Numero; & da essa ogni cosa, 6 semplice, 6 composta, 6 cor- porale, 6 spirituale che sia, uien detta Vna.

TRANSLATION

. . But 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....

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: 12 L'hexachordo maggiore

' Consonanza composta, percioche i minimi termini della

sua proportione, che sono 5 & 3, sono capaci d'un mezano termine, che e il 4-

TRANSLATION The major sixth is a composite Conso- nance, for the minimum limits of its proportions, which are 5 & 3, have a middle term which is 4.

It is unfortunate, perhaps, that Zar- lino, as well as others both ancient and modern, became enamored of the Senario system, because it blinded him to certain fundamental principles of inversion which otherwise might have been obvious. The minute that he considered sixths as composite intervals, he banished the idea that they were also inversions of thirds. At any rate, he continues: 13 Vedsi oltra di questo I'hexachordo maggiore, contenuto in tale ordine tra questi termini 5 & 3, il quale dico esser Con- sonanza composta della Diatessaron & del Ditono: percioche e contenuto tra termini, che sono mediati dal 4.

TRANSLATION 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 4:5. It has a neatness which could easily appeal to the orderly mind.

Figure 114 shows one of the nu- merous 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, Zar- lino has this to say: 15

11 Ibid., Part I, Cap. 12, p. 29. 12 Ibid., Cap. 16, p. 34.

13 Ibid., Cap. 15, p. 33. 14 Ibid., Cap. 15, p. 32. 15 Ibid., Cap. 16, p. 34.


32 Prima Ver& ?ropriet ded momero Senario a delefue parti ; & come tra lorofi ritro&a laforma d'ogni (onfonan(a muficale,

Cap. XV.

w N c o i c H molt fianole proprictd del,numero Scnario; nondimcno. per non andar troppo in lungo, racconter6 folamente quelle che fanno al pro pofito; & la primafara', che egli C tra i Numcri pcrfetti il Primo ; & contic- nein fe Parti, chefono proportionate traloro in tal modo; che pigliandonc

Due qual fli ugliono , hanno tal rclatione, che ne danno la ragione , 6 formia di una delle Proportioni delic muficali confonanze; 6 femplice, 6 compofta ch' ella fia; co- %me fi pu6 uedere nclla fottopofta figura.

Diapafon dia ,

pcntc.

aonics .

04P

Ail tf

C

._.+ /o 0

? :S u c. e

Sonoancorale fue Parti in tal modo collocate & ordinate, chele Forme di ciarcuna delle Due maggiori femplici confonanze, cl quali da i Mufici ucngon chiamate Pecrfet- te; effendo c6tcnute tra Ic parti del Tcrnario,fono in due parti diuife in Harmonica pro portionalit:i,da un tcrmine mczano: conciofia che ritrouandofi prima la Diapafon nella forma & proportione,che C tra 2 & z. fcnz'alcun mezo, e dopoi dal Tcrnarin pollo tra ii 4.& il 2. in due parti diuifi ;

cjo., in due conlbnanze, nella DiactciTron primamcn- tc, cheli ritroua tra 4.& 3.& nella Diapcntc collocata tra il 3. & il 2. Qicfta poi fi ritro-

ua tra 6. & 4. diuifa dal s. in due parti confonanti; cioa', in un Ditono contenuto tra v. & 4. & in un Scmiditono contcnuto tra 6. & j.*Ho dctto, che frmodiuife in Due parti in Figure i



Alquale aggiungeremo il minor Hexa- chordo, che nasce dalla congiuntione della Diatessaron col Semiditono, ... Imperoche ritrouandosi tal proportione tra 8 & 5. tai termini sono capace d'un mezano termine harmonico, ch'e il 6; il quale la divide in questa maniera 8.6.5. in due proportioni minori; cioe, in una Sesquiterza & in una Sesquiquinta.

TRANSLATION Similarly we shall figure the minor Sixth, which is born of the union of the Fourth with the Minor 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: 16 Et benche la sua forma non si troui in atto tra le parti del Senario; si troua nondimeno in potenza; conciosiache ueramente la piglia dalle parti contenute tra esso; cioe, dalla Diatessaron & dal Semiditono; perche di questa due consonanze si compone: la onde tra'l primo numero Cubo, il quale e 8 uiene ad hauerla in atto.

TRANSLATION

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: 17 ..

.Per6 dico .. . che nel Senario; ciol, tra le sue Parti, si ritroua in atto ogni Semplice musical consonanza, & anco le Composte in potenza. ...

TRANSLATION

. . However I say . . . that as every

Simple musical consonance is found in actuality in the Senario, so the composite are found potentially....

And elsewhere, he irrevocably seals the union which cut him off from the invertibility of sixths and thirds."s ... L'hexachordo maggiore, & anco il minore, nascono dalla congiuntione della Dia- tessaron col Ditono, 6 Semiditono; come diligentemente habbiamo dimostrato nel secondo Ragionamento delle Dimostrazioni harmoniche.

TRANSLATION

. . . The 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 Dimostra- zioni harmoniche, it is in the latter work that he gives some hint that he may have understood the invertibility of intervals; for, in the Ra- gionamento Terzo, he gives the following rules: 19 Delle Consonanza e ordinate in cotal guisa, dal fine del Semiditono " quello del Ditono ui e la differenza del Semituono minore; & dal fine del Ditono quello della Diates- saron ui e quella del Semituono maggiore. II fine della Diatessaron da quello della Diapente si troua differente per il Tuono maggiore; & il fine della Diapente da quello dell'Hexachordo minore e 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 e la differenza del Tuono minore. Dal fine dell'Hexa- chordo minore al fine della Diapason si troua la differenza del Ditona. Et dal fine dell'Hexachordo maggiore a quello dell istessa Diapason ui e quella del Semiditono.

16 Ibid. 17 Ibid., p. 35.

Is Ibid., Cap. 16, p. 30. 19 Dimostrazioni harmoniche, Proposta 40,

p. 184.



Simigliantemente il fine della Diapason da quella della Diapason diatessaron e differente per la Diatessaron, & da quello della Diapason diatessaron a quello della Diapason diapente casca la differenza del Tuono maggiore. Vltimamente dal fine dalla Diapason diapente vi e la differenza della Diapente; & da quello della Diapason diapente al fine della Disdiapason si troua la differenza della Diatessaron.

TRANSLATION

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 to 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. Rie- mann thought that he clearly understood the principle, in justifica- tion of which Riemann points to the word

"Replicate" (which will be found in the first quotation shortly after the parenthesis). This he trans- lates as "Oktavversetzungen" or "inversion." 20 However, we believe that

the following statement by Zarlino clearly shows that by "replicate" he meant compound intervals in contra- distinction to simple intervals.21 La onde dico, che gli Elementi del Con- trapunto sono di due sorti; Semplici & Replicati. I Semplici sono tutti quelli In- tervalli che sono minori della Diapason; com'e l'Vnisono, la Seconda, la Terza, la Quarta, la Quinta, la Sesta, la Settima, & l'Ottaua; cio , essa Diapason. Et li Repli- cati 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.

At this point we should again like to digress briefly in order to discuss similar views held by Zarlino's contemporary, Francisco de Salinas ( 1513-90). We do not know whether the two men ever met, but it seems highly probable in view of the fact that Salinas came to Rome in 1538 and remained in Italy until 1561. At least, if they did not meet, the similarity of their basic theories indicates that Salinas was acquainted with Zar- lino's writings.

