Musical system of ancient greece
Encyclopedia
This article concerns itself with the music theoretical and mathematical tone system of ancient Greece. For a discussion of the cultural aspects and history of ancient Greek music, see Music of ancient Greece
.
The musical system of ancient Greece evolved over a period of more than 500 years from simple scales of tetrachord
s, or divisions of the perfect fourth, to The Perfect Immutable System, encompassing a span of fifteen pitch keys (see tonoi below).
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 which includes examples of different kinds of classification while also trying to show the broader form evolving from the simple tetrachord to system as a whole.
Greek theorists conceived of scales from higher pitch to lower (the opposite of modern practice), and 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 image shows the descending two octaves of tones with corresponding modern note symbols and ancient Greek vocal, and instrumental, note symbols in the central columns. The modern note names are merely there for an orientation as to the intervals. They do not correspond to ancient Greek pitches or note names. The section delimited by a blue brace is the range of the central octave. The range is approximately that which we today depict as follows:
The Greek note symbols originate from the work of Egert Pöhlmann (in German), "Denkmäler altgriechischer Musik" = Erlanger Beiträge zur Sprach- und Kunstwissenschaft Bd.31, Nürnberg 1970.
The Greater Perfect System (Systêma Teleion Meizon) was composed of four stacked tetrachords called the (from bottom to top) Hypatôn, Mesôn, Diezeugmenôn and Hyperbolaiôn 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 'Synaphé. At the position of the Paramése which should be the connecting (Synaphé) tone, the continuation of the system encounters a boundary (at b-flat, b). In order to retain the logic of the internal divisions of the tetrachords (see below for more detail) such that méson not consist of three whole tone steps (b-a-g-f), an interstitial note, the diázeuxis ('dividing') was introduced between Paramése and Mése. The tetrachord diezeugménon is the 'divided'. To bridge this inconsistency, the system allowed moving the Néte one step up permitting the construction of the synemmenón ('connecting') tetrachord (see the far left of the diagram).
The use of the synemmenón 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 Hypatôn, Mesôn and Synêmenôn. 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 Mesôn (left side diagram). When viewed together, with the Synêmenôn tetrachord placed between the Mesôn and Diezeugmenôn tetrachords, they make up the Immutable or Unmodulating System (Systêma Ametabolon).
In sum it is clear that the ancient Greeks conceived of a unified system within which the octave acted as the unifying structure (interval). The very last (deepest) tone no longer belongs to the system of tetrachords which is reflected in its name, the Proslambanomenós, the adjoined.
Below is elaborated the mathematics which led to the logic of the system of tetrachords just described.
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 within the octave. Pythagoras's scale consists of a stack of perfect fifths, the ratio 3:2 ( see also Pythagorean Interval
and Pythagorean Tuning
).
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 ( Octave 2:1, Fourth 4:3, Fifth 3:2, 9:8). 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).
The three divisions of the tetrachord
s 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 (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
. In Archytas's case, only the lichanos varies.
More generally, depending on the positioning of the interposed tones in the tetrachord
s, 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 (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.
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.
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, 1964, 1966), C. Andre Barbera (1978, 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). The following reproduces tables from Chalmer which show the common ancient harmoniai, the octave species (tonoi) in all genera and the system as a whole with all tones of the gamut.
names in the following table are the traditional Greek, followed by later alternates, Greek and other. The species and notation are built around the E mode (Dorian).
's enharmonic harmoniai, Henderson's (1942) diatonic and John Chalmers (1936) 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 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.
The Greek scales in the Aristoxenian
tradition were (Barbera 1984, 240; Mathiesen 2001a, 6(iii)(d)):
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)).
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
, 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);), with nominal base pitches as follows (descending order):
, 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.
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)). He held that playing music in a particular harmonia would incline one towards specific behaviors associated with it, and suggested that soldiers should listen to music in Dorian or Phrygian harmoniai to help make them stronger, but avoid music in Lydian, Mixolydian or Ionian harmoniai, for fear of being softened. Plato believed that a change in the musical modes of the state would cause a wide-scale social revolution.
The philosophical writings of Plato
and Aristotle
(c. 350 BCE) include sections that describe the effect of different harmoniai on mood and character formation. For example, Aristotle in the Politics (viii:1340a:40–1340b:5):
In The Republic Plato describes the music to which a person listened as molding the person's character.
The classification of the requirements we have from Proclus
Useful Knowledge as preserved by Photios:
According to Mathiesen:
Music of Ancient Greece
The music of ancient Greece was almost universally present in society, from marriages and funerals to religious ceremonies, theatre, folk music and the ballad-like reciting of epic poetry. It thus played an integral role in the lives of ancient Greeks...
