well either. 19-TET, 22-TET, 31-TET, 41-TET, and 72-TET each offer successively better matches (measured in cents difference) to this interval. Several non-Western and just intonation tunings, such as the 43-tone scale developed by Harry Partch, do feature the (exact) septimal minor third. Listening Because of its position in the harmonic series, the sixth harmonic (frequency ratio 6:1) being a perfect fifth and two octaves above the root, the septimal minor third implies a difference tone a perfect fifth below the lower note in the interval. Depending on the timbre of the pitches, humans sometimes perceive this root pitch even if it is not played. The phenomenon of hearing this root pitch is evident in the following sound file, which uses a pure sine wave. For comparison, the root pitch is played after the interval has been played. References 7-limit tuning and intervals Minor intervals 0007:0006 Thirds (music)