> Another dog sense I've wondered about is hearing. What is our music like to them?

This is a thing I've wondered about too. Their frequency range is only part of it. There's also the frequency weighted sensitivity; it's why we humans perceive music the way we do. A dog might be able to hear a tone at 45kHz, but it might require significant amplitude, e.g. threshold of perception at 45kHz might be 80 dB SPL. The ISO 226:2003 equal loudness contours shows that human sensitivity for high frequencies falls off very sharply after about 16kHz[1]. Looking stuff up for dogs, I'm finding mixed results, so I'm less confident in my assertion here, but it seems to me that dog hearing still falls off sharply near the upper end of it's range. From the charts I find, a dog's sensitive band seems to be wider than humans and centered higher[2], but there's still that sharp upper cutoff.

> Let's consider live music, first. A lot of instruments have significant harmonics well above 20 kHz.

This is heavily dependent on the nature of the instrument. A bass instrument like a tuba or a bass guitar isn't going to have much frequency content once it gets into the mid-to-high hundreds of Hz. A guitar is going to be done between 10-15kHz, and most of it's frequency content that defines its character is going to be down in the mid-range (mid-hundreds to low thousands of Hz). Cymbals? Yeah, I'd be in no way surprised if those contain tons of content above 20kHz that's only detectable with lab equipment or a dog's ears.

> Does the instrument maker take any care to get the harmonics above 20 KHz right? They don't affect how the instrument sounds to humans, so I'd expect not. That could mean that your beautiful violin has a horrible screech that only your dog hears.

Instruments with significant frequency content in our most sensitive bands (e.g. human voice, eletric guitar, trumpet) are often considered 'lead' instruments, and they're are also the ones where getting the frequency balance right to sound good instead of harsh is the trickiest. So, my intuition is that a similar thing plays out with dogs. Those instruments that do contain significant frequency content in the high kHz to low 10s of kHz (e.g. cymbals) are more likely to sound harsh, IMO. Something like a tuba, a dog probably cares less.

> How about recorded music? If my guess is right and our instruments sound bad above 20 KHz, recorded music may be an improvement from the dog's point of view, because we filter out those highs when recording.

> But if live instruments do actually sound OK above 20 KHz, then to a dog our record are going to seem limited at best.

My guess here is that our recordings probably sound unnaturally muffled. In my own study of recording and mixing, it seems common to filter sharply above 20Khz, or maybe a little less, because their's no sense in frying the tweeters with content nobody can hear anyway. Additionally, the DACs in modern recording gear are going to have their filters set to filter sharply above 20kHz anyway, to keep digital aliasing noise from impairing an accurate reproduction of the original analog signal from the digital one. It might not sound bad to the dog, but I'm pretty sure a dog would be able to easily tell the difference between a recording of a cymbal, and a live cymbal.

1. https://en.wikipedia.org/wiki/Equal-loudness_contour

2. https://www.lsu.edu/deafness/HearingRange.html