University of California Publications in Music
Editors (Los Angeles): L. A. Petran, R.
Volume4 pp. xiv
Submitted by editorsJuly 1, 1947; issued November 15, 1951 Price. J12.00
Publishers: Mills Music, Inc.,
NewYork, by arrangement with
the University of California Press, Berkeley and Los Angeles
Copyright 1951 by
MillsMusic, Inc., 1619Broadway,
International Copyright Secured. All Rights Reserved.
Glareanusbrought out his
had beenapparent for a century
morethat the traditional ecclesiastical
modaltheory did not square with the
usage. Glareanus' purpose
wasto reduce the existing practice to a practicable theoretical
Hecould hardlyhaverealized to
waspropheticofthe tonal (Major-minor) period.
Hecould nothave anticipated thathis system oftwelve
would remainpractically unrevised
hundredyears. It is a tribute to the validity of Glareanus' deductions
andconclusions that his
wasnot only recognized asa true interpretation ofhis
immediatepastbut also thathis theories
andso soundly based
on andintegrated with the developing
remainedauthoritative for centurieseven
bythe beginningof the last century there
weresigns that even so cogent a theory as
musteventually be reexamined. All duringthenineteenth centurythe tonalhorizons
comingof the twentieth century the process
In an attemptto
answerthis need, I
madeexhaustive researches into existing practice
arrived ata formulation ofeightDiatonic
the Interchangeability of
on goodusage by recognized
composersof the pastcenturyorso.
Acodification of practice has
meaningfor all musicians, be they performers, theorists, composers,
historians, teachers, or students.
newtheory not only explains
and promotesunderstanding of
whathasbeen done,it alsoprovides asolid
for future progress. It is
hopethat the theories I have advanced will
havesignificance for these important matters.
In recording obligations, itis apleasure to
modaltheories. I wish to record also
myideas during the developing stage; to Dr.
andto Dr. Otto Kinkeldey for their interest
andfor reading themanuscript; to
wayshelped keepthe projectalive. I
MusicLibrary of theBostonPublic Library,
MusicDivision ofthe Library of Congress, the Bibliotheque Nationale of
andthe Staatsbibliothek ofBerlin.
Mygreatest obligations, however,are to
Departmentat theUniversity of California,Los Angeles,ProfessorsRobert U. Nelson,
Rubsamen, andLaurence A. Petran,each of
whomread the text
Brower andother staff
membersof theUniversity of CaliforniaPress,I
muchfor theircareful supervision ofall technicalmatters;
Mills Music, Inc., to
owea debt of gratitude for their unfaltering cooperation
andheart-warming enthusiasm.Iwish to thank
Adams,for her greathelpwith all
andfor typing the bibliography
andindex. Finally, I
must acknowledgethat the
have beenfinished without the inspiration
myappreciation of the courtesy of the
whogave permission to quote
duethe following: American Library of Musicology,
NewYork, by permissionof theGeorgeGradyPress,Inc.,Agent,toquotefrom
ATheoryofEvolving Tonality,by Joseph Yasser
&Co., London,forpermission to quotefrom
HarmonySimplified or theTheory oftheTonal Functions
HugoRiemann, trans, theRev. H. Bewerunge.
Breitkopfund Hartel, Leipzig, for permission toquote fromJ. S. Bach,byJ.A. P. Spitta.
E. C. Schirmet Music Company, Boston,copyright owners, forpermission to quote from Principles ofHarmonic Analysis,byWalter Piston.
&Cie, forpermission toquote from La Musique grecque (Edition Payot), by Theodore Reinach.
G. Schirmer, Inc.,
NewYork, for permission to quote from Sketch of a
NewEsthetic of Music, by Ferruccio Busoni,ttanslated by Th. Baker.
HarvardUniversity,Cambridge,for permissiontoquotefromadoctotalthesis,"TheRelation ofHarmonicTheory and Practice from
Rameauto 1900,"byV. L.Jones.
Henry Holt and Co.,
NewYork, for permission to quote from Jewish Music in its Historical Development, by A. Z.Idelsohn.
Houghton Mifflin Co., Boston, forpetmission to quote from
ModernFrench Music, by Edwatd Burlingame Hill.
&Sons, Ltd.,by petmission of G. Schirmer, Inc.,Agent,toquotefromthePrefaceto
MyLadyeNevells Booke (William Byrd), by Hilda Andrews.
JournaloftheFolk-Song Society, for permission toquote from "Note on the Modal System of GaelicTunes," by Annie G. Gilchtist; "Modal Survivals in Folk-Song," by E. F. Jacques.
Kistnerund Siegel, Leipzig, for petmission to quote ft
NeueHarmonielehre. . . ,byAlois Haba.
La Revue musicale, forpermission to quote from "Cours du College de France," by Jules Combarieu;
"L'Har-monie," by AlfredoCasella.
