Thesaurus of scales and melodic patterns

257 Pages·1947·27.92 MB·English

by  Nicolas Slonimsky

Thesaurus of Seales and Melodic Patterns}

Thesaurus of

Scales and

Melodic

Patterns

Nicolas Slonimsky
Thesaurus of
Scales and
Melodic

Patterns

Nicolas Slonimsky

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CONTENTS

TXPLANATION O8 TERMS,

‘Turon Procession
ual Division at One Octave ieee Two Parss

Dirone Procession
Equal Division of One Octave into Three Ports

Sesqetroxe Peossession
Equu Division of One Occave into Pour Part

WHOLE-ToNE PROGHESSION
Equal Divisioa of One Oxtave inro Six Patts

SEMITOE PROGRESSION
Equal Division of One Octave in Twelve Farts

Quannrtonn Procaisston
Equal Division of Twa Oceaves into Three Parts

SrsquiQuADRTONE PROGRESSION
Equal Division of Thtce Ocraves into Four Parts

QuiIngeETONE ProceessioN
Equel Division of Five Octaves into Six Parcs

Diaressanon Paogusston
Equal Division of Five Oxaves ita Twelve Paces

SermToNe PRogeession
Equa! Division of Seven Qctaves ito Six: Pars

Diarente Prosexssions
Equal Division of Seven Qctaves iano Twelve Patts

Sasquiquasgr eran BKoeAEsHION
qual Divison of Eleven Octaves inco Twelve Parts

Huerarone Scares

Herrarosic ARrEacr0s

3

or

8

106

109

14

135
Peniavonic Scates 160

BerowaL Anesciws 19
‘TwatveTone Parreens (Dodecaphonic) "3
Crossing INTenvats, 196
Drvistow oF weve Tones nvro Foun Muruaniy Bxcuvsive ‘Triads on
QuaoncTONAL ARPEGGIOS ap
InvERTIRLE DopecaPriosic PROGRFSSIONS hy
frervavancie Seares

Ineceasing aod Diminishing Invecvals 186
‘Minxox, uy va. Peocresstons 18,
CoMELEMENLARY ScauEs 188
Penscurarions 188
PaNDIATONIC PROGRESSIONS 192
Dousce Nores 196
LURAL SCALES AND ARPEGGIOS an
Porvronat ScaLes 0
Pouvaseyrsetc ScaLes 24
Pourrona, PoyRinvrioaic SCALES 226
Pauanikonte CANONS 234
AurocnoRnaL HaRWoNtZ<tt0N ak
Hagmonmaarion ix MajoR Truabs an SevaNtti-CHouns 240

Synopsis a” Citoans aye
THESAURUS OF SCALES AND MELODIC PATTERNS

INTRODUCTION

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with we found it EHeonORUS

tom tne co ine misial eits have suggee che posliy of Forming en
trl aew sees based on the divin of the ve inact equa pute Ae ac
41911 dhe lushan musician Doel Alles proposed sich new sale la Hake
In is Neue Harmonilebve (3927), clases a fet puaber of sla tase a el
laterals ancl sugges harmony of these few seen, Tosh Sleticge inthe
posthunowsly published Sebitinger Som of Musee Campuivy cacige nee
teal pogeeinns inthe hapten of Peek Sete

“The sales ant melodic presne inthe textos are genutsed ia a mauer
conveniencr somposers in eaeh of ew mater. The tile Thusats oF cence
tap non rats is doen schaady The tm te ahaa ede
Progresin, either ditonie of cinoma thar rows wimp fa one dio
sseending or descending wl he terminal port sacked A mala pecs on
eke hand, maybe fered by any group of ats tat has acpi, Thee
fae sales of tutes oi an hae ate sles and pacenns uf 1a dete nes Bee
counting repenced nts appetig in dferene nates, 4 sce may have wv mea og
48 FnaioalyAiferae recs, ain te Dison Major Poleenscurd (Ne we)
‘sim melodic pass there i vitally no litem the sume of ave nee

The Trtsaunta i ananged inthe form af pro sales sod melee ead, No
fngeing i given, forthe pian wil teahly tnd the spe of Sigiaren bor aed
the and Ochs fstuceealins, co, wl find mv of the salen melodic peaees
in de Touants adapble (ott inazunents, he nesrionehenighone fear
monte, and acddenas are wed accudng co anvenence Doble dase sa doable
fey te evidently, Pecawsonaty sata sign ate led ete 2 ets oles
4a sonst lad intra] oceans ALC accldenalsec ely the now oeednty
fellowing,

