7.2.2 Principles

same reason, bitonality and polytonality do not exist. Like Schönberg with his twelve-tone technique, Hindemith wanted to save German art music. On page 21 of Der Unterweisung he writes: "Wenn die Verwirrung der Satzkunst nicht noch weiter um sich greifen soll, wenn die zwiespältigen Ergebnisse einer überalterten Lehre zu der Unsicherheit nicht noch ärgeres Unheil bringen sollen, muss endlich wieder ein tragfähiger Unterbau geschaffen werden.“ [“If the confusion of the art of the Satz is not to spread any further, if the ambiguous results of an obsolete theory are not to bring further doom to uncertainty, then a strong basis must finally be created again.”]

7.2.3 THE CHROMATIC TONE ROW Hindemith takes C (64Hz) as starting point. This tone has the harmonic row: C (64Hz) - c (128Hz, 2nd) - g (192Hz, 3rd) - c´ (256Hz, 4th) - e´ (320Hz, 5th) - g´(384Hz, 6th). These are the harmonics 1-6 of C; he ignores the rest of the harmonic row as he is only concerned with the harmonics that together form a major triad. Hindemith places great value in the triad. On page 39 of Der Unterweisung he writes: “So lange es eine Musik gibt, wird sie immer von diesem reinsten und natürlichsten aller Klänge ausgehen und in sich auflösen müssen...In der Komposition kann der Dreiklang oder seine unmittelbaren Erweiterungen nur auf kurze Zeit vermieden werden.“ ["As long as there is music it will always be based on and resolved in this purest and most natural of all sounds … When composing, the triad or its immediate expansion can only be avoided for a little while.”] - From g (192Hz) renumbered as 2nd harmonic the G (96Hz) is derived. - From c’ (256Hz) renumbered as 3rd harmonic the F (85.33Hz) is derived, and renumbered as 5th harmonic the A (102.4Hz) is derived (the root tone here is one octave lower). - From e’ (320Hz) renumbered as 4th harmonic the A (106.66Hz) is derived, and renumbered as 3rd harmonic the E (102.4Hz) is derived. - From g’ (384Hz) renumbered as 5th harmonic the E (76.8Hz) is derived. So now we have C-G-F-A-E-E -A . This is a hierarchic row as well: the lower the number of the harmonic, the more related this tone is with the root tone. Hindemith calls this the father (C) with his six sons. For the other tones he has to call on these sons and the tones derived from them he calls the nephews.