.
The musical system of ancient Greece evolved over a period of more than 500 years from simple scales of tetrachord
Tetrachord
Traditionally, a tetrachord is a series of three intervals filling in the interval of a perfect fourth, a 4:3 frequency proportion. In modern usage a tetrachord is any four-note segment of a scale or tone row. The term tetrachord derives from ancient Greek music theory...
s, or divisions of the perfect fourth, to The Perfect Immutable System, encompassing a span of fifteen pitch keys (see tonoi below).
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 which includes examples of different kinds of classification while also trying to show the broader form evolving from the simple tetrachord to system as a whole.
Systêma Ametabolon, an overview of the tone system
At about the turn of the 5th to 4th century BCE the tonal system, Systeme 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. Please note, this is an as yet not completely translated version of a German illustration, hence, b in the illustration is b-flat and H, b proper.Greek theorists conceived of scales from higher pitch to lower (the opposite of modern practice), and 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 image shows the descending two octaves of tones with corresponding modern note symbols and ancient Greek vocal, and instrumental, note symbols in the central columns. The modern note names are merely there for an orientation as to the intervals. They do not correspond to ancient Greek pitches or note names. The section delimited by a blue brace is the range of the central octave. The range is approximately that which we today depict as follows:
The Greek note symbols originate from the work of Egert Pöhlmann (in German), "Denkmäler altgriechischer Musik" = Erlanger Beiträge zur Sprach- und Kunstwissenschaft Bd.31, Nürnberg 1970.
The Greater Perfect System (Systêma Teleion Meizon) was composed of four stacked tetrachords called the (from bottom to top) Hypatôn, Mesôn, Diezeugmenôn and Hyperbolaiôn 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 'Synaphé. At the position of the Paramése which should be the connecting (Synaphé) tone, the continuation of the system encounters a boundary (at b-flat, b). In order to retain the logic of the internal divisions of the tetrachords (see below for more detail) such that méson not consist of three whole tone steps (b-a-g-f), an interstitial note, the diázeuxis ('dividing') was introduced between Paramése and Mése. The tetrachord diezeugménon is the 'divided'. To bridge this inconsistency, the system allowed moving the Néte one step up permitting the construction of the synemmenón ('connecting') tetrachord (see the far left of the diagram).
The use of the synemmenón 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 Hypatôn, Mesôn and Synêmenôn. 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 Mesôn (left side diagram). When viewed together, with the Synêmenôn tetrachord placed between the Mesôn and Diezeugmenôn tetrachords, they make up the Immutable or Unmodulating System (Systêma Ametabolon).
In sum it is clear that the ancient Greeks conceived of a unified system within which the octave acted as the unifying structure (interval). The very last (deepest) tone no longer belongs to the system of tetrachords which is reflected in its name, the Proslambanomenós, the adjoined.
Below is elaborated the mathematics which 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 where those of PythagorasPythagoras
Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...
to whom was often attributed the discovery that the frequency of a vibrating string is inversely proportional to its length. Pythagoras
Pythagoras
Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...
construed the intervals arithmetically, allowing for 1:1 = Unison, 2:1 = Octave, 3:2 = Fifth, 4:3 = Fourth within the octave. Pythagoras's scale consists of a stack of perfect fifths, the ratio 3:2 ( see also Pythagorean Interval
Pythagorean interval
In musical tuning theory, a Pythagorean interval is a musical interval with frequency ratio equal to a power of two divided by a power of three, or vice versa...
and Pythagorean Tuning
Pythagorean tuning
Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. This interval is chosen because it is one of the most consonant...
).
The next notable Pythagorean theorist we know of is Archytas
Archytas
Archytas was an Ancient Greek philosopher, mathematician, astronomer, statesman, and strategist. He was a scientist of the Pythagorean school and famous for being the reputed founder of mathematical mechanics, as well as a good friend of Plato....
, 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 ( Octave 2:1, Fourth 4:3, Fifth 3:2, 9:8). Euclid
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...
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).
The three divisions of the tetrachord
Tetrachord
Traditionally, a tetrachord is a series of three intervals filling in the interval of a perfect fourth, a 4:3 frequency proportion. In modern usage a tetrachord is any four-note segment of a scale or tone row. The term tetrachord derives from ancient Greek music theory...
s 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 (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
Minor third
In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the minor third is one of two commonly occurring thirds. The minor quality specification identifies it as being the smallest of the two: the minor third spans three semitones, the major...
from the bottom and one whole (major second
Major second
In Western music theory, a major second is a musical interval spanning two semitones, and encompassing two adjacent staff positions . For example, the interval from C to D is a major second, as the note D lies two semitones above C, and the two notes are notated on adjacent staff postions...
