Musical system of ancient Greece


The musical system of ancient Greece evolved over a period of more than 500 years from simple scales of tetrachords, or divisions of the perfect fourth, to The Perfect Immutable System, encompassing a span of fifteen pitch keys
Any discussion of ancient Greek music, theoretical, philosophical or aesthetic, is fraught with two problems: there are few examples of written music, and there are many, sometimes fragmentary, theoretical and philosophical accounts. This article provides an overview that includes examples of different kinds of classification while also trying to show the broader form evolving from the simple tetrachord to the system as a whole.

''Systema ametabolon'', an overview of the tone system

At about the turn of the 5th to 4th century BCE the tonal system, systema teleion, had been elaborated in its entirety. As an initial introduction to the principal names of the divisions of the system and the framing tetrachords, a depiction of notes and positional terms follows. The three columns show the modern note-names, and the two systems of symbols used in ancient Greece, the vocalic and instrumental.. The scales were made up of tetrachords, which were a series of four descending tones, with the top and bottom tones being a fourth apart. The largest intervals were always at the top of the tetrachord, with the smallest at the bottom. The 'characteristic interval' of a tetrachord is the largest one.
The section delimited by a blue brace is the range of the central octave. The range is approximately what we today depict as follows:
The Greek note symbols originate from the work of :de:Egert Pöhlmann|Egert.
The Greater Perfect System was composed of four stacked tetrachords called the Hypaton, Meson, Diezeugmenon and Hyperbolaion tetrachords. Each of these tetrachords contains the two fixed notes that bound it.
The octaves are each composed of two like tetrachords connected by one common tone, the Synaphe. At the position of the Paramese, the continuation of the system encounters a boundary. To retain the logic of the internal divisions of the tetrachords so that meson would not consist of three whole tone steps, an interstitial note, the diazeuxis was introduced between Paramése and Mese. The tetrachord diezeugmenon is the 'divided'. To bridge this inconsistency, the system allowed moving the Nete one step up permitting the construction of the synemmenon tetrachord.
The use of the synemmenon tetrachord effected a modulation of the system, hence the name systema metabolon, the modulating system, also the Lesser Perfect System. It was considered apart, built of three stacked tetrachords—the Hypaton, Meson and Synemmenon. The first two of these are the same as the first two tetrachords of the Greater Perfect, with a third tetrachord placed above the Meson. When viewed together, with the Synemmenon tetrachord placed between the Meson and Diezeugmenon tetrachords, they make up the Immutable System.
In sum, it is clear that the ancient Greeks conceived of a unified system with the octave as the unifying structure. The lowest tone does not belong to the system of tetrachords, as is reflected in its name, the Proslambanomenos, the adjoined.
Below elaborates the mathematics that led to the logic of the system of tetrachords just described.

The Pythagoreans

After the discovery of the fundamental intervals, the first systematic divisions of the octave we know of were those of Pythagoras to whom was often attributed the discovery that the frequency of a vibrating string is inversely proportional to its length. Pythagoras construed the intervals arithmetically, allowing for 1:1 = Unison, 2:1 = Octave, 3:2 = Fifth, 4:3 = Fourth. Pythagoras's scale consists of a stack of perfect fifths, the ratio 3:2.
The next notable Pythagorean theorist we know of is Archytas, contemporary and friend of Plato, who explained the use of arithmetic, geometric and harmonic means in tuning musical instruments. Archytas is the first ancient Greek theorist to provide ratios for all 3 genera. Archytas provided a rigorous proof that the basic musical intervals cannot be divided in half, or in other words, that there is no mean proportional between numbers in super-particular ratio . Euclid in his The Division of the Canon further developed Archytas's theory, elaborating the acoustics with reference to the frequency of vibrations .
The three divisions of the tetrachords of Archytas were: the enharmonic 5:4, 36:35, and 28:27; the chromatic 32:27, 243:224, and 28:27; and the diatonic 9:8, 8:7, and 28:27. The three tunings of Archytas appear to have corresponded to the actual musical practice of his day.
Tetrachords were classified in ancient Greek theory into genera depending on the position of the third note lichanos from the bottom of the lower tetrachord. The interval between this note and the uppermost define the genus. A lichanos a minor third from the bottom and one whole from the top, genus diatonic. If the interval was a minor third, about one whole tone from the bottom, genus chromatic. If the interval was a major third with the 4/3, genus enharmonic. In Archytas's case, only the lichanos varies.
More generally, depending on the positioning of the interposed tones in the tetrachords, three genera of all seven octave species can be recognized. The diatonic genus is composed of tones and semitones. The chromatic genus is composed of semitones and a minor third. The enharmonic genus consists of a major third and two quarter-tones or diesis. After the introduction of the Aristoxenos system, the framing interval of the fourth is fixed, while the two internal pitches are movable. Within the basic forms the intervals of the chromatic and diatonic genera were varied further by three and two "shades", respectively.
The elaboration of the tetrachords was also accompanied by penta- and hexachords. As stated above, the union of tetra- and pentachords yields the octachord, or the complete heptatonic scale. However, there is sufficient evidence that two tetrachords where initially conjoined with an intermediary or shared note. The final evolution of the system did not end with the octave as such but with Systema teleion, a set of five tetrachords linked by conjunction and disjunction into arrays of tones spanning two octaves.
After elaborating the Systema teleion in light of empirical studies of the division of the tetrachord and composition of tonoi/harmoniai, we examine the most significant individual system, that of Aristoxenos, which influenced much classification well into the Middle Ages.
The empirical research of scholars like Richard , C. André and, and John has made it possible to look at the ancient Greek systems as a whole without regard to the tastes of any one ancient theorist. The primary genera they examine are those of Pythagoras, Archytas, Aristoxenos, and Ptolemy . The following reproduces tables from Chalmer show the common ancient harmoniai, the octave species in all genera and the system as a whole with all tones of the gamut.