Librarie Fischbacher, Paris, for permission to quote from LaPluralite des modes et latheorie generale de la
mu-sique, by XavierPerreau.
Librarie Renouard,Paris, forpermissionto quotefrom Histoirede lalanguemusicale,byMaurice Emmanuel. Longmans,Green
&Co.,London, by permission ofAbr. Lundquist,copyright owner, to quote from Sensations of
Tone . . . , byH. L. F. von Helmholtz, translated byA. J. Ellis.
NewYork,for permission to quotefrom Grove's Dictionary ofMusicandMusicians,
Modern Music, forpermission to quote from "Problems ofHarmony," by Arnold Schonberg.
CharlesNef, for permission to quotefrom Histoire de la musique (Paris,Payot).
&Co., London, for permission to quote from Diatonic Modal Counterpoint, byRalph Dunstan; by per-mission of H.
W.GrayCo., Agents,to quote from Theory of Harmony, by MatthewShirlaw.
Oliver Ditson Co., Boston, for permission to quot?from
NewHarmonic Devices, by Horace Alden Miller, and from SeventyScottishSongs,by HelenHopekirk.
Oxford University Ptess, London, for permission to quote from Contrapuntal Technique inthe 16th Century, by
OMorris; and from
AHistory of Music in England, by ErnestWalker.
Preston, London, for permission to quote from
AGeneral Collection of the Ancient Irish Music, by Edward
&Co., London, fot permission toquote from EnglishFolk-Song:
J.Sharp. University ofChicago Ptess,Chicago, for permission toquote from
ATheory ofModulation,by Thorvald Otter-strom.
University of Rochester, Rochester, N. Y., for permission to quote from the doctoral thesis, "The Evolution of
Harmonic Consciousness," by Ruth Hannas.
WinthropRogers,London, by permissionofBoosey
&Hawkes,copyright owners,toquotefromModern Academic
THEORY. . . . • 5
IV. Interchangeability of
VI. Extra-major-minor Chords:
VII. Extra-major-minor Chords: Supertonic
VIII. Extra-major-minor Chords:
Forms, . .
MODES151 Part I: EarlySystems
by Bach and Handel
andthe French Romanticists
OtherManifestations of Modality in the
workdivides itself naturally into
twoparts which, although
moreor less independent, are nevertheless sufficiently related to be treated
twodivisions are roughly: (1) theory,
Theinterchangeability of scale
forms abovea single tonic for the
enrichmentof the melodic
meansis not limited to the juxtaposition of the
Minormodes, butalso includes those diatonic scales
moderncounterpartof theecclesiastical modes.
mutualinterchangeabilityoffers a valid
meansfor a simple
anddiatonicexplanation of the relationship
whichcertain chords (hitherto considered chromatic) bear to the tonic.
havenot lacked logical explanationeither
bythe theories of half-modulationor parenthesis
(Riemann), andof the secondary
haveserved too long
andtoo well to be overthrown,
madeto disprove them.
Theauthor aspires only to present a
onestep to the progress of
twoparts: Early Systems
andthe Genesis of
Twoconcerns chiefly the period since the rise of the
(1600-1900),a sketch of the previous scale history is included in Part
One,for the purpose of orientation aswellasto
throwintorelief thethread ofdiatony,
oneofthe constants of occidental music.
Westerncivilization is their seven-tone diatonism. This
charactisticlinksthe tovoi of ancientGreece,the eight
twoused almost exclusivelyfor the past three centuries. Despite divergent mathematical
andthe differencesin the theory of the function
andrelationship of the
frameworkof all our scales is
anoctave divided into five
two"half" tones, the
lattera fifthor a fourth apart
onthe starting pointof thereckoning.
(Greekmodes, Gregorian modes,
seven octave-species. For purposes ofconvenience, these basicscaleswill becalledthe diatonicmodes. Departures
throughthe use of superimposed "chro-matics."
and sometimeseven smallerintervals)
to the diatonic scales
andare thus not so
muchsmallersubdivisions of the octave astheyare subdivisions oi thewhole-tonesof the diatonicmodes. This statement encompasses the "genera" of
Greekscale-theory, the accidentals of
andthe chromaticism of
Evenafter the general adoption of the
haveoccurred atthe beginningof the seventeenth century,
wefind the so-called ecclesiastical scales persisting.
Toexpose their course through this period, their eventual re-vival,
andthe factors involved is the purpose of the second part of
Thetitle chosenfor thiswork,
maysuggest that the limiting qualification "diatonic" is
anarbitrary one. True, there are
somesuperficial evidence to the contrary, the scale basis of the musical art of
civiliza-tion is diatonic (the diatonic modes). Proof lies in the recorded history of the scale structure
andin the great
nowextant. Since these subjects cannot betreatedadequatelyinthe small space ofan introduction, the readerisreferred to the later chapters for a full exposition of the evidence.
