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Rajko Maksimovic

MORE ON MODESA Step towards a

General Theory of Modes

Belgrade, 1995


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by Rajko Maksimovic

Makenzijeva 3511000 Belgrade

Serbiae-mail: [email protected]

http://www.rajko-maksimovic.net

http://www.myspace.com/rajkomaksimovic
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INTRODUCTION

There is no doubt that a serious crisis of tonal (major-minor) system began with Wagner's chromaticity in Tristane and Ysolde, and later withDebussy's usage of whole-tone scale as well as of the pentatonic scale. Atonalmusic - in the beginning of the XX century - denied all basic principles of thetraditional (tonal) music, and all consequences of those principles - the shape of melody, vertical (harmonic) structure, building of musical forms. Looking fromour standpoint now, it was almost chaos. Soon afterwards Schnberg declared

principles of twelve tone music trying to make order and a new system inorganizing his music of that time. One of his basic principles was absoluteequality among tones, i.e. negation of any possible hierarchy. Indeed, such a"democracy" not only cancelled the supremacy of the tonic and dominant, butalso prevented any possible advantage of any tone in general. Serial music andits last instance integral serialism elaborated Schnberg's principles further, totheir maximum. Aleatory music applied certain features of serial music but inmuch freer form - at least the absolute equality of tones was not under the strictcontrol. Certain inequality of tones might have happened, if not willingly - then

by chance.Many composers tried to make certain order in musical thought in

somehow different way. Olivier Messiaen, one of the leading figures of Frenchmusic in last few decades, was one of them. In his book "Technique de mon

Language Musicale" he proclaimed and explained his modal system andshowed how it worked. He had "invented" 7 modes of limited transposition 1 andfrom them he derived very complex harmonic structures, harmonic progressionsand melody shaping. Probably the second mode 2 was the most attractive and

popular one (thanks to its great richness and vitality) and many composersthroughout the world had had certain experience with it. As a matter of factMessiaen did not invent it, but merely systemized and systematically used it.That mode can be found sporadically in Ravel, Bartok, Stravinsky and even

Scriabine and Korsakow. By the way Scriabine mode means exactly that. Thesame pattern of intervals (121212) 3 can be found in the Istrian scale, but in therange of only a diminished sixth.

1 See more about Messiaen's modes in Chapter I2 2nd mode divides an octave in four identical segments (minor thirds), each one consistingof one minor and one major second. (8 different tones in an octave)3 In this paper I'll use the widely accepted convention for numeric presentation of intervals,as follows:1 = minor second; 2 = major second; 3 = minor third; 4 = major third;

5 = perfect fourth; 6 = tritone; 7 = perfect fifth; 8 = minor sixth;9 = major sixth; 10 = minor seventh; 11 = major seventh; 12 = perfect octave.


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CHAPTER I

STARTING KNOWLEDGE

In my practice as a composer I had used some of the Messiaen's modes(2nd & 3rd), but also the Mediaeval modes Dorian, Phrygean, Lydian,Mixolydian, Aeolian, as well as the (anhemitonic) pentatonic scale (d-e-g-a-c).During the practice I encountered with modal or scale structures which were notin any theory known to me. That forced me to think about the problem and tofind out the way to embrace all possible cases (known to me) such asmediaeval modes, Messiaen's modes, pentatonic and some others, in onesingle theory of modes, where all mentioned ones would be only particular types

or cases. Naturally, to achieve this goal (General Theory of Modes) I had to startfrom already known principles, combine them, make further conclusions and,finally make a larger, all-including system.

a) Principles of mediaeval theory of modes 4 ....... (See sheet 1) Four (diatonic) tones make a tetrachord, which is considered as the basic unitin constructing modes. There were four different tetrachords, here listed by

sharpness, depending on the position of a semitone:lydian 2-2-2 -(1) semitone outside tetrachord. L

mixolydian 2-2-1 (also known as major ) Mdorian 2-1-2 (also known as minor ) Dphrygean 1-2-2 P

Lydian is the "sharpest", phrygean is the "mildest".[We can include here (as an option) the harmonic tetrachord, known as the upper tetrachordin the harmonic minor. It is also known as the

oriental 1-3-1 Osince it is found in many folk scales of the oriental area, like Phrygean minor-major, Gipsyminor and alike].

Two tetrachords standing a whole step apart (called diazeuxis ) make anauthentic mode, with the first tone of the lower tetrachord as the finalis (tonic). Thus:

L M = Lydian mode LydM + D = Mixolydian mode MixD + D = Dorian mode DorP + P = Phrygean mode Phr

4 In fact these names are from the Ancient Greeks which were (wrongly) used later inMiddle Ages


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Here the sign "+" stands for a whole-step diazeuxis, except the Lydian modewhere the sign "" stands for a semitone.When the upper tetrachord becomes the lower one (by the octave transposition)it links with the other one (former lower, now upper) on the synaphe , thus

making a plagal mode:

ML = Hypolydian mode HypolydDM = Hypomixolydian mode HypomixDD = Hypodorian HypodorPP = Hypophrygean Hypophryg

keeping the same finalis as in the authentic mode and differing from it only inmelodic range.

