Greek Music Theory

In treating the theory of ancient Greek music theory theory we shall follow the lines laid down by Aristoxenus, the greatest of Greek theorists, and proceed from the simple musical facts of concords to the complex phenomena of scales, modes, keys, etc.

Concords

The whole material of musical art is supplied by the scales; and a scale is ultimately determined by concords. In the concords, then, we touch the beginnings of all music, and in the scales we have the potentiality of its highest achievement.

A concord contains two elements, a relation and a direction of the relation; that is, in every concord there are two related notes and one of them is more fundamental, more akin to the tonic than the other.

The ancient Greeks recognized as concords or concordant intervals the foundation of a note:

  1. On its fourth above
  2. On its fifth below
  3. On its octave above
  4. On its octave below

Thirds and sixths were discords for the Greek ear.

Scales

The elementary scale is the tetrachord which is built on assumption of the following rules:

  1. The smallest concord is the fourth with the upper note its tonic
  2. This space cannot be divided by more than two intermediate notes
  3. No interval smaller than a quarter tone can be produced or discriminated
  4. In the division of a fourth, when the upper note is tonic, the lowest interval must be equal to or less than the middle, and less than the highest

The recognition of these rules leaves an infinite variety of possible determination of the inner notes of the tetrachord; but three are taken as typical, and the classes represented by these types are called the genera of music, the Enharmonic, the Chromatic, and the Diatonic:

greek1

The sign X signifies that the note to which it is prefixed is sharpened by a quarter tone. The fixed bounding notes of the scale are denoted by minims, the indeterminate passing notes by crotchets.

The three close lying lower notes, occurring only in the Enharmonic and Chromatic (marked by a bracket in the above example), were called the Pyenum. At a later period the Diatonic genus displaced the others.

The enharmonic is no monstrosity, nor is the smallness of its intervals in itself an objection. We cannot appreciate them because we have lost the habit. But its fatal defect is that its notes cannot be determined by the principle of concord. Starting from A we can determine #A by the series of concords:

greek2

But #A cannot be thus determined.

The more ample scales are produced by the collocation of two or more of these tetrachords. Tetrachords can be collocated:

  1. By conjunction, in which case the highest note of the lower tetrachord coincides with the lowest notes of the upper tetrachord. Hence the Heptachord scale:

greek3

The name Hypate signifies the ‘highest’ chord (i.e. the highest in its position on the instrument), Parhypate signifies ‘next the highest,’ Lichanus ‘forefinger,’ Mese ’middle,’ Trite ‘third,’ Paranete ‘next the lowest,’ Nete ‘lowest.’

  1. By disjunction, in which case a tone separates the several tetrachords from one another. Hence the old Dorian Enharmonic scale.

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  1. By alternate conjunction and disjunction. Hence results a non-modulating scale such as that supplied by the white notes of our keyed instruments. The octachord scales are exemplifications of it:

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Paramese signifies ‘beside the middle.’ The last of these methods of collocation practically displaced the others, for it alone was musically satisfactory. The octachord scale alone has a permanent tonic; the others modulate, to use our term, one into the flat, the other into the sharp keys.

Deficient scales are also common e.g. Terpander’s scale:

greek6

a heptachord scale obtained by omission of one note of the octachord; and the enharmonic scale of Olympus, a trichord obtained by omission of one note of the tetrachord.

Modes

Form of the Modes

If in the indefinitely prolonged scale arising from the third method of collocating tetrachords we seek for a segment capable of supplying the notes for the first phrase of ‘Voi che sapete’ we find it in the segment:

greek7

If again we wish to render the opening phrase of ‘Deh vieni, non tardar,’ we are obliged to abandon that segment, and adopt the following:

greek8

Now, since Greek instruments were limited in compass, different instruments or different tunings of the one instrument were necessary in order to obtain such different segments. In this way these segments obtained a certain importance and quasi-independence, and were called modes. The schemes and names of the modes were as follows:

Mixolydian

mixolydian

Lydian

lydian

Phrygian

phrygian

Dorian

dorian

Hypolydian

hypolydian

Hypophrygian

hypophrygian

Hypodorian

hypodorian

Pitch of the Modes

It is a law of Greek music theory – and indeed in the absence of harmony a natural necessity – that the Mese or Tonic must be the predominating or constantly recurring notes in every melody. Therefore every mode will take its pitch character from the position of the Mese or Tonic occupies in it. Thus the Mixlydian is intrinsically high-pitched because, since its tonic lies near its upper extremity, in any melody written in that mode the upper notes will be predominant. Hence we understand Aristotle’s statement that certain low-pitched modes suit the failing voices of old men – they would not have to use their higher notes so much as their lower.

From this intrinsic pitch character arises the relative determination of the pitch of the modes. Since e.g. the Lydian Mese or Tonic (diatonic) is a tone and a half from the opt, and four and a half tones from the bottom of the Lydian mode, while the Dorian Tonic is three and a half tones from the top, and two and a half tones from the bottom, of the Dorian mode, it follows that the Lydian mode is two tones higher than the Dorian.

The following table illustrates the pitch relations of the modes, but it is to be observed that the particular limits of pitch here assumed are arbitrary.

Mixolydian

mixolydian1

Lydian

lydian1

Phrygian

phrygian1

Dorian

dorian1

Hypolydian

hypolydian1

Hypophrygian

hyphohrygian1

Hypodorian

hypodorian1

From this table it appears that the Hypodorian with its tonic F is the lowest of the modes, and the Hypophrygian, Hypolydian, Dorian, Phygian, Lydian and the Mixolydian follow at intervals respectively of a tone, a tone, a semitone, a tone, a tone, a semitone.

Keys

Developed Art called for a more ample scale than the octachord. This was obtained by the addition of tetrachords above and below, so as to form the following type:

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The several tetrachords in it were called respectively, Hypaton, or ‘of the highest’ strings, i.e. lowest notes, Meson or ‘of the middle,’ Diazeugmenon or ‘of the disjunct,’ Hyperbolaeon or ‘of the extreme.’

In this scale was further incorporated a tetrachord united by conjunction to the tetrachord Meson at its upper extremity, and called Synemmenon or ‘of the conjunct,’ and the resulting scheme was known as the complete scale.

The important result of this extension was that the modes (as given in Modes), being all extended to the same type, their independence of form was thereby cancelled; the modes became mere keys.

The subsequent addition of eight keys with their tonics in the spaces left vacant by the tonics of the seven already existing yielded the following complex of scales:

Hyperlydian

hyperlydian

Hyperaeolian

hyperaeolian

Hyperphrygian

hyperphrygian

Hyperionian

hyperionian

Hyperdorian

hyperdorian

Lydian

lydian2

Aeolian

hyperdorianaeolian

Phrygian

phrygian2

Ionian

hypoionian3ionian2

Dorian

dorian

Hypolydian

hypolydian2

Hypoaeolian

hypoaeolian2

Hypophrygian

hypophrygian3

Hypoionian

hypoionian3

Hypodorian

hypodorian3

Ptolemy’s Modes

In the scheme of the mathematician Claudius Ptolemaeus (fl 140-160 A.D.) the fifteen keys were again reduced to seven modes, and a new nomenclature according to position (as opposed to the old nomenclature ‘according to function’) was introduced, by which notes took their names from there mere place in any particular mode:

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Tonality and Modality

The most vexed question presented by ancient Greek music theory is that of its tonality or modality. Modern music exhibits two modalities, that of our major and that of our minor mode. The major and the minor scales differ from one another essentially in this that each admits note-relations that the other excludes. Thus the immediate relation of C# to A – not resolved into any other relations, since A is the tonic – is essential to the scale of A major, but is not to be found in the minor scale.

For though C# an dA both occur in the minor scale of F#, they are there mediated by the relation of both to F# as tonic.

Similarly the immediate relation of C to A, essential to the minor scale of A, is not to be found in the scale of A major. Thus difference of modality means a difference of note relations.

Does, then, ancient Greek music theory admit differences of modality? According to the account given above, it does not; and the only modality to be found in it resembles that of our minor scale without the sharpened leading note:

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But it has been customary to take quite another view of the matter. The modes called Lydian, Dorian, Phrygian, etc. have been commonly regarded as so many modes differing from one another in such a way as our major and minor modes differ, that is, in respect of the note relations which they include. On this view, for example, the opening phrases of ‘God save the King’ would be:

greek13

But apart from its inherent improbability the following arguments may be adduced against this theory:

  1. There is absolutely no reference in the ancient Greek authorities to any such modal distinction
  2. All the analysis of the Greek authorities reduces the scales to tetrachords of the form

greek14

(and of course, its chromatic and enharmonic equivalents) in which extreme notes are determined as notes fixed by concord, while the intermediate notes are variable. Such an analysis would be radically false if modal distinctions in the modern sense existed. Thus any analysis of our major scale of C would be false that failed to recognize C and G as absolutely determined notes.

  1. Distinct ethical character is attributed to the several Greek modes. But it is attributed to them in virtue of their pitch. If now the modes differ in tonality, they cannot differ in pitch. It would be absurd to say that our major scale in general is higher or lower than our minor.
  2. The Greek modes, as we have seen, are regarded as severally suited for voices of different ages. But differences of modality in the modern sense would not account for this. In what way is our major mode more or less adapted to the failing voice of an old man than our minor?

Ethos

The Greeks has a keen appreciation of the potent effects of music on the ethos or mood, and through this on the character; and they are explicit as to the particular moods evoked by particular kinds of music. Thus Diatonic music was held to be manly and severe, Chromatic sweet and plaintive, Enharmonic stirring and pleasing; again high pitched music was felt to be passionate and expressive of violent grief, low pitched music to be sentimental and licentious.

The moods attributed to the modes depended on the intrinsic pitch of the latter.

Singing and Instrumental Music

Music was preeminently song for the Greeks. Instrumental music was mainly accompaniment of the voice. The rise and fall of the melody corresponds in the main to the rise and the fall of the spoken words denoted by the accents, which were marks not of stress but of pitch.

Harmony in the modern sense of the term (as the musical relation of notes sounded simultaneously) was rudimentary among the ancient Greeks, and consisted in an optional, single part accompaniment above the melody, which latter not only was the predominant tune, but also supplied in itself the unity and foundation which the bass and other parts of frequently supply in modern music.

Notation

There are two sets of signs, one for the voice, the other for the instrument. The first are clearly the letters of the ordinary Ionic alphabet; the second have been explained by Vincent and Bellermann as adapted from the cabalistic signs for the heavenly bodies, but with more plausibility by Westphal as the first fourteen letters of an old Doric alphabet. These fifteen characters, and the letters from which they are taken, are as follows:

greek15

The three notes of a Pyenum were denoted by the same sign in different positions; thus

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The order in which these several letters are employed has received as yet no satisfactory explanation.