Consonant and dissonant
Unisons, 3rds, 5ths, 6ths and octaves are consonant, and so are the same intervals an octave higher (a 10th is a 3rd). 2nds, 4ths, 7ths and the tritone are dissonant. In two voices the 4th counts as a dissonance.
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Species counterpoint, after Fux
Write a line and every note is checked against Fux's rules, with the reason. Fix it on the spot, then move on.
First stages freeNo account to startRules from the 1725 treatise
For students
First stages are free, no account needed.
For teachers
Teachers: your first semester is on us. Then $15 a month. See pricing for classes
Parnasso for teachersThe path
Fux's course is a ladder where every species adds one idea to the last. Parnasso lays it out as one trail, three exercises a stage, from a single melody to three and four voices.
Pricing
Lessons, cantus firmus and first species
Second to fifth species, three and four voices
A class of up to 40 students
Up to 120 students
Semester prices are lower. See all plans
Where the rules come from
Parnasso checks the rules of Gradus ad Parnassum (1725). When a note turns red, you see which rule it breaks and why, such as parallel fifths.
A step-by-step way of learning to write independent melodies that sound good together. Johann Joseph Fux set it out in 1725, and it moves from one note against one note to free, florid writing.
No. Every lesson comes with examples to hear, and the first stages explain each note as you write it.
Not to start. An account keeps your progress and streak on every device.
Cantus firmus and first species are free. Second to fifth species and three and four voices are part of Solo, and students in a teacher's class get everything through the teacher's plan.
Composition and music theory students, self-taught composers, and teachers who want exercises that mark themselves.
The first stages are free and need no account.
Parnasso for teachers
Set an assignment in two clicks. Your students write it in the browser, every rule is checked as they go, and you see who is done and where the class got stuck.
Less marking, more teaching. Five things that change when counterpoint homework checks itself.
Parallel fifths, unprepared dissonances, leaps that are never recovered: Parnasso checks them all, as your students write. Nothing slips past, and nothing waits for your pen.
See the mistakes most of your students made, ranked. Spend the lesson on what the class actually got wrong, not on what you guess.
For the next lesson Parallel fifths: bars 4 to 6 of exercise 3.
Choose the species, the stage and how many exercises. Parnasso writes them, in the modes you pick, and you can open and play each one before you give it out.
A student placing a note at eleven at night gets the explanation at once, not at next week’s lesson. They try again right away, so more happens between lessons.
Choose live coaching or marking only after the student presses Check. Read each student’s line, exercise by exercise, and leave a note in your own words. Parnasso checks the rules; you keep the musical judgement.
Good line in bar 3. In 5, check the cadence: the leading tone needs to rise.
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Your first semester is on us: one class, up to 30 students, no card. After that, $15 a month or $45 a semester for up to 40 students across all your classes. Need more? Studio covers 120.
No. Students in your class get everything while the class runs. They sign in with the email you added, or with your class code.
An email address and two minutes. Make an account, make a class, paste your students’ emails or share the invite link, and set a first assignment.
Not yet. You choose the species, the stage and how many; Parnasso builds the exercises, and you can open and play each one before you give them out. Fux’s six cantus firmi are available in the practice room.
The rules of counterpoint are checked by code, so a parallel fifth is always caught and never guessed. Parnasso also comments on the shape of the line. It does not replace your ear: use the results to decide what to talk about.
Only you and the student. Work is stored in the student’s account and is deleted if they leave the class or you remove them.
Writing a cantus firmus, the five species in two voices, and counterpoint in three and four voices, in six modes.
Routes in Fux's order: writing a cantus, the five species, then three and four voices. Every stage has three exercises: solve all three to open the next.
Dimmed options are included in Pro: the Solo, Teacher and Studio plans, or a teacher’s class. See the plans
Note values and accidentals follow Sibelius's keypad (3–6, 7 8 9) and Dorico's keys (= - 0); octave moves work as in Sibelius, Dorico and MuseScore.
Five species, each a small step up from the one before, as Johann Joseph Fux set them out in Gradus ad Parnassum (1725). Start with the basics: they hold in every species.
You get a fixed melody, the cantus firmus: whole notes, mostly by step, starting and ending on the final of its mode. You write a second line above or below it. The rules on this page apply in every species; each species then adds its own.
Unisons, 3rds, 5ths, 6ths and octaves are consonant, and so are the same intervals an octave higher (a 10th is a 3rd). 2nds, 4ths, 7ths and the tritone are dissonant. In two voices the 4th counts as a dissonance.
