On the recommendation of a friend (and Nadia Boulanger), I am working through Hindemith's "Elementary Training For Musicians", with an eye to using a small selection of its exercises for some of my students. However, I am confused by his use of rhythmic proto-notation in the first chapter. Here are the first three exercises:
He has the student beat out the vertical lines in a steady pulse while vocalizing the horizontal arches as "la". Further on, the preliminary skills gained in these exercises are used to introduce basic rhythmic notation:
While I understand the general process at work here, I am confused about his equivalences: the proto-rhythmic unit that is supposed to be equivalent to a whole-note appears instead to be equivalent to a dotted half-note. Or am I reading this wrong? It doesn't appear to be a misprint, as the other smaller units are proportionally related to the whole-note unit. But wouldn't the proto-rhythmic unit in Exercise A be more correctly said to equal a whole-note? And the unit in Exercise C a quarter-note?
In my library I couldn't find much elucidation on the subject, other than this passage from Daniel Kazez's "Rhythm Reading":
Which would seem to concur with my assessment of Hindemith's proto-notation. So, is he mistaken? Or am I failing to understand some fundamental aspect of duration in rhythm? How would these exercises be correctly performed? How does he get from the proto-notation to common rhythmic notation?
In Canada, "Elementary Training For Musicians" is in the public domain. So if you are Canadian, or a scofflaw, you can find a PDF of the book here. The exercises and notation equivalences are on pages 3-4 of the book. Don't know what page of the PDF.