Octave species
Encyclopedia
In early Greek music theory, an octave species (eide diapason) is a sequence of incomposite intervals (ditone
s, minor third
s, whole tones, semitone
s of various sizes, or quarter tone
s) making up a complete octave
(Barbera 1984, 231–32). The concept was also important in Medieval and Renaissance music theory.
, or diatessaron; when filled in with two intermediary notes, the resulting four notes and three consecutive intervals constitute a "tetrachord
" (Gombosi 1951, 22). The species defined by the different positioning of the intervals within the tetrachord in turn depend upon genus first being established (Barbera 1984, 229). Incomposite in this context refers to intervals which are not composed of smaller intervals.
Most Greek theorists distinguish three genera of the tetrachord: enharmonic
, chromatic
, and diatonic
. The enharmonic and chromatic genera are defined by the size of their largest incomposite interval (major third and minor third, respectively), which leaves a composite interval of two smaller parts, together referred to as a pyknon; in the diatonic genus, no single interval is larger than the other two combined (Barbera 1984, 229). The earliest theorists to attempt a systematic treatment of octave species, the harmonicists (or school of Eratocles) of the late fifth century BC, confined their attention to the enharmonic genus, with the intervals in the resulting seven octave species being (Barker 1984–87, 2:15):
Species of the perfect fifth
(diapente) are then created by the addition of a whole tone to the intervals of the tetrachord. The first, or original species in both cases has the pyknon or, in the diatonic genus, the semitone, at the bottom (Cleonides 1965, 41) and, similarly, the lower interval of the pyknon must be smaller or equal to the higher one (Barbera 1984, 229–30). The whole tone added to created the species of fifth (the "tone of disjunction") is at the top in the first species; the remaining two species of fourth and three species of fifth are regular rotations of the constituent intervals, in which the lowest interval of each species becomes the highest of the next (Cleonides 1965, 41; Barbera 1984, 233). Because of these constraints, tetrachords containing three different incomposite intervals (compared with those in which two of the intervals are of the same size, such as two whole tones) still have only three species, rather than the six possible permutations of the three elements (Barbera 1984, 232). Similar considerations apply to the species of fifth.
The species of fourth and fifth are then combined into larger constructions called "systems". The older, central "characteristic octave", is made up of two first-species tetrachords separated by a tone of disjunction, and is called the Lesser Perfect System (Gombosi 1951, 23–24). It therefore includes a lower, first-species fifth and an upper, fourth-species fifth. To this central octave are added two flanking conjuct tetrachords (that is, they share the lower and upper tones of the central octave). This constitutes the Greater Perfect System, with six fixed bounding tones of the four tetrachords, within each of which are two movable pitches. Ptolemy
(1930, D. 49–53; Barbera 1984, 235) labels the resulting fourteen pitches with the (Greek) letters from Α ( Alpha α
) to Ο ( Omega Ω).(A diagram is available at System Ametabolon)
The Lesser and Greater Perfect Systems exercise constraints on the possible octave species. Some early theorists, such as Gaudentius in his Harmonic Introduction, recognized that, if the various available intervals could be combined in any order, even restricting species to just the diatonic genus would result in twelve ways of dividing the octave (and his 17th-century editor, Marcus Meibom, pointed out that the actual number is 21), but "only seven species or forms are melodic and symphonic" (Barbera 1984, 237–39). Those octave species that cannot be mapped onto the system are therefore to be rejected (Barbera 1984, 240).
from the seven diatonic octave species of ancient Greek theory, transmitted to the West through the Latin writings of Martianus Capella
, Cassiodorus
, Isidore of Seville
, and, most importantly, Boethius. Together with the species of fourth and fifth, the octave species continued to be used as a basis of the theory of modes, in combination with other elements, particularly the system of octoechos
borrowed from the Byzantine Church
(Powers 2001).
Ditone
In music, a ditone is the interval 81:64, which is 407.82 cents. It is the major third in Pythagorean tuning. The ditone is evenly divisible by two major tones and is wider than a just major third by a syntonic comma...
s, 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...
s, whole tones, semitone
Semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....
s of various sizes, or quarter tone
Quarter tone
A quarter tone , is a pitch halfway between the usual notes of a chromatic scale, an interval about half as wide as a semitone, which is half a whole tone....
s) making up a complete octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
(Barbera 1984, 231–32). The concept was also important in Medieval and Renaissance music theory.
Ancient Greek theory
Greek theorists used two terms interchangeably to describe what we call species: eidos (εἶδος) and skēma (σκῆμα), defined as "a change in the arrangement of incomposite [intervals] making up a compound magnitude while the number and size of the intervals remains the same" (Aristoxenus 1954, 92.7–8 & 92.9–11, translated in Barbera 1984, 230). The basis of octave species was the smaller category of species of the perfect fourthPerfect fourth
In classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...