Salinas's treatment of consonance is also based upon the Senario and is clear and concise. The accompany- ing figure (Figure 2) is of considerable interest since it helps to clarify the explanation. Thus, concerning the Senario, Salinas says.22

20 Riemann, loc. cit., p. 371. 21 L'istitutioni, Part III, Cap. 3, p. 183. 22 De musica libri VII (Salamanticae: M.


ZARLINO, THE SENARIO, AND TONALITY 35 Et quo clarius Senarii virtus elucescat non solum in eo omnes formae consonantiarum simplicium inveniuntur singulis ejus parti- bus ad proximas et ad quamcunque ejus partem comparata consonantiam facit sim- plicem aut compositam, ut non tantum in sex primis simplicibus sed etiam in sex primis (cum aequa) multiplicibus inven- iantur, in tripla sicut in sesquialtera, in quadrupla sicut in dupla, in quintupla sicut in sesquiquarta et in sextupla sicut in tripla et sesquialtera. Neque ultra sextuplam in proportione septupla consonantiam inven- iri, sicut neque in sesquisexta ultra ses- quiquintam .... Sciendum est, intervalla nunc secundum Arithmeticam divisionem disponi nunc secundum Harmonicam. Di- visione Arithmetica aequales esse differ- entias ac spacia, inaequales vero proportiones ... talem autem divisionem in primo Senario reperiri satis et praecedenti figura liquet.

TRANSLATION And to what extent the real value of the Six begins to shine forth not only in all forms of simple consonances to 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 i:3 just as in 2:3, in x:4 just as in 1:2, in 1:5 just as in 4:5 and in 1:6 just as in 1:3 and 2:3. And neither beyond 1:6 in the ratio 1:7 is a consonance to be found, just as not in 7:6 beyond 6:5 . . It is understood, intervals are distributed now according to the Arithmetic division and now according to the Harmonic. Arith- metic 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

sufficient and this is evident from the foregoing figure. [See Figure 2 below.]

The 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 Arith- metica ut in priori chorda dispositae sunt.

TRANSLATION 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 real- izing 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 prope similem concentum auribus effeciunt. Et mult6 manifestius experimur Diapente, & Diatessaron esse tamquam germanas gemel- las eodem partu editas

"

Diapason; & soldim quantitate differre, quoniam altera minor, altera maior sit.

TRANSLATION

... Between the two extremes of an Oc- tave 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.

Gastius, 1577), Lib. II, Cap. 12, pp. 61-62. The Senario concept continued to be quoted in later years, as by Descartes, Compendium Mu- sices, written in h168, published in 1650; English trans. Renatus Des-Cartes Excellent Compendium of Musick (London: T. Harper, 1653), pp. 9-Io. And Kircher, Musurgia uni- versalis (Romae: F. Corbelletti, 1650), Lib. III, Cap. V, p. 100oo.

23 Salinas, op. cit., p. 63. 24 Ibid., Cap. 25, p. 90.



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Huiusfigure explicatio. Bafi ihulus fgurx tribus fpacijsquartuorlineisinterceptis , conflat :quorum fuperius

continet chordx n xquas partesdiuifr iniclaiones;proximum p3rtium,feu inci(iotiu nu- niero;infi mum fonos literi(c laues vocant pradici)defignatos.Co terum finguix inter C- collatx incifioncs,feu parte quas proportiones,atque interualla conflituant ; id dire-

c' illis fubiec'i numcri,& fonorum claues docent.Sed qui numeri quas proportiones ef ficiant,tatis in primno lbro dictum eft.qubus autem fonis qux proportionabus rcfpondi tiainterualla contincantur,id binxab ncifionum pundis egrcdi:ten linex ( qux cum Bari triangulum conftituunt)oflendunt:angulo enim,qucm concurr entes confiituunt, nomina interualloram infcripta fint. Vnum hoc ad monendus cft Le.tor,chord hIli# principium defiderari:diuifa enim efi in fex partes xquales,quarurn fxta comprehendi- tur inter numeros 6.& 5,quinta inter .& 4,quarta inter 4.& 1,tertia inter ;.& 2,fecun da inter 2.& s,prima inter I,& chordx principium,quod dlcfidratur.nec