‘The tls and pans in the “Thetatnus ate arceage seconling co the principal
icra ofeach parila section In cet wo avoid ueneintion with debete eel,
use basi neva are here refed ro by Latin and Greek ames diva ow okt
tage In addin, new erm hat eo be cine fr inal toxin the ten ol hoe
teaes Io these now tes the probe vega! sands forthe addon oneal oo
cove Ths, Signe i 1% tone, a arinoe tid, Sesuiguadstone tf; tones, oF
+ major ith; and Ssiguloqueons 51s toes, ett apr seventy
“The table of intecvats from the semivone co the major seventh zppeats as follows:

Seonitone. ince Second Tebone Auginenced Fourth

Whole Tone .... Maye Second Diepewe Pestace Flt

Sexyuatone Miner Third (Quadvitoye. ... Minoe Sie

Dior, Majer Thiel Seoguiguadritone...Majoe Sth

Dilatetaror. .... Pefece Powe Quingesrone..... . Migor Seventh
‘Seequiguinguctone Major Seventh

‘The interval of a major alich is called Septitone, to indicate that it contains 7 whole

‘These basic intervals ate tegardel a8 fractions of one or mote octaves. Thus, che
Tritone Progression cepresents the division af the octave into 2 equal pars, and ir
produves sequencial scales and patterns, The Ditane Progression is the division of the
etave into 3 equal parts, and is intervallially identical seh che augmenced criad,
‘The Sesquicone Progression is the division of che octave into 2 equal parts and is ideo:
tical with the familiar diminished-sevonth chard, The Whole-Tune scale represents
tte equal division of the octave into 6 parts. The Semitune Progression is equivalent
vw the chromatic scale. By the process of permutation the cheamatic scale is productive
‘of characteristic paetns of the 12-one technique

‘Bp deveding 2 ocraves into 3 equat parts we obtain the Quadricone Progeession,
which is closely relaced on che Dizone Progression, being in fact # epread-our angenented
triad. By dividing 3 actaves inro 4 equal parts wo obtain the interval nf the majar sixth
“This is the Seequiquadsitane Progression, which is an unfolded Sesquitone Progees
sion, productive of pamemns celated ro dinynished seventh, harmonics.

Ti the eye of scules the interval of a pesfect fifth is one-cwelfch pare of 7 actaves,
aad ie is 20 reprcscaced in the Diapence Progression. A perfeer fourth is onerwelfh
part of 5 octaves, and is classified as such ia the section Diacessaron Progression,

Poruing « similar process, we find cha the Sesquiquinguecone Progression, ar the
progression of majoc scvenths, is che result of che equal division of 14 oetaves ito 42
ARS, Finally, rhe Sepeitone Progression is the equal division of 7 octaves into 6 pares,
with dhe Basie interval uf a ajoe auth

Scales and melodic patterns ase formed by dhe processes of Interpolation, Infra-
polacion, and Llecapelacion, The ward Jnterpolarion is in cummon usage; here it
signifies the insertion of une or several notes berween te principal cones, lnfrapolation.
and Uetapolution ate coined words, Jafrapolation indicares the addition of a noce
below a principal rene; Ulteapotation is the addition of a nete above the next peincipal
tone, Infrapolation and Littapolution result in che shife of dicection, with the melodic
line progressing in 2igeags. lafcapolation, leccepolarion and Uhrapalacion may be
feeely combined, resulting in hyphenated forms: Tnfrs-Toterpolation, InfraHleapola
‘90, end Tafa Tater-Ultrapalation

gece neratinn _ tng Jafrapalation
=e =o S= a
Tafra-Taterpolation —_afeaTitrapolation _Infee-Inter-Titrepolation

=e =
Progeessions and patterns bused on uncqual division of the octave are exemplified
bby Heptatonic scales and Perearonic scales, Amony Heptatoaic scales, or tone scales,
aie our famitias major and minor scales as well as the chucch modes, tu the section
Hiepratouie Arpeggios che scates ave speead out in thieds. In the section Biconal Apege
ios the C major aepeggio is combined wieh aepeggios in all other 23 cajor ‘and
sinor keys

Busoui, who bed eamestly explored new musical resources, found x3. diffecene
sales of 7 notes. Meotioning 2s an example the sale: C, Db, Eb, Ta, Gb, Ab, Bb. ©
(itis No. 1035 io che Tassanars), he writes in his Fntwwe cincr wenem Acstbetib
ster Tonumats "These is a significant Uilfereuce between the sound af this aew scale
when (is taken as the tonic and when ie is taker ax che Jeadiing tone of the seale of
Db minor. By hesmonizing the conic with the cusomary € major tiad as a fundamental
chord, a novel hacmonic sensation is obtaizwed.”

