Greek musical notation

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, into several complex systems encompassing tetrachords and octaves, as well as octave scales divided into seven to thirteen intervals.

Any discussion of the music of ancient Greece, 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. The empirical research of scholars like Richard Crocker, C. André Barbera, and John Chalmers 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 and the Pythagorean school, Archytas, Aristoxenos, and Ptolemy (including his versions of the genera of Didymos and Eratosthenes).

Overview of the first complete tone system

As an initial introduction to the principal names and divisions of the Ancient Greek tone system we will give a depiction of the "perfect system" or systema teleion, which was elaborated in its entirety by about the turn of the 5th to 4th century BCE.

The following diagram reproduces information from Chalmer. It shows the common ancient ''harmoniai'', the ''tonoi'' in all ''genera'', and the system as a whole in one complete map.

The central three columns of the diagram show, first the modern note-names, then the two systems of symbols used in ancient Greece: the vocalic (favoured by singers) and instrumental (favoured by instrumentalists). The modern note-names are given in the Helmholtz pitch notation, and the Greek note symbols are as given in the work of . Note that the pitches of the notes in modern notation are conventional, going back to the time of a publication by in 1840; in practice the pitches would have been somewhat lower.

The section spanned by a blue brace is the range of the central octave. The range is approximately what we today depict as follows:

Note that Greek theorists conceived of scales as descending from higher pitch to lower (the opposite of modern practice).

The earliest Greek scales were tetrachords, which were series of four descending tones, with the top and bottom tones being a fourth apart in modern terms. The sub-intervals of the tetrachord were unequal, with the largest intervals always at the top, and the smallest at the bottom. The 'characteristic interval' of a tetrachord is its largest one.

The Greater Perfect System (''systema teleion meizon'') was composed of four stacked tetrachords called (from lowest to highest) the ''Hypaton'', ''Meson'', ''Diezeugmenon'' and '' Hyperbolaion'' tetrachords. These are shown on the right hand side of the diagram. Octaves were composed from two stacked tetrachords connected by one common tone, the ''synaphe''.

At the position of the ''paramese'', the continuity of the system encounters a boundary (at b-flat, b). To retain the logic of the internal divisions of the tetrachords and avoid the ''Meson'' being forced into three whole tone steps (b–a–g–f), an interstitial note, the ''diazeuxis'' ('dividing'), was introduced between the ''paramese'' and ''mese''. This procedure gives its name to the tetrachord ''diezeugmenon'', which means the 'divided'.

To bridge the inconsistency of the ''diazeuxis'', the system allowed moving the ''nete'' one step up, permitting the construction of the ''Synemmenon'' ('conjunct') tetrachord – shown at the far left of the diagram.

The use of the ''Synemmenon'' tetrachord effected a modulation of the system, hence the name ''systema metabolon'', the modulating system, also called the Lesser Perfect System. This 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 System, with a third tetrachord placed above the ''Meson''. When all these are considered together, with the ''Synemmenon'' tetrachord placed between the ''Meson'' and ''Diezeugmenon'' tetrachords, they make up the Immutable (or Unmodulating) System (systema ametabolon). The lowest tone does not belong to the system of tetrachords, as is reflected in its name, the ''Proslambanomenos'', the adjoined.

In sum, it is clear that the Ancient Greeks conceived of a unified system with the tetrachord as the basic structure, but the octave as the principle of unification.

Below we elaborate the mathematics that led to the logic of the system of tetrachords just described.

The Pythagoreans

After the discovery of the fundamental intervals (octave, fourth and fifth), 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 (see also Pythagorean Interval and Pythagorean Tuning).

The earliest such description of a scale is found in Philolaus fr. B6. Philolaus recognizes that, if we go up the interval of a fourth from any given note, and then up the interval of a fifth, the final note is an octave above the first note. Thus, the octave is made up of a fourth and a fifth. ... Philolaus's scale thus consisted of the following intervals: 9:8, 9:8, 256:243 hese three intervals take us up a fourth 9:8, 9:8, 9:8, 256:243 hese four intervals make up a fifth and complete the octave from our starting note This scale is known as the Pythagorean diatonic and is the scale that Plato adopted in the construction of the world soul in the ''Timaeus'' (36a-b).

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. Euclid further developed Archytas's theory in his ''The Division of the Canon'' (''Katatomē kanonos'', the Latin ''Sectio Canonis''). He elaborated the acoustics with reference to the frequency of vibrations (or movements).

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 (octave 2:1, fourth 4:3, fifth 3:2, 9:8).

Archytas was also the first ancient Greek theorist to provide ratios for all 3 genera. The three genera of tetrachords recognized by Archytas have the following ratios:
*The enharmonic – 5:4, 36:35, and 28:27
*The chromatic – 32:27, 243:224, and 28:27;
*The diatonic – 9:8, 8:7, and 28:27.
These three tunings appear to have corresponded to the actual musical practice of his day.