This will be
morefully treated in the chapters
(Book One,pp. 6-15;
It will be notedthatthe
withproving the existenceoftwelve
AQA EKAXOP AON
Hyperaeolius Mar. Cap.
Hyperiastius velHyperionicusMar. Cap.
GHypoionicus F* Hyperphrygius
Hyperlydius Politia,sed est errar.
EPhrygius F Lydius
Hyperphrygius Mar. Cap.
Hyperlydius Mart. Cap.
Porphyrio iastius Apuleius
wasrejected because of its diminished fifth, is usually given the designation, Locrian.
anyusefulpurposeitserveddisappeared along withthe cantus firmus,
was mainly anacademic distinction of melodic ambit.
Thereare several other systems of
onechosen has several advantages:
andin English-speakingcountries. (InFrancethree systems
b) It iscomplete since it encompasses a scale
oneachofthesevendiatonic degrees. (This important
qualification is lackingin the
pseudo-Greeklisting asgiven by Koechlin in hisadmirable
rules of counterpoint.2)
donot carry the inextricablepreconceptions
Greek enumerationor the ecclesiastical classification
bynumbers. (Itisclearthat certainderails about ancient
remainnebulous, although everything
numbersaretoo closely identi-fiedwith certainfunctions oftones,i.e.,traditionaltheoretical dominants, mediants, participants, absolute
andconceded modulations, cadences, etc.)
Althoughthe essential diatonism of our music has
undergonecomparatively little evolution since the earliest records, the superimposed internal
con-figurations,thatis, tonal functions
andtheir manifesta-tion in
morethan superficial resemblanceto that ofanother age. Inthis
Greekchromaticismwith that of
musictheoryisa history of the revision ofviewpointin
changingrelationships of these variables to the constant of diatony.
study, ithas been thought wellto divestthe diatonicbasisofmusicofitsoverlying complications inorder
The namesDorian, Phrygian,
havea solid historical justificationsincethey
morethan a thousandyears. It is true that they result
froma misinterpreta-tionoftheir original
Greeksignificance,but the sanction of ten centuriescannot be overlooked.
wouldserveverywell but for
twoobjections. First, they
wouldresultinsuch complexities as
This terminology proves very confusing in analyses
'Charles Koechlin, Precis des Regiesdu Contrepoint (Paris,
Aon D. CD- Aeolian) .
For the foregoing reasons the nomenclature chosen seemsthe best of the several existing systems.It
harmonictheory that a tonality is not
overthrown bya single chord
whichnormally belongs to anotherkey.
-a-c in thefollowing
exampledoes not upset the C-tonality in spite of thefactthat it is
mannerthe chordg-b-d-fdoes notindicate a
Bothof these types of
harmonicprogressionare juxtaposedinthefollowingexcerpt.This onlyserves
modulationisintended, since thekey
imprac-ticalinso short a space.
Copyright 1928 by Novello&Co.,Ltd.Viedby permissionofH.W. GrayCo.,Agents.
Suchapparent violations of key
have beengiven various
whichindicated their transient
themas fleetingmodulations, considering thatareal
wasbrought about only bya subsequent full cadencetoaffirm the
newtonality. Piutti1recognized the ambiguity ofsuch chords
Ausweichungis quite descriptive ofthe digressive character.
Riemann2 explains the
Aus-weichung bya system of substitution (the substitute-klang).
Carl Piutti,RegelundErlduterungen zum Studium der
Mu-siktheorie (1883). SeealsoD. G. Mason, "A Neglected
Contri-bution to Harmonic Theory
—Piutti's Parenthesis Chords,'
NewMusic Review (April, 1908), pp. 299-303.
"Dr. Hugo Riemann, Harmony Simplified or the Theory of theTonal functions of Chords, trans, the Rev. H. Bewerunge (London, AugenerandCo.).
dominantsare thus related to thetriads of the
major mode: V,IV, II, VI,
minorthe list is
V<7) ofIV, etc.,
andnor-mally resolve to thechord to
anextension of the principle, the
(Neapolitansixth) isallowed, 6
N8 as a "half modulation." Piston8
"Vrt .,** if1* r uf-" «J
O. _ -**
CMajorI III6 VI IV of IV
comeabout because of the inadequacy of the
which hadto resort to continuous
modulationto explain the relationship of certain chords.
N6,etc.) as violations of the key.
Theincreasing complexity of the
harmonicmaterials forced a progressivelybroader
came twosignificant changes:
berelated to the tonic.
Underthe parenthesis-chord system of Piston
byrecognizing relationships is once removed.9 For example,
ordinarily closely associated with the
anintermediate chord to
whichboth are in simple relationship.
