Music theory

This page is a short course in the ideas that Greek music rests on. It starts from nothing. Each tab explains one idea in plain words, then lets you hear it, then gives the Greek terms, and ends with what the Greeks themselves said about it. The later Music pages assume these ideas, so this is the place to begin.

High and low

Some sounds are high and some are low. A small bird sings high. A large drum booms low. This quality of a sound is called its pitch.

Every sound is a vibration. When a lyre string is plucked, it swings quickly to and fro. Each swing pushes the air beside it, and the air passes the movement on to the ear.

A string that vibrates faster gives a higher note. A string that vibrates more slowly gives a lower one.^[1] The number of vibrations in one second is called the frequency of the note. Frequency is counted in hertz, written Hz: a note of 220 Hz vibrates 220 times every second.

Pitch is not the same as loudness. A string plucked hard swings wider, so it sounds louder. But it still swings to and fro at the same rate, so its pitch stays the same.^[2]

Hear it

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Naming the notes

Musicians name notes with the letters a to g. After g the letters start again, because the eighth note above a sounds like a higher a.^[3] To tell the different a’s apart, this site uses a common convention. Capital letters stand for the lowest octave used, A to G. Plain small letters stand for the next octave up, a to g. A stroke marks each octave above that: a′, then a″.^[4]

On this page the note a sounds at 220 Hz. That is the a below middle c on a piano. The modern editions write the Greek note sign C as this a.^[5]

We do not know the exact pitch the Greeks sang at. Pitch may also have differed from one performance to the next.^[4] The modern editions write the notes by a convention, and that convention probably sounds about a minor third too high.^[5] You can hear the difference further on.^[6]

The Greek terms

The Greeks did not usually call notes “high” and “low”. They called them “sharp” and “heavy”.^[7] The word phthongos could mean any sound made by the voice. In the theory of music it means a single note.^[8] It is the second half of the English word “diphthong”.

What the Greeks said

The first Greek account of sound comes from Archytas of Tarentum, a friend of Plato. He taught that there is no sound without an impact of one moving body on another. He also thought that a faster impact gave a higher note.^[9] His examples mixed up pitch and loudness, but he had found the link between motion and pitch.

A short treatise of about 300 BC, the Sectio Canonis, “The Division of the Ruler”, states the true cause. Notes are made of movements. Movements that come closer together give a higher note, and movements spaced further apart give a lower one.^[10] That is what we now call frequency.

Aristoxenus, the great theorist of the fourth century BC, began from what the ear hears. He noticed that a speaking voice slides up and down without settling on any pitch. A singing voice, by contrast, holds one pitch and then moves cleanly to the next.^[11] Music, for him, is made of these held pitches and the steps between them.^[12]

Notes

1. ^ West 1992, p. 8.
2. ^ Landels 1999, c. p. 136.
3. ^ See the Octave tab.
4. ^ ^{a b} West 1992, p. 12.
5. ^ ^{a b} Pöhlmann and West 2001, p. 7.
6. ^ See the Notation tab.
7. ^ West 1992, p. 64 n. 73.
8. ^ Landels 1999, c. p. 87.
9. ^ Landels 1999, c. pp. 137–138.
10. ^ Landels 1999, c. pp. 145–147.
11. ^ West 1992, pp. 43–44; Landels 1999, c. pp. 86–87.
12. ^ See the Tone and semitone tab.

Sing a note, and then ask a child to sing “the same note”. The child will usually sing a higher note that still sounds like yours. The two notes are an octave apart.

Two notes that sound alike

Notes an octave apart blend so well that, sounded together, they seem almost to be one note. That is why they share a letter name. A scale that starts on one a feels complete when it reaches the next a above. The keyboard of a piano shows this. Its pattern of white and black keys repeats every octave.^[1]

The reason lies in the vibrations. The higher note of an octave vibrates exactly twice as fast as the lower one. Their ratio is 2 to 1, written 2:1. So every peak of the slower wave meets every second peak of the faster wave. The more often the peaks meet, the better two notes blend.^[1]

The same ratio holds for the length of a string. Take two strings of the same material, thickness and tension. A string half as long as the other sounds an octave higher. So does one string stopped at its middle point.^[2]

Hear it

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Octaves and their letters

Because the octave repeats, notes an octave apart get the same letter. The octave marks tell them apart. On this site A is 110 Hz, a is 220 Hz, a′ is 440 Hz and a″ is 880 Hz.^[3] Each a vibrates twice as fast as the one below it.