Above the cantus: unison, 5th or octave. Below it: unison or octave only, so the mode stays clear.
And use the unison nowhere else: in the middle the two voices merge into one.
Close with a major 6th opening to an octave (line above) or a minor 3rd closing to a unison (line below). In every mode except Phrygian this means raising the leading tone, here C to C♯.
Two perfect intervals of the same size in a row, with both voices moving, make the voices lose their independence. Parallel 3rds and 6ths are fine.
Approach a perfect interval by contrary or oblique motion, never with both voices moving the same way.
The upper line normally stays above. Fux lets the counterpoint cross the cantus for a moment when that avoids a worse progression, so Parnasso marks it as a suggestion. Keep the voices within a 10th where you can.
Perfect to perfect: contrary or oblique motion only. Perfect to imperfect: any motion. Imperfect to perfect: contrary motion only. Imperfect to imperfect: any motion. Oblique motion is allowed with every progression.
An octave reached on the downbeat from a 10th, with both voices stepping towards each other, is called the battuta. Fux says the use or avoidance is up to you: "it is of little importance". Parnasso does not mark it.
More than three 3rds or 6ths in a row, or too many bare 5ths and octaves, make the two lines sound like one.
Allowed leaps: 3rds, perfect 4ths and 5ths, the rising minor 6th and the octave. Avoid the tritone, 7ths and augmented intervals: they are hard to sing.
After a large leap, step back in the opposite direction. Avoid two leaps in the same direction.
Give the line one highest note, away from the cantus's high point, and keep its range singable: within a 10th.
When the line runs in one direction from F up to B (or down from B to F), the ear hears the tritone between its ends, even though every move is a step. Turn back before you reach it, or carry on past it.
The counterpoint may repeat a note occasionally, but the same note should not be repeated more than once (Fux). Parnasso suggests a change from the second repeat on.
Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Ionian, on several finals each. Stay inside the mode. The only chromatic note is the raised leading tone at the cadence; Phrygian never raises it. Fux leaves out the mode on B: it has no perfect 5th above the final, so it cannot end a piece.
If the cantus is on top, count intervals down from it.
A 10th is a 3rd an octave higher. Write in neighbouring clefs so simple intervals stay easy to tell apart.
Fill in a skip of a 5th with passing notes and two 5ths in a row appear.
The start expresses perfection and the end relaxation. Imperfect consonances sound fuller, so they should outnumber the perfect ones.
Only the leading tone at the cadence, and to avoid mi against fa. Never decoration.
Poor, especially into a unison or into an octave from a distant consonance. Fux tolerates it only where the cantus forces it.
The counterpoint begins and ends in the cantus's mode: opening on G over a D cantus forces it out.
Every cantus in all six modes, line above and below, then the cantus in each voice. A year or two of practice before free composition.
Fux gives no rule beyond singability: take a chorale or invent one.
One line
Before writing against a cantus, write one. A cantus firmus is a short, plain melody in whole notes: it sets out the mode, moves mostly by step and has a clear arc. Every species exercise starts from one.
The first and last notes are the final of the mode, in the same octave. That is what makes the mode clear.
Usually from the note above. A step up from the leading tone below also works, but the cantus itself stays in the mode.
One to three leaps give the line character. After a leap, step back the other way; never two leaps in a row.
The highest note comes once, somewhere in the middle. Keep the whole line within about a 10th, with no repeated notes and nothing outside the mode.
A cantus firmus is a single melody, usually in whole notes, that the other voices are written against. In Fux's method it begins and ends on the final, moves mostly by step, and has one highest note.
Eight to twelve notes is usual. Shorter lines give too little shape, and longer ones are hard to keep coherent.
1 : 1
One whole note against each note of the cantus. With no rhythm to hide behind, every interval counts. All the basics apply, plus two rules.
No dissonances at all: each bar is a unison, 3rd, 5th, 6th or octave, or a compound of these.
With one note per bar, a repeated note stalls the line. Fux allows one repeat in the whole exercise, no more: move on, by step if you can.
The 7th degree rises at the cadence in Dorian, Mixolydian and Aeolian. In Fux's cantus firmi the next to last note is the 2nd degree of the mode.
Write the interval over each note and the bar numbers below, to prove each progression is deliberate.
Contrary and oblique motion make mistakes easier to avoid. Take more care with direct motion.
2 : 1
Two half notes against each cantus note. The line opens with a half rest and ends on a whole note. The second half of a bar can now carry a dissonance, if it passes.
The first half note of every bar follows the first-species rules for harmony.
