In the

musical system of ancient Greece The musical system of ancient Greece evolved over a period of more than 500 years from simple scales of tetrachords, or divisions of the perfect fourth, into several complex systems encompassing tetrachords and octaves, as well as octave scales d ...

, an octave species (εἶδος τοῦ διὰ πασῶν, or σχῆμα τοῦ διὰ πασῶν) is a specific sequence of

intervals Interval may refer to: Mathematics and physics * Interval (mathematics), a range of numbers ** Partially ordered set#Intervals, its generalization from numbers to arbitrary partially ordered sets * A statistical level of measurement * Interval e ...

within an

octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...

. In ''

Elementa harmonica ''Elementa harmonica'' is a treatise on the subject of musical scales by Aristoxenus, of which considerable amounts are extant. The work dates to the second half of the 4th century BC. It is the oldest substantially surviving work written on the s ...

'',

Aristoxenus Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been ...

classifies the species as three different

genera Genus ( plural genera ) is a taxonomic rank used in the biological classification of living and fossil organisms as well as viruses. In the hierarchy of biological classification, genus comes above species and below family. In binomial nomenclat ...

, distinguished from each other by the largest intervals in each sequence: the diatonic, chromatic, and enharmonic genera, whose largest intervals are, respectively, a

whole tone In Western music theory, a major second (sometimes also called whole tone or a whole step) is a second spanning two semitones (). A second is a musical interval encompassing two adjacent staff positions (see Interval number for more deta ...

, a

minor third In music theory, a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval number). The minor third is one of two com ...

, and a

ditone In music, a ditone (, from , "of two tones") is the interval of a major third. The size of a ditone varies according to the sizes of the two tones of which it is compounded. The largest is the Pythagorean ditone, with a ratio of 81:64, also cal ...

;

quarter tone A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, a ...

s and

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. It is defined as the interval between two adjacent no ...

s complete the

tetrachord In music theory, a tetrachord ( el, τετράχορδoν; lat, tetrachordum) is a series of four notes separated by three intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency propo ...

s. The concept of octave species is very close to tonoi and akin to

musical scale In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale. Often, especially in the ...

and

mode Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is ...

, and was invoked in Medieval and Renaissance theory of

Gregorian mode A Gregorian mode (or church mode) is one of the eight systems of pitch organization used in Gregorian chant. History The name of Pope Gregory I was attached to the variety of chant that was to become the dominant variety in medieval western and ...

and Byzantine

Octoechos Oktōēchos (here transcribed "Octoechos"; Greek: ;The feminine form exists as well, but means the book octoechos. from ὀκτώ "eight" and ἦχος "sound, mode" called echos; Slavonic: Осмогласие, ''Osmoglasie'' from о́см� ...

Ancient Greek theory

Greek theorists used two terms interchangeably to describe what we call species: ''eidos'' (εἶδος) and ''skhēma'' (σχῆμα), defined as "a change in the arrangement of incomposite ntervalsmaking up a compound magnitude while the number and size of the intervals remains the same"., translated in

Cleonides Cleonides ( el, Κλεονείδης) is the author of a Greek treatise on music theory titled Εἰσαγωγὴ ἁρμονική ''Eisagōgē harmonikē'' (Introduction to Harmonics). The date of the treatise, based on internal evidence, can be e ...

, working in the Aristoxenian tradition, describes three species of

diatessaron The ''Diatessaron'' ( syr, ܐܘܢܓܠܝܘܢ ܕܡܚܠܛܐ, Ewangeliyôn Damhalltê; c. 160–175 AD) is the most prominent early gospel harmony, and was created by Tatian, an Assyrian early Christian apologist and ascetic. Tatian sought to comb ...

, four of

diapente In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval from the first to the last of fi ...

, and seven of diapason in the diatonic genus.

Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...

in his ''Harmonics'' calls them all generally "species of primary consonances" (εἴδη τῶν πρώτων συμφωνιῶν). In the

Latin West Greek East and Latin West are terms used to distinguish between the two parts of the Greco-Roman world and of Medieval Christendom, specifically the eastern regions where Greek was the '' lingua franca'' (Greece, Anatolia, the southern Balkans, t ...

Boethius Anicius Manlius Severinus Boethius, commonly known as Boethius (; Latin: ''Boetius''; 480 – 524 AD), was a Roman senator, consul, ''magister officiorum'', historian, and philosopher of the Early Middle Ages. He was a central figure in the tr ...