The octave is large. Between its two notes a scale fits several smaller steps. A modern scale has seven different notes in the octave, and the eighth is the first again.

The Greeks built their octave in a special way. They did not divide it straight away into small steps. They first split it into two smaller frames, a fourth and a fifth, and filled those in.^[4] These two frames come next.^[5]

Men and boys

When men and boys sing the same tune together, the boys’ voices sound an octave higher. The Greeks knew this well. Men and boys sometimes sang together in this way. Octaves are the only parallel singing that the Greek sources recognise, and other kinds are expressly denied.^[6] Notes an octave apart were thought of as practically the same note.^[7]

The Greek terms

The verb magadizein means to produce an octave concord. It does not mean “to play the harp”, although later writers took magadis for a kind of harp.^[8]

What the Greeks said

The Problems, a collection of questions and answers that goes under Aristotle’s name, discuss singing in parallel. They allow only the octave, and they deny that voices sing together at any other interval.^[9] The same collection uses the verb magadizein for sounding the octave.^[10]

Pindar thought about where the low-pitched lyre called the barbitos came from. He guessed that it was invented to answer the deep Lydian harp, which played its tune doubled at the octave.^[11]

Notes

1. ^ ^{a b} West 1992, p. 8.
2. ^ West 1992, p. 8 n. 12.
3. ^ West 1992, p. 12.
4. ^ West 1992, pp. 160–161.
5. ^ See the Intervals tab.
6. ^ West 1992, pp. 40–41.
7. ^ Landels 1999, c. pp. 106–107.
8. ^ West 1992, pp. 72–73; Anderson 1994, p. 178.
9. ^ West 1992, p. 41 and n. 13.
10. ^ West 1992, p. 73 n. 108.
11. ^ West 1992, p. 58 n. 41.

A tune moves from note to note in steps. Most steps are small. This tab explains the three small steps that Greek music used: the tone, the semitone and the quarter-tone.

The tone

The tone is the ordinary step of a scale. Sing the first two notes of a major scale, “do” and “re”, and you have sung a tone.

The Greeks found the tone in a neat way. It is the difference between two larger distances, the fifth and the fourth.^[1] Go up a fifth from a note, then come down a fourth. You land one tone above where you began.^[2] The higher note of a tone vibrates 9 times for every 8 vibrations of the lower. So the tone’s ratio is 9:8.

A lyre was tuned in exactly this way. The player set one string by ear or from a small pitch-pipe. He then tuned the others from it by fifths and fourths. This method was called “taking by concords”.^[3] Aristoxenus defined his tone by the same rule: up a fifth, then down a fourth.^[4]

The semitone

The semitone is half a tone, more or less. On a piano it is the step from a white key to the black key beside it, or from e to f.

A fourth holds two tones and a semitone. But if you take two true 9:8 tones out of a fourth, the piece left over is not quite half a tone. It is about 12 per cent smaller.^[2] The Pythagoreans called this leftover step the leimma, “the remainder”. Its ratio is 256:243.^[5]

Musicians did not worry about such fine differences. A Greek called any step of about half a tone a hemitonion, just as we say “semitone”.^[6]

The quarter-tone

Greek music also used steps smaller than a semitone. The smallest was the quarter-tone, half of a semitone. A modern keyboard cannot play it, because it falls between the keys.

Aristoxenus held that a quarter-tone is about the smallest step the voice can sing accurately. It is also about the smallest that the ear can recognise.^[7] Quarter-tones belong to the enharmonic genus, one of the three ways of filling a fourth.^[8]

Hear it

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Measuring in cents

The steps are easier to compare with a single measure. Musicians today use the cent. An octave has 1,200 cents, and a modern semitone has exactly 100.^[9] On this scale the Greek tone of 9:8 measures 204 cents. The leimma measures 90 cents, a little less than half a tone.^[10] A quarter-tone is about 50 cents.

Aristoxenus worked by ear rather than by number. In practice his tone was close to 200 cents, which he could halve and quarter.^[11]

The Greek terms

The word diesis changed its meaning over time. Philolaus, a Pythagorean of Socrates’ day, used it for a semitone. Aristoxenus used it only for steps smaller than a semitone.^[12] It may have begun as a pipers’ word, meaning a “letting through” of a little air from a finger-hole.^[13]

What the Greeks said

Aristoxenus began his account of melody with the voice. In speech, he said, the voice slides up and down and never seems to settle on any pitch. In song it holds each pitch and leaps cleanly to the next, so that the pitches between are not heard.^[14] The last two buttons in the figure play both kinds of voice.

