sus2 chord and sus4 chord

The two formulas, and the third they leave out

The only note that changes between the two chords is the second against the fourth: 2 semitones above the root against 5, which is 3 semitones apart. The fifth is 7 semitones above the root in both. A major triad puts its third 4 semitones above the root and a minor triad puts its third 3 semitones above it, so the sus2 sits 2 semitones below the major third and the sus4 sits 1 semitone above it.

Twelve roots, both chords

Each row is one root with both chords spelled out. Every name in the two note columns comes from the chord formula: root, then the note 2 semitones up and the note 7 semitones up for sus2, and the note 5 semitones up and the note 7 semitones up for sus4. This table gives note names only; the fret numbers for every root are on the suspended chord page.

One finger, two roots

The same root played twice: once as the sus2 and once as the sus4, on a root that sits on the sixth string and a root that sits on the fifth. In both pairs the two grips differ on one string, and the note on that string moves 3 semitones. Every fret and note name below was built by the site's suspended-chord module and checked note by note against the chord formula.

The two intervals, measured

A sus2 chord puts a major second above its root and a sus4 chord puts a perfect fourth there. Both intervals can be measured on their own, without a chord around them. The reading below uses two adjacent notes of one bar in a public-domain piano recording.

C4 is 262.87 Hz and D4 is 295.28 Hz. 295.28 ÷ 262.87 = 1.12329, and 1200 × log2(1.12329) = 201.27 cents for the interval itself. Equal temperament puts two semitones at 2^(2 ÷ 12) = 1.12246, which is 200.00 cents, so this one is 1.27 cents wider. A just 9:8 interval is 1.12500, or 203.910 cents, and this one is 2.64 cents narrower than that.

A4 is 442.95 Hz and D5 is 590.36 Hz. 590.36 ÷ 442.95 = 1.33278, and 1200 × log2(1.33278) = 497.33 cents for the interval itself. Equal temperament puts five semitones at 2^(5 ÷ 12) = 1.33484, which is 500.00 cents, so this one is 2.67 cents narrower. A just 4:3 interval is 1.33333, or 498.045 cents, and this one is 0.72 cents narrower than that.

The same rule on a second fourth, this time in the following bar: D4 is 295.21 Hz and G4 is 394.50 Hz. 394.50 ÷ 295.21 = 1.33632, and 1200 × log2(1.33632) = 501.91 cents for the interval itself. Equal temperament puts five semitones at 2^(5 ÷ 12) = 1.33484, which is 500.00 cents, so this one is 1.91 cents wider. A just 4:3 interval is 1.33333, or 498.045 cents, and this one is 3.87 cents wider than that.

Both readings come from Prelude No. 1 in C major, BWV 846, played by Kimiko Ishizaka and released under CC0 1.0. Johann Sebastian Bach died in 1750, and Book I of the Well-Tempered Clavier is dated 1722. The 1893 G. Schirmer edition prints the second bar over a C in the bass, and the pitches the analyser finds there are C, D, A and F. Neither bar is a suspended chord; what the recording supplies here is the width of the two intervals, not a chord. Bar 2 runs from 5.71 to 9.94 seconds; the second is read in a window from 5.98 to 7.18 seconds and the fourth in a window from 6.47 to 7.67 seconds, so both windows sit inside that bar. Bar 3 runs from 9.94 to 14.26 seconds and its fourth is read from 10.49 to 11.69 seconds. Each window starts at the later of the two note onsets and lasts 1.2 second, and it is the same rule for all three. Hear on this page uses the site's sampled guitar, not that recording.

The recording's credit and licence are on sound credits.

Three places players use them

1. G, Gsus4, G. G, C, D drops the fourth C by one semitone onto the third B of G, B, D. The root and the fifth stay where they are, which is why the change reads as a lift and a landing rather than a chord change.
2. D, Dsus2, D. D, E, A raises the second E by 2 semitones onto the third F# of D, F#, A. This is the move a sus2 makes when it does settle: the note that was a step above the root becomes the third.
3. A, Asus4, D. A, D, E holds two notes of A, C#, E, the root and the fifth, and replaces the third C# with the fourth D. That fourth, D, is the root of the next chord, D, F#, A, and the fifth of the first chord, E, is a note of the second. Nothing jumps: one note stops, one becomes the new root.

Questions people ask about sus2 and sus4

Can someone explain sus chords once and for all?

A sus chord takes the third out and puts a different note in its place. In a sus2 chord that note is the second, 2 semitones above the root; in a sus4 chord it is the fourth, 5 semitones above it. On C the whole answer is two lines: Csus2 is C, D, G, Csus4 is C, F, G, and C is C, E, G.

Is a sus2 chord the same as an add9 chord?

No. C, E, G, D is an add9 chord on C and it still contains the third E; Csus2 is C, D, G and contains no third at all. The add9 has four notes, the sus2 has three, and only the add9 is major.

Does a sus4 chord have to resolve?

Not always. On C the fourth is F, one semitone above the major third E and two semitones above the minor third C minor's Eb. In classical writing the fourth usually steps down onto the third; in jazz the sus4 often stays put; in popular music it is left unresolved just as often. The arithmetic above is what the ear is following.

Why are they called suspended?

The name comes from the suspension in counterpoint, where a note of one chord is held over into the next and then resolves. A suspended chord keeps that held-over note as a chord tone instead of treating it as a passing dissonance.

What are the two cents numbers on this page?

C4 is 262.87 Hz and D4 is 295.28 Hz. 295.28 ÷ 262.87 = 1.12329, and 1200 × log2(1.12329) = 201.27 cents for the interval itself. Equal temperament puts two semitones at 2^(2 ÷ 12) = 1.12246, which is 200.00 cents, so this one is 1.27 cents wider. A just 9:8 interval is 1.12500, or 203.910 cents, and this one is 2.64 cents narrower than that. The fourth: A4 is 442.95 Hz and D5 is 590.36 Hz. 590.36 ÷ 442.95 = 1.33278, and 1200 × log2(1.33278) = 497.33 cents for the interval itself. Equal temperament puts five semitones at 2^(5 ÷ 12) = 1.33484, which is 500.00 cents, so this one is 2.67 cents narrower. A just 4:3 interval is 1.33333, or 498.045 cents, and this one is 0.72 cents narrower than that.

Where the other sus pages fit

Suspended chord is the reference: twelve roots, both chords, the fret numbers for each, and a switch between the sus2, the sus4 and the major triad on one root. This page is the pair: two formulas, the note names for every root, one shape per root string, and two measured intervals. The single roots keep their own pages: C sus2 guitar chord, D sus2 guitar chord, C sus 4 chord guitar, G sus4 guitar chord, B sus4 guitar chord, E sus4 guitar chord and A sus chord guitar.