Genus (music)
In the musical system of ancient Greece, genus is a term used to describe certain classes of intonations of the two movable notes within a tetrachord. The tetrachordal system was inherited by the Latin medieval theory of scales and by the modal theory of Byzantine music; it may have been one source of the later theory of the jins of Arabic music. In addition, Aristoxenus calls some patterns of rhythm "genera".
Tetrachords
According to the system of Aristoxenus and his followers—Cleonides, Bacchius, Gaudentius, Alypius, Bryennius, and Aristides Quintilianus—the paradigmatic tetrachord was bounded by the fixed tones hypate and mese, which are a perfect fourth apart and do not vary from one genus to another. Between these are two movable notes, called parhypate and lichanos. The upper tone, lichanos, can vary over the range of a whole tone, whereas the lower note, parhypate, is restricted to the span of a quarter tone. However, their variation in position must always be proportional. This interval between the fixed hypate and movable parhypate cannot ever be larger than the interval between the two movable tones. When the composite of the two smaller intervals is less than the remaining interval, the three-note group is called pyknon.The positioning of these two notes defined three genera: the diatonic, chromatic, and enharmonic. The first two of these were subject to further variation, called shades—χρόαι —or species—εἶδη. For Aristoxenus himself, these shades were dynamic: that is, they were not fixed in an ordered scale, and the shades were flexible along a continuum within certain limits. Instead, they described characteristic functional progressions of intervals, which he called "roads", possessing different ascending and descending patterns while nevertheless remaining recognisable. For his successors, however, the genera became fixed intervallic successions, and their shades became precisely defined subcategories. Furthermore, in sharp contrast to the Pythagoreans, Aristoxenos deliberately avoids numerical ratios. Instead, he defines a whole tone as the difference between a perfect fifth and a perfect fourth, and then divides that tone into semitones, third-tones, and quarter tones, to correspond to the diatonic, chromatic, and enharmonic genera, respectively.
Diatonic
Aristoxenus describes the diatonic genus as the oldest and most natural of the genera. It 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 according to the tunings of the various shades.Etymology
The English word diatonic is ultimately from the, itself from, of disputed etymology.Most plausibly, it refers to the intervals being "stretched out" in that tuning, in contrast to the other two tunings, whose lower two intervals were referred to as, from. This takes, to mean "interval of a tone"; see Liddell and Scott's and Barsky, below.
Alternatively, it could mean "through the tones", interpreting as "through". See also Barsky: "There are two possible ways of translating the Greek term 'diatonic': 'running through tones', i.e. through the whole tones; or a 'tensed' tetrachord filled up with the widest intervals".
The second interpretation would be justified by consideration of the pitches in the diatonic tetrachord, which are more equally distributed than in the chromatic and enharmonic tetrachords, and are also the result of tighter stretching of the two variable strings. It is perhaps also sounder on linguistic morphological grounds. Compare diameter as "across/width distance".
A completely separate explanation of the origins of the term diatonic appeals to the generation of the diatonic scale from "two tones": "Because the musical scale is based entirely on octaves and fifths, that is, two notes, it is called the 'diatonic scale' ". But this ignores the fact that it is the element di- that means "two", not the element dia-, which has "through" among its meanings. There is a Greek term, which is applied to an interval equivalent to two tones. It yields the English words ditone and ditonic, but it is quite distinct from διάτονος.
The Byzantine theorist George Pachymeres consider the term derived from, meaning "to stretch to the end", because "...the voice is most stretched by it".
Yet another derivation assumes the sense "through the tones" for διάτονος, but interprets tone as meaning individual note of the scale: "The word diatonic means 'through the tones' ". This is not in accord with any accepted Greek meaning, and in Greek theory it would fail to exclude the other tetrachords.
The fact that τόνος itself has at least four distinct meanings in Greek theory of music contributes to the uncertainty of the exact meaning and derivation of διατονικός, even among ancient writers: τόνος may refer to a pitch, an interval, a "key" or register of the voice, or a mode.
Shades or tunings
The diatonic tetrachord can be "tuned" using several shades or tunings. Aristoxenus describes two shades of the diatonic, which he calls συντονόν and μαλακόν. Syntonón and malakón can be translated as "tense" and "relaxed", corresponding to the tension in the strings. These are often translated as "intense" and "soft", as in Harry Partch's influential Genesis of a Music, or alternatively as "sharp" and "soft". The structures of some of the most common tunings are the following:The traditional Pythagorean tuning of the diatonic, also known as Ptolemy's ditonic diatonic, has two identical 9:8 tones in succession, making the other interval a Pythagorean limma :
hypate parhypate lichanos mese
4:3 81:64 9:8 1:1
| 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 an 8:7 tone and the superparticular 28:27 instead of the complex 256:243 for the lowest interval:
hypate parhypate lichanos mese
4:3 9:7 9:8 1:1
| 28:27 | 8:7 | 9:8 |
-498 -435 -204 0 cents
Didymus described the following tuning, similar to Ptolemy's later tense diatonic, but reversing the order of the 10:9 and 9:8, namely:
hypate parhypate lichanos mese
4:3 5:4 9:8 1:1
| 16:15 | 10:9 | 9:8 |
-498 -386 -204 0 cents
Ptolemy, following Aristoxenus, also described "tense" and "relaxed" tunings. His "tense diatonic", as used in Ptolemy's intense diatonic scale, is:
hypate parhypate lichanos mese
4:3 5:4 10:9 1:1
| 16:15 | 9:8 | 10:9 |
-498 -386 -182 0 cents
Ptolemy's "relaxed diatonic" was:
hypate parhypate lichanos mese
4:3 80:63 8:7 1:1
| 21:20 | 10:9 | 8:7 |
-498 -413 -231 0 cents
Ptolemy described his "equable" or "even diatonic" as sounding foreign or rustic, and its neutral seconds are reminiscent of scales used in Arabic music. It is based on an equal division of string lengths, which implies a harmonic series of pitch frequencies:
hypate parhypate lichanos mese
4:3 11:9 10:9 1:1
| 12:11 | 11:10 | 10:9 |
-498 -347 -182 0 cents
Byzantine music
In Byzantine music most of the modes of the octoechos are based on the diatonic genus, apart from the second mode 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 third mode and two of the grave modes are based, and the "soft diatonic" on which the first mode and the fourth mode 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.Chromatic
Aristoxenus describes the chromatic genus as a more recent development than the diatonic. It is characterized by an upper interval of a minor third. The pyknon, consisting of the two movable members of the tetrachord, is divided into two adjacent semitones.The scale generated by the chromatic genus is not like the modern twelve-tone chromatic scale. The modern well-tempered chromatic scale has twelve pitches to the octave, and consists of semitones of various sizes; the equal temperament common today, on the other hand, also has twelve pitches to the octave, but the semitones are all of the same size. In contrast, the ancient Greek chromatic scale had seven pitches to the octave, and had incomposite minor thirds as well as semitones and whole tones.
The scale generated from the chromatic genus is composed of two chromatic tetrachords:
File:Greek Dorian chromatic genus.png|thumb|center|250px|Chromatic genus of the Dorian octave species
whereas in modern music theory, a "chromatic scale" is:
Shades
The number and nature of the shades of the chromatic genus vary amongst the Greek theorists. The major division is between the Aristoxenians and the Pythagoreans. Aristoxenus and Cleonides agree there are three, called soft, hemiolic, and tonic. Ptolemy, representing a Pythagorean view, held that there are five.Tunings
gives an incomplete account of Thrasyllus of Mendes' formulation of the greater perfect system, from which the diatonic and enharmonic genera can be deduced.For the chromatic genus, however, all that is given is a 32:27 proportion of mese to lichanos. This leaves 9:8 for the pyknon, but there is no information at all about the position of the chromatic parhypate and therefore of the division of the pyknon into two semitones, though it may have been the limma of 256:243, as Boethius does later. Someone has referred to this speculative reconstructions as 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 used the simpler and more consonant 9:7, which he used in all three of his genera. His chromatic division is:
hypate parhypate lichanos mese
4:3 9:7 32:27 1:1
| 28:27 | 243:224 | 32:27 |
-498 -435 -294 0 cents
According to Ptolemy's calculations, Didymus's chromatic has only 5-limit intervals, with the smallest possible numerators and denominators. The successive intervals are all superparticular ratios:
hypate parhypate lichanos mese
4:3 5:4 6:5 1:1
| 16:15 | 25:24 | 6:5 |
-498 -386 -316 0 cents