I dunno about that. Standing in the bar of the Hong Kong Aviation club when the last scheduled Dragonair 737-200 service departed runway 13, the JD-8Ds brought to almost max power before brakes released. Windows shook, flat beer revived, conversation drowned, pretty charismatic to me.
Then I have memory of the comforting sound of the big radials fitted to DC3s or Bristol Freighters droning overhead my house at 1 am on their way to Tasmania from Essendon, pushing into a 50 knot headwind on a Melbourne winter's stormy night as they made for Bass Strait. I say comforting as I was tucked up in bed.

Growing up next to LHR in 50s and 60s one got very attuned to the many different engine sounds and could be very accurate about guessing the type from the noise . Even able to distinguish different type same engine, Comet /Caravelle for instance.

But that's along long time ago and cant be too fussy these days but having been in Czech rep last week the town i was in has a small but pool table flat grass field which I always check out when there. s i drove up this time Iwas treated toa gang of skydivers climbing aboard an AN2 . great cloud of blue smoke and rattling at start up and tremendous rumbling and clunking radial noise when taxying , so rare to hear any radial now.

They really a re quite amazing planes it was full of jumpers but was airborne in a tiny fraction of the runway length and 10 mins later up at dropping height , 8000ft?? maybe it had no apparent forward motion at all on a windy day . Lovely twenty minutes spent there..

i think it is often the sound that gets ones attention too and if it heralds something unusual even better, a few years back when I lived in Camberley I was out walking the dog and heard a very very unusual sound and a F4U Corsair hove into view, a real thrill. Also one still evening , again dog walking a most unusual clattering rumbling noise a long way off, luckily aclear sky and a clear view revealed a dark speck moving very slowly north to south and a good five minutes later it reveals itself a s its a JU52 , Never ever though i would see one , unbelievable slow and a wonderful sound (

Ditto. Our house was under the approach path for runway 28L. Other distinctive engine tones: the crackle of Wright turbo-compounds on Super Connies and DC-7s and the low-pitched whine of the Centaurus on BEA's Elizabethans.

Our TVs also served as aircraft detection systems: before the engines could be heard the TV picture (405 lines, black-and-white) would start to fluctuate in brightness (presumably as the signal reflected from the approaching aircraft interfered with the ground wave). As the aircraft got closer the fluctuations would increase in intensity but slow down in frequency, eventually to a constant brightness. Then the sequence would reverse as the aircraft flew on towards LHR.

I'd suggest taking a look at the dictionary then. Hence my comment.

The New Oxford American Dictionary - Charisma is compelling attractiveness or charm that can inspire devotion in others.

As we often talk of aircraft in the feminine and talk of a particular aircrafts characteristics, some appealing, some not, as in, she's a bitch, I think it's fair to say they have charisma, or not. Some I've flown have inspired devotion, some I fair lust after.

Just trying to get to the crux of the OP's intent: hence I think we mean 'charming' or possibly 'evocative'. I doubt many engine sounds inspire devotion unless the sound of a Merlin has made you go out and buy a Spifire.

But in terms of 'engine sounds I like', for some bizarre reason, I do enjoy the sound of Diamond Twin Star diesels! Make sense of that :)

Oh, I don't know, an R-1820 in a T-28 inspires devotion in me, not when its in a DC-3 though. (Heading out to hit the boat)


https://cimg7.ibsrv.net/gimg/pprune....4eb108831d.jpg

Based at RAF Thornhill (5 FTS) in S. Rhodesia 1951 - 1953, individual Harvards were noisy, but we got used to it. However, a formation of 21 flew down to RAF Kumalo for a football final at which Thornhill were playing. So one Harvard can be noisy, but 21 together can be very noisy.
Formation photographed by me at the time.

https://cimg0.ibsrv.net/gimg/pprune....e643b39ebb.jpg
21 Harvards together

I don't think that any gas turine can compete with a merlin
I never found the Dart noise very exciting and as
for the manic screeching of the CSDS on the 1-11
when we were always waiting for an overspend and a get your hands dirty standing on a bar box under the the engine to do a reset

With the handle of a hammer.

Discord

I had forgotten aboutt he TV phenomenum.
Where I lived, Stanwell, we were not far from the extended centre line of 23R . With strong south westerlies a common occurrence that runway was used a lot especially in winter and as you say as the aircraft taking off approached the TV would start to flicker , that would increase until it started to fade gain.
I was told it was a sort of radar effect with the TV signals being reflected by the props . I dont recall that many jets used 23R and cannot remeebr noticing any difference , they were probably a lot higher passing my road than DC7s and the like. Although out delivering papers one Sunday morning around 7am a sadistic Pan am skipper decided he would awake the snoozing populace with a full power take off on 23R in the period when it wasnt used much but was still available for use

PB

Since it says "Engine sound" and not "Aero-engine sound", can I forward a 3 cylinder Lister diesel in a narrowboat?

Don't know that one but if we allow narrow boat engines nothing beats the single-cylinder two-stroke Bolinder semi-diesel:

Whilst I like the sound of old narrow boats as they pass, I think the thump, thump, all day would get to me.
My narrow boat has a Barrus Shire engine with a hospital silencer and thick rubber insulation under the rear deck. I can hardly hear the engine at normal canal speeds and often get asked if I'm electric.

For non-aviation I'd have to say the Deltic, a sound like no other diesel I've ever heard.
And the opposite extreme to a high revving engine, not charismatic but I'm fascinated by the old Field-Marshall tractor which I believe had a massive single-cylinder engine which fires about once a fortnight on tick-over.

something different..
 

Well my vote is for the wonderful Detroit 2-stroke diesel, especially the 8V-91. On acceleration it sounds incredible but even better when slowing down using the jake (Jacobs) brake. Visceral...

Well if we're determined to ignore the OP's first explanatory post that specified aircraft engines ...

https://cimg3.ibsrv.net/gimg/pprune....2b24a744ba.jpg

:O

Well if we're going to open it up to non-aviation, a auto racing V-12 at speed is music to my ears. First one I heard in person was an IMSA Jaguar big V-12 - first time it went at an IMSA race in Portland, by my buddy and I just looked at each other and smiled.
The Ferrari F-1 engine in the late 1980's to mid 1990s was even better, reving up to over 15,000 rpm - simply beautiful. I actually bought a CD of V-12 engine sounds back in the 1990s :O

Okay, I'll bite. What engine sounds like making love to a not so beautiful woman? :)

While here, I never picked a single engine sound as the one. Hearing a multi-ship of C-130s taxi out, going in and out of reverse and/or 'low-speed ground idle' setting always did it for me.