The function of modulation and tonality is as important as the degree. Classical forms and harmony are inseparable. Throughout the nineteenth century the dominant was being supplanted by more remote keys - for instance the mediant in the Waldstein. Keys were chosen for expressive rather than structural reasons. Drama or a programme added another dimension to this. Associating particular keys with events or people or moods necessitated a radically different conception of tonality and structure. The conflict of programme and absolute music was a major issue of the nineteenth century, and one which Wagner ignored, by writing opera and saying that absolute music bored him because it was "unspecific". While he did use keys as dramatic representatives, or as in Tristan emphasising the change that occurs during the opera (begins in a minor, ends in B major), it was left to others, such as Mahler, to incorporate this into symphonic works. Such key usage has a conservative effect on harmony, as it requires that keys are established obviously. Mahler wrote many clear diatonic passages in his 4th symphony, which progresses through G from B to E, but with meticulous conventional structures. Strauss, who made less use of progressive tonality, was more prone to continuous chromatic modulation. When Strauss did associate keys dramatically, it would be contrasts - such as C and B in Also Sprach Zarathustra (a contrast which exists at all levels from structural downwards), or unresolved polytonal effects - such as A major and Eb minor in Elektra,or D minor and B major in Salome (represented a demand that Herod be silenced).
There is a fine line between extreme modulation and chromatic wandering. Liszt was known to pass it (deliberately in his last piano works), but Wagner was one of the first. His traditional method was to add an unimportant note to a normal triad, and force modulation by emphasising this note. That in itself was not a breakthrough. What mattered was whether that note was the agent or the decider of the modulation. Frequently in Wagner, there is a clear root harmony served by such agents. There are times though in Tristan where the only connection between chords seems to be semitonally. Where this happens one can speak only of chords, not modulation. The Tarnhelm motif in the Ring is a good example. Schoenberg was to follow this up from his beginning. Verklärte Nacht was rejected as having a single undefinable chord - one created by semi-tonal movement. Mahler's more chromatic passages are frequently driven by internal part movement.
The role of melodies and motifs within a texture was bound up with the desire for unity. The discovery of Bach had prompted a huge interest in miniatures, which contrasted with Romantic monumentalism. Wagner's use of leitmotifs showed part of the way for detailed motivic working that was not necessarily dramatic, however Wagnerian leitmotif (and the seamless texture it derived) came to a dead end with Strauss (Debussian leitmotifs were something altogether subtler and more ambiguous). Wagner generally used combinations and transformations in a manner clearly derived from Liszt, but it was Brahms built melodies, chords, tonal associations, and whole structures around tiny motifs that pointed towards unity of horizontal and vertical musical space that was so influential in the Second Viennese School. Schoenberg's statement that he owed most to Bach comes in part from this, and “through Brahms” can be added. Wagner, for all the melodic and chordal use of the Tristan idea, never developed this far.
Wagner's innovations in rhythm are perhaps more influential than in harmony. While there was a very strong beat, there was no regular strong/weak pulse of the sort that characterised music of the past two centuries. This was partly due to the elaborate setting of words to melody. There is an endless range of emphasis which serves to create a free and flexible metre that serves the words. Within orchestral parts there is immense rhythmic subtlety and detail, which sometimes leads to a diffuse rather than free sound. The setting of Stabreim verse to music had great effect on Schoenberg, who frequently created musical prose in his efforts serve the words. Strauss attempted similar things, but while at first glance the vocal lines are similar, they lack Wagner's subtle correspondance of word to music. Brahms' rhythmic subtlety was in the school of Mozart and Beethoven - pliability within a fixed framework. The rhythmic expansion and contraction of motifs - no innovation in itself - was against a very clear metre. Reger's freedom, particularly to write out accelerations, derives largely from this. Schoenberg on the other hand followed it in his neo-classical works but not in his expressionist ones.
Wagner's treatment of voices and orchestra had a similar aim to his treatment of rhythm. He wished to create something which followed the precepts of what he knew of Ancient Greece, which included the synthesis of music, drama (including poetry and acting). His vocal lines are exceptionally taxing for singers, yet the orchestral backing makes them singable, especially at Bayreuth where the orchestral sound bounces off the parabola and comes at the audience after sound produced simultaneously on stage. The essentially symphonic nature of his voice and orchestra blend was to influence Mahler greatly. Das Klagende Lied, a Wagnerian cantata, has a very intense and prominent vocal line. The Wunderhorn songs are noted for their powerful melodies supported by strong yet clear orchestral accompaniment. By his maturity and old age, his vocal writing was changing though, musical prose was moving towards recitative in parts of Das Lied von der Erde - once more, Wagner influence at first, but displaced by earlier German composers' influences - in this case most of all Bachian church cantatas and Passions.