In his Chronicle of My Musical Life Rimsly-Korsakow exativns che vse he made
cof an 8-tone seale, foruted by alteroading majar and minor sevunds. This is Seale No.
303 in the THresAimus. Sporadic uscs of che Whole-Tone scale ure found in Glinks
and even in Morarc (as a jest co mock the inept Dorfreaanten), bur it did) not
Decome a deliberare device before Debussy. In Detsiy's piano piece Voiles the prin
sipal melodic sruucure is in the Whole'Tone seale, but the iaiddle part is written
exclusively on the black keys, exemplifying the Pentstonic scale.

‘The Whule-Tone scale has 6 nores co he octave; the Fencatonie scale has fire. The
‘Whole“tione scale is possible in only one form on a given nore, but there can be many
Pentaronie scales, There aie 4y Peacaronic scales in the Teesatrer,

‘The r2-Tone Techaique of enmpocition promnlgated by Schoenberg is based on
ermuracions of the Scmitoue sesle, Vasious 2-tonc patecas ate found in che THE-
SAUkuS jn exampios No. 1214 t No, 13:8. For example, it is possible co arvange the
a chroobatic tones in 2 euajor and 2 minox irieds withour repeating 4 note. It is alsa
possible co form 4 mumally exclusive acgmented criads using all x2 chramacic tones
‘The theme of Liszt's Faust Symphony is composed of 4 augmented triads. Tc is further
possible 10 split the chromatic seale inco a dimwinithed iad, @ minor triad, a major
(iad, and an augmenced cciad. ‘These motvally exclusive criads can be srcanged in the
Fonn of Quadtitomil Aspeygies

A revene development of the 12-Tone Teebnique isthe at-interval techaique, which
prescribes dhe formarion of progressions containing rr different intervals, The idea was
fist inroduced by the Austrian musician Trice Klein in tyar i a curious composition
entitled Die Mucbine, with the subtitle Ex-Tondl SelfSatie. The aame uf the cony
Doser was coneraled behind « characteristic nam de plume Hesutentincenumeives which
‘rans Self-Toreurer. To zhis piece Klein ieccadused a Mocher Chotd which contains
not ony all rr different incervals, but r2 difteront notes as well.

A further elaboration on the Mother Chord i an inverible tr-ioveeval, 12-one
chord ineroduced by che authut and appropcately cbristened Grandmother Chord. Tr
has all the ievervallic properties of the Mother Chard plus an especial order of inter
vals 0 arranged thar diey atc altemnately odd-numbered and cver-oumbered when
counted in semitones, with che row of odd-numbered inteevale farming # decceasiog,
arithmetical peogeession and the cow of eveiaumbered intervals forming. an. incieas.
ing asivhmetical progression. The order of neces in the Grandmother Chord is idcasical
with the c2-one Spiral Pattern No. 12524
|AIL chorcis composed of 14 different intervals add up co the inserval of 46 semi
ones, which is che soca of the arithmetical progression fxom + to 21. The interval of
66 somizones oquals 31% ectaves, and so forins a ‘Vritone between the lowest and rhe
pighese cones in the Pyramid Chord, Machor Chord, Grandmoches Chord, ud wer
siclorerval sipneures

‘Scales and patieras liswd in the unin body of the Tarsatcaus readily lend dhecn
solves co new melodic possibilities. For instance, a dewxuling scale may be prayed in
the form of the melodic inversion of rhe ascecding scale, as suggested in thie section
Mirror Tnterval Peogccssions, Te is possible es foun complemencary scales in the range
of 2-extives, hy nsiog in che second detave the notes noe used iu the fest. Ocher posti
bilities for the focraation of cew patcerns are demonstrated in the sectcnt om: Peuur

‘A Diatonic counrespart of the 12-Tone Technique is ete system af Pandiaconic,
coopasition, The cerm Pacdistonic, fst incroduced hy this wricec in 137, denotes che
free use of all 7 ones of the diatonic scale, both exwludscally and fuarponically. in
‘one-pact Pandiaconic Progressions, the elody is exede up of 7 different noees of the
Aliaronic scale. Such a prugeession onay chen be melodically inverted, read hackorard, o¢
bork, sesuleing in 2 ddfferone forms. Pandiaemie Councerpaine in serio syle uses
progeessions of 7 differene mures in each voice, with 0 vertical duplication,

?Pandiaronic Harmony is the cwcatieth cenrury counterpart of ‘classical emus
Modern compusets of such varied backgrounds and munsical pernasions 1s Ravel,
Stinvinsky, Heedomich, Méllaud, Coplaud and Roy Harcis make use of this echo'aue,
arriving at i by differenc creative processes, Jaxz coroposes, 100, have found, ay sheer
expeciuentition, effective application tor the enriched chords of Pandiamnie forex:
tions. Ics a common practice to ené an archescal arrangenuent of a popular song by
the enriched major etitd with an added shwth, sevench, of vith.