, or diatessaron; when filled in with two intermediary notes, the resulting four notes and three consecutive intervals constitute a "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...
" (Gombosi 1951, 22). The species defined by the different positioning of the intervals within the tetrachord in turn depend upon genus first being established (Barbera 1984, 229). Incomposite in this context refers to intervals which are not composed of smaller intervals.
Most Greek theorists distinguish three genera of the tetrachord: 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...
, 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...
, and 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...
. The enharmonic and chromatic genera are defined by the size of their largest incomposite interval (major third and minor third, respectively), which leaves a composite interval of two smaller parts, together referred to as a pyknon; in the diatonic genus, no single interval is larger than the other two combined (Barbera 1984, 229). The earliest theorists to attempt a systematic treatment of octave species, the harmonicists (or school of Eratocles) of the late fifth century BC, confined their attention to the enharmonic genus, with the intervals in the resulting seven octave species being (Barker 1984–87, 2:15):
| Mixolydian Mixolydian mode Mixolydian mode may refer to one of three things: the name applied to one of the ancient Greek harmoniai or tonoi, based on a particular octave species or scale; one of the medieval church modes; a modern musical mode or diatonic scale, related to the medieval mode.-Greek Mixolydian:The idea of a... |
¼ | ¼ | 2 | ¼ | ¼ | 2 | 1 |
| Lydian Lydian mode The 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... |
¼ | 2 | ¼ | ¼ | 2 | 1 | ¼ |
| Phrygian Phrygian mode The Phrygian mode can refer to three different musical modes: the ancient Greek tonos or harmonia sometimes called Phrygian, formed on a particular set octave species or scales; the Medieval Phrygian mode, and the modern conception of the Phrygian mode as a diatonic scale, based on the latter... |
2 | ¼ | ¼ | 2 | 1 | ¼ | ¼ |
| Dorian Dorian mode Due 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 :... |
¼ | ¼ | 2 | 1 | ¼ | ¼ | 2 |
| Hypolydian Hypolydian mode The 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... |
¼ | 2 | 1 | ¼ | ¼ | 2 | ¼ |
| Hypophrygian Hypophrygian mode The 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... |
2 | 1 | ¼ | ¼ | 2 | ¼ | ¼ |
| Hypodorian Hypodorian mode The 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... |
1 | ¼ | ¼ | 2 | ¼ | ¼ | 2 |
Species of the perfect fifth
Perfect fifth
In classical music from Western culture, a fifth is a musical interval encompassing five staff positions , and the perfect fifth is a fifth spanning seven semitones, or in meantone, four diatonic semitones and three chromatic semitones...
(diapente) are then created by the addition of a whole tone to the intervals of the tetrachord. The first, or original species in both cases has the pyknon or, in the diatonic genus, the semitone, at the bottom (Cleonides 1965, 41) and, similarly, the lower interval of the pyknon must be smaller or equal to the higher one (Barbera 1984, 229–30). The whole tone added to created the species of fifth (the "tone of disjunction") is at the top in the first species; the remaining two species of fourth and three species of fifth are regular rotations of the constituent intervals, in which the lowest interval of each species becomes the highest of the next (Cleonides 1965, 41; Barbera 1984, 233). Because of these constraints, tetrachords containing three different incomposite intervals (compared with those in which two of the intervals are of the same size, such as two whole tones) still have only three species, rather than the six possible permutations of the three elements (Barbera 1984, 232). Similar considerations apply to the species of fifth.
The species of fourth and fifth are then combined into larger constructions called "systems". The older, central "characteristic octave", is made up of two first-species tetrachords separated by a tone of disjunction, and is called the Lesser Perfect System (Gombosi 1951, 23–24). It therefore includes a lower, first-species fifth and an upper, fourth-species fifth. To this central octave are added two flanking conjuct tetrachords (that is, they share the lower and upper tones of the central octave). This constitutes the Greater Perfect System, with six fixed bounding tones of the four tetrachords, within each of which are two movable pitches. Ptolemy
Ptolemy
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...
(1930, D. 49–53; Barbera 1984, 235) labels the resulting fourteen pitches with the (Greek) letters from Α ( Alpha α
Alpha (letter)
Alpha is the first letter of the Greek alphabet. In the system of Greek numerals it has a value of 1. It was derived from the Phoenician letter Aleph...
) to Ο ( Omega Ω).(A diagram is available at System Ametabolon)
The Lesser and Greater Perfect Systems exercise constraints on the possible octave species. Some early theorists, such as Gaudentius in his Harmonic Introduction, recognized that, if the various available intervals could be combined in any order, even restricting species to just the diatonic genus would result in twelve ways of dividing the octave (and his 17th-century editor, Marcus Meibom, pointed out that the actual number is 21), but "only seven species or forms are melodic and symphonic" (Barbera 1984, 237–39). Those octave species that cannot be mapped onto the system are therefore to be rejected (Barbera 1984, 240).