Archytas, a Pythagorean of Plato’s time, proved that a tone of 9:8 cannot be split into two equal halves by any ratio of whole numbers. So the Pythagorean semitone, the leimma, had to come out smaller than half a tone.^[15] Aristoxenus ignored the arithmetic. A semitone, for him, was simply a step that sounded like half a tone.^[4]

Notes

1. ^ See the Intervals tab.
2. ^ ^{a b} West 1992, p. 10.
3. ^ Landels 1999, c. p. 93.
4. ^ ^{a b} Landels 1999, c. p. 91.
5. ^ Nowacki 2020, p. 173.
6. ^ Landels 1999, c. p. 90.
7. ^ Landels 1999, c. p. 87.
8. ^ West 1992, p. 162; see the Tetrachord tab.
9. ^ West 1992, p. 11.
10. ^ West 1992, p. 12.
11. ^ West 1992, pp. 166–167.
12. ^ Nowacki 2020, p. 172.
13. ^ Hagel 2009, pp. 443–444.
14. ^ West 1992, pp. 43–44; Landels 1999, c. p. 87.
15. ^ West 1992, pp. 11–12, 235–237.

The distance between two notes is called an interval. A tone is an interval, and so is an octave. This tab is about the intervals the Greeks built their music on, and how they measured them on a string.

Concords and discords

Some intervals sound smooth when their two notes are played together. The notes seem to fit. The Greeks called such an interval a concord. Every other interval was a discord.^[1]

The Greeks recognised only three concords: the fourth, the fifth and the octave. Larger intervals made from them, such as an octave and a fourth, counted too.^[1] Even the intervals we call the major and minor third were discords to a Greek ear.^[2] A discord was not forbidden. It was perfectly acceptable in a melody, but it could not serve as the frame of a scale.^[1]

The names count notes. From e up to a is a fourth, because e, f, g and a are four notes. From e up to b is a fifth: e, f, g, a, b. The fourth and the fifth together make an octave, from e to e′.

Why concords sound smooth

The answer lies in the vibrations again.^[3] In a fifth the higher note vibrates 3 times while the lower vibrates twice. Its ratio is 3:2. In a fourth the ratio is 4:3. So the peaks of the two waves meet often: at every second or third vibration.^[4] Only the octave, at 2:1, has its peaks meet more often.

Ratios combine by multiplying. A fifth and a fourth make an octave because 3/2 × 4/3 = 2.^[5] The tone is what is left when a fourth is taken from a fifth: 3/2 ÷ 4/3 = 9/8.

The monochord

String lengths show the same ratios. Stop a string at its middle and the sounding half gives the octave. Stop it a third of the way along, so that two thirds sound, and you hear the fifth. Let three quarters sound and you hear the fourth.^[6]

The Pythagoreans tested this on the monochord. It is a single string stretched over a ruler, with a bridge that can slide along it.^[7] They called it the kanōn, “the measuring rod”.^[8]

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Measuring in cents

Ratios are hard to compare by eye. Is 32:27 bigger than 9:8, and by how much? So musicians today measure intervals in cents. The octave is divided into 1,200 equal parts, and each modern semitone has 100.^[9] Cents can be added like ordinary numbers. The fifth is 702 cents and the fourth 498, and together they make 1,200.^[10] A fifth on a modern piano is 700 cents, so the Greek fifth is a hair wider.

To turn a ratio into cents, multiply the logarithm of the ratio by about 3,986.^[11] The monochord above does this for you.

The Greek terms

The names of the fourth and the fifth come from the strings of the lyre. They count the strings that the interval reaches across.^[12] The octave is dia pasōn.^[13]

What the Greeks said

Every Greek writer on tuning took it as settled that the octave is 2:1, the fifth 3:2 and the fourth 4:3.^[14] How these numbers were first found is not known.