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& feq uenti,& plurimis alijs,quxe fatm a' numcro nci, int, princaipiui deeftlquod fa-tum ewf, nequod fpicium relinqueretur vacuum, quod prxrcr chordmi nihil contincret.id enim non modo fuperuacincumn futurum,fed & fi;uram dcformatu rum videbatur.in multisetiam figuris illud ob chartx angufviamn ncccllfrio prxternmate dum f it.Quare admonitum Le-'torem hoc capite volutniu,non in hifkcc tant"mrn libr?a, fed & apud Bo'tium,& quotlibet alios Muficom in plkrifql figuriN cliordx principiai defi dcrari;eiufquc rci vrucum fignum clc,il flatim a numero figura incipist.Prxterea ne ea- dcem interualla in fequenti tr'po fruftra repetita videantur,fciendlum eft, interualia nunc fecund'rm Arithmeticanm diuifonem difponi,nunc fecundtnm Harmnonicam.Diui(ione Arith-

Figure 2

This is actually considerably clearer than Zarlino's statement.

In either case, while the final con- clusion is never reached, it is symp- tomatic of the new harmonic think- ing and shows a definite break from the past.

In the foregoing study of consonance it is interesting that, 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



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 ' da auertire, che quella

Compositione si puo chiamar Perfetta, nella quale in ogni mutatione di chorda, tanto uerso '1 grave, quanto uerso l'acuto, sempre si odono tutte quelle Consonanze, che fanno uarieta di suono ne i loro estremi. Et quella e ueramente Harmonia perfetta; ch' in essa si ode tal consonanze; ma i Suoni ' Consonanze che possono far diversita al sentimento sono due, la Quinta & la Terza, ouer le Replicate dell' una & dell' altra; percioche i 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 Terza, ne per il contrario; ... dobbiamo per ogni modo (accioche habbiamo perfetta cotale harmonia) cercare con ogni mostro potere, di fare udir nelle mostre Compositione questa due consonanze pid che sia possi- bile, ouer le loro Replicate.

TRANSLATION Another thing which you should heed is that that composition is called Perfect in which every change of harmony, whether up 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

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) to find out how each of us can use in our Composi- tions those two consonances as much as possible, or 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, & e ben fatto. Ma si de auertire, che quando si porr" in una delle parti la detta Sesta sopra'1 Basso, di non porre alcun' altra parte; 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 ... Os- seruara adunque il Compositore questo, c'h6 detto nelle sue compositione; cioe, di far pitt ch'ello potra, che si ritroui la Terza, & la Quinta, & qualche siate la Sesta in luogo di questa, 6 le Replicate; accioche la sua Cantilena uenghi ad esser sonora & piena. ....

TRANSLATION

It is indeed true that many times Com- posers 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 parts 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

25 L'istitutioni, Part III, Cap. 59, pp. 299- 300. The Harmonia perfetta had many follow- ers. Lippius, Synopsis musicae novae (Argen- torati: Ledertz, 1612), p. 16, states: "In practica observa Triadem harmonicam." G. Doni, Compendio del trattato dM'generi, e de'modi (Rome: Fei, 1635), p. 387, says "In quanti modi si possa practicare l'accordo per- fetto nelle Viole." And Mersenne, Harmonie universelle (Paris: Cramoisy, 1636-37), First Book of Consonance, ". .. que l'on appelle ordinairement Harmonie parfaite." 26 L'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 chord with a fifth--thus, again indicating that he did not grasp the invertibility of chords; and (2) he speaks of using a "Sixth above the Bass."

