Chromatic genus
Encyclopedia
In Ancient Greek
music theory, the chromatic genus (also known as chrōma, from the Greek
word χρώμα, "colour") is a genus of the tetrachord
characterized by an upper interval of a minor third
. The two middle notes of the tetrachord were movable (kinoumenoi) while the two outer notes were immovable (hestōtes) (Mathiesen 2001, 6.iii.c). The movable members of the tetrachord (the pyknon) is divided into two adjacent semitone
s (hence this genus is the origin of the modern term, chromatic
).
Note that the scale generated by the chromatic genus is not like the modern chromatic scale
. The modern (18th century) well-tempered
chromatic scale has 12 pitches to the octave
, and consists of semitones of various sizes; the equal temperament
common today, on the other hand, also has 12 pitches to the octave, but the semitones are all of the same size. In contrast, the ancient Greek chromatic scale had seven tones to the octave (assuming alternating conjunct and disjunct tetrachords), and had undivided minor thirds as well as semitones.
The (Dorian) scale generated from the chromatic genus is composed of two chromatic tetrachords:
Whereas in modern music theory, a chromatic scale is:
gave the traditional Pythagorean tuning
of the chromatic genus:
hypate parhypate lichanos mese
4/3 81/64 32/27 1/1
| 256/243 | 2187/2048 | 32/27 |
-498 -408 -294 0 cents
Archytas
replaced the 81/64 with the simpler and more consonant 9/7, which he used in all three of his genera:
hypate parhypate lichanos mese
4/3 9/7 32/27 1/1
| 28/27 | 243/224 | 32/27 |
-498 -435 -294 0 cents
Didymus
's chromatic has only 5-limit
intervals, with the smallest possible numerators and denominators. Also note that the successive intervals are all superparticular numbers:
hypate parhypate lichanos mese
4/3 5/4 6/5 1/1
| 16/15 | 25/24 | 6/5 |
-498 -386 -316 0 cents
the chromatic genus is the genus on which the 2nd mode and 2nd plagal mode are based. The "extra" mode nenano
is also based on this genus.
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...
music theory, the chromatic genus (also known as chrōma, from the Greek
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...
word χρώμα, "colour") is a genus 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...
characterized by an upper interval of 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...
. The two middle notes of the tetrachord were movable (kinoumenoi) while the two outer notes were immovable (hestōtes) (Mathiesen 2001, 6.iii.c). The movable members of the tetrachord (the pyknon) is divided into two adjacent 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 (hence this genus is the origin of the modern term, chromatic
Chromatic scale
The chromatic scale is a musical scale with twelve pitches, each a semitone apart. On a modern piano or other equal-tempered instrument, all the half steps are the same size...
).
Note that the scale generated by the chromatic genus is not like the modern chromatic scale
Chromatic scale
The chromatic scale is a musical scale with twelve pitches, each a semitone apart. On a modern piano or other equal-tempered instrument, all the half steps are the same size...
. The modern (18th century) well-tempered
Well temperament
Well temperament is a type of tempered tuning described in 20th-century music theory. The term is modelled on the German word wohltemperiert which appears in the title of J.S. Bach's famous composition, The Well-Tempered Clavier...
chromatic scale has 12 pitches to the 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"...
, and consists of semitones of various sizes; the equal temperament
Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
common today, on the other hand, also has 12 pitches to the octave, but the semitones are all of the same size. In contrast, the ancient Greek chromatic scale had seven tones to the octave (assuming alternating conjunct and disjunct tetrachords), and had undivided minor thirds as well as semitones.
The (Dorian) scale generated from the chromatic genus is composed of two chromatic tetrachords:
Whereas in modern music theory, a chromatic scale is:
- D D E F F G G A A B C C D D E ...
Tunings of the chromatic
Thrasyllus of MendesThrasyllus of Mendes
Thrasyllus of Mendes, whose full name was Tiberius Claudius Thrasyllus , was an Egyptian Greek grammarian and literary commentator from Mendes, Egypt...
gave the traditional 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...
of the chromatic genus:
hypate parhypate lichanos mese
4/3 81/64 32/27 1/1
| 256/243 | 2187/2048 | 32/27 |
-498 -408 -294 0 cents
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
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....
replaced the 81/64 with the simpler and more consonant 9/7, which he used in all three of his genera:
hypate parhypate lichanos mese
4/3 9/7 32/27 1/1
| 28/27 | 243/224 | 32/27 |
-498 -435 -294 0 cents
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
Didymus
Didymus the Musician
Didymus the Musician was a music theorist in Rome of the end of the 1st century BC or beginning of the 1st century AD, who combined elements of earlier theoretical approaches with an appreciation of the aspect of performance...
's chromatic has only 5-limit
Limit (music)
In music theory, limit or harmonic limit is a way of characterizing the harmony found in a piece or genre of music, or the harmonies that can be made using a particular scale. The term was introduced by Harry Partch, who used it to give an upper bound on the complexity of harmony; hence the name...
intervals, with the smallest possible numerators and denominators. Also note that the successive intervals are all superparticular numbers:
hypate parhypate lichanos mese
4/3 5/4 6/5 1/1
| 16/15 | 25/24 | 6/5 |
-498 -386 -316 0 cents
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
Byzantine Music
In Byzantine musicByzantine music
Byzantine music is the music of the Byzantine Empire composed to Greek texts as ceremonial, festival, or church music. Greek and foreign historians agree that the ecclesiastical tones and in general the whole system of Byzantine music is closely related to the ancient Greek system...
the chromatic genus is the genus on which the 2nd mode and 2nd plagal mode are based. The "extra" mode nenano
Nenano
Phthora Nenano is the name of one of the two "extra" modes in the Byzantine Octoechos—an eight mode system, which was created by a reform of the Monastery Agios Sabas, near Jerusalem, during the seventh century...
is also based on this genus.
Sources
- Mathiesen, Thomas J. 2001. "Greece, §I: Ancient". 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.