A famous story tells how Pythagoras passed a smithy and heard the hammers ringing in concords. He found that the hammers’ weights stood in the same ratios. The story is false. The pitch of an anvil depends on the anvil, not on the hammer.^[15] The discovery may have been made by watching a player stop a string, but how is unknown. The monochord was probably built later, to test a theory that was already believed.^[16]

Aristoxenus measured intervals differently. For him an interval was a distance heard by the ear, not a ratio of lengths.^[17] The quarrel between his followers and the Pythagoreans is told elsewhere.^[18]

Notes

1. ^ ^{a b c} West 1992, p. 160.
2. ^ Landels 1999, c. p. 93.
3. ^ See the Octave tab.
4. ^ West 1992, pp. 8–9.
5. ^ West 1992, p. 9.
6. ^ Landels 1999, c. p. 130.
7. ^ West 1992, pp. 240–242.
8. ^ Landels 1999, c. p. 132.
9. ^ Nowacki 2020, p. 171.
10. ^ West 1992, pp. 11–12.
11. ^ Landels 1999, c. pp. 264–266.
12. ^ Landels 1999, c. p. 35; Nowacki 2020, p. 175.
13. ^ Landels 1999, c. p. 95.
14. ^ West 1992, p. 11.
15. ^ West 1992, p. 234; Landels 1999, c. p. 131.
16. ^ Landels 1999, c. pp. 131–132.
17. ^ Landels 1999, c. p. 88.
18. ^ See the Aristoxenus and the Pythagoreans tab of the Scales page.

A modern musician thinks of a scale as an octave cut into steps. A Greek musician started from something smaller: the fourth. Every Greek scale is built out of fourths, each filled with two extra notes.^[1] This four-note unit is the key to the rest of Greek music theory.

Four notes in a fourth

A tetrachord is a group of four notes that spans a fourth. The name means “four strings”. Take the notes e, f, g and a. The outer notes, e and a, are a fourth apart. The two inner notes, f and g, divide the fourth into three steps: a semitone and two tones.^[2]

The two outer notes never change. They are called the standing notes. The two inner notes can move, and they are called the moving notes.^[3] Where the moving notes are placed decides the character of the tetrachord.

The three genera

There are three main ways to place the moving notes. Each way is called a genus (plural genera), Greek for “kind”.^[4]

• In the diatonic genus the steps are a semitone, a tone and a tone: e f g a. This is the pattern most familiar to us.
• In the chromatic genus the steps are a semitone, a semitone and a minor third: e f f♯ a.
• In the enharmonic genus the steps are a quarter-tone, a quarter-tone and two whole tones: e e↑ f a. The arrow marks a note raised by a quarter-tone.

In the chromatic and the enharmonic the two moving notes crowd together at the bottom. The three close notes at the bottom make a cluster called the pyknon, “the close-packed”.^[4] By definition the pyknon is smaller than the large step above it.^[5]

The words “chromatic” and “enharmonic” mean something quite different in modern music.^[6] Here they are only the names of these three ancient patterns.

Hear it and move the notes

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Shades

The three genera are not three fixed points. The moving notes could be placed a little higher or lower, and Aristoxenus named six standard positions, called shades.^[7] They are the enharmonic, three kinds of chromatic and two kinds of diatonic:^[8]

The enharmonic has no variants.^[9] For the Greek writers its most typical sound was not the tiny quarter-tones but the wide gap of two tones above them.^[10]

The Greek terms

What the Greeks said

The music of the fifth century, the century of Pindar and the tragedians, was normally enharmonic. The chromatic, the “colouring”, came in with the professional lyre-singers around the middle of the century. Some held that it made men soft.^[12]

By Aristoxenus’ day, the later fourth century, taste had changed. He complained that performers “sweetened” the small enharmonic steps until they drifted towards the soft chromatic.^[9] Much later, Aristides Quintilianus explained the three genera by the skill they demand. The diatonic is natural to everyone. The chromatic is for trained musicians. The enharmonic is for the most accomplished, and most people cannot sing it at all.^[13]

How the genera began is disputed.^[14]

Notes

1. ^ West 1992, pp. 160–161.
2. ^ Landels 1999, c. pp. 88–89.
3. ^ West 1992, p. 162; Nowacki 2020, p. 175.
4. ^ ^{a b} West 1992, p. 162.
5. ^ Nowacki 2020, pp. 174–175.
6. ^ West 1992, p. 162 n. 1.
7. ^ West 1992, pp. 168–169.
8. ^ Landels 1999, c. pp. 91–92; Nowacki 2020, p. 171.
9. ^ ^{a b} Landels 1999, c. p. 92.
10. ^ Nowacki 2020, p. 172.
11. ^ Landels 1999, c. p. 90.
12. ^ West 1992, pp. 164–165.
13. ^ West 1992, pp. 165–166.
14. ^ See the Tetrachords and genera tab of the Scales page.