The 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, Zar- lino speaks in the following manner: 27

. . I Musici nelle lor cantilene sogliono il pii dlle uolte porre Quattro parti, nelle quali dicono contenersi tutta la perfettione dell'harmonia. Et perche si compongono principalmente de cotalai parti, perb le chiamarono Elementali della compositione, alla guisa de i quattro Elementi la onde si come '1 Fuoco nutrisce et e cagione di far produrre ogni cosa naturale che si troua ad ornamento et a conservatione del Mondo cosi ii Compositore si sforzara di far che la parte piu acuta della sua cantilena habbia bello, ornato ed elegante procedere di maniera che nutrisca et pasca l'animo che ascoltano. Et si come la Terra e posta per fondamento de gli altri Elementi; cosi 1'Basso ha tal proprietY, che sostiene, stabi- lisce, fortifica, & da accrescimento all' altre parti; conciosiache e" posto per Basa & fondamento dell'Harmonia; onde ' detto Basso quasi, Basa, & sostenimento dell' altre parti. Ma si come auerebbe, quando l'Ele- mento della Terra mancasse (se cib fusse possible) che tanto bell' ordine di cose ruinarebbe, & si guastarebbe la mondana, & la humana Harmonia; cosi quando '1 Basso mancasse, tutta la cantilena si emperebbe di confusione, & di dissonanza, & ogni cosa andarebbe in ruina. Quando dunque il Compositore componer' 1'Basso della sua compositione, procedera per mouimenti alquanto tardi, & separati alquanto, ouer

lontani piiu de quelli, che si pongono nell' altre parti; accioche le parte mezani pos- sino procedere con movimenti eleganti, & congiunti, & massima mente il Soprano; percioche questo e '1 suo proprio. Debbe adunque esser' il basso non molto diminu- ito; ma procedere per la maggior parte con nell' altre parti; & debbe esser' ordinato di maniera, che faccia buoni effetti, & che non sia difficil da cantare; & cosi l'altre Parti si potranno collocare ottimamente ne i propij luoghi nella cantilena. Il1 Tenore segue immediatamente l'Basso uerso l'acuto, ilqual' e quella parte, che regge, & governa la cantilena, & C quella, che mantiene '1 Modo, o Tuono, nelquale ? composto; ... osseruando di far le Cadenze a i luoghi proprij, & con proposito.

TRANSLATION

. .. The Musicians in their song settings

most of the time put them in four parts, in which they say are contained all the per- fections of the harmony. And because it is composed of such parts, for that reason they call the Elements of the composition after the manner of the four Elements whence as the Fire is fed and is the cause of producing every natural thing which is found in the ornamentation and conserva- tion of the world so the Composer strives to make the upper part of the song more beautiful, ornate, and elegant in a way which feeds and maintains the listening spirit. And as the Earth is held to be the fundament of all the other elements; so the Bass has such a propriety, which sus- tains, stabilizes, fortifies, and gives support to all the other parts; because it is the Base and fundament of the Harmony; whence it is called the Bass, as a Base and support of the other parts. But as when an Element of the Earth is missing (and this may be possible) which may ruin the good order of things and spoil the worldly and the human Harmony, so when the Bass is lack- ing, the whole song is filled with confusion and dissonance and everything goes to ruin. When then the Composer composes the Bass of his composition, he will proceed in a manner somewhat more slow, and different as far as possible, from the other parts; so that the middle parts can proceed with elegant and united animation, 27 Ibid., Cap. 58, pp. 293-94.


ZARLINO, THE SENARIO, AND TONALITY 39 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.

The 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 up until this time.28

Nevertheless, four pages later Zar- lino qualifies this view, since it is not really in keeping with the rest of the statement.29 Ma si debbe anco ouertire, che quantunque il basso possa alle uolte tenere ii luogo del Tenore, & Cosi l'una dell' altre parti, quel dell'altra; nondimeno si de fare, che '1 Basso finisca sempre sopra la Chorda rego- lare & finale del Modo, sopra '1 quale C composta la cantilena, & cosi 1' altre parti Si lor luoghi proprii; percioche da tal

chorda haueremo , giudicare il Modo. Et se bene il Tenore uenisse a 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

..

