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 (see tonoi below) (Chalmers 1993, chapt.
6, p. 99)
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 (favoured
by singers) and instrumental (favoured by
instrumentalists). (Note that the pitches
of the notes in modern notation are conventional,
going back to the time of a publication by
Friedrich Bellermann in 1840; in practice
the pitches would have been somewhat lower
(Pöhlmann and West 2001, 7).
Greek theorists conceived of scales as descending
from higher pitch to lower (the opposite of
modern practice). 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
(or the 'tone' in the case of the 'tense/hard
diatonic' genus).
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 Egert Pöhlmann (1970).
The Greater Perfect System (systema teleion
meizon) was composed of four stacked tetrachords
called the (from bottom to top) Hypaton, Meson,
Diezeugmenon and Hyperbolaion tetrachords
(see the right hand side of the diagram).
Each of these tetrachords contains the two
fixed notes that bound it.
The octaves are each composed of two like
tetrachords (1–1–½) connected by one
common tone, the Synaphe. At the position
of the Paramese, the continuation of the system
encounters a boundary (at b-flat, b). To retain
the logic of the internal divisions of the
tetrachords (see below for more detail) suo
that meson would not consist of three whole
tone steps (b-a-g-f), an interstitial note,
the diazeuxis ('dividing') 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 ('conjunct') tetrachord
(see 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 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 (right side diagram),
with a third tetrachord placed above the Meson
(left side diagram). When viewed together,
with the Synemmenon tetrachord placed between
the Meson and Diezeugmenon tetrachords, they
make up the Immutable (or Unmodulating) System
(systema ametabolon).
In sum, it is clear that the ancient Greeks
conceived of a unified system with the octave
as the unifying structure (interval). 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
(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 [these three intervals take
us up a fourth], 9:8, 9:8, 9:8, 256:243 [these
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).
(Huffman 2011)
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 (Chalmers 1993, chapt. 6, p. 99). 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) (Huffman
2011; Barker & 1984–89, 2:46–52). Euclid
in his The Division of the Canon (Katatomē
kanonos, the Latin Sectio Canonis) further
developed Archytas's theory, elaborating the
acoustics with reference to the frequency
of vibrations (or movements) (Levin 1990,).
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
(Huffman 2011). The three tunings of Archytas
appear to have corresponded to the actual
musical practice of his day (Barker & 1984–89,
2:46–52).
Tetrachords were classified in ancient Greek
theory into genera depending on the position
of the third note lichanos (the indicator)
from the bottom of the lower tetrachord (in
the upper tetrachord, referred to as the paranete).
The interval between this note and the uppermost
define the genus. A lichanos a minor third
from the bottom and one whole (major second)
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 (or a semitone
from the bottom), genus enharmonic (Chalmers
1993, chapt. 5, p. 47). 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 (Cleonides
1965, 35–36). After the introduction of
the Aristoxenos system (see below), the framing
interval of the fourth is fixed, while the
two internal (lichanoi and parhypate) pitches
are movable. Within the basic forms the intervals
of the chromatic and diatonic genera were
varied further by three and two "shades" (chroai),
respectively (Cleonides 1965, 39–40; Mathiesen
2001a, 6(iii)(e)).
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 (above),
a set of five tetrachords linked by conjunction
and disjunction into arrays of tones spanning
two octaves (Chalmers 1993, chapt. 6, p. 99).
After elaborating the Systema teleion in light
of empirical studies of the division of the
tetrachord (arithmetical, geometrical and
harmonious means) 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
Crocker (1963) (also Crocker 1964 Crocker
1966), C. André Barbera (1977) and Barbera
(1984), and John Chalmers (1990) 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 (school),
Archytas, Aristoxenos, and Ptolemy (including
his versions of the Didymos and Eratosthenes
genera) (Chalmers 1993, chapt. 5, pp. 48–51).
The following reproduces tables from Chalmer
show the common ancient harmoniai, the octave
species (tonoi) 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 (Dorian). Although the Dorian,
Phrygian, and Lydian modes have distinctive
tetrachordal forms, these forms were never
named after their parent modes by any of the
Greek theorists. In the chromatic and enharmonic
genera the tonics of the species are transformed.
(Chalmers 1993, chapt. 6, p. 103)
=== 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
​1⁄2-flat (a quarter-tone flat) from the
preceding 'd', and the same d- about ​1⁄2-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 out of the tetrachord scheme.
These tables are a depiction of Aristides
Quintilianus's enharmonic harmoniai, the diatonic
of Henderson (1942) and John Chalmers (1936)
chromatic versions. Chalmers, from whom they
originate, states
In the enharmonic and chromatic forms of some
of the harmoniai, it has been necessary to
use both a d and either a d♭ or d♭♭
because of the non-heptatonic nature of these
scales. C and F are synonyms for d♭♭ a
g♭♭. The appropriate tunings for these
scales are those of Archytas (Mountford 1923)
and Pythagoras. (Chalmers 1993, chapt. 6,
p. 109)
The superficial resemblance of these octave
species with the church modes is misleading.
