Collection of chords

Way too many chords.

This page covers chords with fewer than 5 pitch classes. At 5 pitch classes or above, the "chord" becomes more treatable as a scale, and may be found at Collection of scales.

Chords here are rotation-agnostic.

Triads

A triad is a chord containing 3 pitch classes. That is, C-E-G is a triad, but C-E-C is not a triad because even though the Cs may be separated by an octave, they are the same pitch class. Some theorists restrict the word 'triad' to exclusively refer to tertian triads, composed of two stacked thirds.

Fifth-bounded triads

These triads are bounded by a perfect fifth.

Suspended triad

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Intervals: Unison - Perfect Fourth - Perfect Fifth, Unison - Major Second - Perfect Fifth

Just tunings: Usually 6:8:9; 8:9:12

The suspended triad refers to two triads, sus4 and sus2, which are often each other's inversions. The sus4 triad is usually tuned with the perfect fourth and fifth octave complements, so it is the inversion of a corresponding sus2 triad. Sus triads are the simplest kind of triad in Pythagorean tuning, however they are considerably less concordant than other triads, especially with flatter tunings of the fifth (and thus sharper tunings of the fourth, and flatter tunings of the second).

Tendo triad

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Intervals: Unison - Ultramajor Third - Perfect Fifth

Just tunings: 16:21:24, 10:13:15

The tendo triad is generally similarly consonant to the sus4 triad. The intervals themselves are more complex, but the smaller interval is also wider, making the triad feel more open. Notably, the tendo triad's third is separated from that of the arto triad by over 200 cents, meaning both can be played at the same time and avoid clashes, similarly to a suspended chord.

Supermajor triad

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Intervals: Unison - Supermajor Third - Perfect Fifth

Just tunings: 14:18:21

The supermajor triad contains a supermajor third, and is usually seen as a 7-limit triad containing the interval 9/7. It is interestingly the *less* stable of the two basic 2.3.7 triads, despite being major, giving 2.3.7 harmony a unique sound.

Major triad

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Intervals: Unison - Major Third - Perfect Fifth

Just tunings: 4:5:6, 64:81:96

The major triad is one of the two standard varieties of triad. It has a stable, rooted sound coming from its simple enumeration and low placement in the harmonic series. It is represented in 12edo and in the standard tuning of the diatonic scale.

Neutral triad

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Intervals: Unison - Neutral Third - Perfect Fifth

Just tunings: 18:22:27, 26:32:39, 2:sqrt6:3

The neutral triad is associated with the 11-limit and 13-limit. It exists between major and minor triads, and often wants to resolve to either one, creating a tense, unstable sound similar to that of a diminished triad, or in other cases an "ambiguous" quality. While 2:sqrt6:3 isn't strictly just intonation, it is the tuning that utilizes the equal division of the perfect fifth into two identical neutral thirds, so it is in a sense as fundamental as the JI tunings for this particular case.

Minor triad

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Intervals: Unison - Minor Third - Perfect Fifth

Just tunings: 10:12:15, 16:19:24, 54:64:81

The minor triad is the other of the two standard triads, appearing in and giving its name to the minor scale. While it is conventionally less stable than the major triad, the influence of 16:19:24 in 12edo, according to some, gives it a sense of stability. It is represented in 12edo and in the standard tuning of the diatonic scale.

Subminor triad

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Intervals: Unison - Subminor Third - Perfect Fifth

Just tunings: 6:7:9

This type of triad is usually thought of in the 7-limit, where it is significantly more stable than its major counterpart, owing to its much simpler position in the harmonic series. This essentially makes the 2.3.7 subgroup work somewhat backwards melodically compared to the 5-limit - melodically similar chords are stable in 2.3.7 and unstable in 2.3.5.

Arto triad

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Intervals: Unison - Inframinor Third - Perfect Fifth

Just tunings: 14:16:21, 26:30:39

The arto triad is the "minor" counterpart of the tendo triad, and serves a similar role in harmony to a standard minor chord, allowing arto and tendo triads to, in a sense, fully replace minor and major ones and form their own system of harmony. As mentioned previously, the two chords can be played both at once, avoiding clashes.

Other triads

Augmented triad

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Intervals: Unison - Major Third - Augmented Fifth

Diminished triad

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Intervals: Unison - Minor Third - Diminished Fifth

Major latal triad

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Intervals: Unison - Subminor Third - Perfect Fourth

Minor latal triad

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Intervals: Unison - Supermajor Second - Perfect Fourth

Tetrads

Arto-tendo tetrad

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Intervals: Unison - Inframinor Third - Ultramajor Third - Perfect Fifth

Just tunings: [1/1 15/13 13/10 3/2]

The combination of the arto and tendo triads. See #Arto triad and #Tendo triad above.

Major seventh tetrad

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Intervals: Unison - Major Third - Perfect Fifth - Major Seventh

Just tunings: 8:10:12:15

Minor seventh tetrad

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Intervals: Unison - Minor Third - Perfect Fifth - Minor Seventh

Just tunings: 10:12:15:18

Dominant tetrad

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Intervals: Unison - Major Third - Perfect Fifth - Minor Seventh

Just tunings: [1/1 5/4 3/2 16/9]

Contains a tritone from the third to the seventh, and is thus generally a tense chord. Found on the V of major diatonic scales, where it resolves to the tonic.

Harmonic tetrad

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Intervals: Unison - Major Third - Perfect Fifth - Subminor Seventh

Just tunings: 4:5:6:7

This tetrad approximates the harmonic series and can be seen as a tetradic analogue of 4:5:6 that extends it to the 7-limit.

Minor harmonic tetrad

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Intervals: Unison - Minor Third - Perfect Fifth - Supermajor Sixth

Just tunings: 70:84:105:120

Exists in JI, but in jubilic temperaments it becomes a clear "minor" counterpart to the harmonic tetrad. Below are the major and minor harmonic tetrads in 22edo.

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Essentially tempered chords

An essentially tempered chord is a chord whose structure is dependent on a temperament.

Slendric tetrad

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Intervals: Unison - Supermajor Second - Subfourth - Perfect Fifth

Temperament: Gamelic

Distances: 8/7, 8/7, 8/7

Just tuning: [1/1 8/7 21/16 3/2]

A special case of an arto-tendo chord where all three distances between the notes are equal and equated to 8/7, while the chord's span is a perfect fifth 3/2. This can only happen in Slendric temperament.

Symmetric augmented triad

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Intervals: Unison - Major Third - Minor Sixth

Temperament: Augmented

Distances: 5/4, 5/4

Just tuning: [1/1 5/4 8/5]

Symmetric diminished tetrad

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Intervals: Unison - Minor Third - Tritone - Major Sixth

Temperament: Diminished

Distances: 6/5, 6/5, 6/5

Just tuning: [1/1 6/5 36/25 5/3]