) from the top, genus diatonic
Diatonic genus
In ancient Greek music theory, the diatonic genus is the division of the tetrachord from which the modern diatonic scale evolved. The distinguishing characteristic of the diatonic genus is that its largest interval is about the size of a major second...
. If the interval was a minor third, about one whole tone from the bottom, genus chromatic
Chromatic genus
In Ancient Greek music theory, the chromatic genus is a genus of the tetrachord characterized by an upper interval of a minor third. The two middle notes of the tetrachord were movable while the two outer notes were immovable...
. If the interval was a major third with the 4/3 (or a semitone from the bottom), genus enharmonic
Enharmonic genus
The enharmonic genus has historically been the most mysterious and controversial of the three Greek genera of tetrachords. Its characteristic interval is a major third, leaving the remainder of the tetrachord to be divided by two intervals smaller than a semitone...
. In Archytas's case, only the lichanos varies.
More generally, depending on the positioning of the interposed tones in the tetrachord
Tetrachord
Traditionally, a tetrachord is a series of three intervals filling in the interval of a perfect fourth, a 4:3 frequency proportion. In modern usage a tetrachord is any four-note segment of a scale or tone row. The term tetrachord derives from ancient Greek music theory...
s, 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 (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.
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.
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, 1964, 1966), C. Andre Barbera (1978, 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). The following reproduces tables from Chalmer which 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 speciesOctave species
In early Greek music theory, an octave species is a sequence of incomposite intervals making up a complete octave...
names in the following table are the traditional Greek, followed by later alternates, Greek and other. The species and notation are built around the E mode (Dorian).
Diatonic
| Tonic | Name | Mese |
|---|---|---|
| (A | Hypermixolydian, Hyperphrygian, Locrian | D) |
| B | Mixolydian, Hyperdorian | E |
| C | Lydian | F |
| D | Phrygian | G |
| E | Dorian | A |
| F | Hypolydian | b |
| G | Hypophrygian, Ionian | c |
| a | Hypodorian, Aeolian | d |
Chromatic
| Tonic | Name | Mese |
|---|---|---|
| (A | Hypermixolydian, Hyperphrygian, Locrian | D) |
| B | Mixolydian, Hyperdorian | E |
| C | Lydian | F |
| D | Phrygian | G |
| E | Dorian | a |
| F | Hypolydian | b |
| G | Hypophrygian, Ionian | c |
| a | Hypodorian, Aeolian | D |
Enharmonic
| Tonic | Name | Mese |
|---|---|---|
| (A | Hypermixolydian, Hyperphrygian, Locrian | D) |
| B | Mixolydian, Hyperdorian | E |
| C- | Lydian | F- |
| D | Phrygian | G |
| E | Dorian | a |
| F- | Hypolydian | b |
| G | Hypophrygian, Ionian | c- |
| a | Hypodorian, Aeolian | d |
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. The (d) listed first for the Dorian is the Proslambanómenos which was appended as it were and falls out of the tetrachord scheme. These tables are a depiction of Aristides QuintilianusAristides Quintilianus
Aristides Quintilianus was the Greek author of an ancient musical treatise, Perì musikês , who probably lived in the third century AD. According to Marcus Meibomius, in whose collection Aristides Quintilianus (Greek: Ἀριστείδης Κοϊντιλιανός) was the Greek author of an ancient musical treatise,...
's enharmonic harmoniai, Henderson's (1942) diatonic and John Chalmers (1936) chromatic versions. Chalmers, from whom they originate, states
The superficial resemblance of these octave species with the church modes
Musical mode
In the theory of Western music since the ninth century, mode generally refers to a type of scale. This usage, still the most common in recent years, reflects a tradition dating to the middle ages, itself inspired by the theory of ancient Greek music.The word encompasses several additional...
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.