TRANSLATION 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

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 re- spects the needs of this study, we should like to digress briefly and en- large somewhat on the above topic of maintaining the mode or tone of a composition.

In the middle of the i6th century there was a growing desire for the expressive treatment of the text in what Adrian Coclico described as musica reservata, a style of treatment which could scarcely fail to disrupt the character of the modes, which is precisely what happened. It is interesting to read what another contemporary of Zarlino's had to say concerning this problem. We are referring to Nicolo Vicentino (ca. 1511-72), who was one of the first theorists to experiment with the res- toration of the Greek modes and genera which he considered as more expressive, since the Greek philoso- phers had ascribed great powers to their music. At 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, 6 dal'Organo, come saranno alcune

28 E.g., Pietro Aaron, Trattato della natura e cognizione di tutti gli toni di canto figurato; in Oliver Strunk, Source Readings in Music History (New York, 1950), p. 209. 29 L'istitutioni, Cap. 59, p. 298.

30 N. Vicentino, L'antica musica ridotta alla moderna prattica (Roma: A. Barre, 1555), Lib. III, Cap. 15, p. 48.



altre compositione Latine che ricercher- anno mantenere il proposito del tono, & altre uolgari lequali hauranno molte diuer- sit' di trattare molte & diuerse passioni, come saranno sonetti, Madrigali, 6 Can- zoni, che nel principio, intraranno con allegrezza nel dire le sue passioni & poi nel fine saranno piene di mestitia, & di morte, & poi il medesimo uerra per il con- trari6; all'hora sopra tali, il compositore potr' uscire fuore dell'ordine del Modo, & intrerb in un'altro, perche non haura ob- ligo di rispondere al tono, di nissun choro, ma sara solamente obligato dar l'anima, a quelle parole, & con l'armonia di mos- trare le sue passione, quando aspre, & quando dolci & quando allegre, & quando meste, & secondo il loro suggietto; & da qui si cauera la ragione, che ogni mal grado, con cattiua consonanza, sopra le parole si potra usare, secondo il loro effetti, adunque sopra tali parole si potra comporre ogni sorte de gradi, & di armonia, & andar fuore di tono & regersi secondo il suggietto delle parole uolgare, secondo che di sopra s'ha detto; . . . & sara molto in proposito per hora dire della commistione de toni, che ne canti figurati si ritruoua, laquale da adintendere che nis- suno compositore ha offeruato ne osserua il tono, e le sue compositione le dimostre- ranno a ogniuno, che cognoscera la natura & i termini, & le compositione demodi....

TRANSLATION If one composes ecclesiastical works, & those which are to be sung by a Chorus, or for Organ, as will any other Latin compositions which seek to maintain the purpose of the tone, & other common pieces, there may be many diverse ways of treat- ing many & diverse passions, such as in sonnets, Madrigals, or Canzoni, which in the beginning may deal with joyfulness in speaking of the passions, & then at the end will be full of sadness, & of death, & then the same thing in reverse; now for such a work the composer will have to go outside of the ordinary Mode, & enter into another, so that he will not be obliged to answer to the tone, but will only be obli- gated to give the spirit to the words, & with the harmony to show forth the passions, when harsh, when sweet, when joy-

ful, & when sad, & according to the subject; & from this the reason will be seen, that any bad degree [altered tone] can be used with an imperfect consonance over the words, according to their effects, so that above such words can be composed every type of note, & of harmony, & one can go outside of the tone and govern himself according to the subject of the common words, according to what has been said above; ... & there are many at the present time to speak of the mixture of modes, which may be found in canti figurati, in which the composer has paid no intention toward observing the mode, and his compositions demonstrate this to everyone, who recognizes the nature & limitations of the mode....