"Adolph Weidig,HarmonicMaterialandits Uses (Chicago, Clayton
SummyCo., 1923), chap.xvi.
'Walter Piston. Principles of Harmonic Analysis (Boston,
E.C. Schirmet Co- 1933).
lbid., p. 1.
"Weidig, op. cit., pp. 344-345.
'Daniel Jelensperger, Die Harmonie in Anfange des
neun-zehnten Jahrhunderts und die Artsiezuerlernen, trans. A. F.
Haser (Leipzig,BreitkopfundHartel, 1833),p. 34.
Piston, op cit.,p. 45, (IV of IV). Principles of Harmonic Analysis does notmention
Vof V, but the expression
isused in hisclassroom. ''
harmonicpassages could be accounted for withina single tonality. This
only recognized intheory a fact long apparent to theear: anestablished tonalityisreallydifficultto over-throw; itpersists until another is well-established
andobscures the first in the consciousness.
illustration of this persistenceofa tonic:
sMixolydian VII [IV of IV]
GMajor I IV
Althoughthe chords are identical, there is
no doubtabout the tonality of either, if considered
CMajor,the final chord
CMajor: the penultimate chord,
not satisfactory asafinal. Similarly, tobegin in
Majoristo feel any other close unsatisfactory:
wecan-not add another chord
(C Major)atthe end.
Theadvantages ofthe broader conceptionof the limitsof
major-minortonality are in the directness of perspective
andcomprehension. In the following
example fromBeethoven,the entirepassage isheard
in relationto the tonic
maybe regarded as a series of modulations only by a kaleidoscopic analysis
whichmisses the point of the music,
upin the relationship
whichthe chromatic section bears to the D-tonic. In a
mannerof speaking, the middle partis
Atraditional analysis fails to
whilean analysisby the parenthesis-chordsystemrenders fullaccountof the chord-by-chord relationships, yet constantly relates the
whole harmonictexture tothe ruling center of gravity (
Op.18, 3. Finale.
jij ]> v7
VofIV 7 IVofIV
VofIV 7 [iv]
V7 of IV
V7 ofIV tones
EminorII4 TT 6 II 4 III I
V°f (!) ofII
Visusedto designate achord ofdominantfunctionin
modulationhas at least
onevirtue: the diatonic character of the
musicis recognized in the figured bass.
sug-gests a diatonic scale
Its disadvantages are that, although it emphasizes the diatonic element, (1) itfails torecognize the
andto the established tonality;
and(2) it resorts to too frequent modulation.
Theresultisa lack of
harmonicperspective. Specifically, the
methodrecognizes the impor-tance of the rolesplayed by the
and dominantchords in determining
patterns. Ithas long been
atthe interval of afourthor afifth.
remainedto be recognized
wasthat the chords concerned in such progressions
haverelationships not unlike those of the true V-I
Theprinciples of the
and pseudosubdominanttonal functions, although unformulated,
andthe theories of
grewout of afait accompli.
Theprimary concern of these theories is to accountfortheprogressions involved,
evenattheriskof neglecting the relationship
componentchords beartothe tonic.
a fuller understandingof the progressions are not to beminimized, but certain
drawbacksinherentinthe system shouldbe noted:
Theessential diatonyof the
harmonyis slighted. (2)
maybe permitted toextend
somewhatarbitrary.This arbi-trariness is probably
whatPiston hasreference to
Although theuse of suchterms as IIof IV, IIofV,etc.,wouldbestretchingtheboundsoftonality toperhapsan
impossible extreme, there are
manyinstances to befound in which the expression IV of
V[sic] seems reasonable.11
boundsoftonality, the chords designated assecondary
=" arenot admitted to
havea primaryrelationshiptothe center ofgravity.Instead,as
shownearlier in the chapter, the relationship is onlyestablished through
Wherethe chords called
VorIV, justificationfor thenomenclature islost,
Copyright 1913 byHeugel &Cie, Paris.Used by permission.
It isthe object ofthe present
Throughan extended concept of diatony,
chords in the parenthesis-chord system
haveadirect relationshiptothetonic.In other words,certain chro-matically conceived chordsare actually diatonic. (2)
numberof chords not
commonpractice12 are well within the confines of tonality. (3)
Thecomplete diatonic system defines the limits
boundsof tonality to
whichthe juxtaposition of chords
The"extended conception ofdiatony" is a principle
whichincludes the interchange of
andthe resulting increase of
harmonicpossibilities. Substantiation of this theory as
will be the object of Chapters III
andIV. Later, everychordofthe
themusic ofrecognized composers of the past
Theestablishment of the theory of interchange of
whichgrants tonality toeachofthe diatonic modes.