The second half may be dissonant only as a passing tone: reached by step and left by step in the same direction, filling in a 3rd.
5ths or octaves on two downbeats in a row are heard as parallels, even with a note between them. A leap of a 4th or more around that note makes the ear forget the first downbeat, so the parallel no longer counts.
Fux mentions triple time only briefly: three notes can stand against one. If all three move by step, the middle one may be dissonant; if one of them leaps, all three must be consonant. Parnasso has no exercises for it.
No repeated notes. The cadence sits on the last half note: a major 6th above, or minor 3rd below, then the final.
Fux asks to avoid sequences (monotonia) as far as possible, in every species from here on. A figure of two or three moves that is simply repeated again and again makes the line monotonous: change its shape the second time. Parnasso suggests it.
A skip of a minor 6th or an octave can turn a direct approach into a contrary one.
It may stand in the next to last bar when two half notes cannot reach the cadence.
The 5th is dissonant, so write a 6th in the next to last bar instead.
It is the hardest bar. Look one or two bars ahead before you write.
The line may start with a half rest instead of a half note.
4 : 1
Four quarter notes against each cantus note, opening with a quarter rest. The downbeat is consonant; the other three quarters may be dissonant, handled in one of three ways.
On any of the three weak quarters: reached and left by step in the same direction.
On the 2nd or 4th quarter: a step away from a consonance and straight back to it.
On the 2nd quarter: step down to the dissonance, leap a 3rd down to a consonance, then step up. The one dissonance in species counterpoint that is left by leap.
No repeated notes, no parallels across the barline, no 5ths or octaves on successive downbeats.
1st and 3rd consonant; the 2nd may be dissonant; the 4th only if the 5th is consonant.
If the 2nd and 4th quarters are consonant, the 3rd may be dissonant: it only fills in a 3rd.
A quarter rest may open the bar. No eighths yet: they belong to fifth species.
Fux accepts it in one old model because it is easier to sing. Most teachers avoid it.
A leap from a strong to a weak quarter is hard to sing in the Palestrina style (Jeppesen). This is not Fux's rule.
Avoid melodic sequences, and plan the next bar before you write.
Ties
Half notes, shifted: each note is struck on the second half of the bar and tied over the barline into the next downbeat. When the cantus moves under the tie, you get a suspension.
It resolves the last suspension and prepares the next one.
Above the cantus use 7–6, 4–3, 9–8 or 2–1. Below the cantus use 2–3. A 9–8 resolves onto a bare octave, so 7–6 and 4–3 are preferred.
Fux forbids a 2–1 suspension that comes after a unison, and a 9–8 after an octave. Take the tie away and you hear two unisons or two octaves in a row. A 3rd or 10th leading into the 2nd or 9th is fine.
Fux asks for a tie in every bar where one is possible. Where none works, write plain half notes until a tie fits again, and never repeat the same note. The same ties may also be varied: two eighths on the 2nd and 4th beats, or the note struck again, keep the idea but liven the line.
If the tied note is consonant against the new cantus note, the next note may step or leap.
The classic 7–6 above (2–3 below), resolving to the octave or unison, with the leading tone raised.
Sometimes no tie leads anywhere good: every suspension would make parallels or an unresolvable dissonance. Then Fux breaks the chain for one bar: the note is not tied, and the next bar starts with a fresh, consonant note, as in second species. Use it once at most. In Parnasso, select the note and press + to break or restore its tie.
Fux leaves the case of an ascending tie for later.
It would resolve to an octave, which the masters never wrote.
Avoid repeating the same tie figure bar after bar.
In three voices a tie over a pedal point may be dissonant throughout.
Avoid sequences as far as possible.
Florid
All the species mixed, bar by bar: halves, quarters, a pair of eighths, and ties that make suspensions. Choose a rhythm for each bar, then write the notes.
Struck downbeats are consonant. Dissonant halves pass; dissonant quarters pass, neighbour or form a cambiata; dissonant ties resolve down by step.
In and out, usually as a pair on the 2nd or 4th quarter of the bar.
In florid counterpoint a suspension may be ornamented before it resolves: short consonant notes after the tie, most often a 3rd down and back up, as long as the step down arrives by beat 4.
A dotted quarter and an eighth, or a dotted half and a quarter, give the line a lilt. Dotted notes start on a beat; the eighth after a dotted quarter moves by step. Press . to dot the selected note.
The same rhythm three bars in a row sounds like a lower species. Let the line speed up and slow down.