One tetrachord spans only a fourth. A tune needs more room. So the Greeks joined tetrachords together, and the way they joined them shaped their whole system of scales.

Two ways to join

Two tetrachords can be joined in two ways.^[1]

• They can share a note. The top note of the lower tetrachord is the bottom note of the upper one: e f g a, then a b♭ c′ d′. This is called conjunction. It gives seven notes spanning a seventh.
• They can be kept a tone apart: e f g a, then b c′ d′ e′. This is called disjunction. It gives eight notes spanning a full octave. The tone between them, from a to b, belongs to neither tetrachord. It is called the disjunction too.

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The two-octave ladder

By the fourth century BC theorists had joined five tetrachords and one extra note into a ladder of two octaves.^[2] It is called the Perfect System, meaning the complete scale.^[3] It was not a tune. It was a map of every note a scale could use. A musician cut the scale for a piece out of it.^[4]

The ladder runs from A up to a′. Its middle note is mesē, the a. From the bottom it goes like this:^[5]

1. A single extra note at the bottom, A. It is called the proslambanomenos, “the note taken in addition”, because it stands outside the tetrachords.^[6]
2. The tetrachord hypatōn, B to e.
3. The tetrachord mesōn, e to a. It is joined to the one below.
4. A tone of disjunction, a to b.
5. The tetrachord diezeugmenōn, b to e′.
6. The tetrachord hyperbolaiōn, e′ to a′. It is joined to the one below.

This ladder is the Greater Perfect System. There is also a shorter one, the Lesser Perfect System. It goes up only to d′. Above mesē it takes a different tetrachord, synēmmenōn, a to d′, which is joined to mesē instead of standing a tone above it. This brings in a b♭.^[7] The two together were called the Unmodulating System, because a musician could move between them without, in theory, changing key.^[8]

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The note names

The names come from the strings of the lyre. They describe each string’s place on the instrument, not its sound.^[9] That is why the lowest note is called hypatē, “topmost”. The player held the lyre tilted away from him, so the lowest-sounding string was the highest one in space.^[10] For the same reason the highest note is nētē, “bottom”.

Each name is a position in the ladder, like “do” or “re” in sol-fa. It does not fix an exact pitch.^[11] The same name is used in more than one tetrachord, so a second word says which one: hypatē hypatōn is “the topmost of the topmost notes”, the B. Hypatē mesōn is “the topmost of the middle notes”, the e.

The Greek terms

What the Greeks said

Mesē was the heart of the system. The Problems note that good melodies keep coming back to it.^[12] If any other string is out of tune, only that note sounds wrong. If mesē is out of tune, the whole melody suffers.^[13] A singer pitched his mesē where his voice was comfortable, and the rest of the scale followed.^[11]

Notes

1. ^ Landels 1999, c. p. 89; West 1992, pp. 160–161.
2. ^ West 1992, pp. 221–222.
3. ^ Nowacki 2020, pp. 172–173.
4. ^ West 1992, pp. 222–223.
5. ^ Nowacki 2020, pp. 172–173; Anderson 1994, pp. 199–201.
6. ^ Landels 1999, c. p. 89.
7. ^ Nowacki 2020, pp. 173–174.
8. ^ West 1992, p. 223; Landels 1999, c. pp. 97–98.
9. ^ West 1992, p. 64.
10. ^ West 1992, p. 64; Hagel 2009, p. 5 n. 21.
11. ^ ^{a b} West 1992, p. 222.
12. ^ West 1992, p. 219.
13. ^ Landels 1999, c. p. 97.

Names like Dorian, Phrygian and Lydian run all through Greek writing about music. They are used for two different things. One is the octave species, a pattern of steps within an octave. The other is the older harmonia, a whole style of tune. This tab takes them one at a time.

The octave species

Play the white keys of a piano from e up to e′. You hear an octave with its semitones in two particular places. Now play from d up to d′. It is still an octave, but the semitones fall in different places, so the scale sounds different.

The Perfect System has the same property.^[1] An octave can be cut out of it starting on any of seven notes. Each cut gives a different order of tones and semitones. Each of these orders is called an octave species.^[2]

Before Aristoxenus, a theorist called Eratocles had already listed the seven species and given them the old regional names.^[3] In the diatonic genus they are:

The Dorian species, e to e′, is the centre of the system. It is made of two tetrachords, e–a and b–e′, with the tone of disjunction between them.