, in his ''Fundamentals of Music'', calls them "species primarum consonantiarum". Boethius and

Martianus Martianus Minneus Felix Capella (fl. c. 410–420) was a jurist, polymath and Latin prose writer of late antiquity, one of the earliest developers of the system of the seven liberal arts that structured early medieval education. He was a nati ...

, in his ''De Nuptiis Philologiae et Mercurii'', further expanded on Greek sources and introduced their own modifications to Greek theories.

Octave species

The most important of all the consonant species was the octave species, because "from the species of the consonance of the diapason arise what are called ''

modes Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is ...

''". The basis of the octave species was the smaller category of species of the

perfect fourth A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending interval from C to ...

, or ''diatessaron''; when filled in with two intermediary notes, the resulting four notes and three consecutive intervals constitute a "

". The species defined by the different positioning of the intervals within the tetrachord in turn depend upon

genus Genus ( plural genera ) is a taxonomic rank used in the biological classification of extant taxon, living and fossil organisms as well as Virus classification#ICTV classification, viruses. In the hierarchy of biological classification, genus com ...

first being established. Incomposite in this context refers to intervals not composed of smaller intervals. Greek Phrygian enharmonic genus

Most Greek theorists distinguish three genera of the tetrachord:

enharmonic In modern musical notation and tuning, an enharmonic equivalent is a note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently. The enharmonic spelling of a written n ...

chromatic Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, ...

, and

diatonic Diatonic and chromatic are terms in music theory that are most often used to characterize Scale (music), scales, and are also applied to musical instruments, Interval (music), intervals, Chord (music), chords, Musical note, notes, musical sty ...

. 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. 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: : Species of the

perfect fifth In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval fro ...

(''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 and, similarly, the lower interval of the ''pyknon'' must be smaller or equal to the higher one. The whole tone added to create 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.( 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. 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. 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 labels the resulting fourteen pitches with the (Greek) letters from Α ( Alpha α) to Ο ( Omega Ω). (A diagram is shown at systema 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". Those octave species that cannot be mapped onto the system are therefore rejected.

Medieval theory

In chant theory beginning in the 9th century, the ''New Exposition'' of the composite treatise called ''Alia musica'' developed an eightfold modal system from the seven diatonic octave species of ancient Greek theory, transmitted to the West through the Latin writings of

Martianus Capella Martianus Minneus Felix Capella (fl. c. 410–420) was a jurist, polymath and Latin prose writer of late antiquity, one of the earliest developers of the system of the seven liberal arts that structured early medieval education. He was a nati ...

Cassiodorus Magnus Aurelius Cassiodorus Senator (c. 485 – c. 585), commonly known as Cassiodorus (), was a Roman statesman, renowned scholar of antiquity, and writer serving in the administration of Theodoric the Great, king of the Ostrogoths. ''Senator'' w ...

Isidore of Seville Isidore of Seville ( la, Isidorus Hispalensis; c. 560 – 4 April 636) was a Spanish scholar, theologian, and archbishop of Seville. He is widely regarded, in the words of 19th-century historian Montalembert, as "the last scholar of ...

, and, most importantly, Boethius. Together with the species of fourth and fifth, the octave species remained in use as a basis of the theory of modes, in combination with other elements, particularly the system of

octoechos Oktōēchos (here transcribed "Octoechos"; Greek: ;The feminine form exists as well, but means the book octoechos. from ὀκτώ "eight" and ἦχος "sound, mode" called echos; Slavonic: Осмогласие, ''Osmoglasie'' from о́см� ...

borrowed from the

Eastern Orthodox Church The Eastern Orthodox Church, also called the Orthodox Church, is the second-largest Christian church, with approximately 220 million baptized members. It operates as a communion of autocephalous churches, each governed by its bishops via ...

. Species theory in general (not just the ''octave'' species) remained an important theoretical concept throughout Middle Ages. The following appreciation of species as a structural basis of a mode, found in the ''Lucidarium'' (XI, 3) of Marchetto (ca. 1317), can be seen as typical:

We declare that those who judge the mode of a melody exclusively with regard to ascent and descent cannot be called musicians, but rather blind men, singers of mistake... for, as
Bernard Bernard (''Bernhard'') is a French and West Germanic masculine given name. It is also a surname. The name is attested from at least the 9th century. West Germanic ''Bernhard'' is composed from the two elements ''bern'' "bear" and ''hard'' "brav ...
said, "species are dishes at a musical banquet; they create modes."

References

Sources * * * * * * * * * *

Ancient Greek theory

Octave species

Medieval theory

References

Further reading