A chord of three tones none of which is an octave transposition of another.
The Major Triad in Just Intonation contains three tones whose frequency relations are 4:5:6 or 1/1 5/4 and 3/2.
The Minor Triad is 10:12:15 or 1/1 6/5 and 3/2.
Other triads such as the Septimal Minor 6:7:9 or 1/1 7/6 and 3/2 are used in extended Just Intonation tuning systems.
"Common-practice" (classical) music-theory is based on triads, built upwards or downwards by stacking the various types of 3rds (intervals), resulting in 4 different types of triads. Below is a table showing the interval-string (is) for all 4 types and their inversions, in 12-edo tuning:
12-edo interval strings of the 4 main chord types (triads) and their inversions
chord-members are listed in ascending pitch order, from left to right
(parentheses indicate the last interval which completes the octave)
diminished
Root 3rd 5th Root 3rd 5th
Position:
Root 3 3 (6)
1st-inv 3 6 (3)
2nd-inv 6 3 (3)
minor
Root 3rd 5th Root 3rd 5th
Position:
Root 3 4 (5)
1st-inv 4 5 (3)
2nd-inv 5 3 (4)
major
Root 3rd 5th Root 3rd 5th
Position:
Root 4 3 (5)
1st-inv 3 5 (4)
2nd-inv 5 4 (3)
augmented
Root 3rd 5th Root 3rd 5th
Position:
Root 4 4 (4)
1st-inv 4 4 (4)
2nd-inv 4 4 (4)
Any other possible chord types in 12-edo are found by using different combinations of intervals.
Below are links to download .pdf files of 12-edo diagrams of the triads in all the major and minor keys of traditional 31-tone musical notation:
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