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The harmoniai

Long before anyone counted species, Greek musicians spoke of the Dorian or Lydian harmonia. The word means a “fitting together”. It was first the tuning of a lyre’s strings for music of a particular kind.^[4]

A harmonia was more than a scale. Each had its own set of notes and its own range. It also had typical turns of melody, typical rhythms, and a typical height, high or low.^[5] Down to the fifth century each harmonia stood on its own. Only later were they treated as slices of one master scale.^[6]

For this reason the word is not well translated by “mode”. The harmoniai were idioms of song, with the tunings that went with them.^[7]

Six old tunings

One list claims to give the actual notes of six old harmoniai. It survives in Aristides Quintilianus, a writer of about AD 300, who says they were used by “the most ancient” musicians. They may go back to Damon, an Athenian teacher of music in the later fifth century BC.^[8] All six are enharmonic. Some span less than an octave, some more, and several skip notes.^[9]

Whether the list can be trusted is disputed. Aristides wrote some seven hundred years after the music he describes. Most musicologists, Nowacki reports, will not take the scales as evidence for fifth-century practice.^[10] Hagel, on the other hand, accepts them as genuine fifth-century material.^[11] Listen to them as a possibility, not as a certainty.

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The Greek terms

Greek writers could also use adverbs instead of the noun, and speak of music made “in the Dorian way”.^[12]

What the Greeks said

Plato sorted the harmoniai by their effect on character. He called some “tense”, such as the Mixolydian, and fit for laments. He called others “slack”, such as the Ionian and Lydian, and fit for drinking parties. He kept only the Dorian and the Phrygian for his ideal city.^[13] The Dorian was the most widely respected of all, solemn and manly, and it was the first tuning a boy learned.^[14]

These verdicts belong to the debate about musical character, which is told elsewhere.^[15]

Notes

1. ^ See the Joining tetrachords tab.
2. ^ Anderson 1994, p. 201; Nowacki 2020, p. 175.
3. ^ West 1992, pp. 227–228.
4. ^ Landels 1999, c. pp. 100–101.
5. ^ West 1992, pp. 177–178.
6. ^ Anderson 1994, p. 198.
7. ^ Nowacki 2020, pp. 11, 22–23.
8. ^ West 1992, p. 174.
9. ^ West 1992, pp. 174–175.
10. ^ Nowacki 2020, pp. 20–21.
11. ^ Hagel 2009, pp. 390–392.
12. ^ Nowacki 2020, p. 12.
13. ^ West 1992, p. 179.
14. ^ West 1992, pp. 179–180.
15. ^ See the Harmoniai and ethos tab of the Scales page.

Sing “Happy Birthday” starting on a low note. Then sing it again starting higher. The tune is the same, but it sits at a different height. Moving a whole tune or scale up or down like this is called transposition. A Greek tonos, or key, is the Perfect System transposed to a particular height.^[1]

The same ladder at different heights

The note names of the Perfect System say where a note stands in the ladder. They do not fix its pitch.^[2] The tonos fixes the pitch. Set mesē a tone higher, and every other note of the ladder moves up a tone with it. The word tonos means “tension”. A lyre put into another tonos had its strings at a different tension.^[3]

The keys took the old regional names: Dorian, Phrygian, Lydian and the rest. The Lydian, Phrygian and Dorian appear in every ancient list, a tone apart from each other.^[4] The prefix hyper- came to mean a key a fourth higher, and hypo- a key a fourth lower.^[4]

Why keys were needed

The seven octave species are seven slices of one ladder.^[5] So they lie at seven different heights. The Mixolydian slice, B to b, lies low. The Hypodorian slice, a to a′, lies high. A tune in the Hypodorian would sit too high for a comfortable voice.

The keys solved this. Shift the whole ladder down, and the Hypodorian slice comes down into the singer’s comfortable octave. Shift it up, and the low Mixolydian slice rises into the same octave.^[6] Each key was named after the species it brought into the middle octave.

