Diatonic genus
Encyclopedia
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 other two intervals vary among different tunings.
The word is derived either from the Greek, dia (διά) and tonos (τόνος), meaning "proceeding by whole tones" (Drabkin n.d.), or "through, at the interval of" a "tone" (OED), or from Greek dia and tonikos, meaning "at intervals of a tone" (Dunsby 2002).
of the diatonic, also known as Ptolemy
's "ditonic diatonic", has two identical 9/8 tones in succession, making the other interval 256/243:
hypate parhypate lichanos mese
| 256/243 | 9/8 | 9/8 |
-498 -408 -204 0 cents
However, the most common tuning in practice from about the 4th century BC to the 2nd century AD appears to have been Archytas
's diatonic, or Ptolemy's "tonic diatonic", which has the superparticular 28/27 instead of the complex 256/243 for the lowest interval:
hypate parhypate lichanos mese
| 28/27 | 8/7 | 9/8 |
-498 -435 -204 0 cents
Ptolemy described his "equable" or "even diatonic" as sounding foreign or rustic, and its neutral second
s are reminiscent of scales used in Arab music
. It is based on an equal division of string lengths, which implies a harmonic series
of pitch frequencies:
hypate parhypate lichanos mese
| 12/11 | 11/10 | 10/9 |
-498 -347 -182 0 cents
most of the modes of the Octoechos
are based on the diatonic genus, apart from the 2nd mode (both authentic and plagal) which is based on the chromatic genus
. Byzantine music theory distinguishes between two tunings of the diatonic genus, the so-called hard diatonic on which the 3rd mode and two of the grave modes are based, and the soft diatonic on which the 1st mode (both authentic and plagal) and the 4th mode (both authentic and plagal) are based. The hard tuning of the diatonic genus in Byzantine music may also be referred to as the enharmonic genus; an unfortunate name that persisted, since it can be confused with the ancient enharmonic genus
.
Ancient Greece
Ancient Greece is a civilization belonging to a period of Greek history that lasted from the Archaic period of the 8th to 6th centuries BC to the end of antiquity. Immediately following this period was the beginning of the Early Middle Ages and the Byzantine era. Included in Ancient Greece is the...
music theory
Music theory
Music theory is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers' techniques across or within genres, styles, or historical periods...
, the diatonic genus is the division 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...
from which the modern diatonic scale
Diatonic scale
In music theory, a diatonic scale is a seven note, octave-repeating musical scale comprising five whole steps and two half steps for each octave, in which the two half steps are separated from each other by either two or three whole steps...
evolved. The distinguishing characteristic of the diatonic genus is that its largest interval
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...
is about the size of a 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...
. The other two intervals vary among different tunings.
The word is derived either from the Greek, dia (διά) and tonos (τόνος), meaning "proceeding by whole tones" (Drabkin n.d.), or "through, at the interval of" a "tone" (OED), or from Greek dia and tonikos, meaning "at intervals of a tone" (Dunsby 2002).
Tunings of the diatonic
The traditional Pythagorean tuningPythagorean 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 diatonic, also known as 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...
's "ditonic diatonic", has two identical 9/8 tones in succession, making the other interval 256/243:
hypate parhypate lichanos mese
| 256/243 | 9/8 | 9/8 |
-498 -408 -204 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...
However, the most common tuning in practice from about the 4th century BC to the 2nd century AD appears to have been 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....
's diatonic, or Ptolemy's "tonic diatonic", which has the superparticular 28/27 instead of the complex 256/243 for the lowest interval:
hypate parhypate lichanos mese
| 28/27 | 8/7 | 9/8 |
-498 -435 -204 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...
Ptolemy described his "equable" or "even diatonic" as sounding foreign or rustic, and its neutral second
Neutral second
A neutral second or medium second is a musical interval wider than a minor second and narrower than a major second. Three distinct intervals may be termed neutral seconds:...
s are reminiscent of scales used in Arab music
Arab music
Arabic music or Arab music is the music of the Arab World, including several genres and styles of music ranging from Arabic classical to Arabic pop music and from secular to sacred music....
. It is based on an equal division of string lengths, which implies a harmonic series
Harmonic series (mathematics)
In mathematics, the harmonic series is the divergent infinite series:Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are 1/2, 1/3, 1/4, etc., of the string's fundamental wavelength...
of pitch frequencies:
hypate parhypate lichanos mese
| 12/11 | 11/10 | 10/9 |
-498 -347 -182 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...
most of the modes of the 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...
are based on the diatonic genus, apart from the 2nd mode (both authentic and plagal) which is based on the chromatic genus
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...
. Byzantine music theory distinguishes between two tunings of the diatonic genus, the so-called hard diatonic on which the 3rd mode and two of the grave modes are based, and the soft diatonic on which the 1st mode (both authentic and plagal) and the 4th mode (both authentic and plagal) are based. The hard tuning of the diatonic genus in Byzantine music may also be referred to as the enharmonic genus; an unfortunate name that persisted, since it can be confused with the ancient enharmonic genus
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...
.
See also
- Genus (music)
- Chromatic genusChromatic genusIn 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...
- Enharmonic genusEnharmonic genusThe 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...
- Diatonic and chromaticDiatonic and chromaticDiatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to intervals, chords, notes, musical styles, and kinds of harmony...
- Pythagorean intervalPythagorean intervalIn 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...
Further reading
- Chalmers, John H. Jr. Divisions of the Tetrachord. Frog Peak MusicFrog Peak MusicFrog Peak Music is a composer's collective that produces and distributes experimental works, and functions as a home for its artists. It was co-founded in 1984 by Jody Diamond and Larry Polansky....
, 1993. ISBN 0-945996-04-7