It should be noted that the Lydian and Mixolydian modes have a major triad on the finalis and form the major type, while the Dorian and Phrygeanmodes have a minor triad on the finalis and form the minor type.

Each one of the modes is featuring one particular interval as itsrepresentative, or characteristic one (counting from the finalis):

lydian fourth (augm. 4) lyd.4 for Lydian modemixolydian seventh (minor 7) mix.7 for Mixolydian modedorian sixth (major 6) dor.6 for Dorian modephrygean second (minor 2) phr.2 for Phrygean mode

We may call lyd. 4 and phr. 2 as primarily characteristic since theseintervals show up uniquely, only in "their modes". Mix.7 and dor.6 are

secondarily characteristic, though, since these intervals as such can be found inother modes (minor 7 in Phrygean and Dorian; major 6 in Lydian andMixolydian), but they are considered characteristic in respect to thecorresponding tonic triad, i.e. minor 7 in spite of the major triad in Mixolydianand major 6 in spite of the minor triad in Dorian mode.

Later practice of post-renascence period brought up two modes more:Ionian and Aeolian. As a matter of fact they were the result of chromaticalterations of real modes. Flattening of augm. 4 in Lydian mode to avoid thetritone jump, or sharpening of min. 7 in Mixolydian mode to obtain the leadingtone in cadences and elsewhere produced the Ionian mode (later called: major scale); flattening of maj. 6 in Dorian mode (what was considered as normal since early times) created Aeolian mode (later called: natural minor scale).Some theorists claim that these modes have characteristic intervals, too, aeolian sixth (min.6) and ionian seventh (maj. 7), respectively, but we think

opposite: both of them are middle solutions, the result of a compromise, since both of them became by truncation (or negation) of real characteristics of real


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modes therefore, they are uncharacteristic modes having no characteristicinterval! Nevertheless we can include them in our list arranged by sharpness:mode tetrachords interval characteristic

Lydian LM lyd 4 ** (strong) Ionian M+M (none) Mixolydian M+D mix 7 * (medium)

Dorian D+D dor 6 *Aeolian D+P Phrygean P+P phr 2 **

It should be noted that these modes are made either of identical or similar (adjacent in our list) tetrachords. So called Locrian mode is out of this discussion since it has no consonant triad on the tonic (it has a diminished triad)and besides it is structurally unbalanced (it links two extreme tetrachords).

Nevertheless it may be of our particular interest:

Locrian PL loc 5 (dim.5th) *** (strongest)

b) Principles of Messiaen's modal theory............. (See sheet 2)

An octave is divided on 2, 3, 4 or 6 identical segments (tritones, maj. 3rds,min. 3rds, maj. 2nds).

All the segments of a mode have the identical internal structure.The segments are linked by a common tone - (the synaphe).

In respect to the size of the constitutional segments, corresponding mode haslimited number of possible transpositions, as follows:

mode pattern num. of segm. range of segm. num. of transp.

1st mode 2-2-2-2-2-2 6 2 1 + 12nd mode 12-12-12-12 4 3 1 + 23rd mode 211-211-211 3 4 1 + 34th mode 1131-1131 2 6 1 + 55th mode 141-141 2 6 1 + 56th mode 2211-2211 2 6 1 + 57th mode 11121-11121 2 6 1 + 5

It is never said in the book, but it is obvious, that the (perfect) octave isconsidered as the measure of periodicity. That means that all modes repeat


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themselves in upper or lower octaves, i.e. after the completion of an octave they proceed the same pattern out of it.All these modes generate very specific harmonic structures and progressions. Itis possible to make chords of 3, 4, 5 or more tones either by skipping one tone

and take every other or to skip two tones and take every third. It is possible tocombine both these ways.

c) Principles of the pentatonic mode................ (See sheet 3)

The semitone is avoided.The maj.2 and min.3 alternate until the octave is reached. Then the tones repeatthemselves.Two consecutive maj.2 may happen

There are three types of pentatonic rows (using here only white piano keys):

c-d -e-g-a-c-d-e...; c-d-f -g -a-c-d-f...; e-g- a -h-d-e-g-a...;

Thanks to the absence of a semitone and tritone, tonal feeling is very doubtful. Any of the tones may act as a tonic, so: no one is a real tonic. It is true thatamong five tones, only one of them (marked bold) has major seconds on bothsides, but this is not enough to promote that tone as a real tonic.

In the harmonic elaboration this mode eliminates chords by thirds. Instead,chords (of no matter how many tones) consist of the combination(s) of perfectfourths and fifths, major seconds and minor thirds.