This explains a puzzle in the names. The Mixolydian species is the lowest slice, but the Mixolydian key is the highest key. The Hypodorian species is the highest slice, but the Hypodorian key is the lowest.^[7]

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Seven, thirteen or fifteen

The number of keys grew over time. Aristoxenus set out thirteen keys a semitone apart. Later writers added two more, making fifteen in five groups of three.^[8] The fifteen are the keys of the surviving scores. Ptolemy, in the second century AD, argued that seven are enough: one for each species, as in the figure.^[9]

A key is not a mode

In the later scores the key works like a key signature. It tells the reader where the notes lie. It does not tell the reader the character of the tune. The Seikilos song, for example, is written in the Iastian key, but its melody moves in the Phrygian species.^[10] To change key in the middle of a piece was called metabolē, “change”.^[11]

The Greek terms

What the Greeks said

Aristoxenus complained that the theorists before him could not agree how many keys there were. Nor could they say why the keys stood a semitone, three quarter-tones or a tone apart.^[13] He compared their confusion to the calendars of the Greek cities, where the tenth of the month at Corinth was the fifth at Athens.^[14]

Ptolemy objected to the long lists. Only seven keys, he said, are needed to bring every species into the singing octave, and the rest repeat one another. His objection came too late. The fifteen keys were already fixed in the notation.^[15]

Notes

1. ^ Nowacki 2020, p. 24.
2. ^ See the Joining tetrachords tab.
3. ^ Landels 1999, c. p. 98; Nowacki 2020, pp. 26–27.
4. ^ ^{a b} Landels 1999, c. p. 98.
5. ^ See the Species and harmoniai tab.
6. ^ West 1992, p. 228; Nowacki 2020, pp. 26–27.
7. ^ Anderson 1994, p. 202; Landels 1999, c. p. 99.
8. ^ West 1992, pp. 230–231; Hagel 2009, p. 4.
9. ^ West 1992, pp. 232–233; Nowacki 2020, pp. 29–33.
10. ^ West 1992, pp. 185–186; Nowacki 2020, pp. 28–29.
11. ^ Nowacki 2020, p. 174.
12. ^ Nowacki 2020, p. 12.
13. ^ West 1992, pp. 228–229.
14. ^ West 1992, p. 228.
15. ^ West 1992, pp. 232–233.

Pitch is one half of music. The other half is time: how long each note lasts, and how the notes group into a beat. This is rhythm. Of all ancient Greek music, rhythm is the part we know best. The tunes are almost all lost, but the poems survive, and their metres record the rhythm.^[1]

Long and short

Greek verse is built from long and short syllables.^[2] In song, a long syllable took a long note and a short syllable a short note. The long note lasted twice as long as the short one.^[3] The words themselves carried the rhythm.^[4]

This is quite unlike English verse. English poetry arranges stressed and unstressed syllables. Greek poetry arranges durations.^[5]

The time-unit

Aristoxenus gave the short note a name: the prōtos chronos, “first time”, the smallest unit of time in a piece. A long note is two of these units.^[6] Greek rhythm is built up from these units, added one after another. A modern bar works the other way: it is a fixed length that is then divided.^[7]

Feet

A short group of longs and shorts that repeats is called a foot. A foot has two parts. The thesis is the down-beat, where a dancer’s foot came down. The arsis is the up-beat, where it lifted.^[8]

The theorists grouped feet by the ratio between their down and up parts. In the dactyl the two parts are equal, 1:1. The iambus is 1:2, and the cretic or paeon 2:3.^[9] In a dactyl the long is the thesis and the two shorts the arsis.^[10] An iambic metron is two iambs; its first half is the thesis and its second the arsis.^[11]

Hear it

This figure needs JavaScript to draw and play.

Epic: a softer rhythm

The first line of the Iliad is a dactylic hexameter: six feet, each a dactyl or a spondee. In Homer’s time such verse was sung to the lyre.

The long note of epic song may not have been exactly twice the short. West argues, from a remark of Dionysius of Halicarnassus and from the verse itself, that the ratio was less than 2 to 1, perhaps about 5 to 3, and could not be measured exactly.^[12] That is nearer the rhythm of ordinary speech. The figure lets you hear both versions of the line.

