I have a very, very vague memory that some loony conspiracy theorists in the 1960s thought that you could pick up esoteric, alien messages by playing one of The Beatles’ albums backwards (something to do with ‘Klaatu’, whatever that was all about).
But of course those were the days when Charles Manson’s ‘Family’ cult picked up messages from ‘Helter Skelter’ on The White Album that led them to murder the lovely Sharon Tate.
It’s a strange old world out there!!
Messiaen would have an answer.
Most of the suggestions so far are pre 20th century. But there is a lot of really good classical music since then.
20th century music is much more varied so if you dislike one piece there are lots of other pieces (by other composers) that are quite different.
Here are some suggestions …
Shostakovich: Symphony no 5
Bartok: Concerto for Orchestra
Bartok: Music for Strings, Percussion and Celeste
Stravinsky: Firebird
Stravinsky: Petrushka
Stravinsky: Rite of Spring
Stockhausen: Stimmung
If you are interested in Beethoven, note that 2020 was a significant anniversary and you can get a box set of his complete works (over 100 CD’s) for about £100. (There are various labels doing such sets).
I have to say, there’s a lot of bombast in some of the suggestions. The Beethoven cycle is a great first choice though.
I’m listening to Beethoven Symphony No.3 Op.55
Conducted by Simon Rattle at the moment … it’s bombastic 
I’ll take the advice above and will take a week listening to just classical ( it might include some Howard Shore LOTR 
) and see how I get on
Thanks again for all the recommendations
Could I gently recommend some Boccherini?
Janacek Sinfonietta is lovely, startling and never to be forgotten.
Watching several Great Whites circle the boat in South Africa , I could swear I heard music …
You already have some excellent recommendations; if you like violin music I would recommend Sibelius’s violin concerto. If you like his darker moods then try his symphonies and tone poems.
I don’t think that Sibelius symphonies are his darker moods necessarily. They always speak to me of the uplifting great open spaces of Northern Finland. They are lovely to listen to, I agree.
On R3 Essential Classics every morning is excellent as is the live concert at lunchtime.
Besides birdsong … his Quator pour le fin de temps is very meditative - since you’ve mentioned meditative regarding the Feldman piece.
The Sibelius symphonies are wonderful pieces, and they have been ‘lucky’ in the recording studios: Bernstein in NewYork (CBS, now Sony) and later in Vienna (DGG), Karajan in Berlin (4 to 7 on DGG, and later, complete on EMI), Colin Davis (in Boston, Philips, and LSO Live) to name just a few that I know well. The first serious recordings were made under Anthony Collins, which flit into and out of the catalogues over the years, and which are said to be very special indeed - I have never been able to get hold of copies.
Quick thread heist. Talking of great 20th century symphonies, there is a really excellent programme about RVW’s 6th symphony by Simon Heffer on BBC Sounds “Such stuff as Dreams are made on” (Broadcast Sunday, 6.45pm)
Back to the thread: For something which is rather more off the beaten track but highly enjoyable nonetheless is George Lloyd’s 5th Symphony. The recording conducted by the composer is good, the one conducted by Edward Downes is, in my view, better. (Both available on Qobuz).
I recommend Blomstedt (San Francisco SO) on Decca or Vanska (first cycle with Lahti SO) on BIS. Give them a listen some time 
Minor comment - to my knowledge Von Karajan never recorded Sibelius’ third symphony.
Thank you, WW, I shall try to do so, if the opportunity ever presents itself.
You may well be right, I currently have no means of checking at present. I know that, in the early DG cycle, Karajan only recorded the Fourth to the Seventh, with someonre else, Okku Kamu (?), taking over for the first three.
I thought that Karajan had recorded all seven for his later EMI set, but I may well be misremembering that.
I have had fun and success picking up Classical Vinyl from a local charity shop in the last couple of years. Need to search through for condition and then assessing whether you might like it. At about £1.50 or £2 a shot it is low risk. I have picked up about 40 albums in 3 visits about 9 months apart. I guess they are from house clearances and quite a lot are as new. Very few I have not liked.
@Thomas gave me this list a few months ago which I really enjoy. I’m also clueless in Classical.