Suchaconception can hardly be controversial but, in an effort to avoid any possible misunderstanding about the subject, the following chapter provides a consideration ofmodality
Piston, op.cit.,p.45 "IVofV"seemstobeatypographical
..."An authoritative list of the chords of common practice is
componentsounds in this basic pattern are called tones
andare represented in notation
bya series of lines
andspaces called a staff.
termtoneis also used to indicate the larger of the
kinds ofconjunct interval in the pattern, the smaller being a semitone.
minorsecond forthe latter are better terms: their
meaningis not ambiguous.
Thebasic pattern is giventhe qualifying
(Greekdiet ,acrossorthrough,plus xovog
synonymouswith the phrase by conjunct staff-degrees,
it is principallyused to denote conformity of ascale to the
Western European Schema.
Theseventones of the
byby the first seven letters of the alphabet although the correspondence
andthe tones is
Di T ,F. A
Western European TonalSchema
For the purposes ofserial
enumeration anytone of the
maybe chosen as a starting point. This
maygive theresult: cycle
wasarbitrarilychosen each oftheother tones
maysuccessively serve as initials. 1
Theseoctave species, although not yet assigned musical functions,
maybe called diatonic modes, since each
conformsto a cycle of the
mostprimitive tonal function isthemelodicfinalortonic.
mayserve in this capacity. It is impossible, however, to conceive a tonality consisting of but a
singletone: at least
Musichaving a tonic
whichthe other tonal
minimumis only rudimentary: street cries
somePentatonic melodies are illustrative.
After the tonic, the
mostimportant function is thatof the dominant.
Mostoften it is placedat the interval of a fifth
abovethe tonic but, as in the plagals of the ecclesiastical modes, it
the fourth, or
eventhethird. Itsfunctionsare: (1) to be conspicuous asa notein the
melody and/oras a chord in the
harmony, andso be definitive ofthe tonic
bythe pro-gression (melodic or harmonic),
dominantis a fifth
maybe a certain physical basis for its domination,
but this cannot be claimed
whenit is placed at
someother interval. In the latter case the ruling
whollyconditioned by conventionalized usage,
and evenwith the
mustbe partly operative.
and dominantof a
have beenassigned their respective roles
andconventionalized to the extent thattheir
anarchy hasbeen banished
from sound andorderhas taken the place of chaos.
beenlimited in order that those remaining can be
andsince they are
less extensive, there is a corresponding gain in
cometo understand that in a tonal scheme, the
two mostimportanttones are the tonic
anddominant, that they aremutuallydefinitive,
from oneto the other is cadential (dominant-to-tonic being the stronger),
andthat the tonicis thefinal.
Theseare the least conditionsof tonality, although
manyother established conventions
Accordingto this view, it isclear thatthe ecclesiastical
havetonality, but it
under-stood that it is a different tonality
fromthat of the
major-minorsystemof the past three
owingto the lackof uniformity inthe matter of
andother tonal conventions, the strength
andqualityof tonality varied
amongthe several modes.
someothers because ofits
wasdeclared defective because of its
Since the character of a particular tonality is theproduct of a certain setofformalized tonal usages,
changein these will produce corresponding mutationsinthat character.
fromthe original b to c.
Churchtheory (the Ionian)
modernMajor; but before this point is discussed
mustbe taken of the matter of intonation of the intervals of the scales.
wasin use untillong after the riseofpolyphony. In thissystemthe
wereof the proportion 8:9, semitones
wereclassed as dissonant.
the influence of
beganto be questioned and,afterthe tenth century,the"natural" third (4:5) gradually
cameinto use. Zarlino
(1517-1590)completedthe process with hissenario theory. Equal
temperamentis astill laterdevelopment.
Thesechanges undoubtedly altered the character of the scales, but the adoption of the
newtuning cannot be said automatically to
havegiven rise to the Major. Indeed, the Ionian
modestill exists today despite the
preeminenceof the Major, although its effect isdescribed,
somewhatdisparagingly, as pseudo-modal.
modeof Glareanus, with its
onthe fifth of the scale,
samediatonic form: T-T-S-T-T-.T-S.
twois marked. Inspite of the fact that
wouldmistake the effect of
oneforthe other, the matter has
diffi-cult to put into words.
onthedissimilarityof internal tonal con-ventions. Further light will be
onthis question laterin the chapter by a
conven-tions of tonalitycharacteristicofmedieval
polyphonyascontrasted with thoseof the
Aphysical basis of tonality rests
grounddespite courageous attempts to estab-lish it. Shirlaw
Riemann's andbrings very
evi-dence tobear against their propositions.
wasthe first to formulate a complete theory of the
duethe credit for the practical idea that the
V7 contains within
itself the limits ofthe
andso unmistakably defines the key. This is very
andis probably the
mostimportant single principle of
Fetisconsidered that the necessityof resolving the dissonance of the 3rd
and7th of the
deter-minesthe tonality of
andtaught that the
wasthe result of Monteverdi's3 supposed introduction of the use of the
. . .tonality resides in themelodic and harmonicaffinites of the sounds of the scale,which determine the successions
and aggregations of these sounds.
