A perfect third is a music term where the periods of two periodic signals (sounds) have a frequency ratio of 4:5. Including this shows the LLM can integrate knowledge from different domains: music, math, flags of the world, and Mathematica.
There's no such thing as a perfect third in music theory, only perfect 4ths and 5ths, which explains the 4:5 ratio. There's major/minor (imperfect) thirds.
While "perfect third" may not exist as a name for an interval, it does make sense to apply the adjective "perfect" to the interval "third" in order to distinguish a just intonation third (4/5) from a well-tempered intonation third (1/2)^(4/12).
You can construct a system under which the phrase makes sense but musicians and musicologists will look at you weird if you say it. The LLM just forges bravely on, however.
I don't think of it as a failure. The LLM figured out a reasonable interpretation for a term it did not know. It might be better to come back with "do you mean pure ptolemaic major third?" instead of assuming, but the way it does it now might be better for programmatic requests.
Comments
A perfect third is a music term where the periods of two periodic signals (sounds) have a frequency ratio of 4:5. Including this shows the LLM can integrate knowledge from different domains: music, math, flags of the world, and Mathematica.
There's no such thing as a perfect third in music theory, only perfect 4ths and 5ths, which explains the 4:5 ratio. There's major/minor (imperfect) thirds.
Interesting test of LLMs, this one failed.
While "perfect third" may not exist as a name for an interval, it does make sense to apply the adjective "perfect" to the interval "third" in order to distinguish a just intonation third (4/5) from a well-tempered intonation third (1/2)^(4/12).
You can construct a system under which the phrase makes sense but musicians and musicologists will look at you weird if you say it. The LLM just forges bravely on, however.
Example usage here,
https://archive.org/details/onsensationston01helmgoog/page/3...
(by Helmholtz of Helmholtz Equation)
I'm very impressed that you were able to find this.
I don't think of it as a failure. The LLM figured out a reasonable interpretation for a term it did not know. It might be better to come back with "do you mean pure ptolemaic major third?" instead of assuming, but the way it does it now might be better for programmatic requests.
4:5 is a major third. "Perfect third" isn't really a thing in western music theory. Just found it odd the LLM didn't pick up on that.