With music, it is well known that two notes that are adjacent to each other, such as C and C#, can sound dissonant when played together. This is especially significant in the lower frequency region (below or near middle C) where the fundamental frequency difference between C and C# can be on the order of only 15 Hz. Musical note spacing (and its harmonics) should be on the order of at least 25 dB for there to be no dissonance.
This is one of the reasons why frequency lowering can be problematic when it comes to amplified music—unintentionally causing some harmonic elements of one note to be too close to another note that is played at the same time.
But perhaps this is too simplistic of a conclusion?
This staircase is a visual analog of musical dissonance. One staircase has equally spaced poles or harmonics from one note but when overlaid with another part of the staircase (another note), the vertical poles/harmonics can be anywhere including almost (but not quite) adjacent harmonics that will sound dissonant.
We have all been to birthday parties where the guest of honor is the recipient of the well-known happy birthday song. One person singing the song may have a fundamental frequency of 125 Hz, and another 128 Hz, while yet another person has a fundamental frequency of 233 Hz.
When singing together, many of the harmonics may be only several Hz apart, yet it sounds pretty good—context can be everything.
Context can also be affected by cultural elements. For example, in Hindustani Vedic music it is commonplace to have “quarter tones” where two adjacent notes may only have a frequency difference of 6 or 7 Hz, especially in the lower frequency region.
The same can be said of Celtic music where bagpipes have a drone whose harmonics may only be several Hz away from the fundamental or a harmonic of the melody. One may not like the sound of bagpipes, but nobody would use the word “dissonant” to describe their sound… well, maybe they would, but that’s merely a personal preference.
But using pure tones or single musical notes can be problematic.
Audio File 1, below, is in an ABA format where the A part is the note A (440 Hz) on a violin, and the B part is a slight detuning of all harmonics above 1500 Hz but by only ½ of one semi-tone.
Compared with the A part, the B part sounds dissonant and “out of tune.”
Audio File #1
Harmonic complexity can also be an issue that can make a dissonant sound appear to be quite nice. Audio File 2, below, includes the two notes C and C#, which are adjacent to each other on the piano keyboard. Around middle C these two notes are only about 15 Hz apart, and indeed, when played together, sound dissonant.
However, when these two dissonant notes are played as part of a more complex chord, they sound quite nice. For example, the C# major 7 chord is made up of C#, C, F, and G#. It still contains both C and C#, but with F and G# also added in, together the chord sounds quite good.
Audio file #2 includes several examples of the C and C# notes played simultaneously, and then again in a chord along with F and G#. All together they make up the very pleasant-sounding C# major 7 chord. In fact, this would be the case for all major 7th chords in music where a second—a ½ semitone above the root key—is played concurrently with the root of the chord and all sounds quite nice.
Audio File #2
Context and complexity can go a long way toward making what one person may consider dissonant, yet another person may consider to be not only acceptable, but an improvement upon the sound’s musicality.
**Note: Some parts of this blog entry were previously published in Sept 2024 issue of the Hearing Review