'Matthew Shirlaw, Theory of Harmony (London, Novello S
J. F. Fetis, "Monteverdi," Esquisse de I'histoire de
I'har-andCo., Ltd.,1917?). monie (Paris, 1830).
J.-Ph.Rameau,Traitede I'harmonie (1722); idem,
they assumed the formof ourMajorand Minormodes. It would be correct to say that harmony banished these old
modesout of existence.5
wecorrectly interpret the phrase "old
thesii ofthe present
workassumes the present-day existence of
modesidentical in their diatonism with those called "the ecclesiastical modes."
wastoo specific in assigning tonality only to the
Schonbergis too general
It [tonality] has alwaysbeenthe referring ofall resultsto a center, to afundamentaltone,to an emanationpoint oftonality,whichrendered importantservice tothe composerinmatters of form. All the tonalsuccessions,chords,and
chord-successionsin apiece achievea unifiedmeaningthroughtheir definiterelationto atonalcenterandalsothrough
This statement does not
modesother thanthemajor-minor, but it
Helmholtzspecifically includes the
earliest Christian period
andemphasizes the importance of the final tothe tonality.
Asthefundamental principle forthedevelopment ofthe Europeantonalsystemthe wholemass of tonesand the connection of harmonies must stand in close and always distinctly perceptible relationship to some arbitrarily selected tonic, and the-mass of tone which forms the wholecompositionmustbe developedfromthis tonic,andmust
Theancientworld developedthis principle in homophonic music: the modern world in harmonic
Piston's statement about tonality
moreclearlyincludes the diatonic
Thepresence ofa centerofgravity,ortonic,being thesolerequisiteforthepresence ofatonality,itwillbeseen
numberof variations inthe
Recognizinganeglectedpointintonalitydefinitions, a distinction
elements, Yasser still does not
showtheimplications of theidea.
Tonality is a principle which organically and tonocentrically unitesthemelodic andharmonicfunctionsofa cer-tain numberof systematically arranged sounds as mostsirrplyrepresented inamusical scale.
Toexpand this definition and describe the twofundamental aspectsinreference toourpresent (diatonic) system which isgoverned by theaboveprinciple,
mayaddthatthe tonal center represents a single note (tonic) from the
melodicpoint of view, and a chordof three notes arrangedby thirds (tonictriad) fromtheharmonicpoint of view.
Again, that in the melodic aspect this system manifests a characteristic distribution of its seven regular (diatonic) degreeswithin an Octave, forming various chains of whole steps and half steps (Modes) . . . Finally, from the
har-monicviewpointthis systemdivides all its possible tonalcombinations into two distinctly opposed groups of
conso-nances and dissonances, the latter inevitably "requiring" resolution into the former.8
All the usual definitions of tonality
havea certain logic, but there
seemsto be a general lack of recognition of thedifferentiations
moreparticularized,exclusive statements dealingwith existingsubdivisionsoftonality.Intheabsence of definitions
whichtake cognizance of these distinctions,the followingdefinitions areproposed.
GeneralTonality is that principle
mentalgrasp of the musical texture is maintained
is thus the tonal center
andordinarily the final.
Tonality in Plain
Chantis a system
unaccompaniedmelodic line is
througha system of linear tonal conventions. Conspicuous
Idem,TraitecompletdelatheorieetdelapratiquedeI'har- 'H. L. F. von Helmholtz, Sensations of Tone, trans. A. J.
monie (Paris, 1844),p. 249. Ellis (London, 1885), P. Ill, chap. 13.
Shirlaw,op. cit.,p. 337. "Piston, Principles of HarmonicAnalysis,p. 60.
"Arnold Schonberg, "ProblemsofHarmony," ModernMusic "Joseph Yasser,
ATheory ofEvolving Tonality (American (May-June, 1934),p. 177. Library of Musicology,
NewYork, 1932),p. 331.
dominantrecitingnote,the absolute initials, the mediant,
andthestylized final cadence: a progression
to the final
fromthe note immediately above. It thusonly
makesuse of themelodic phaseofthegeneral principleoftonality.
texture is maintainedpartly
mainlyto the cantus firmus,
componenttriads tothe triadof the final
whichhas taken the place of the simple final.
mustbe conspicuous; the progression
dominanttriad to tonic triad
becomesthe principal cadence; there are other conventional cadences
onthe important degrees of the scale;
andthe final cadence
usually be perfect, thatis, the tonic note in the top voice as well as in the lowest. It is important to
re-memberthat in spite of these
wasstillhorizontal,notvertical: each ofthe voices
wasregarded as a melody.
Thedual nature ofthis tonality should be noted becauseit
wasundoubtedlya factor in theeventual capitulation tothe
Major-MinorTonality is a system by
mentalgrasp of the musical texture is maintained
through a very circumscribed
meansof relatingall melodic
harmonicelements tothe tonic or itstriad.
Amongthe differentiae are: a) Cadential conventions:
(1) V-l and IV-V-I are the normal formulae.
Themajor thirdof the
Vnormally progressesuptothe tonicandactssomewhatlikearedarrow point-ing to it.
Theseventh of the
Vhas a normal resolution downwards to the thirdof the tonic.
ThearrestingIfis normally usedbefore the
Vin the cadence.
b) Restricted arethe progressions II-I, V-IV,
employmentof the secondary
triadsII, III, VI,
Thechromatic conventions require that each chromatic note or chromatic chord lean
Quite arbitrarily the descriptive
beenapplied to the
andobserving its conventions.
Thethree centuries of
fromthe established conventions of this tonality are called extra-tonal or modal.
termused to designate emphasisofthesecondary chordsII, III,VI, and
VII° in the
Major mode, whichresults in a
weakeningof its tonalquality.
Tothe three subdivisions of
GeneralTonality (tonality in plain chant, tonality in Renaissance Poly-phony,
oneother kind: the tonality of the diatonic
Book Two,all the diatonic
modesare to be
foundin the music of the present epoch. Their scale types are the
modesbut there the similarity ceases: the plagalforms
and mostof the oldconventions of
beensuperseded. Certain conventionsofthe
have been imposed
uponthese scales: the
dominantis always a fifth
abovethe tonic, the texture is essentially
harmonic(vertical) instead of con-trapuntal (horizontal),
andthe dissonances of the seventh
andninth areusedfreely (subject to the
principles of resolution
whichapply to such dissonances inClassical
Modes,10since their tonality is the result of superimposing Classic
knownasLydian,Mixolydian, Dorian, Aeolian, Phrygian,
onecannot grant tonality to the
abovewithout further proof, the matter
maybe considered asa hypothesis,
and agreementreserved until therehas been submittedthe additional evidence
embodiedin Chapters III
onthe principle of interchangeability ofmodes.
The genesis of the Harmonic Modes is the subject of the second part ofBook Two.
Sincetheirtime tuning has
anditsinversion, the fourth,
dominantsof five of the six recog-nized authentic
onthe fifth of the scale,
Afavorite device for "explaining" the derivation
majorscale istorefer to a
series ofsevenperfect fifths
beenembarrassingforthe theory is:
Whydoes thescale begin
c, the second
componentof the series, instead ofthe first? In order to avoid this stumbling block it is
sometimessaid thatthe seriesbegins
Thefinal fifthis diminished
andthis is said to "close theseriesin order topreventits continuing indefi-nitely." Inspite of the neatness of thisexplanation it is clearly
anevasion because theseries is not
Notheorist has demonstrated
meansof theseries offifthsthatthe
onescaleofa complete diatonicscale system.
onthe second fiftb of the series
componenttones of a series ofsevenperfect fifths to the
and dothis seven times
byadopting eachof the tones in turn as a beginning.
formedthe seven diatonic scales
knownas Lydian, Major, Mixolydian, Dorian, Aeolian, Phrygian,
Specific citationsare notgiven in this briefmentionof the
subject.It issufficientto say thattheseries of perfectfifthsasa possibletheoretical basisfortherelationshipof the tones of the major scale has tempted every theorist from Rameau to
F = Lydian
C; Major *!:«»
If the initials of the
abovescales are written in scale
on"F", a diatonic series of
initials is formed. This
makesa convenient table of the tonics of the seven modes.
Eachof these tonics
is, of course, the firstnotes of its respective
mode, andall the seven
modesin thispresentation are
samediatonic series. Since the initials or tonics themselves are indiatonic order, the table pro-duced is called the OrdinalIndex.
*«- XI. Dorian
modesofthe Ordinal Indexis
comparableto that of
Major andits relative
A-Aeolianis the relative Aeolian of C-Major,
G-Mixolydianis the relative
D-Dorian, andso on.
Suchrelationships, however, involve a
changeoftonic: inorder to shift
in the Ordinal Index there
mustbe a corresponding modulation. In other words, althoughthe
tones of the musical texture
remainthe same, the tonal center of gravityis
onetoanotherof these notes.
Theconverse of this operation is to retain the tonic while substitutinganother of the scales
for the original. This is interchange of
andthe relationships in this category are those of the Lateral Index,
whichis derived as follows:
wecontinue a series of fifths untilthe cycle is complete, that is, until the first tone recurs, there will be thirteen integrants
CompleteCycle in Fifths3
See chap, iv for further discussion of the interchange of mode.
groupofseven4 consecutive tones
fromthis cycle will
commonto all: the middle tone (d in this case). If taken as the
commontonic of the seven possible
modes(by a process
whichisthe converseof that described in the derivation of theOrdinalIndex),this
whichbinds theseveral derivative scales into lateral relationships.
