I own a number of Ps and one sort of mongrel Mustang (recent Squire Mustang body, JMJ Mustang pick guard and pickup, killer 70s Fender Musicmaster neck currently strung with LaBella Mustang Deep Talkin' flatwounds). They can definitely fill in similar sonic roles, but back to back and in a mix they can also be pretty distinct especially with flatwounds.
My comparison here will be assuming both instruments are loaded with similar flatwounds- if you are using bright roundwounds I think a lot of the tonal signatures of certain instruments can get lost under all the harmonics so I can see how the sound could be less distinct for those using brighter tones.
P-basses are midrange machines, which is why I suspect they fit so well into just about any genre where they fill the right space above the bass drum without messing with the guitar as long as you are careful with your tone and playing. A P-bass also has a sort of rounder or compressed attack and potentially fairly long sustain (unless you are using some sort of muting techniques or very old strings). A Mustang (consistent with many short-scales) has less harmonic stuff going on, so notes up and down the neck tend to sound fatter and it seems like in general the sound is taking up less sonic space than a P but somewhat more forceful in the space it does occupy. Mustangs also have a sharper attack (amplitude envelope vs frequency- more “plunk” than a P-basses “thump”) and less sustain in general (the pickups have a single pole located directly under the string vs the "split-pole" design of a P-bass pickup and more consistent with Fender guitars, the original single-coil P-bass, or instruments like Rickenbacker 4001/4003). I think the combination of all these factors makes tight melodic lines really punch through a mix on a Mustang with ease (especially with a pick, but possible with finger style too- mine sounds particularly great using palm-muted thumb/fingerstyle techniques) in a way that a P-bass requires more manipulation/care to achieve- it can be fat and clear with each note in a really distinct way. I'm not sure I'd choose the Mustang specifically in a role where I didn't want the bassline to stick out.
Of course the playing feel of a short-scale and long-scale is way different! In general I find long-scales easier to control due to my large hands and the tighter string tension and so I only choose the short-scales for tonal reasons when I think they'd be right. The Musicmaster neck on my Mustang is super thin and fast, but I can tend to dig in too hard or fumble around a bit with my fretting hand unless I spend awhile rehearsing on short-sale before a gig to refresh my muscle memory. I do find the Mustang tonally to be somewhat forgiving of digging in too hard in a way that some of my P-basses might not be (the setup on my neck is really nice though, may not be as great on lesser necks).
My comparison here will be assuming both instruments are loaded with similar flatwounds- if you are using bright roundwounds I think a lot of the tonal signatures of certain instruments can get lost under all the harmonics so I can see how the sound could be less distinct for those using brighter tones.
P-basses are midrange machines, which is why I suspect they fit so well into just about any genre where they fill the right space above the bass drum without messing with the guitar as long as you are careful with your tone and playing. A P-bass also has a sort of rounder or compressed attack and potentially fairly long sustain (unless you are using some sort of muting techniques or very old strings). A Mustang (consistent with many short-scales) has less harmonic stuff going on, so notes up and down the neck tend to sound fatter and it seems like in general the sound is taking up less sonic space than a P but somewhat more forceful in the space it does occupy. Mustangs also have a sharper attack (amplitude envelope vs frequency- more “plunk” than a P-basses “thump”) and less sustain in general (the pickups have a single pole located directly under the string vs the "split-pole" design of a P-bass pickup and more consistent with Fender guitars, the original single-coil P-bass, or instruments like Rickenbacker 4001/4003). I think the combination of all these factors makes tight melodic lines really punch through a mix on a Mustang with ease (especially with a pick, but possible with finger style too- mine sounds particularly great using palm-muted thumb/fingerstyle techniques) in a way that a P-bass requires more manipulation/care to achieve- it can be fat and clear with each note in a really distinct way. I'm not sure I'd choose the Mustang specifically in a role where I didn't want the bassline to stick out.
Of course the playing feel of a short-scale and long-scale is way different! In general I find long-scales easier to control due to my large hands and the tighter string tension and so I only choose the short-scales for tonal reasons when I think they'd be right. The Musicmaster neck on my Mustang is super thin and fast, but I can tend to dig in too hard or fumble around a bit with my fretting hand unless I spend awhile rehearsing on short-sale before a gig to refresh my muscle memory. I do find the Mustang tonally to be somewhat forgiving of digging in too hard in a way that some of my P-basses might not be (the setup on my neck is really nice though, may not be as great on lesser necks).
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