Reading through Intervals 1 & 2 earlier made me realize that I left out a very important part of learning intervals: consonance and dissonance. These are loosely defined at the most basic level as “sweet” sounding or “harsh” sounding. I also like to use analogies like blending vs. clashing or restful vs. tense or stable vs. unstable. However, consonance and dissonance are not binary, but rather more like a spectrum.
The most consonant interval is an octave or a unison. This is two notes that have the same name in different registers, or two instruments or voices playing the same note. Part of why we hear octave equivalence (using the same name for notes in multiple registers) is that the sound waves have peaks and troughs the sync up. So a soprano might sing an A at 440 Hz (440 cycles of the sound wave in a second), but an alto or a tenor might sing A 220 Hz, and a Bass might sing A 110 Hz. These three notes sound similar because the for each cycle of the sound wave that the bass sings, the other singers match the peak by double (and then double again).
When the sound waves don’t match up on peaks and troughs, the sound waves compete an interfere with each other contributing to our perception of dissonance. (Some types of dissonance are learned too.) So a perfect fifth might match up sound waves most of the time but not as much as an octave, so it sounds pretty consonant, but we can still tell that there are two different pitches. Something like a minor second matches up almost never and sounds very dissonant.
Here is an approximate ranking of consonance to dissonance (but this may change depending on the style of music you are in) from most consonant to least consonant:
Perfect 5th/4th (tho 4ths are weird and have to be judged in context)
Minor 3rd/major and minor 6th (sixths are tricky because of their association with certain types of chords)
Major 2nd/minor 7th
Tritone and other augmented/diminished intervals
Audio for those intervals in that order (sorry for midi violin/bassoon sound, but it’s better than trying to hear the difference between two same midi piano sounds):
Note that intervals and their inversions are pretty much the same consonance level. Intervals greater than an octave are mostly reduced down to the similar interval less than an octave (a 10th is a 3rd plus an octave, so we talk about 3rds instead) except for 9ths (2nd + octave) which most often have a different usage and impact than 2nds.
Minor seconds sound pretty much the most dissonant because they are so small. Tritones and other augmented or diminished intervals often sound more dissonant in context, especially with certain types of chords, but out of context on their own the sound wave interference isn’t necessarily as audible.