Major Thirteenth
Definition & Properties
The major thirteenth is a compound interval spanning an octave plus a major sixth. It adds warmth and complexity to extended jazz chords, completing the thirteenth chord family.
| Property | Value |
|---|---|
| Abbreviation | M13 |
| Semitones | 21 |
| Quality | Major |
| Just Ratio | 10:3 |
| Cents from Equal | -15.64 |
| Harmonic Character | warm extension |
Ear Training Reference
The Major Thirteenth (M13) is commonly recognized by the ascending motion of: Compound major sixth; jazz chord color.
Practice direction: ascending — sing from the lower note up by 21 semitones.
Note Pair Examples
| Note 1 | Note 2 | Interval | Semitones |
|---|---|---|---|
| C | A (+ octave) | Major Thirteenth | 21 |
| G | E (+ octave) | Major Thirteenth | 21 |
| D | B (+ octave) | Major Thirteenth | 21 |
| F | D (+ octave) | Major Thirteenth | 21 |
Intonation by Temperament
The Major Thirteenth measures 10:3 in just intonation (-15.64 cents from equal temperament). This deviation affects ensemble tuning and instrument voicing.
| Temperament | C4 (Hz) | A5 (Hz) |
|---|---|---|
| Equal Temperament | 261.626 | 880.000 |
| Pythagorean | 260.740 | 880.000 |
| Just Intonation | 261.626 | 872.085 |
Instrument Tuning Context
Compound intervals (21 semitones) span more than an octave and appear in extended harmony and orchestral voicings.
Chords & Scales Containing This Interval
The Major Thirteenth is present in all diatonic contexts. See the Chord Reference for chord types that incorporate this interval.
Scales
These scales include the Major Thirteenth as a structural interval: