Do harmonics work the same on bass guitar as is the case with a regular guitar (Natural harmonics at the 7th and 12th frets) or is it different on the bass?
It's the same as on a guitar. Harmonics occur at equal divisions of the string length. Half the string is the location of the 12th fret. This produces a harmonic at twice the frequency of the open string, which is one octave higher.
Dividing the string into thirds, which is at the 7th fret, produces the fifth of the 12th fret harmonic. (Halfway between the 7th fret and the bridge, at the 19th fret, you'll find the same harmonic.)
This continues to work up the harmonic series. If you divide the string in equal fourths (which occur at the 5th and 24th frets), you'll get a pitch two octaves higher than the open string.
By dividing a string, you can find these same harmonics on any stringed instrument, though you don't necessarily have frets as a convenient reference.
Harmonics are always at the same (proportional) spaces on any string.
The only thing that matters when determining where harmonics appear on a string would be length of the string. The 1st harmonic will always appear halfway inbetween the endpoints of the string (if it's fretted, count that as the endpoint), the next one divides the string into 3rds, etc...
That also means that the harmonics will always be in the same location relative to the fretboard (for instruments that have them), so as an example, the bass guitar and the guitar will both have a harmonic over the 12th fret on an open string.
Yes, the harmonics work exactly the same way on guitar and bass. Actually it's somewhat easier to produce higher harmonics on bass (at least with fresh roundwound strings), due to the longer scale length, but they are in principle the same.
Here's a listing of the (IMO) usable harmonics on the A string (lower clef “where you finger” the flageolett-nodes, upper clef resultant sounding note):
X:1 L:1/4 M: K: %%score T1|B V:T1 clef=treble V:B clef=bass-8 % 1 [V:T1] "15mb"A,|"8vb"A,|E,2 |A,2 |^C4 |E |G3 |A |B| s: (×1) |(×2) |(×3) |(×4)|(×5) |(×6)|(×7) |(×8)|(×9)| [V:B] A,, |A, |E, E |D, A|^C, ^F, ^C ^F|=C, |=C, _E, G, |B,,|B,,| s: 0 |12 |7 19|5 24|4 9 16 21|3 |2.7 6 9.8|2.4|2.2|
Of course, the pitches are in just intonation: the 5-limit C♯ and particularly the 7-limit G are noticably flatter then their closest 12-edo representatives.
You can go even a bit higher, but from the 8th harmonic it starts to become unreliable which multiple you actually hit – though this can be improved by fingering two nodes on the string. It generally seems to work best to finger both the second and third node, counting from the nut.
Ordered sequence of notes that can be played as natural harmonics on a 4-string bass (preferring the lowest position on the neck that responds well and avoiding 7-limit versions, when there are multiple options):
X:1 L:1/4 M: K: %%score T1|B V:T1 clef=treble V:B clef=bass-8 % 1 [V:T1] ^G, A, B, ^C D E ^F G ^G A B | s: E×5 A×4 E×6 A×5 D×4 A×6 D×5 G×4 E×10 D×6 G×5 | [V:B] ^G,, D, =G,, ^C, G, =C, ^F, C [^G,,_B,,] =F, B, | s: 4 5 3 4 5 3 4 5 4;6.3 3 4 | [V:T1] c ^c d e f ^f g a b c' | s: D×7 A×10 G×6 D×9 G×7 D×10 G×8 G×9 G×10 D×14 | [V:B] _A, [^C,_E,] _B, [^F,A,] ^C [^F,_A,][A,C] [B,D] [B,_D][=F,_G,] | s: 5.9 4;6.3 3 4.4;7 5.9 4;6.3 2.4;5 4.4;7 4;6.3 2.7;4.3 |
To flesh out the other answers with some practical pointers, try the fifth fret (gives you two octaves above the open string), and the fourth (produces a third plus two octaves above the open string). There are are further harmonics to be found, both above frets and between them, but the two mentioned above will be easisest to find and play (as well as the 7th and 12th frets, of course).