The genera arose after the framing interval of the tetrachord was fixed, because the two internal notes (called ''lichanoi'' and ''parhypate'') still had variable tunings. Tetrachords were classified into genera depending on the position of the ''lichanos'' (thus the name ''lichanos'', which means "the indicator"). For instance a ''lichanos'' that is a minor third from the bottom and a major second from the top, defines the genus diatonic. The other two genera, chromatic and enharmonic, were defined in similar fashion.

More generally, three ''genera'' of seven octave ''species'' can be recognized, depending on the positioning of the interposed tones in the component tetrachords:

*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.

Within these basic forms, the intervals of the chromatic and diatonic genera were varied further by three and two "shades" (''chroai''), respectively .

The elaboration of tetrachords was also accompanied by penta- and hexachords. The joining of a tetrachord and a pentachord yields an octachord, i.e. the complete seven-tone scale plus a higher octave of the base note. However, this was also produced by joining two tetrachords, which were linked by means of an intermediary or shared note. The final evolution of the system did not end with the octave as such but with the ''Systema teleion'', a set of five tetrachords linked by conjunction and disjunction into arrays of tones spanning two octaves, as explained above.

The system of Aristoxenus

Having elaborated the ''Systema teleion'', we will now examine the most significant individual system, that of Aristoxenos, which influenced much classification well into the Middle Ages.

Aristoxenus was a disciple of Aristotle who flourished in the 4th century BC. He introduced a radically different model for creating scales, and the nature of his scales deviated sharply from his predecessors. His system was based on seven "octave species" named after Greek regions and ethnicities – Dorian, Lydian, etc. This association of the ethnic names with the octave species appears to have preceded Aristoxenus, and the same system of names was revived in the Renaissance as names of musical modes according to the harmonic theory of that time, which was however quite different to that of the ancient Greeks. Thus the names Dorian, Lydian etc. should not be taken to imply a historical continuity between the systems.

In contrast to Archytas who distinguished his "genera" only by moving the ''lichanoi'', Aristoxenus varied both ''lichanoi'' and ''parhypate'' in considerable ranges. Instead of using discrete ratios to place the intervals in his scales, Aristoxenus used continuously variable quantities: as a result he obtained scales of thirteen notes to an octave, and considerably different qualities of consonance.

The octave species in the Aristoxenian tradition were:

* Mixolydian: ''hypate hypaton–paramese'' (b–b′)
* Lydian: ''parhypate hypaton–trite diezeugmenon'' (c′–c″)
* Phrygian: ''lichanos hypaton–paranete diezeugmenon'' (d′–d″)
* Dorian: ''hypate meson–nete diezeugmenon'' (e′–e″)
* Hypolydian: ''parhypate meson–trite hyperbolaion'' (f′–f″)
* Hypophrygian: ''lichanos meson–paranete hyperbolaion'' (g′–g″)
* Common, Locrian, or Hypodorian: ''mese–nete hyperbolaion'' or ''proslambanomenos–mese'' (a′–a″ or a–a′)

These names are derived from:
*an Ancient Greek subgroup (Dorians),
*a small region in central Greece (Locris),
*certain neighboring (non-Greek) peoples from Asia Minor ( Lydia, Phrygia).
*The prefixes ''myxo'' and ''hypo'' were added to these to form associated scales above and below.

Aristoxenian ''tonoi''

The term ''tonos'' (pl. ''tonoi'') was used in four senses, for it could designate a note, an interval, a region of the voice, and a pitch.

The ancient writer Cleonides attributes thirteen ''tonoi'' to Aristoxenus, which represent a transposition of the tones of the Pythagorean system into a more uniform progressive scale over the range of an octave.

According to Cleonides, these transpositional ''tonoi'' were named analogously to the octave species, supplemented with new terms to raise the number of degrees from seven to thirteen. In fact, Aristoxenus criticized the application of these names by the earlier theorists, whom he called the "Harmonicists".

According to the interpretation of at least two modern authorities, in the Aristoxenian ''tonoi'' the Hypodorian is the lowest, and the Mixolydian is next-to-highest: the reverse of the case of the octave species. The nominal base pitches are as follows (in descending order, after Mathiesen; Solomon uses the octave between A and a instead):

The octave species in all genera

Based on the above, it can be seen that the Aristochene system of tones and octave species can be combined with the Pythagorean system of "genera" to produce a more complete system in which each octave species of thirteen tones (Dorian, Lydian, etc.) can be declined into a system of seven tones by selecting particular tones and semitones to form genera (Diatonic, Chromatic, and Enharmonic).

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 template of the Dorian.

Diatonic

Chromatic

Enharmonic

The oldest ''harmoniai'' in three genera

In the notation above and below, the standard double-flat symbol is used to accommodate as far as possible the modern musical convention that demands every note in a scale to have a distinct, sequential letter; so interpret only as meaning the immediate prior letter in the alphabet. This is a complication unnecessary in Greek notation, which had distinct symbols for each half-flat, flat, or natural note.

The superscript symbol after a letter indicates an approximately half-flattened version of the named note; the exact degree of flattening intended depending on which of several tunings was used. Hence a three-tone falling-pitch sequence d, d, d, with the second note, d, about -flat (a quarter-tone flat) from the first note, d, and the same d about -sharp (a quarter-tone sharp) from the following d.