The Greek terms

What the Greeks said

The Greeks counted rhythm the soul of music. One of the Problems says that melody is slack until rhythm gives it an edge.^[13] Damon, in the fifth century, first sorted rhythms by whether their up and down parts were equal or unequal.^[14]

Aristoxenus separated rhythm from the things it shapes. Words, melody and the dancer’s movement are the material. Rhythm is the ordering of their durations. He therefore refused to measure rhythm by counting syllables, because one syllable can last longer than another: what is fixed is the time.^[6] The Rhythm page follows his theory further.^[15]

Notes

1. ^ West 1992, pp. 129–130.
2. ^ See the 3. Long or short? tab of the Start here page.
3. ^ West 1992, pp. 130–131.
4. ^ Landels 1999, c. pp. 110–111.
5. ^ Landels 1999, c. pp. 111–113.
6. ^ ^{a b} West 1992, pp. 244–245.
7. ^ West 1992, pp. 131–132.
8. ^ West 1992, pp. 133–134; Landels 1999, c. p. 114.
9. ^ West 1992, pp. 130–131, 140–141.
10. ^ West 1992, p. 136.
11. ^ West 1992, p. 137.
12. ^ West 1992, p. 135.
13. ^ West 1992, p. 129.
14. ^ West 1992, pp. 243–244.
15. ^ See the Aristoxenus’ rhythmics tab of the Rhythm page.

The Greeks could write music down. By the third century BC professional musicians had a settled system for it.^[1] This tab explains its basic idea. The Notation page then reads real scores sign by sign.^[2]

Letters above the words

A Greek score is a text with letters written above its syllables. Each letter stands for a note.^[3] There were two sets of signs. Singers read ordinary letters of the alphabet. Players read an older set of signs. Many of them look like letters of a local Greek script, but how the set came about is still unexplained.^[4]

The singers’ letters run down the scale in alphabetical order. The central octave, from f′ down to f, uses the whole alphabet. Every third letter marks a plain note: Γ Ζ Ι Μ Ο Ϲ Φ Ω are f′ e′ d′ c′ b a g f.^[5] The C-shaped letter Ϲ is the lunate form of sigma.

Naturals and sharps

The letters work in groups of three. The third letter of each group is the plain note, called the natural. The two letters before it raise that note a little. They are its first and second sharps.^[6] So Ρ and Π are the two sharps of Ϲ, the note a.

How far a sharp raises the note depends on the genus.^[7] In the enharmonic the first sharp is a quarter-tone up and the second a semitone. In the chromatic they are a semitone and a tone. A first sharp is used only for the lower moving note of a tetrachord.^[8] There is no sign for lowering a note.^[9]

This figure needs JavaScript to draw and play.

How high did it sound?

The letters give the notes relative to each other. They do not tell us the exact pitch. In 1847 the scholars Bellermann and Fortlage chose modern equivalents for the signs. They matched them so that the key written with the plain signs needed no sharps or flats. By his convention the Greek Ϲ is written as a, the a below middle c.^[10] Editions still use this convention, and so does this site.

The convention is only a convenience. The editors agree that it sets everything about a minor third too high.^[11] The real Ϲ was probably near f♯, not a. The figure lets you hear both.

Hagel goes further. He argues that the transcriptions should be built on a different key, the Lydian, which would write every note a fourth lower than now. The sound would then be within about a semitone of the real pitch.^[12]

Rhythm in the score

Most scores do not mark rhythm at all. The metre of the words supplies it: a short syllable is one unit, a long syllable two.^[13] Where a composer wanted something else, he added small marks above the letters.^[14] The Seikilos stone carries such marks, and the figure follows them.

The Greek terms

What the Greeks said

Aristoxenus thought little of notation. Writing down a melody, he said, is not the same as understanding it. A written fourth looks the same wherever it falls in the scale, and someone can write out a Phrygian melody without knowing what makes it Phrygian.^[16]

Notes

1. ^ Hagel 2009, p. 1.
2. ^ See the Two sign systems tab of the Notation page.
3. ^ West 1992, p. 254.
4. ^ West 1992, p. 254; Hagel 2009, pp. 1–2.
5. ^ Nowacki 2020, pp. 44–45.
6. ^ West 1992, pp. 255–256; Nowacki 2020, p. 45.
7. ^ See the Tetrachord tab.
8. ^ West 1992, pp. 255–256.
9. ^ Nowacki 2020, p. 43.
10. ^ Hagel 2009, p. 9; Pöhlmann and West 2001, p. 7.
11. ^ Pöhlmann and West 2001, p. 7; West 1992, pp. 273–276; Anderson 1994, p. 204.
12. ^ Hagel 2009, pp. 452–453.
13. ^ Pöhlmann and West 2001, p. 7; see the Rhythm tab.
14. ^ See the Rhythmic signs tab of the Notation page.
15. ^ Landels 1999, c. p. 207.
16. ^ West 1992, pp. 263–264.