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Every chord in the standard jazz toolbox! Interval formulas below refer to the chord root’s major scale (e.g. Cmaj7: 1–3–5–7 = tones 1–2–3–4–5–6–7 from the Cmaj scale). Also note a few other nomenclature quirks…

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—Interval Formulas—

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• Power: 1-5 [C5]

• Major: 1-3-5 [C, Cmaj]

• Minor: 1-b3-5 [Cm, Cmin]

• Diminished: 1-b3-b5 [Cdim, C°]

• Augmented: 1-3-#5 [C+, Caug]

• Sus. 2nd: 1-2-5 [Csus2]

• Sus. 4th: 1-4-5 [Csus4]

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• Major 7th: 1-3-5-7 [Cmaj7, C^▵7]

• (Dominant) 7th: 1-3-5-b7 [C7]

• Minor 7th: 1-b3-5-b7 [Cm7, C–7]

• Half-Dim. 7th: 1-b3-b5-b7 [Cm7^b5, C^ø7]

• Dim. 7th: 1-b3-b5-bb7 [Cdim7, C°7]

• Aug. 7th: 1-3-#5-b7 [Caug7, C+7, C7^#5]

• Min-Maj. 7th: 1-b3-5-7 [Cm(maj7)]

• Dim-Maj. 7th: 1-b3-b5-7 [Cdim(maj7)]

• (Major) 6th: 1-3-5-6 [C6, Cmaj6]

• Minor 6th: 1-b3-5-6 [Cm6, Cmin6]

• Add 9th: 1-3-5-9 [Cadd9, Cadd2]

• Add 11th: 1-3-5-11 [Cadd11, Cadd4]

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• Major 9th: 1-3-5-7-9 [Cmaj9]

• (Dom.) 9th: 1-3-5-b7-9 [C9]

• Minor 9th: 1-b3-5-b7-9 [Cm9]

• 6th/9th: 1-3-5-6-9 [C6/9, C6add9]

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• Major 11th: 1-3-5-7-9-11 [Cmaj11]

• (Dom.) 11th: 1-3-5-b7-9-11 [C11]

• Minor 11th: 1-b3-5-b7-9-11 [Cm11]

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• Major 13th: 1-3-5-7-9-11-13 [Cmaj13]

• (Dom.) 13th: 1-3-5-b7-9-11-13 [C13]

• Minor 13th: 1-b3-5-b7-9-11-13 [Cm13]

—Chordal Quirks—

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• Bespoke names: virtually all other chords can be deduced via the info above, e.g. ‘C7#9(no5)‘ has no 5th, ‘C6(b9)‘ just adds a b9 to a Cmaj6, etc. Rare exceptions include compound ‘polychords’, which are written as their ‘sum’ – e.g. ‘Cmaj + Emaj‘ (C-E-G-E-G#-B) is much clearer than ‘G#aug(#9)/C‘, although they both mean the same thing [also check this lookup site]

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• Inversions: chords where the root isn’t the lowest-pitched tone – notated like ‘D/F#‘ with the lowest tone after the slash (often, this note is ‘ignored’ in naming the rest of the chord, e.g. ‘Am/G‘: an Am triad doesn’t contain a G, but the pre-slash part isn’t renamed to reflect its presence)

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• Altered dominants: any dominant 7th with an ‘altered’ upper extension, i.e. 1-3-5-b7 plus a 9/11/13 which is ‘altered’ by an accidental – which in practice is limited to combinations of b9/#9/#11/b13 (e.g. C7b9, C7#9^(b13)). Generally, altered dominants can be treated interchangeably, mostly due to their tritonal overlaps (i.e. try playing any in the place of any other…)

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• Omitting tones: often, playing all notes of a complex chord isn’t practical (e.g. a guitar’s 6 strings can’t play all 7 notes in a 13th chord) – therefore, tones tend to be omitted as per a rough hierarchy: usually the 5th is the first one to go, often followed by the root – and the most important tones to keep are the 3rd, 7th, plus any extensions which are specified in the name

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• Nicknames: many chords also have special names, which often refer to specific voicings rather than generic formulas – e.g. the ‘Hendrix chord‘ (1-3-b7-#9), Scriabin’s ‘Mystic chord‘ (1-3-b7-9-#11-13), Strauss’ ‘Elektra chord‘ (Emaj + C#maj), Stravinsky’s ‘Petrushka chord‘ (Cmaj + F#maj), La Monte Young’s ‘Dream chord‘ (1-4-5-#11), Schoenberg’s ‘Farben chord‘ (1-3-6-7-b13) and ‘Napoleon chord‘ (1-3-6-b9-11-b13)…