Dorian
| Genus | Tones |
|---|---|
| Enharmonic | (d) e f- g a b c- d' e' |
| Chromatic | (d) e f g a b c d' e' |
| Diatonic | (d) e f g a b c d' e' |
Phrygian
| Genus | Tones |
|---|---|
| Enharmonic | d e f- g a b c- d' d' |
| Chromatic | d e f g a b c d' d' |
| Diatonic | d e f g a b c d' |
Lydian
| Genus | Tones |
|---|---|
| Enharmonic | f- g a b c- d' e' f-' |
| Chromatic | f g a b c d' e' f' |
| Diatonic | f g a b c d' e' f' |
Mixolydian
| Genus | Tones |
|---|---|
| Enharmonic | B c- d d e f- g b |
| Chromatic | B c d d e f- g b |
| Diatonic | B c d e f(g) (a) b |
Syntonolydian
| Genus | Tones |
|---|---|
| Enharmonic | B C- d e g |
| Chromatic | B C d e g |
| Diatonic | c d e f g |
| 2nd Diatonic | B C d e g |
Ionian (Iastian)
| Genus | Tones |
|---|---|
| Enharmonic | B C- d e g a |
| Chromatic | B C d e g a |
| Diatonic | c e f g |
| 2nd Diatonic | B 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 considereable ranges.The Greek scales in the Aristoxenian
Aristoxenus
Aristoxenus of Tarentum was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been lost, but one musical treatise, Elements of Harmony, survives incomplete, as well as some fragments concerning rhythm and...
tradition were (Barbera 1984, 240; Mathiesen 2001a, 6(iii)(d)):
- Mixolydian: hypate hypaton – paramese (b – b′)
- LydianLydian modeThe Lydian musical scale is a rising pattern of pitches comprising three whole tones, a semitone, two more whole tones, and a final semitone. This sequence of pitches roughly describes the fifth of the eight Gregorian modes, known as Mode V or the authentic mode on F, theoretically using B but in...
: parhypate hypaton – trite diezeugmenon (c′ – c″) - Phrygian: lichanos hypaton – paranete diezeugmenon (d′ – d″)
- DorianDorian modeDue to historical confusion, Dorian mode or Doric mode can refer to three very different musical modes or diatonic scales, the Greek, the medieval, and the modern.- Greek Dorian mode :...
: hypate meson – nete diezeugmenon (e′ – e″) - HypolydianHypolydian modeThe Hypolydian mode, literally meaning "below Lydian", is the common name for the sixth of the eight medieval church modes . The name is taken from Ptolemy of Alexandria's term for one of his seven tonoi, or transposition keys...
: parhypate meson – trite hyperbolaion (f′ – f″) - HypophrygianHypophrygian modeThe Hypophrygian mode, literally meaning 'below Phrygian', is a musical mode or diatonic scale in medieval chant theory, the fourth mode of church music. This mode is the plagal counterpart of the authentic third mode, which was called Phrygian...
: lichanos meson – paranete hyperbolaion (g′ – g″) - Common, LocrianLocrian modeThe Locrian mode is either a musical mode or simply a diatonic scale. Although the term occurs in several classical authors on music theory, including Cleonides and Athenaeus , there is no warrant for the modern usage of Locrian as equivalent to Glarean's Hyperaeolian mode, in either classical,...
, or HypodorianHypodorian modeThe Hypodorian mode, a musical term literally meaning 'below dorian', derives its name from a tonos or octave species of ancient Greece which, in its diatonic genus, is built from a tetrachord consisting of a semitone followed by two whole tones. The rising scale for the octave is a single tone...
: 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
Locris
Locris was a region of ancient Greece, the homeland of the Locrians, made up of three distinct districts.-Locrian tribe:...
), and certain neighboring (non-Greek) peoples from Asia Minor
Asia Minor
Asia Minor is a geographical location at the westernmost protrusion of Asia, also called Anatolia, and corresponds to the western two thirds of the Asian part of Turkey...
(Lydia
Lydia
Lydia was an Iron Age kingdom of western Asia Minor located generally east of ancient Ionia in the modern Turkish provinces of Manisa and inland İzmir. Its population spoke an Anatolian language known as Lydian....
, Phrygia
Phrygia
In antiquity, Phrygia was a kingdom in the west central part of Anatolia, in what is now modern-day Turkey. The Phrygians initially lived in the southern Balkans; according to Herodotus, under the name of Bryges , changing it to Phruges after their final migration to Anatolia, via the...
). The association of these ethnic names with the octave species
Octave species
In early Greek music theory, an octave species is a sequence of incomposite intervals making up a complete octave...
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". CleonidesCleonides
Cleonides is the author of a Greek treatise on music theory titled Eisagōgē harmonikē . The date of the treatise, based on internal evidence, can be established only to the broad period between the 3rd century BCE and the 4th century CE; however, treatises titled eisagōgē generally began to appear...
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
Cleonides
Cleonides is the author of a Greek treatise on music theory titled Eisagōgē harmonikē . The date of the treatise, based on internal evidence, can be established only to the broad period between the 3rd century BCE and the 4th century CE; however, treatises titled eisagōgē generally began to appear...
