Chapters 1-2
Chapters 3-8
Impure Consonance
Galilei's Convenient Division
Tuneful Melody
Kepler Modes
Ecclesiastic Modes

©2006 LaRouche Youth L.L.P.
Untitled Document

Naturally Tuneful and Suitable Melody

We have come to the point where we have obtained the lawful melodic scales known as the hard and soft. But with the acceptance of the the imperfect consonances we can go beyond one octave and even compose melody in the octaves other than the one we have found, in other modes. This begs the question of what melodic is. Certainly many sounds can be put together in a way that is unmelodic, as in the following Turkish example that Kepler gives.

But, what makes this next one melodic?

In the thirteenth chapter of Book III of the Harmony of the World, Kepler lists the aspects of melody, which he then uses to evaluate which modes created by the system of a double octave are appropriate for melody.

Elements of Melody

There are four elements of melody that Kepler attributes to Euclid. These are: αγωγε (approach), τωνη (emphasis), πεττεια (playing), πλοκη (twining). The melody above supplies examples of these elements.

Αγωγε is like a direct motion, πλοκη like a variable motion; whereas τωνη is, so to speak, the termination of motion, or rest in the position of the system which has been the aim, πεττεια is many terminations of rather tiny motions, like rests. In our example, the syllables '-demit oves Christus in-' are a sort of continuous τωνη with the exception of two syllables; but, the syllables '' exhibit πεττεια. But if in this tune you inspect the tied syllables, 'laud-, an-, patr-, -tor-,' and consider them as having two notes, then there will be no pure and simple αγωγε in it. But if you consider them as having how it has come about in the style of folksong the from a note which was to be sung in a rather drawn out way has been made a double note which rises at the end, and if to these syllables you restore the simple drawn out note which is the first of the tie, you will find a pure αγωγε in 'Paschali laudes,' also in 'immolent,' also in 'Christiani', also in 'innocens patri,' and a short one in 'catores'; but there is a pure πλοκη, although not a natural one, in the Turkish example.

Therefore as the skeleton is to the body for anatomists, so in a single system of an octave are the sounds which are consonant, both among themselves and with the point of origin or base of the octave, to the actual tune or melody. For just as flesh fills out the curves of the bones, and clothes them to make them comely, so the componenets which have been listed fill out the skeleton of the octave, especially αγωγε and πεττεια, and straying over the dissonant postions which are scattered among the consonant notes shape and give body, so to speak, to the tune.

And a little later, Kepler says about αγωγε and πεττεια,

For frequently these components in the middle of the course of a rather lond tune occupy positions which are dissonant with the first point of origin; but that is done for the sake of variety, and it is just as if with the former tune there were mingled a new tune, and some new starting point were fixed for it which was dissonant with the former, or the skeleton of a new octave were signified. It is like an interlude or digression in a speech; so we do not linger over such matters but revert quickly, so to speak, to the principal skeleton. And as long as τωνη or πεττεια occupies dissonances, we understand that the melody is not yet finished; for at the actual true finish it must return not just to consonant notes, in fact regularly, but also to the actual point of origin of the proper octave. From this structuring of the melody, and strining for consonances, the ancients seem even to have called simple melody 'harmony' exactly as if the fitting and suitable correspondence of the limbs, which is the soul of form, were called harmony, or as it were beauty; for Harmony was also the name of a woman.


The Laws of Melody

I.  A diesis is not performed before or after a semitone.

II.  Two semitones cannot be performed by three successive tones, but must be joined with other elements to form two tones.

III.  Two semitones cannot be encompassed in a single fourth or fifth.  In that case,the fourth or fifth tone would not be consonant with the first tone, either perfectly or imperfectly.

IV.  Four tones are not played in succession, except in the top part of the octave.

V.  Sevenths and dissonances above the octave are not normally played, with a few exceptions.

VI.  Sixths are rarely admitted, and only minor sixths.

VII.  Two tetrachords are rarely performed.

VIII.  Three tones in succession are not played in the lowest position in the octave.

IX.  It is not natural to combine two semitones to form a whole tone.  The result would be unmelodic.

X.  Any system which does not setup a fourth and fifth below is unmelodic.

Kepler Modes