The (d) listed first for the Dorian is the ''Proslambanómenos'', which was appended as it was, and falls outside of the linked-tetrachord scheme.

These tables are a depiction of Aristides Quintilianus's enharmonic ''harmoniai'', the diatonic of Henderson and 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 (such as C D E F followed by D E F G) is incorrect. The species were re-tunings of the central octave such that the sequences of intervals (the cyclical modes divided by ratios defined by genus) corresponded to the notes of the Perfect Immutable System as depicted above.

Dorian

Phrygian

Lydian

Mixolydian

Syntonolydian

Ionian (Iastian)

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 (comparable to the modern conception of building all seven modal scales on a single tonic). 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 (c. 350 BCE) include sections that describe the effect of different ''harmoniai'' on mood and character formation (see below on ethos). For example, in the ''Republic'' (iii.10–11) 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'' (viii:1340a:40–1340b:5):

Aristotle remarks further:

Ethos

The ancient Greeks have used the word ''ethos'' (ἔθος or ἦθος), in this context best rendered by "character" (in the sense of patterns of being and behaviour, but not necessarily with "moral" implications), 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 (for instance, Plato, in the ''Republic'' (iii: 398d–399a), attributes "virility" to the " Dorian," and "relaxedness" to the " Lydian" mode), instruments (especially the aulos and the cithara, but also others), 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 (cited in Pseudo-Plutarch, ''De Musica'' 32: 1142d ff; see also Aristides Quintilianus 1.12). The Greeks were interested in musical ethos particularly in the context of education (so Plato in his ''Republic'' and Aristotle in his eighth book of his ''Politics''), 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 (or value) of particular musical features or styles, while others, in particular Philodemus (in his fragmentary work ''De musica'') and Sextus Empiricus (in his sixth book of his work ''Adversus mathematicos''), 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 (''On Music'', i.12), 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 (diastaltic), depressing (systaltic), or soothing (hesychastic).

The classification of the ''requirements'' we have from Proclus ''Useful Knowledge'' as preserved by Photios:
* for the gods—hymn, prosodion, paean, dithyramb, nomos, adonidia, iobakchos, and hyporcheme;
* for humans— encomion, epinikion, skolion, erotica, epithalamia, hymenaios, sillos, threnos, and epikedeion;
* for the gods and humans—partheneion, daphnephorika, tripodephorika, oschophorika, and eutika

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.

See also

* Alypius of Alexandria
* Delphic Hymns
* Seikilos epitaph
* Mesomedes
* Oxyrhynchus hymn

References

Sources

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Further reading

* (1840).
Die Hymnen des Dionysius und Mesomedes: Text und Melodieen nach Handschriften und den alten Ausgaben bearbeitet von Dr. Friedrich Bellermann
'. Berlin: Albert Förstner.
* Jan, Karl von (ed.) (1895). ''Musici scriptores graeci: Aristoteles, Euclides, Nicomachus, Bacchius, Gaudentius, Alypius et melodiarum veterum quidquid exstat''. Bibliotheca scriptorum graecorum et romanorum Teubneriana. Leipzig: B. G. Teubner.
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* Mathiesen, Thomas J. (2001d). "Alypius lupios. ''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
* Meibom, Marcus (ed.) (1652). ''Antiquae musicae auctores septem: Graece et latine'', 2 vols. Amsterdam: Apud Ludovicum Elzevirium. Facsimile reprint in Monuments of Music and Music Literature in Facsimile, Second Series: Music Literature 51. New York: Broude Bros., 1977. .
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* Winnington-Ingram, Reginald P. (1954). "Greek Music (Ancient)". ''Grove's Dictionary of Music and Musicians'', fifth edition, edited by Eric Blom. New York: St. Martin's Press.

External links

* Elsie Hamilton
booklet on the modes of ancient Greece
with detailed examples of the construction of Aolus (reed pipe instruments) and monochord, which might help reconstruct the intervals and modes of the Greeks
* Nikolaos Ioannidis musician, composer, has attempted t

from a combination of the ancient texts (to be performed) and his knowledge of Greek music.
* A mid-19th century, 1902 edition, Henry S. Macran
''The Harmonics of Aristoxenus''
The Barbera translation cited above is more up to date.
* Joe Monzo (2004)
Analysis of Aristoxenus
Full of interesting and insightful mathematical analysis. There are some original hypotheses outlined.
* Robert Erickson, American composer and academic
Analysis of Archytas
something of a complement to the above Aristoxenus but, dealing with the earlier and arithmetically precise Archytas:. An incidental note. Erickson is keen to demonstrate that Archytas tuning system not only corresponds with Platos Harmonia, but also with the practice of musicians. Erickson mentions the ease of tuning with the Lyre.
* Austrian Academy of Science
examples of instruments and compositionsEnsemble Kérylos
a music group led by scholar Annie Bélis, dedicated to the recreation of ancient Greek and Roman music and playing scores written on inscriptions and papyri.

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Ancient Greek music
Ancient Greek music theory
Melody types

Musical tuning