Hi, I understand that beats are the difference between two sounds having different frequencies, which propagate simultaneously in the same body that produces them.
Therefore, I wonder what hyper-beating intervals like major or minor thirds, sixths, tenths, and seventeenths are?
Therefore, I wonder what hypo-beating intervals like fourths, fifths, and elevenths are?
Since PURE intervals such as octaves and sixteenths do not have beats, can I use them as a comparison to understand if the piano is in tune? So, in the case that I hear beats, is the instrument out of tune?
For hyperbeats or hypo-beats, one refers to the "speed" (give me the correct term) with which these occur. The faster the beats, the further they deviate from the pure interval.
You stated that octaves are correct: this is only true in theory because they must be widened based on the inharmonicity of the instrument: on the bass notes, fifths may need to be tuned correctly and use sevenths as a reference. It is a very difficult subject: I hope I have conveyed the idea, even if with improper terminology.