Berlioz had been instrumental in a revolution in orchestration. Wagner's orchestration, while competent and imaginative (particularly in Parsifal), was never as innovative. He enlarged his orchestra (particularly brass), and further intertwined orchestration with initial composition; but relied on rich harmonies and suspensions for the full sound he created. Mahler's successive enlargement of his orchestras was of an entirely different nature - variety of sound was the driving force. His theatrical effects such as on- and off-stage musicians can be trtaced back far before Wagner. His increasingly economical and clear orchestration was if anything a reaction to Wagner's influence. The chamber-textures he could produce from full orchestra have no match in Wagner - the beginning of Lohengrin for instance derives much of its strength from being so obviously the sound of a large orchestra. The true chamber textures the Second Viennese School moved to after the luxuriance of such as Gurrelieder however are as likely to have been forced by financial considerations as artistic.
Strauss is also one of the great masters of orchestration. Like Wagner and Mahler he was a talented conductor, and knew how to create virtuosic effect with realistic effort in much the way Liszt understood the workings of piano technique. He also could create chamber music delicacy - for instance parts of Symphonie Domestica - but he is most memorable for the amazing pyrotechnics of Don Juan, Also sprach Zarathustra, and other tone poems. He was also brilliant at creating moods with orchestration, and very realistic musical pictorialism (such as Don Quixote and the Alpine Symphony). In this he went further than Wagner, who was at his most detailed in the Ring with such as the Rhine and the woodbird. The divide between programme and absolute music is relevant here - Wagner music dramas and especially Strauss tone poems made accurate musical descriptions, Mahler symphonies (and Webern orchestral pieces such as Op.10/2) would make symbolic sounds often in the sense of Naturlaute.
Wagner exerted some philosophical influence on Mahler. His vision of German art revitalising German culture and society and giving the artist new almost religious importance was much discussed by groups such as Vienna's Academic Wagner Society. Mahler was closely linked to some of these, through friends such as Siefried Lipiner. Alma Mahler writes that Gustav thought that only Wagner (in Beethoven) and Schopenhauer had anything to say on the essence of music. However, Mahler began reading Nietzsche seriously after composing, and found it “epoch making”. The Wunderhorn songs are primitive folk-songs, not colossal world myths. Nietzsche also found that Wagner had ignored his quest for Beethoven universality in his pursuit of ever greate sensuousness and emotion in his music. Mahler, in his intensely personal works, has an element of self-parody which allows the listener to step back slightly.
Wagner's wish for higher standards in performance was echoed by Mahler and Strauss, and his innovations in terms of increasing power of the conductor over soloists were influential. Bayreuth was never to be repeated though. The design remains to this day unique - although music rooms are all accoustically designed now. Even though no other Germanic composer ever had monarchical backing, is still doubtful whether Schoenberg or his contemporaries would have wanted so precisely tailored a performance house - their works were so diverse.
Mahler, Strauss and Schoenberg all followed the pattern of writing initially in an individual yet Wagnerian manner, but quite quickly moved onto quite separate paths, as if reacting violently to Wagner. The increasing desperation and savagery of Strauss and Schoenberg's works, such as Elektra and Erwartung can be seen in this light, but also as a product of other factors. The increasing social and moral decay exemplified by turn of the century Vienna is one. The nature of the harmonic language is another. Flowing Wagnerian textures are ideally suited the mood of Parsifal, more concentrated, dissonant, motivic (rather than leitmotivic or thematic) textures of 1905-8 Strauss and 1905-12 Schoenberg are suited to the expressionistic torment and macabre of Elektra and Pierrot.
Wagner's direct influence was very specific in comparison with that of someone like Debussy. His chromatic harmonic language sometimes driven internally, his leitmotive, his word setting, and his form, the Music Drama. He had shown with Tristan that music is a language that can be changed with a single work (which speech cannot be). He had no successors, only followers and chronologically later rivals. He contributed to the loss of tonality's monopoly over harmony in the way that Berlioz and Mahler had contributed to ever subtler orchestration. But Bach and Brahms were to be the primary influences on Schoenberg, Berg and Webern. Even before the Great War, their dominance was present if not obvious.