, 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);), with nominal base pitches as follows (descending order):
| f: | Hypermixolydian | also called Hyperphrygian |
| e: | High Mixolydian | also called Hyperiastian |
| e♭: | Low Mixolydian | also called Hyperdorian |
| d: | High Lydian | |
| c♯: | Low Lydian | also called Aeolian |
| c: | High Phrygian | |
| B: | Low Phrygian | also called Iastian |
| B♭: | Dorian | |
| A: | High Hypolydian | |
| G♯: | Low Hypolydian | also called Hypoaeolian |
| G: | High Hypophrygian | |
| F♯: | Low Hypophrygian | also 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. PtolemyPtolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
, 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
Eratosthenes
Eratosthenes of Cyrene was a Greek mathematician, poet, athlete, geographer, astronomer, and music theorist.He was the first person to use the word "geography" and invented the discipline of geography as we understand it...
and Didymos
Didymos
Didymos was an ancient Greek music theorist in the last century before Christ. He was a predecessor of Ptolemy at the library at Alexandria.- Theory :We know of his theory only indirectly from the works of Porphyry and Ptolemy...
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 (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
Melody type
In ethnomusicology and musicology, a melody type is a set of melodic formulas, figures, and patterns which are used in the composition of an enormous variety of music, especially non-Western and early Western music. Such music is generally composed by a process of centonization, either freely In...
characteristic of Greeks speaking the Aeolic dialect than of a scale pattern (Anderson and Mathiesen 2001).
In the Republic, Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
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)). He held that playing music in a particular harmonia would incline one towards specific behaviors associated with it, and suggested that soldiers should listen to music in Dorian or Phrygian harmoniai to help make them stronger, but avoid music in Lydian, Mixolydian or Ionian harmoniai, for fear of being softened. Plato believed that a change in the musical modes of the state would cause a wide-scale social revolution.
The philosophical writings of Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
and Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
(c. 350 BCE) include sections that describe the effect of different harmoniai on mood and character formation. For example, Aristotle in the Politics (viii:1340a:40–1340b:5):
In The Republic Plato describes the music to which a person listened as molding the person's character.
Ethos
The word ethos in this context means "moral character", and Greek ethos theory concerns the ways in which music can convey, foster, and even generate ethical states (Anderson and Mathiesen 2001).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 (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
Proclus
Proclus Lycaeus , called "The Successor" or "Diadochos" , was a Greek Neoplatonist philosopher, one of the last major Classical philosophers . He set forth one of the most elaborate and fully developed systems of Neoplatonism...
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:
See also
- Alypius (music writer)Alypius (music writer)Alypius of Alexandria was a Greek writer on music who flourished c. 360. Of his works, only a small fragment has been preserved, under the title of Introduction to Music .-Works:...
which we have from Meibom -> Karl von Jan (17th, 19th century respectively) and then later in the 20th century in English from Strunk?
See also
These are as yet incomplete.- Winnington-Ingram, R.P. (1932). Aristoxenus and the intervals of Greek music. The Classical Quarterly XXVI, Nos. 3–4, pp. 195–208.
- Winnington-Ingram, R.P. (1936). Mode in Ancient Greek Music. Cambridge University Press, London, England.
- Winnington-Ingram, R.P. (1954). "Greek Music (Ancient)." In Grove's Dictionary of Music and Musicians, Volume 3, 5th ed., E. Blom, Editor. St. Martin's Press, Inc., New York, 1970.
External links
- Some useful biographical information
- Neume Notation Project, "is principally an exploration of data representations for medieval music notations and data streams"
- Booklet on the modes of ancient Greece with detailed examples of the construction of Aolus (reed pipe instruments) and monochord with which the intervals and modes of the Greeks might be reconstructed http://www.nakedlight.co.uk/pdf/articles/a-002.pdf
- Divisions of the Tetrachord is a methodical overview of ancient Greek musical modes and contemporary use, including developments to Xenakis. And a backup link. Divisions of the Tetrachord. The frogpeak page http://www.frogpeak.org/unbound/index.html points to the same resource.
- 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.
- relatively concise overview of ancient Greek musical culture and philosophy
- mid-19th century, 1902 edition, Henry S. Macran, The Harmonics of Aristoxenus. The Barbera translation cited above is more up to date.
- Analysis of Aristoxenus from Joe Monzo. Full of interesting and insightful mathematical analysis. There are some original hypothesis outlined.
- Robert Erickson, American composer and academic in California, 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