Bitonality, or the use of two distinct musical keys simultaneously, is a technique which has been used since the Classical era and seized the interest of many twentieth century composers. Igor Stravinsky, Ferrucio Busoni and Kaikhosru Sorabji were all very much involved with this approach and the latter's Transcendental Etude No. 10, a display of polytonal arpeggios, is an effective and vehement melange. His etude is strictly arpeggiated, which led me to believe that the examples from the Thesaurus can not only be musically relevant but may form the basis of a musical piece if one wishes to be so bold.
The focus of the bitonal arpeggio section in the Thesaurus is to exhibit the combination of the C major triad (C, E, G) with each of the 23 major and minor triads available. Some of the results are fascinating (CM+F#M, an implied Petrushka chord), others are musically consonant (CM+DM) and a few are slightly harder to appreciate (CM+C#m). The exercises, when played on guitar, can be beneficial in a couple of ways. Primarily, they are great for training the ear to hear triads; the alternation between the two distinct chords trains the ear to differentiate and focus on where the switch takes place. And of course the exercises are really taxing (at first) because of their bizarre shapes, and they demand larger than normal stretches in the fretting hand. I have included my preferred fingerings for each example but I have chosen not to include picking patterns because the examples are all played against C major and they change dramatically. I strive for the sweeping approach because it sounds a lot better if you can get it under the fingers, but at times there are two note per string patterns present and need to be approached with your choice of hammering or picking. I usually alternate pick more often than not but my personal choice in these exercises is the hammer-on because it mixes well with the sweeping that can be done when the triads align in their conventional form. One last thing before the examples - the T with the fingering numbers means a tap is required and there are exercises with three notes tapped in a row, this is treated as a tap-slide. But if you want to get crazy you can always manipulate the fret hand but be sure to avoid anything painful; I've already had a bad bout with tendinitis. Enjoy!