The conventional representation as a section
(such as CDEF followed by DEFG) 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
(Chalmers 1993, chapt. 6, p. 106).
=== Dorian ===
=== Phrygian ===
=== Lydian ===
=== Mixolydian ===
=== Syntonolydian ===
=== Ionian (Iastian) ===
== 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 (Chalmers
1993, chapt. 3, pp. 17–22). In contrast
to Archytas who distinguished his genera only
by moving the lichanoi, Aristoxenus varied
both lichanoi and parhypate in considerable
ranges (Chalmers 1993, chapt. 5, p. 48).
The Greek scales in the Aristoxenian tradition
were (Barbera 1984, 240; Mathiesen 2001a,
6(iii)(d)):
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 Ancient
Greek subgroups (Dorians), one small region
in central Greece (Locris), and certain neighboring
(non-Greek) peoples from Asia Minor (Lydia,
Phrygia). 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 (Mathiesen 2001a,
6(iii)(d)).
=== Aristoxenus's tonoi ===
The term tonos (pl. tonoi) 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 1965, 44) Cleonides attributes
thirteen tonoi to Aristoxenus, which represent
a progressive transposition of the entire
system (or scale) by semitone over the range
of an octave between the Hypodorian and the
Hypermixolydian (Mathiesen 2001a, 6(iii)(e)).
Aristoxenus's transpositional tonoi, according
to Cleonides (1965, 44) 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
(Mathiesen 2001a, 6(iii)(e); Solomon 1984,),
with nominal base pitches as follows (descending
order):
== 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 (Chalmers 1993, chapt. 2, p. 10).
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 (Mathiesen 2001a, 6(iii)(e); Mathiesen
2001c). 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 (Chalmers 1993,
chapt. 6, p. 99).
== 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 (Mathiesen 2001b).
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 (Winnington-Ingram
1936, 3). 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
(Anderson and Mathiesen 2001).
In the Republic, Plato uses the term inclusively
to encompass a particular type of scale, range
and register, characteristic rhythmic pattern,
textual subject, etc. (Mathiesen 2001a, 6(iii)(e)).
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):
But melodies themselves do contain imitations
of character. This is perfectly clear, for
the harmoniai have quite distinct natures
from one another, so that those who hear them
are differently affected and do not respond
in the same way to each. To some, such as
the one called Mixolydian, they respond with
more grief and anxiety, to others, such as
the relaxed harmoniai, with more mellowness
of mind, and to one another with a special
degree of moderation and firmness, Dorian
being apparently the only one of the harmoniai
to have this effect, while Phrygian creates
ecstatic excitement. These points have been
well expressed by those who have thought deeply
about this kind of education; for they cull
the evidence for what they say from the facts
themselves. (Barker & 1984–89, 1:175–76)
Aristotle remarks further: From what has been
said it is evident what an influence music
has over the disposition of the mind, and
how variously it can fascinate it—and if
it can do this, most certainly it is what
youth ought to be instructed in. (Aristotle
1912, book 8, chapter 5)
== 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."
(Anderson and Mathiesen 2001). 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 (Kramarz 2016).
== 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"
(Cleonides 1965, 35)—which, together with
the scales, tonoi, and harmoniai resemble
elements found in medieval modal theory (Mathiesen
2001a, 6(iii)). 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)
(Mathiesen 2001a, 4).
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 eutikaAccording
to Mathiesen:
Such pieces of music were called melos, which
in its perfect form (teleion melos) comprised
not only the melody and the text (including
its elements of rhythm and diction) but also
stylized dance movement. Melic and rhythmic
composition (respectively, melopoiïa and
rhuthmopoiïa) were the processes of selecting
and applying the various components of melos
and rhythm to create a complete work. (Mathiesen
1999, 25)
== 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:
== See also ==
Alypius of Alexandria
Music of ancient Greece
Delphic Hymns
Seikilos epitaph
Mesomedes
Oxyrhynchus hymn
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== Further reading ==
Winnington-Ingram, Reginald P. (1932). "Aristoxenus
and the Intervals of Greek Music". The Classical
Quarterly. 26 (3–4): 195–208. doi:10.1017/s0009838800014415..
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, Inc.
== 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 to reconstruct ancient Greek music
from a combination of the ancient texts (to
be performed) and his knowledge of Greek music.
A relatively concise overview of ancient Greek
musical culture and philosophy (archive from
9 October 2011).
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 Sciences examples of instruments
and compositions
Ensemble 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.
