so at my lesson today we began learning some harmonics, and he said the 12th, 7th, and 5th, frets were the basic harmonics and so on.. but I don't understand how a harmonic over a fret is not the same note if ur finger is pressed down on that fret and played, and is there a pattern to the harmonic notes?

i couldn't find this on the search bar so if this thread does exist plz link me, thanks
Every note has a harmonic series, and by shortening the string length at the fret but not pinching the string, you isolate certain frequencies to hear that particular overtone. If you take any theory classes you learn about harmonics and how they work. Suffice to say for now that fractional amounts of string length (1/4, 1/3, 1/2 for starters) produce those overtones when plucked but not fretted. By actually pushing down on the string you shorten the string length and create a different pitch. By gently stopping the string on the fret, you maintain the fundamental pitch (ie. G for your G string, A for your A string) but isolate and hear the overtone from the point where you put your finger. Theoretically, any fret will produce a harmonic, and on good (stress the word good) guitars you can easily produce harmonics from the 3rd, 9th, 15th, 8th, and 2nd frets as well as the typical 5th, 7th, and 12th frets.
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Basically, your harmonic is playing a note in the overtone series of the string. Octave, octave and a fifth, out of tune octave and a minor seventh, two octaves and so on. The only place on the neck where the fretted note is the same as the harmonic is twelfth, 24th, and I suppose 36th.
on bass, some harmonix are hard to hit. the basic ones are 5,7,12,17,19,24 depending on how many fretts you have. how it produces the same pitch as the fretted note is all in the shortening of the string like musicology said. but instead of giving the pitch of the freted note, it gives the pitch of the note at higher octaves. the more advanced you get, and the better your touch becomes, you can start hitting harmonix from the 2nd fret all the way beyond your neck. its much easier to do this on guitar, but a bassist can learn them if he tries.
Harmonics actually ring out much nicer on a bass than a guitar. It doesn't depend on the amount of frets as harmonics are completely based on the physics of your string and can be found on the string, regardless of the number of frets. You actually can't hit harmonics anywhere, there's a very specific overtone frequency series. You can get psuedo-overtones that are just the harmonic played incorrectly, that souind different, but are in reality the same thing. And finally, the harmonic does not produce the fretted note at a higher octave. Fifth fret harmonic is two octaves. The fifth fret is not an octave of that string.