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CHAPTER II

EXPANDING OF BASIC PRINCIPLESOF EARLIER THEORIES

First of all we have to see what is our goal, i.e. what is the meaning of this paper?Brief answer might be in following few statements:

a) Looking throughout the (European) history of music we notice that in alltimes some kind of a tonal feeling was more or less present; from Gregorianor Byzantine monophonic singing up to Stravinsky's polytonality we couldrecognize the gravitational force of one (or two or even more) tone(s).

b) We can conclude that some kind of a tonal feeling helps both in organizingmusical form (time) by the composer and to its comprehensiveness by the

listener.

c) Among many problems of our time, one might be how to establish the senseof tonic and yet to avoid worn out traditional solutions (especially of major-minor system).

d) I think that the variety of modes I am going to present in this paper may be agood base to start off. Naturally, I always underline that any method or systemor knowledge are just tools. Without the real talent of the user they remain an

empty shell without the living body. On the contrary: a talented personwithout knowledge (tools) remains the poor talent. Therefore, only thetalented and earnest person equipped with the broad knowledge, up-to-dateinformation and good taste may be one to create something really new and of good quality.

*

At the very beginning I took the Messiaen's modal system and asked two

basic questions: Why all the segments of a mode must be identical?


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Why the range of a mode must be an octave? What to do with the tone-rowswhich following certain logic or pattern quite normally and smoothly

skip the tone of the first octave above?

When I began thinking this way I realized that the octave though the firstnatural transposition as a mode frame is too cramped.

To answer the first question I was helped by the Mediaeval modes. Three of them (Ionian, Dorian and Phrygean) are made of two identical tetrachords,

but the others (Lydian, Mixolydian, Aeolian and Locrian) have different ones.That encouraged me to dig up even the Messiaen's modes! I took the thirdone 211-211-211, and made another pattern: 211-121-112. (See figure onsheet 4). That's different. That's the new mode! Then, I tried some unusualcombinations of tetrachords and also got the result (See sheet 4).

Then I "attacked" the octave range. I began from a scale (mode) known intheory as the Antique Major which links several major (Mixolydian)tetrachords on the synaphe, like a chain. (See figure on sheet 3). Though mostof the tones have their octave transpositions, it is obvious that octave is not the interval of periodicity of the mode as a whole. We may notice that "bnatural" and "e natural" in upper octaves have flats! For that reason themixolydian segment transforms into aeolian one in the upper octave. If, for instance, we want the first tetrachord (g-a-b-c) to find transposed somewhereelse in the mode but in exactly the same sequence of tones (g-a-b-c), we haveto wait not less than 5 octaves! The interval of its periodicity is 5 octaves!So the next thing I had realized was that:

similarly to the interval of one octave which is reachable either in 6 whole-tone steps, or in jumps of 4 minor-thirds, 3 major-thirds, 2 tritones(Messiaen's modes)

interval of two octaves may be reached in 3 minor-sixth jumps,

three octaves may be reached in 4 major-sixth jumps,

five octaves may be reached in 12 perfect-fourth jumps,

seven octaves may be reached in 12 perfect-fifth jumps.

These jumps which evenly divide ranges of 1 octave, 2 octaves, 3 octaves, 5

octaves and 7 octaves I named modules. And modules happen to be the basic units in mode construction.


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WARNING!

All what is shown here ought to be understood only as an attempt to establisha kind of order among tones, potential relations among them and especially

the gravitational power of tonic.The worst thing would be is to understand this as a recipe for successfulcomposing! It should never be forgotten that great masters from the past aregreat, among other merits, because they used to outrun the system they hadinherited! Remember multiple appogiaturas in Bach's organ and piano works(which are out of chord ), also his chromatic alterations of a given scale; or take Beethoven and his frequent changes of tonality; and many, many other cases.

And now we come to the crucial question: what is the relation (if any) between the rational element in music (knowledge, theories, systems etc.)and irrational one commonly called inspiration (or intuition)?

We state that both elements have always been present in compositional practice more or less, and in best examples they show beautiful andharmonic interdependence. On the other hand extreme cases, from our pointof view, are clear: strongly predominant rational element kills musical being, while the absolute lack of it gives an illiterate product. Therefore, I think that

both elements are essential with light predominance of intuition.This opinion is based on experience: it is much easier to "civilize" a "savage"musical idea than to add some kind of spontaneity to a piece rigidly writtenaccording to a certain system.

Its the time to quote Anatole France here: The art is being threatened by twomonsters: the Artist who is not master and the Master who is not artist.

IN SHORT: Theoretical knowledge and in general rational experience givesthe music its body whilst inspiration is the soul of music.

[This paper was prepared for a group of Greek graduate students of composition who in 1995 attended my course in Karditza, Greece]

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