Septimal minor third

From Wikipedia, the free encyclopedia

In music, the septimal minor third, also called the subminor third (by eg Helmholtz) is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies. In terms of cents, it is 267 cents, a quartertone of size 36/35 flatter than a just minor third of 6/5.

The septimal minor third has a darker but generally pleasing character when compared to the 6/5 third. A triad formed by using it in place of the minor third is called a septimal minor or subminor triad; however in fact that chord is a part of the overtone series, or in other words is an otonal chord, with ratios of 6:7:9, whereas the ordinary minor third is a utonal chord. While the septimal minor third is classed as a 7-limit interval, and the septimal minor triad as a 9-limit chord, the fact that the chord is otonal makes it sound perhaps about as consonant as the just minor triad.

In the meantone era the interval made its appearance as the alternative minor third in remote keys, under the name augmented second. Tunings of the meantone fifth in the neighborhood of 1/4 comma meantone will give three septimal minor thirds among the twelve minor thirds of the tuning; since the wolf fifth appears with an ordinary minor third, this entails there are three septimal minor triads, eight ordinary minor triads and one triad containing the wolf fifth arising from an ordinary minor third followed by a septimal major third.

[edit] In Equal-Temperament

The widely used 12-ET does not provide a good match for this interval, and even quarter tones (24-ET) do not match it well. 19-ET, 22-ET, 31-ET, 41-ET, and 72-ET each offer successively better matches (measured in cents difference) to this interval. 34-ET has a poor match to this interval.

[edit] Listening

Septimal Minor Third (just intonation, 7:6 ratio), sawtooth wave

The file plays A440, followed by 528 Hz, followed by both tones together.

Problems listening to the file? See media help.

Because of its position in the harmonic series, the sixth overtone being a perfect fifth above the root, the septimal minor third implies a root note 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.

Septimal Minor Third (just intonation, 7:6 ratio), sine wave

The file plays A880, followed by 1026.67 Hz, followed by both tones together, followed by the implied root frequency of 586.67 Hz, a fifth below the A.

Problems listening to the file? See media help.

[edit] See also

Septimal major third

[edit] References

Hermann Helmholz and Alexander Ellis (trans), On the Sensation of Tone, Dover Publications