The concluding soctions of che Tessauntts demonst-aee the variass methods by
which ronal macerials ny be used to beat avanrage. The section Double Notes shows
the combinacions derived from corwspanding scales aul peucurs, Plural Scales and
[Arpeggios give examples af common major and minor peogtessinns arranged cousecu
lively in chromatic ctensposicion. Polytonal Scales are simulewievas progressions in
different keys. Polychythralc Scales ere progressions in diferent shythms, Palyranal
Polychyebanic Seales combine ditferec chyehoss iu dalferene conalitis

‘A special word is to be said about Palindromic Canoos. Patindromnes arc words or
sentences that eead the same forward or buckward, ax the seareace Atte Wac I Fre
Saw 82be {applied 0 Napalein). Similarly, Paliodzomic Canons read che sacze back:
‘ward oc forward, The ewe Palindromic Canens based on Pateera No. 72 are pacticlarly
interesting, They cesule in a progzession af enharmonic teiads ve their inversions, aloe
tating in major and minor keys

Fragments of the scales acd paticins ia che THesaiitrs may be used as motives
and taemes, The rhythmical claboration is lofe co che ‘nuginacion of de composes. Tiy
using @ portion of a pattem in forward und cetrugeade trotian, ia varied chythms
swichin a given meter, iis passible to form ac untimiced surber of coelodie figuses,

Rhythmic Development
eae

Spe

Pattarn 1104
‘Tr formulas ae use in the harmonization of the scales and pattems: one hy coun
aman eriads, and one by sevench-ciuris. tn the hacinntzacion by couton tials, only
oor posiions of major eciaus in close hartmany are applied. Figher the race, ehe third
cor the ffch may appear in the nielody. These positions are referred eo ax Octave, Ter
doa, and Quintun, or in figures, 8, 5, and 5, Wacn the melody ascends, dintonically or
caramatically, the postions dtaoge from the Octave ro the Tertan to the Quintan
to the Ocave, Wheo the melody descends, the onder of the pmstions in rovecsed.
Fortheruce, the order of positions may be reversed at che end of @ cadence ever
ascending motion. When the melody ‘s staiouany, the order of pasitions is free. The re
sulting harmony traverses severat ronalities in an alternarion of successive major chocds,

Harmonization in Major Teiads
(Piguros Indioats latervals Bolwrera fhe Blalody tad the Base)

re ot 7 ESSE

(6

— Pan de

¥ 7 a 7

‘The barmonizatoa in major tad is found in dee music of Debussy, Mousorgsks,
aud ether composes of the Trench and Russian schools A clasieal example f the
scene in dhe monk’ cell in Moussrgsky’s opecn Bor Gidunoo, To the second ace af
Peccii's opece Tosca the Whole-Tane scale in the bas 8 huemonized by artsy oF
sinjor ttads with the prions fellowing the Octave-Terdan-Quioean (83-5) total

Mounaveginy: Borie Gadus Sein: Foven (Whale-Toas Scalia the Basel
i

a

‘The seonad sype of harwonization is effecced by misans of Master Chotds, “These
Master Chel re daminanrseventk chords wich the filth emitted, Ia. catubination
with melodic elements of a given scale or patzern, dese chords Form hacenoaie stu
cuces of che @ype of screnth-chords, ninch-chotds, ar wholerone choeds, The Mascer
Choeds are indicated for ascending scales and parterns in the stations Tritooe Pro-
gression, Ditone Progression and Sesquitone Progecssion by figures within cecles, as,
3nd are used co basmouie an entice shythmic group in a given progression. Ie

Yaitoue and Sesysitone Progeessians ic is alu possible co hanunonize che entice occa
range with 4 single Master Chosd. Furthermore, any Master Chord suitsble for ha

coizatnn of a given progcession may be transposed @ uitoue ep or down with satisfactory

cenale,
Harmonization with Master Chords

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