On a related topic, Navani's research aligns really well with some cool music theory principles about tones and how "tuning" an interval actually works.
Like Serack described, sound waves "beat" against each other because of their relative frequencies. Sometimes, this interaction sounds pleasing, or consonant, and sometimes it does not. In general, the more consonant intervals correspond to simple, whole number ratios between the frequencies of the two notes. For example, an octave is 1:2, and a perfect fifth is 2:3.
Another way to describe the frequency of a note is to subdivide an octave into 12 equal pieces. Each subdivision is called a half-step or semitone . A perfect fifth corresponds to a difference of 7 semitones between the two notes being played, while an octave is separated by all 12 semitones. Using these measurements, if we start at a note and move up in pitch by a perfect fifth 12 times, we should arrive at the same pitch / frequency as if we had started at the same place and moved up by an octave 7 times (7*12 = 12*7).
However, going back to our definition of an interval as "simple ratios", we now run into a problem. Namely, if we take the ratio of 12 perfect fifths from our starting note, it is not exactly the ratio of 7 octaves ((3/2)^12 does not equal 2^7). It is close, but not exactly the same. This difference is called a "Pythagorean comma", and means that our two definitions of notes (frequency ratios and a 12 tone system) do not agree, meaning we must choose one or the other. In music theory, the ratio system is called just intonation, and splitting an octave into 12 equal pieces is called pure intonation. Each system has its own advantages and disadvantages.
The major benefit of pure intonation is that is always the same. Each note will always have the same frequency, regardless of what key the piece is in, or what other notes are being played with it. This means individual notes can be tuned exactly, and used in any piece (useful so that you don't have to retune an entire piano in between songs that are in different keys). However, to a careful ear, pure intervals often sound slightly off.
Just intervals (tuned using frequency ratios) usually sound slightly better, but are more context dependent, since they are defined as a ratio with respect to some other frequency. The choice of the frequency to define all other notes relative to corresponds to choosing a key for a piece of music, and will very slightly offset the positions of notes from where they would be in pure intonation.
OK, now that the context is out of the way, onto the connection to Navani's research. She ends up finding tones that correspond to Honor and Odium. At one point, she tries to sing Honor's tone at the same time as Raboniel sings Odium's, but something is wrong at first. Though they are each "pure" tones on their own, they are just slightly off when put together. This corresponds exactly to how individual notes can be tuned perfectly with pure intonation, but when they are put together in an interval, they sound just a little bit wrong! It is only after making a slight change to both frequencies that they truly combine, to create the Rhythm of War. This is exactly what just intonation does; it moves each note slightly from where it would normally be on its own, but as a result makes the interval formed by both notes sound better!
Anyways, I have no idea if this was intentional, but there are certainly some neat parallels between the way Sanderson wrote the magic system and real world math and music theory.