In florid counterpoint Fux likes to reach each downbeat with a tie or by oblique motion: it gives the greatest beauty and keeps the line out of trouble. A singable melodic line matters more than anything else in this species, and Fux tells his student to spend most time here.
Fux advises against two quarters at the start of a bar followed by a half note that is not tied on: the line seems to lag. Tie the half over the barline, or add more quarters. Parnasso suggests it.
A rest may stand in place of a note when the line has nowhere good to go.
Every struck downbeat note is consonant.
Fux says to work at it more than at any other.
Mix the other species freely, but let the line stay singable.
3–4 voices
After the five species in two voices, Fux adds voices. The cantus may sit in the bass, the middle or on top; the other voices move note against note, or one of them in a higher species. Every rule still holds between every pair of voices, and each chord is now heard from the bass.
A 4th above the bass is a dissonance. Between two upper voices it is fine: in C–G–C the G and C make a 4th, but each is consonant with the bass.
In the middle of the exercise, give each chord a 3rd (or a 6th) above the bass. Don't double the raised leading tone. A tritone between upper voices is allowed but tense.
When the bass has the third degree of the mode (B in Dorian, the "mi"), put a 6th above it, not a 5th: the 5th would be diminished. A 3rd and a 6th make the chord.
Put the 5th low and the 3rd high: a 3rd close to the bass sounds dull (Fux). Voices that sit close together sound fuller. Double the octave first; if a progression forbids that, double the 3rd, more rarely the 5th or 6th. In a suspension double the 2nd, not the 4th.
On each downbeat use the full triad, a 3rd and a 5th above the bass, unless the melody or a parallel forbids it. Then take a 6th or an octave instead of the 5th. Prefer the version in which every voice moves smoothly and no note is doubled for no reason.
The downbeat should carry a full chord; the upbeat may be thinner. In ties and quarters, give the note against the whole notes the consonances it would have if the tie were taken away.
No parallel 5ths or octaves between any two voices. Direct 5ths and octaves matter most between the outer voices, when the top voice leaps.
The bass stands on the final. Above it: the octave and the 5th. Leave out the 3rd when you can; if the 5th would make parallels, take a major 3rd, never a minor one, which Fux finds too weak to end on.
One voice rises from the raised leading tone to the final, as in two voices; when the bass is free, it often leaps from the 5th to the final.
With more voices, a repeated note, a unison or a brief crossing is sometimes the best way through, and a hidden 5th or octave is tolerated between inner voices when the voice leading is otherwise good, more than between the outer ones. Use them sparingly; Parnasso marks them as suggestions, not errors. The more voices, the looser the rules.
When one voice moves in halves, quarters, ties or florid rhythm, it follows that species' rules against every other voice; the rest move note against note.
Practise with the cantus in the top, the middle and the bottom voice.
Stay within the five lines of the staff and prefer an octave to a unison.
It is wrong between any two voices, not only against the bass.
One voice moves in halves and the others in wholes; each half note must be consonant with both whole notes.
A half note may excuse two parallel 5ths by a skip of a 3rd, if that keeps the triad.
A rest in one voice can hide a hidden 5th between the others.
Give the first quarter the triad. If that fails, use the 2nd or 3rd quarter.
Double the 3rd rather than writing a unison on a downbeat.
A 4th between inner voices acts like an imperfect consonance.
Allowed in an accompanying voice when no other solution exists; Fux avoids it where he can.
A direct move into a perfect interval is easier to accept descending than ascending (Beethoven).
With no perfect 5th, the final chord and cadence need a different solution.
The rules loosen further. Fux ends the book here.
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A practice room for composers who learn on their own and have no teacher to mark their exercises.
Every exercise is short: a cantus firmus and a line to write against it. The rules of counterpoint are checked by code, so a parallel fifth is always caught and never guessed. On top of that, Parnasso comments on the shape of your line: its climax, its leaps, how independent it is from the cantus.
The name comes from Mount Parnassus, home of the Muses. In 1725 Johann Joseph Fux called his counterpoint textbook Gradus ad Parnassum, "steps to Parnassus": a climb toward mastery, one exercise at a time. That book taught Haydn, Mozart and Beethoven. Parnasso follows the same path, starting with counterpoint and climbing toward harmony and beyond.
Parnasso is made by one person who wanted this tool to exist. (Placeholder: a short name and note will go here.)
Piano, cello and violin samples from tonejs-instruments (MIT licence). Playback by Tone.js. Notation engraved with VexFlow (MIT) in the Bravura music font (SIL Open Font License). The opening exercise uses Fux's Dorian cantus firmus.
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Last updated 31 October 2026.
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