#tonoi

Unfortunately, there are no surviving writings by either Pythagoras or his followers (although some of his followers are quoted by later authors).  The earliest surviving Greek works on music theory are by Aristoxenus (360 – 300 BC), a pupil of Aristotle.  They are Harmonic Elements and Rhythmic Elements, both written around 330 BC.  Cleonides (c. 100's/200's BC), Claudius Ptolemy (100 – 170 AD) and Aristides Quintilianus (35 – 100 AD) were also important later writers.

These Greek musical theorists defined concepts that we still use today, and concepts that only the Greeks used.  The Greeks valued abstract thought, logic, and systemic definition & classification – this approach has influenced all later Western writings on music. Their writings also showed the Greeks' love of variety, as they describe many different notes, intervals and scales.

Only part of Aristoxenus' Rhythmic Elements survives.  What is left shows that the Greeks considered musical rhythm to be closely aligned with poetic rhythm.  Aristoxenus defines note durations as multiples of a basic unit of time – this is like Greek poetry, which uses patterns of long & short syllables, rather than the stressed & unstressed syllables in English poetry.

In Harmonic Elements, Aristoxenus describes two different types of movement of the voice.  1) Continuous movement (stepwise) going up & down as in speech; 2) Diastematic (intervallic), moving between sustained pitches that are separated by distinct intervals.

A melody consists of a series of notes, each of which are on a single pitch.  An interval is formed between two differently-pitched notes; a scale is a series of 3+ different pitches, going up or down.

These definitions are simple to us, but they formed the basis of Greek musical theory, and all later music theory.  And this system was a great step forward – for example, the Babylonians (a millennium earlier) only had interval names for those formed by certain pairs of open strings on the lyre or harp.

Tetrachords & Genera

The word “tetrachord” literally means “four strings”.  It was four notes spanning a perfect 4th, and there were three genera (sing. genus) – diatonic, chromatic and enharmonic.  The outer two notes were considered to be stationary, while the inner two notes varied to change the genus.  Usually, the smallest intervals were at the bottom, and the largest intervals at the top.

Diatonic genus – Two tones and a semitone (moving downwards).

Chromatic genus – Top interval is a tone and a half (minor 3rd), leaving two semitones below it.

Enharmonic genus – Top interval is two tones (major 3rd), leaving two approximate quarter-tones below it.

The intervals within a genus could vary slightly, giving “shades” within each genus.

Aristoxenus stated that the diatonic genus was the oldest & most natural; the chromatic genus was more recent; and the enharmonic genus was the most refined & difficult to hear.  The Babylonian system used the diatonic system.

The Greater Perfect System

Tetrachords were combined to create a larger range.  The Greater Perfect System was made up of four tetrachords, and the proslambanomenos at the bottom (an “added” note to complete the two octaves).

Two tetrachords were conjunct if they shared a note, but disjunct if they did not.  Tetrachords 1-2 and 3-4 were conjunct, whereas tetrachords 2-3 were disjunct.

The middle note was the mese (middle).  The 3rd tetrachord (below the mese) was the meson, and the 4th tetrachord was the hypaton (first).  The 2nd tetrachord (above the mese) was the diezeugmenon (disjunct), and the 1st tetrachord was the synemmenon (conjunct).

There were no set pitches – what mattered were the intervals between the notes & tetrachords.

Cleonides' Species of Consonances

Κλεονείδης (Cleonides) wrote a treatise on music theory Εἰσαγωγὴ ἁρμονική (Introduction to Harmonics), probably in the 00's AD.

The three main consonances are the 4th, 5th and octave.  Cleonides wrote that within the diatonic genus, these consonances were subdivided into tones and semitones (T & S), but there were a limited number of ways to do this (i.e. a limited number of T/S patterns within them).  He called these patterns species. They are useful in understanding Greek melodies, medieval plainchant, Renaissance polyphony, and even contemporary music.

The diatonic genus usually has the biggest interval (T) at the top, followed by T & S.  But the middle two notes could vary, causing different intervals within the tetrachord.  The defining aspect of the diatonic genus seems to be that the largest interval is a tone, rather than that it is the top interval.

So within the diatonic genus, there are three species of perfect 4th – 1) ascending STT, 2) ascending TTS, 3) ascending TST.

Now for the species of perfect 5th – there are four possible species within the diatonic genus.  They are also ascending – 1) STTT, 2) TTTS, 3) TTST, 4) TSTT.  So there can only be one semitone, and the species depends on where it falls – if there was another semitone, then one of the tones would have to become a minor 3rd, thus changing the genus.

There are seven species of octave.  Each octave is made up of a 4th followed by a 5th (sharing a note where they overlap, so conjunct).  The first three are a 4th + 5th; the last four are a 5th + 4th.

Mixolydian – STT STTT

Lydian – TTS TTTS

Phrygian – TST TTST

Dorian – STTT STT

Hypolydian – TTTS TTS (basically, switching the two sections of the Lydian)

Hypophrygian – TTST TST (switching the Phrygian)

Hypodorian – TSTT STT (This sort of switches the Dorian. But instead of just changing the 4th & 5th around, the new 5th starts on the second note of the old 5th.)

Cleonides gave these octave species the names that “the ancients” apparently used.  Also, the octave species parallel the seven diatonic tunings used by the Babylonians – so that practice was quite likely continued, and there was possibly a continuation of music theory as well.

Later on in the Middle Ages, some music theorists used the same names for the modes, but the note-patterns within them did not match up with the octave species.  Also, an important defining aspect of the modes is that the melody is expected to end on the principal note – this was not the case with the Greek octave species.

Tonoi

The names of the octave species were used for other things, too. Lydian, Phrygian and Dorian were ethnic names that were originally associated with styles of music practised in certain regions of the Greek world.

Plato & Aristotles used these names for ἁρμονίαι (referring to scale types or melodic styles).  Prefixes such as hypo- meant there were more such names in use.

Later, writers such as Aristoxenus, Cleonides and Aristides Quintilianus used these names for up to 15 different τόνοι (tonoi).  A τόνος (tonos) was a scale or set of pitches within a certain region/range of the voice.  Basically, the system of tones was transposed up or down a certain number of semitones.

Cleonides said that the word τόνος was used for four different things: “note, interval, region of the voice, and pitch.  We use it for the region of the voice whenever we speak of Dorian, or Phrygian, or Lydian, or any of the other tones.”

Different τόνοι were associated with different characters & moods, like ἁρμονίαι.  The higher τόνοι were energetic, and the lower τόνοι were sedate.