Edit: Most of the explanation I came up with for this turns out to be wrong. I will update when I understand more thoroughly.
I recently had a conversation with my dad regarding “overtones” (a note that can be heard in a chord that is not acutally being sung). He informed me that what we in the barbershop community call overtones can be more accurately called sum tones, or as wikipedia calls them combination tones. The explination is that all tones, or sounds that we percieve as a single note, are actually comprised of that note, and an infinite number of notes above it (overtones). These notes are arranged according to the harmonic series: the root and octave above, the fifth above that, the root above that, the third above that, and so on with the intervals between these notes getting smaller as we go higher. The strength of each of these overtones depends on the vowel being sung, and the wave form of the tone (e.g. sine wave, sawtooth wave, square wave). When a sum tone is heard, it is because the overtones of two or more notes overlap on at least one overtone. This overtone, because it is present in more than one note, is therefore heard much louder than the other overtones and therefore can be heard as its own note.
My dad has also told me that square wave-type tones create more overtones. At least I think that’s what he said. So, in an attempt to create a sum tone, as well as hear a robot barbershop quartet, I recorded a barbershop tag in my robot voice, which seems to me to have some of the qualities of a square wave.
In the following recording, on the last half of the last chord, if you listen on good spearker or headphones, you can hear the overtones overlaping on the 9th of the chord forming a strong sum tone. If you have trouble hearing it, try singing the 9th right at the beginging of the chord, so you know what to listen for.
This tag was recorded with no post processing - equalization, reverb, special effects - at 4am (I am sure my neighbors think I am very weird) and is from this collection. I have changed the word “born” to “made” for both a brighter vowel, and because its being sung by robots. It is also the tag I changed the words to for my mom’s mother’s-day gift.
Things I still don’t understand:
- My calculations show only one voice contains the sum tone that can be heard in my recording.
- Why do different wave forms have different overtone content?
- What are odd harmonics and even harmonics?
- Which octave is the sum tone actually in?
Things I would like to create to illustrate this phenomenon:
- A stereo audio file with the unaltered tag in one channel and just the frequency of the sum tone (extracted from the actual audio of the tag) in the other.
- The overtone content of each note in the chord written out in staff notation showing which notes contain the sum tone.