The octave species in all genera

The order of the octave species names in the following table are the original Greek ones, followed by later alternatives, Greek and other. The species and notation are built around the E mode.

Diatonic

Chromatic

Enharmonic

The oldest ''harmoniai'' in three genera

The sign - indicates a somewhat flattened version of the named note, the exact degree of flattening depending on the tuning involved. Hence a three-tone falling-pitch sequence d, d-, d, with the second note, d-, about -flat from the preceding 'd', and the same d- about -sharp from the following d.
The listed first for the Dorian is the Proslambanómenos, which was appended as it was, and falls out of the tetrachord scheme.
These tables are a depiction of Aristides Quintilianus's enharmonic harmoniai, the diatonic of and John Chalmers chromatic versions. Chalmers, from whom they originate, states
The superficial resemblance of these octave species with the church modes is misleading. The conventional representation as a section is incorrect. The species were re-tunings of the central octave such that the sequences of intervals corresponded to the notes of the Perfect Immutable System as depicted above.

Dorian

Phrygian

GenusTones
Enharmonicd e f- g a b c- d' d'
Chromaticd e f g a b c d' d'
Diatonicd e f g a b c d'

Lydian

GenusTones
Enharmonicf- g a b c- d' e' f-'
Chromaticf g a b c d' e' f'
Diatonicf g a b c d' e' f'

Mixolydian

GenusTones
EnharmonicB c- d d e f- g b
ChromaticB c d d e f- g b
DiatonicB c d e f b

Syntonolydian

GenusTones
EnharmonicB C- d e g
ChromaticB C d e g
Diatonicc d e f g
2nd DiatonicB C d e g

Ionian (Iastian)

GenusTones
EnharmonicB C- d e g a
ChromaticB C d e g a
Diatonicc e f g
2nd DiatonicB C d e g a

Classification of Aristoxenus

The nature of Aristoxenus's scales and genera deviated sharply from his predecessors. Aristoxenus introduced a radically different model for creating scales. Instead of using discrete ratios to place intervals, he used continuously variable quantities. Hence the structuring of his tetrachords and the resulting scales have other qualities of consonance. In contrast to Archytas who distinguished his genera only by moving the lichanoi, Aristoxenus varied both lichanoi and parhypate in considerable ranges.
The Greek scales in the Aristoxenian tradition were :
These names are derived from Ancient Greek subgroups, one small region in central Greece, and certain neighboring peoples from Asia Minor. The association of these ethnic names with the octave species appears to precede Aristoxenus, who criticized their application to the tonoi by the earlier theorists whom he called the Harmonicists.

