12 trichord set classes (Forte 3-1 through 3-12)

Their are twelve transpositions of each set class. A set class groups a prime form and its inversion together under one Forte number. They share the same interval vector or the same interval content. A good way to learn to hear sets is in terms of intervals. A trichord contains three intervals.

Consider 3-2 (013). It contains a m2, M2, and m3. C, C#, and D# is one arrangement with the inner intervals of m2 and M2 and an outer interval of m3. Swapping the inner intervals to M2 and m3 produces C, D, and Eb. One way to differentiate these is to think of of C, C#, D# as (013) and C, D, Eb as (023). The first is in prime form and the second is in normal form. Both sets are (013). The order of intervals has been switched, so these two sets are related by inversion.

5 of the 12 trichords are symmetrical, meaning they do not have and ordering of intervals that produces an inverted set. Consider the augmented triad 3-12 (048). It contains two M3 and an A5. You can't switch the M3's, you just end up with the same intervals. No meaningful inversion, just the same chord. The 5 symmetrical trichords are built from stacks of the same interval:

• 3-1 (012) minor 2nds, chromatic cluster
• 3-6 (024) major 2nds, Do Re Mi
• 3-9 (036) minor 3rds, diminished triad
• 3-12 (048) major 3rds, augmented triad
• 3-9 (027) perfect 4ths/5ths, quartal or sus4

The other seven set classes contain a pair of sets related by inversion. A different order of intervals produces the inverted set. There are a total of 19 trichords, including inversions. Major and minor triads belong to the same set class, 3-11 (037).

Another useful approach to learning trichords is to break them into families or type based on the smallest interval. Type 1 contains a minor second, Type 2 contains a major second, and Type 3 contains major and/or minor thirds.

■ Type 1: Chromatic (5 classes)
3-1 (012)   3-2 (013)   3-3 (014)   3-4 (015)   3-5 (016)
At least one semitone.

■ Type 2: Whole-tone (4 classes)
3-6 (024)   3-7 (025)   3-8 (026)   3-9 (027)
No semitones. Whole steps, thirds, fourths. Modal, pentatonic.

■ Type 3: Triads (3 classes)
3-10 (036)   3-11 (037)   3-12 (048)
3-10 = diminished triad   3-11 = consonant triads (major, minor)   3-12 = augmented triad

Two answer modes

Set class: 12 answers, one per Forte number. The deck plays both the prime form and its inversion randomly — you identify the set class regardless of which orientation you hear. This is the primary ear-training task.

Interval direction: 19 answers, prime and inversion treated separately. You must identify not just the set class but which orientation is sounding. This works best with ascending or descending playback.

Suggested progression

Start: Isolate each family → Ascending playback → Set class (to limit choice) → Root = C
Then: Both Type 1 and Type 2 with C as root → Ascending/Descending playback
Advanced: Chord/Random playback, 0 = any pitch for transpostions.

How it works

You have three attempts before the answer is revealed. After 20 answers, an general assessment is offered. Click the refresh button at the top right of the app to clear the attempts. Without refreshing, the questions will adapt to your answers. Asking incorrect sets more frequently and correct sets less freqently.