Medieval theory
In chant theory beginning in the 9th century, the New Exposition of the composite treatise called Alia musica developed an eightfold modal systemMusical 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...
from the seven diatonic octave species of ancient Greek theory, transmitted to the West through the Latin writings of Martianus Capella
Martianus Capella
Martianus Minneus Felix Capella was a pagan writer of Late Antiquity, one of the earliest developers of the system of the seven liberal arts that structured early medieval education...
, Cassiodorus
Cassiodorus
Flavius Magnus Aurelius Cassiodorus Senator , commonly known as Cassiodorus, was a Roman statesman and writer, serving in the administration of Theodoric the Great, king of the Ostrogoths. Senator was part of his surname, not his rank.- Life :Cassiodorus was born at Scylletium, near Catanzaro in...
, Isidore of Seville
Isidore of Seville
Saint Isidore of Seville served as Archbishop of Seville for more than three decades and is considered, as the historian Montalembert put it in an oft-quoted phrase, "le dernier savant du monde ancien"...
, and, most importantly, Boethius. Together with the species of fourth and fifth, the octave species continued to be used as a basis of the theory of modes, in combination with other elements, particularly the system of octoechos
Octoechos
Oktōēchos is the name of the eight mode system used for the composition of religious chant in Syrian, Coptic, Byzantine, Armenian, Latin and Slavic churches since the middle ages...
borrowed from the Byzantine Church
State church of the Roman Empire
The state church of the Roman Empire was a Christian institution organized within the Roman Empire during the 4th century that came to represent the Empire's sole authorized religion. Both the Roman Catholic Church and the Eastern Orthodox churches claim to be the historical continuation of this...
(Powers 2001).
Sources
- AristoxenusAristoxenusAristoxenus 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...
. 1954. Aristoxeni elementa harmonica, edited by Rosetta da Rios. Rome: Typis Publicae Officinae Polygraphicae. - Barker, Andrew (ed.) (1984–89). Greek Musical Writings. 2 vols. Cambridge & New York: Cambridge University Press. ISBN 0-521-23593-6 (v. 1) ISBN 0-521-30220-X (v. 2).
- Barbera, André. 1984. "Octave Species". The Journal of Musicology 3, no. 3 (Summer): 229–41.
- CleonidesCleonidesCleonides 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...
. 1965. "Harmonic Introduction," translated by Oliver Strunk. In Source Readings in Music History, vol. 1 (Antiquity and the Middle Ages), edited by Oliver Strunk, 34–46. New York: W. W. Norton. - Gombosi, Otto. 1951. "Mode, Species". Journal of the American Musicological Society 4, no. 1 (Spring): 20–26.
- Powers, Harold SHarold PowersHarold Stone Powers was an American musicologist.Powers attended Stanford University and then Syracuse University, where he received a BMus in 1950. He obtained his Ph.D. from Princeton University in 1959 after studying music theory under Milton Babbitt and Edward T. Cone, and musicology under...
. 2001. "Mode §II: Medieval Modal Theory". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley SadieStanley SadieStanley Sadie CBE was a leading British musicologist, music critic, and editor. He was editor of the sixth edition of the Grove Dictionary of Music and Musicians , which was published as the first edition of the New Grove Dictionary of Music and Musicians.Sadie was educated at St Paul's School,...
and John TyrrellJohn Tyrrell (professor of music)John Tyrrell was born in Salisbury, Southern Rhodesia in 1942. He studied at the universities of Cape Town, Oxford and Brno. In 2000 he was appointed Research Professor at Cardiff University....
. London: Macmillan Publishers. - PtolemyPtolemyClaudius 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...
. 1930. Die Harmonielehre des Klaudios Ptolemaios, edited by Ingemar Düring. Göteborgs högskolas årsskrift 36, 1930:1. Göteborg: Elanders boktr. aktiebolag. Reprint, New York: Garland Publishing, 1980. - Ptolemy. 2000. Harmonics, translated and commentary by Jon Solomon. MnemosyneMnemosyne (journal)Mnemosyne is an academic journal of Classical Studies published by Brill Publishers. It was established in 1852 as a journal of textual criticism. It publishes articles in English, French, German, and Latin. The journal is abstracted and indexed in the Arts and Humanities Citation Index, Current...
, Bibliotheca Classica Batava, Supplementum, 0169-8958, 203. Leiden and Boston: Brill. ISBN 9004115919 - Solomon, Jon. 1984. "Towards a History of Tonoi". The Journal of Musicology 3, no. 3 (Summer): 242–51.
Further reading
- http://www.britannica.com/eb/article-9056731/octave-species
- Chalmers, John H. Jr. 1993. Divisions of the Tetrachord. Hanover, NH: Frog Peak Music. ISBN 0-945996-04-7 available on-line http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/index.html