Aristoxenus's ''tonoi''

The term tonos was used in four senses: "as note, interval, region of the voice, and pitch. We use it of the region of the voice whenever we speak of Dorian, or Phrygian, or Lydian, or any of the other tones" Cleonides attributes thirteen tonoi to Aristoxenus, which represent a progressive transposition of the entire system by semitone over the range of an octave between the Hypodorian and the Hypermixolydian. Aristoxenus's transpositional tonoi, according to were named analogously to the octave species, supplemented with new terms to raise the number of degrees from seven to thirteen. However, according to the interpretation of at least two modern authorities, in these transpositional tonoi the Hypodorian is the lowest, and the Mixolydian next-to-highest—the reverse of the case of the octave species, with nominal base pitches as follows :
f:Hypermixolydianalso called Hyperphrygian
e:High Mixolydianalso called Hyperiastian
e♭:Low Mixolydianalso called Hyperdorian
d:High Lydian-
c♯:Low Lydianalso called Aeolian
c:High Phrygian-
B:Low Phrygianalso called Iastian
B♭:Dorian-
A:High Hypolydian-
G♯:Low Hypolydianalso called Hypoaeolian
G:High Hypophrygian-
F♯:Low Hypophrygianalso called Hypoiastian
F:Hypodorian-

Ptolemy and the Alexandrians

In marked contrast to his predecessors, Ptolemy's scales employed a division of the pyknon in the ratio of 1:2, melodic, in place of equal divisions. Ptolemy, in his Harmonics, ii.3–11, construed the tonoi differently, presenting all seven octave species within a fixed octave, through chromatic inflection of the scale degrees. In Ptolemy's system, therefore there are only seven tonoi. Ptolemy preserved Archytas's tunings in his Harmonics as well as transmitting the tunings of Eratosthenes and Didymos and providing his own ratios and scales.

''Harmoniai''

In music theory the Greek word harmonia can signify the enharmonic genus of tetrachord, the seven octave species, or a style of music associated with one of the ethnic types or the tonoi named by them.
Particularly in the earliest surviving writings, harmonia is regarded not as a scale, but as the epitome of the stylised singing of a particular district or people or occupation. When the late 6th-century poet Lasus of Hermione referred to the Aeolian harmonia, for example, he was more likely thinking of a melodic style characteristic of Greeks speaking the Aeolic dialect than of a scale pattern.
In the Republic, Plato uses the term inclusively to encompass a particular type of scale, range and register, characteristic rhythmic pattern, textual subject, etc..
The philosophical writings of Plato and Aristotle include sections that describe the effect of different harmoniai on mood and character formation. For example, in the Republic Plato describes the music a person is exposed to as molding the person's character, which he discusses as particularly relevant for the proper education of the guardians of his ideal State. Aristotle in the Politics :
Aristotle remarks further:

Ethos

The ancient Greeks have used the word ethos, in this context best rendered by "character", to describe the ways music can convey, foster, and even generate emotional or mental states. Beyond this general description, there is no unified "Greek ethos theory" but "many different views, sometimes sharply opposed.". Ethos is attributed to the tonoi or harmoniai or modes, instruments, rhythms, and sometimes even the genus and individual tones. The most comprehensive treatment of musical ethos is provided by Aristides Quintilianus in his book On Music, with the original conception of assigning ethos to the various musical parameters according to the general categories of male and female. Aristoxenus was the first Greek theorist to point out that ethos does not only reside in the individual parameters but also in the musical piece as a whole. The Greeks were interested in musical ethos particularly in the context of education, with implications for the well-being of the State. Many other ancient authors refer to what we nowadays would call psychological effect of music and draw judgments for the appropriateness of particular musical features or styles, while others, in particular Philodemus and Sextus Empiricus, deny that music possesses any influence on the human person apart from generating pleasure. These different views anticipate in some way the modern debate in music philosophy whether music on its own or absolute music, independent of text, is able to elicit emotions on the listener or musician.

Melos

Cleonides describes "melic" composition, "the employment of the materials subject to harmonic practice with due regard to the requirements of each of the subjects under consideration" —which, together with the scales, tonoi, and harmoniai resemble elements found in medieval modal theory. According to Aristides Quintilianus, melic composition is subdivided into three classes: dithyrambic, nomic, and tragic. These parallel his three classes of rhythmic composition: systaltic, diastaltic and hesychastic. Each of these broad classes of melic composition may contain various subclasses, such as erotic, comic and panegyric, and any composition might be elevating, depressing, or soothing .
The classification of the requirements we have from Proclus Useful Knowledge as preserved by Photios:
According to Mathiesen:

Unicode

Music symbols of ancient Greece were added to the Unicode Standard in March, 2005 with the release of version 4.1.
The Unicode block for the musical system of ancient Greece, called Ancient Greek Musical Notation, is U+1D200–U+1D24F: