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A piano reference: chords, scales, theory & ear training.

A chord is built from a root that names it, a third that makes it major or minor, and a fifth, with any further notes stacked above.

Anatomy of a Chord

Open any chord page and you will see the same chord described four ways: as notes, as intervals, as a formula, and as scale degrees. They are not four different chords. They are four lenses on the same one, and once you can switch between them, every chord in the catalogue gets simpler.

Anatomy Explorer

One chord, four ways of describing it.

Pick a root and a quality. The same chord appears as notes, intervals, formula and scale degrees, all updating together.

Root note

Chord quality

Now showing

F♯ (Major)

C1C2C3C4C5C6C7C8F♯A♯C♯

Root3rd5th

Build it tone by tone

F♯ is F♯, A♯, C♯. Bright and settled. The major 3rd is what makes it sound open.

1. Notes

F♯·A♯·C♯

The actual letter names you press.

2. Intervals

P1·M3·P5

Each note’s distance up from the root.

3. Formula

1·3·5

The recipe, read against the major scale of the root.

4. Scale degrees

1·3·5

Which degrees of the parent scale the chord occupies.

1. The notes

The most concrete description of a chord is the list of notes in it. F♯ major is F♯, A♯, C♯. Three notes, three keys you press, done. No Roman numerals, no arithmetic, just letter names.

What looks arbitrary at first, why A♯ and not B♭, is a deliberate spelling choice. A triad uses every other letter going up: F, then A, then C, skipping G and B. Spelling that middle note B♭ instead of A♯ gives you exactly the same key on the piano, but on the page F♯ up to B♭ reads as a fourth rather than a third, and the chord stops looking like a triad at all. The accidental follows from the letter, and the letter follows from the chord.

When notes are most useful: sight-reading, looking up a fingering, or playing a chord you have never seen. Notes tell you exactly which keys to press, right now.

Same root, different qualities

All seven chords below share the root C. The 3rd, the 5th and sometimes the 7th change to make each quality. Watch the letters stay put: C diminished is C, E♭, G♭, never C, E♭, F♯, because the 5th has to be a G of some kind.

C1C2C3CEGC5C6C7C8

Root3rd5th

C is C, E, G (P1, M3, P5)


2. The intervals

An interval is the distance between two notes. Every chord can be described as a set of intervals measured up from the root.

A major triad has a major 3rd and a perfect 5th above its root, so its interval list is P1, M3, P5. A minor triad swaps the major 3rd for a minor 3rd: P1, m3, P5. That one half step in the middle is the whole difference between the two most common chords in music.

Interval names have two parts. The number counts letter names inclusively, so C up to E is a third because C, D, E is three letters. The quality word fixes the exact size: perfect (unisons, 4ths, 5ths, octaves), major and minor (2nds, 3rds, 6ths, 7ths, a half step apart), diminished (a half step below perfect or minor) and augmented (a half step above perfect or major).

When intervals are most useful: working out why a chord sounds the way it does, or moving it to another key. Intervals are key-independent. A major 3rd is a major 3rd whether the root is C or F♯.

Interval ladder

Click any key to measure its distance from C. The interval name carries two pieces of information: the number counts letters, the quality word measures the exact size.

C1C2C3CGC5C6C7C8

C, the reference noteNote you picked

From C to G: P5 (Perfect 5th, 7 half steps)


3. The formula

The formula is the most compact description. It uses degree numbers from the major scale of the root, with sharps and flats marking where a note has been raised or lowered.

Major triad: 1-3-5. Take the 1st, 3rd and 5th notes of the major scale of your root. For C that is C, E, G. For F♯ it is F♯, A♯, C♯. Same recipe, different ingredients.

Minor triad: 1-♭3-5. Same three degrees, but lower the 3rd by a half step. C major’s 3rd is E; lower it to E♭ and you have C minor.

Why it is built on the major scale: convention, and a useful one. The major scale is the shared reference grid, so 1-3-5-♭7 means the same thing on every root: take 1, 3 and 5 from that root’s major scale, then flatten the 7th. Learn the major scales and every formula resolves without thinking.

The seven qualities in this article, written on C.
ChordSymbolFormulaIntervalsOn C
MajorC1-3-5P1, M3, P5C, E, G
MinorCm1-♭3-5P1, m3, P5C, E♭, G
DiminishedC°1-♭3-♭5P1, m3, d5C, E♭, G♭
AugmentedC+1-3-♯5P1, M3, A5C, E, G♯
Major 7thCmaj71-3-5-7P1, M3, P5, M7C, E, G, B
Dominant 7thC71-3-5-♭7P1, M3, P5, m7C, E, G, B♭
Minor 7thCm71-♭3-5-♭7P1, m3, P5, m7C, E♭, G, B♭

When the formula is most useful: learning a new chord type, transposing on the fly, or comparing two chords side by side. The formula is what makes the family resemblance visible. Major and minor differ by one symbol; dominant 7th and major 7th differ by one symbol.


4. The scale degrees

Scale degrees describe a chord’s position inside a parent key. They answer a different question: if we are in C major, what is this chord doing?

Every major scale carries seven triads, one on each degree, all built only from notes of that scale. In C major: C is the I chord, D minor is ii, E minor is iii, F is IV, G is V, A minor is vi, and B diminished is vii°. The numeral gives the degree, and the case gives the quality.

Formula against scale degrees, the subtle difference: the formula describes a chord on its own, always relative to the major scale of that chord’s root. Scale degrees describe the chord’s role inside a key. F major’s formula is always 1-3-5, but in C major F is the IV chord and in F major it is the I chord. Same notes, different job.

Diatonic chords in C major

Each degree of the C major scale carries a chord built from notes of that same scale. Pick a Roman numeral to see which degrees light up.

C1C2C3CDEFGABCDEFGABC6C7C8

Chord toneOther scale tone

The I chord is C, E, G (degrees 1, 3, 5 of C major). Quality: Major.


All four together: F♯ major

Every chord page on this site stacks the same four pieces of information in its header. Here is what each line is telling you.

F♯ major

Notes
F♯, A♯, C♯
The keys you press.
Intervals
P1, M3, P5
Each note’s distance up from the root.
Formula
1, 3, 5
The 1st, 3rd and 5th of the F♯ major scale.
Scale degrees in F♯ major
1, 3, 5 (the I chord)
F♯ is the home chord of its own key.

None of the four is more correct than the others. They are different tools. Notes are best for sight-reading, intervals for analysis, formulas for memorising chord types, scale degrees for understanding harmony in context. Fluent musicians switch between them without noticing.


Frequently asked

Why are some 3rds called major and others minor?
A major 3rd is four half steps; a minor 3rd is three. Both span three letter names, so both are a kind of third, but one is a half step wider than the other. Which 3rd sits between the root and the middle note is what decides whether a triad is major or minor.
Is the formula always relative to the major scale?
Yes, by convention. Chord formulas use the major scale of the chord’s own root as the reference grid. Even for a minor chord, the formula 1, ♭3, 5 is read against the major scale: lower the 3rd by a half step. That way every chord type has one canonical formula no matter which key you are in.
What is the difference between the formula and the intervals?
They describe the same thing in two notations. The formula 1, 3, 5 maps to the intervals P1, M3, P5; the formula 1, ♭3, 5 maps to P1, m3, P5. Formulas are compact and good for quick lookup. Interval names are explicit and good for analysis.
Why do scale degrees use Roman numerals instead of ordinary numbers?
Two reasons. Roman numerals signal that the number refers to a chord rather than a single note, so ii means the chord built on the 2nd degree, not the second note. And the case carries the quality: capitals for major, lowercase for minor, with a degree symbol added for diminished.
Why does the spelling matter if the note sounds the same?
Because the letters are what make a chord readable. A triad uses every other letter, so C augmented has to be C, E, G♯. Spelling that last note A♭ gives the same key on the piano but puts C, E and A on the page, which reads as a sixth chord rather than an augmented triad. The sound is identical; the meaning is not.
Do I need to memorise all of this?
Not at once. Most people start with notes, which keys to press, then learn formulas so they can build any chord on any root, then pick up intervals and scale degrees as they get into harmony and song analysis. Each layer adds depth, and you can play music well at every stage.
How does this connect to fingering?
Fingering is a fifth, more practical layer on top of the four here. Once you know the notes, fingering tells your hand which finger plays which one. For a root position triad the standard right hand is 1, 3, 5 (thumb, middle, little finger) and the standard left hand is 5, 3, 1.

Where to go next

Related Tools

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