Musical system of ancient Greece
Note that Greek theorists described scales as descending from higher pitch to lower, which is the opposite of modern practice and caused considerable confusion among Renaissance interpreters of ancient musicological texts.
To retain the logic of the internal divisions of the tetrachords and avoid the Meson being forced into three whole tone steps (b–a–g–f), an interstitial note, the diazeuxis ('dividing'), was introduced between the paramese and mese.
To bridge the inconsistency of the diazeuxis, the system allowed moving the nete one step up, permitting the construction of the Synemmenon ('conjunct') tetrachord, shown at the far left of the diagram.
In sum, it is clear that the Ancient Greeks conceived of a unified system with the tetrachord as the basic structure, but the octave as the principle of unification.
[12] The next notable Pythagorean theorist known today is Archytas, contemporary and friend of Plato, who explained the use of arithmetic, geometric and harmonic means in tuning musical instruments.
[13] Archytas provided a rigorous proof that the basic musical intervals cannot be divided in half, or in other words, that there is no mean proportional between numbers in super-particular ratio (octave 2:1, fourth 4:3, fifth 3:2, 9:8).
[1] The three genera of tetrachords recognized by Archytas have the following ratios: These three tunings appear to have corresponded to the actual musical practice of his day.
[14] The genera arose after the framing interval of the tetrachord was fixed, because the two internal notes (called lichanoi and parhypate) still had variable tunings.
The joining of a tetrachord and a pentachord yields an octachord, i.e. the complete seven-tone scale plus a higher octave of the base note.
[1] Having elaborated the Systema teleion, the most significant individual system, that of Aristoxenos, which influenced much classification well into the Middle Ages, will be examined.
[23] The ancient writer Cleonides attributes thirteen tonoi to Aristoxenus, which represent a transposition of the tones of the Pythagorean system into a more uniform progressive scale over the range of an octave.
[18] According to Cleonides,[23] these transpositional tonoi were named analogously to the octave species, supplemented with new terms to raise the number of degrees from seven to thirteen.
[19] According to the interpretation of at least two modern authorities, in the Aristoxenian tonoi the Hypodorian is the lowest, and the Mixolydian is next-to-highest: the reverse of the case of the octave species.
[a] The double-flats () are used merely to adhere to the modern convention of that all standard pitches in an octave are assigned a distinct, sequential alphabetic letter.
The superscript symbol after a letter indicates an approximately half-flattened version of the named note; the exact degree of flattening intended depending on which of several tunings was used.
[25]The superficial resemblance of these octave species with the church modes is misleading: The conventional representation as a section (such as C D E F followed by D E F G) is incorrect: The species were re-tunings of the central octave such that the sequences of intervals (the cyclical modes divided by ratios defined by genus) corresponded to the notes of the Perfect Immutable System described above.
[32] When the late 6th-century poet Lasus of Hermione referred to the Aeolian harmonia, for example, he was more likely thinking of a melodic style characteristic of Greeks speaking the Aeolic dialect than of a scale pattern.
[33] In the Republic, Plato uses the term inclusively to encompass a particular type of scale, range and register, characteristic rhythmic pattern, textual subject, etc.
[18] The philosophical writings of Plato and Aristotle (c. 350 BCE) include sections that describe the effect of different harmoniai on mood and character formation (see below on ethos).
[35])The ancient Greeks have used the word ethos (ἔθος or ἦθος), in this context best rendered by "character" (in the sense of patterns of being and behaviour, but not necessarily with "moral" implications), to describe the ways music can convey, foster, and even generate emotional or mental states.
Aristoxenus was the first Greek theorist to point out that ethos does not only reside in the individual parameters but also in the musical piece as a whole (cited in Pseudo-Plutarch, De Musica 32: 1142d ff; see also Aristides Quintilianus 1.12).
The Greeks were interested in musical ethos particularly in the context of education (so Plato in his Republic and Aristotle in his eighth book of his Politics), with implications for the well-being of the State.
Melic and rhythmic composition (respectively, melopoiïa and rhuthmopoiïa) were the processes of selecting and applying the various components of melos and rhythm to create a complete work.