Such desire for expression could only result in the dissolution of the diatonic modes and, coupled with the basic affections by which Zar- lino had dichotomized the expanded modal system, it is evident that the church modes were on the decline. In the period I540 to I580 only 34% of the music analyzed subscribed to a relatively pure modal standard; the remainder being monal (a mixture of modal and tonal elements81) and tonal.

Our final consideration is that concerning the part played by dissonance, a factor concomitant with that of expression. We need not go into the problem with the same de- tail as we did in regard to consonance, suffice it to say that all intervals not in the Senario, actually or potentially, or their compounds, are classed as dissonant; in addition, of course, the fourth is also handled as a dissonance. Again, we state that it is not the purpose of this study to deal with rules of counterpoint; there are sufficient books available on this subject. Rather, we want to point out aspects of the evolving theories

sl See the author's article, "English Theor- ists and Evolving Tonality," Music & Letters XXXVI (I955), p. 378.



of harmony which indicate the changes which 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 Zar- lino, who says: 32 Le Compositione si debbono comporre primieramente di Consonanze & dopoi per accidente di Dissonanze.

TRANSLATION

Compositions ought to be made up primarily of Consonance & thereafter per- chance by Dissonance.

He then continues: 33 ... La Dissonanza fa parer la Consonanza, la quale immediatemente la seque, pid diletteuole.

TRANSLATION S.. 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. (We have already indicated that he was the first theorist to begin a serious consideration of chordal structure with his Har- monia perfetta, or common chord.) The increasing use of both the V7 and the I in the final cadence shows that Zarlino's opinion was pretty

generally held. It is also indicative of the growing awareness of the vertical concept. In analyzing the music of the period I500 to I700 we pointed earlier to the almost uni- versal use of the third in the final chord during Zarlino's time. In addition to its significance as the Har- monia perfetta is the added importance of the inclusion of the final third for the use of the passing pen- ultimate dominant seventh. Zarlino'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 I , in the final cadence. During the forty years from I580 to I620 the music examined shows a total use of the V7 in almost ten per cent of all closes, and of the I 6 in eleven per cent. In both cases this represents a five fold increase over the preceding forty years. The greatest use of the V7 in the period around i6oo is to be found with the English composers, who used it in some 22.2z% of all final cadences. If I may quote from my article referred to above: "The importance of the V, in delineating the tonic triad can scarcely be overesti- mated and, coupled with England's over-all tonal feeling, is of the greatest significance in the mutual inter- relationship of tonality and the authentic dominant-seventh cadence.""4

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 s32 L'istitutioni, Part III, Cap. 27, p. 212. 33 Ibid. 34 Op. cit., p. 382.


Article Contentsp. 27p. 28p. 29p. 30p. 31p. 32p. 33p. 34p. 35p. 36p. 37p. 38p. 39p. 40p. 41

Issue Table of ContentsJournal of the American Musicological Society, Vol. 12, No. 1 (Spring, 1959), pp. 1-104Volume InformationFront MatterThe Diatonic "Chromaticism" of the "Enchiriadis" Treatises [pp. 1-6]A Possible Cantus Firmus among Ciconia's Isorhythmic Motets [pp. 7-15]The "Chanson rustique": Popular Elements in the 15th- and 16th-Century Chanson [pp. 16-26]Zarlino, the Senario, and Tonality [pp. 27-41]Charles Darwin on Music [pp. 42-48]English Models for the First American Anthems [pp. 49-58]ReviewsReview: untitled [pp. 59-65]Review: untitled [pp. 65-71]Review: untitled [pp. 71-74]Review: untitled [pp. 75-78]Review: untitled [pp. 78-80]Review: untitled [pp. 80-83]Review: untitled [pp. 83-86]Review: untitled [pp. 86-88]Review: untitled [pp. 88-90]Review: untitled [pp. 90-91]Review: untitled [pp. 91-93]

Abstracts [pp. 94-99]Communications [pp. 100-104]Back Matter

zarlino, the senario, and tonality

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