D-Major D= Mixolydian
D=Aeolian D= Phrygian
modesto their scale
commontonic d, the
maybe calledthe Lateral Index. Lateral
D=Locrian t±-Natural Signature
This index constitutes the theoretical basis of the principle of Interchangeability of
abovea single tonic. Further consideration of the principle
andproof of its
foundin the next chapter.
which'died withits jealous guardians. In his Musical Offering
and Artof the
Bachused inversions butthese
modaltype, being confined to the
whichthe original edition appeared in 1725.
madeintwoways:bysimplecontrarymotion,and by invertedcontrarymotion.
contrary motion is
whenthe self-same notes ate merely turned upside-down so that those notes which first
nowdescend.Thisis donewithoutthe slightestattention to the semitones. For example, seethatwhich has
been'given so often:
Model Simple contrary motion
waythatsemitonesremain semitones and
Theexact manner inwhich this is doneisshowninthe followingillustration. 6
Compare the ascendingnotesatthe left with thosedesending attheright:
Dis inverted, itremains D;
invertedbecomes C; F inverted becomesB;
Gbecomes A; etc. Thisprocess applied tothe originalmodel willbe as follows:5
Inverted contrary motion
onephase or anotherof inversion.
Thesubjectistreated inRousseau's Dictionnaire (before
1740)in the article "Systeme" written
creditfor beingthefirstto notethatthe Phrygian
modeisthe inverse oftheMajor,6 although
mode"semi-mineur" because of the
mentionedagain until a century later
Johann JosephFux, Salitaal Parnasso, trans, into Italianby Alessandro Manfredi (Capri, 1761),p. 181.
AdamSerre,Letterappendedto EsiaissurlesPrincipes deI'Harmonie (Paris,PraultFils, 1753), pp. 143-144.
H.L. F.von Helmholtz, Lehre von den Tonempfindigungen
alsphysiologischeGrundlagefur dieTheoriederMusik (1863). Artur vonOettingen, Harmoniesystem in dualerEntwickelung (1866). Dr. Hugo Riemann, Vereinfachte Harmonielehre (1893). Hermann Schroder, Die symmetrische Umkehrung in derMusik,Beiheht 8 der Publikationen deI
Bernhard Ziehns carried the idea
ofitself, the Aeolian inverts to Mixolydian,
andthePhrygianistheantithesisof theIonian or Major. For
somereason he omits
mentioningthat the Lydian
andLocrian are inverted
formsof each other. Otter-strom, however,gives thefollowing list,
Ionian becomes Phrygian.
Dorian remains Dorian.
Phrygian becomes Ionian.
Lydian becomes Locrian.
Mixolydian becomes Aeolian Aeolian becomes Mixolydian. Locrian becomes Lydian.
"Thesecuriosities belong to the
realmof amuse-ment. . . ."
Whetheror not this is true
andtake into consideration every possibility offered for the
develop-mentof thematic material, the statement is misleading.
Spiegel-bilder (retrograde inversions). Lydian
mUEijoav Dorian "-*
no onehas demonstrated that the
wholediatonic system is symmetrically invertible.
Dorianwith its identicaltetrachords
forms the center, since itinverts without
most majorof the three
modes(those with a
majorthird) since every scale degreeis atits
the mirrored reciprocal of the
most minor mode,the Locrian.
twofollowing diagrams illustrate the symmetrical invertibilityofthecompletediatonicsystem.
Thefirstis concerned with the OrdinalIndex, the second with the Lateral Index.
Bernhard Ziehn, Canonical Studies;
NewTechnic in "Thorvald Otterstrom,
ATheory of Modulation (Chicago, Composition (Milwaukee,
Wm.A. Kaun Music Co., 1912), University ofChicagoPress, 1935),p. 131.
maybe defined as: the substitution of
yet maintaining a single tonic. In effect, this
oneof the diatonicscales
maytake the place ofanyother above
anygiventonic. For example,forthe
maybe substituted the tonic Minor, the tonic Aeolian, the tonicPhrygian,
Minor (Harmonic or melodic)
o«» Phrygian t i t>'
Sofar as the free alteration of
major and minorare concerned the practiceis recognized in theory
andhas long been in use.
Strange, thatone shouldfeel majorandminorasopposites. They both present the same face,
nowmore serious; and a mere touch of thebrushsuffices to turn the one into the other.
Thepassage from either to the other is easy and imperceptible;
whenit occurs frequently and swiftly,the two begin to shimmer and coalese indistinguishably.1
Ferruccio Busoni, Sketchof a
NewEstheticof Music, trans.
Dr. Th. Baker (New York, G.Schirmer, 1911),p. 21.