(Too long...I'm sorry! I meant only to mention Busoni

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I must say, dlu, I share your love for Mahler, and your need to be better acquainted with his music. I have the scores of his songs and symphonies, and at least 30+ recordings and performances of each symphony, including nearly 70 of the 6th Symphony (!), and still there is this wall, and this constant begging desire that I approach it with a baton and an orchestra...alas a "need," at this point, I quite honestly know not how to fill.
I've wanted to come across a composer (who wrote for the piano) that was/is a master manipulator of the tonal system; someone who could convey overwhelming emotions; music that is tragic and unharnissed and full of drama.
For me, the answer is Ferruccio Busoni, whose pianistic legend has sadly placed his wealth of compositional talent in an unfair shadow. I was reading through the Elegies today and there is an obvious Mahlerian influence, especially in All'italia which is very close in language to some of Mahler's Wunderhorn songs...the almost manic play on the major-minor progressions and the emotional language...The mood swings produced are a Mahler finger print. This small etching of influence is not to take a way from Busoni's fantastically original sound-world, as anyone who has experience with the operas, the elegies, the Fantasia contrappuntistica, etc. very well knows.
Incidentally, Busoni performed with Mahler's orchestras (or at least the Philharmonic Society of New York), and the last concert Mahler conducted included the premiere of Busoni's Berceuse elegiaque, which is of course, the orchestration of the 7th Elegy; this originally piano composition is the seed that blossomed into this orchestral vision - as unique and beautiful a work as has been penned by man (and I mean that! Completely transcendent). Have a look! You can stand up for his compositions which desperately need to be performed and remembered!
Also, do not neglect the so called, Second Viennese School, Schoenberg, Berg and Webern. They were born out of the vast romanticism of Wagner, Bruckner and Mahler (and I'll include Brahms!). A little study shows their great respect for Mahler in particular...Schoenberg's writings, Berg's claim that "There are only two 6th Symphonies...Beethoven's and Mahler's..." and that the 6th was the first symphony of a new era. This does leave you with only a few options, and on paper these options may seem the ascetic opposite of Mahler, but they are highly concentrated and an inward answer to Mahler's outward language (I'm not going to try to work that out...). Of the three, Berg is the closest, that leaves you with that Op. 1 sonata (a masterpiece!) and a chamber concerto, if you wish to be so involved.
How about Britten?
Both Britten and Shostakovich were famously fond of Mahler, though both fall well short of the type of musical complexity Mahler's music displays. Let that simplicity come as refreshment to your mind, as there is much to love and experience. Britten inherits the same usage of folk song and common elements (not banality!) which Mahler inherited from Schubert. I'm afraid I cannot speak with any depth on any solo piano pieces Britten may have written, as I'm much more familiar with the larger orcherstral works and the opera's, but there is a piano concerto which is lean and energetic with a neoclassical tilt, and do find some singers to go there some of his songs! You'll find singers love singing them, and you'll love playing them, and will be much better for the collaboration.
Shostakovich, of course has two sonatas, two sets of preludes, ala Chopin...ala Bach (preludes and fugues), which speak for themselves. Shostakovich has in his works, little hidden tributes to composers he's loved and been influenced by, such as Bizet's Carmen in the 5th Symphony, Berg's Violin Concerto and Beethoven's Moonlight sonata in the Viola Sonata, etc. and I think you'll find many small, if indefinable illusions to Mahler also. The conception of the Viola Sonata itself, may elude to Mahler's 9th Symphony!
On this note, back in February I was fortunate enough to play an atypical, but very rewarding recital with a cellist. We had started making plans in October, at which point she offered a 30 minute slot in the recital all to myself (a bit rare!). So the program was as follows: Vivaldi Concert in G minor for two cellos, Shostakovich's Cello Sonata, and Beethoven's Op. 111 Piano Sonata. Now, sometimes in working on certain pieces of music, what might be a universal constant can hit you in different ways...seeing things through the eyes of other things, whether they have much to do with each other at all - It's quite fascinating, and in working with the Shosty Cello Sonata, moments from Mahler's 7th Symphony often crept in my mind (especially in the first movement's second theme). Now in this case, probably a coincidence relating to a familiarity with the Mahler 7th, and the phenomenon of the above universal constant.
But the Beethoven brought something much more revealing - and here is a point... you can travel backwards in time, as well as forwards, i.e. searching for things which brought about Mahler (or think of how amazing the comparison between, works of other composers, such as the astounding shared nature of the harmonic mountains in the developement of Schubert's G major Sonata, and the slow movement of Bruckner's 8th Symphony!). In practicing the trills which close Beethoven's op. 111, I was overwhelmed with this deja vu, that I'd tasted this feeling before. Indeed it was the "Ewiger" of Das Lied von der Erde on the tip of my tongue, and it is a startling similarity...that holding on and seeping out. Even more amazing is the discovery of Mahler's own experience with Op. 111 as written by Fritz Loerh:
"He could never have given an account of how he achieved what he did; every thought of technical difficulty was utterly cancelled out; all was disembodied, purely contemplative, passionately and spiritually concentrated on all that, without conscious physical contact, passed from the keys into his being. In a way all his own, comprehending it with the energy and accomplishment of genius, bringing out every nuance, every shade of expression, he caused the music to ring out with all the force with which it had gushed forth from the soul of its creator. In Beethoven's Sonata Op. 111 (No. 32), for instance, the storm at the beginning broke out in a terrible maestoso, shatteringly intense, with a wild ferocity such as I have never heard again; and similarly the finale faded out, pure, utterly luminous, in loveliest beauty, softly and softlier still, from closest touch with this earth out into eternity."
As well as the knowledge of Mahler's quoting and eluding to Beethoven's Op. 135 in his 3rd Symphony, and Op. 27 no. 1 in the 4th Symphony. Add to this the possible illusion to the first movement, Op. 111 in the build up and march of the finale of Mahler's 2nd Symphony!
This could go on and on, and looking up, it appears it has, and I'm sorry I've written so much, at least for the sake of my current exhaustion (which somehow lends itself to on and on writing...hm). I hope at least some of this is helpful...Beethoven, Schubert leading to Mahler; Busoni, Britten, Shostakovich taking from Mahler, etc, with no end.
Ah....good night, or morning or whatever it is!