# Six questions about Rule 21 in Hindemith's Craft of Musical Composition, book 2: Exercises in two-part writing [closed]

I am a musician reading Hindemith's Craft of Musical Composition, book 2: Exercises in two-part writing by myself. I have some questions about Rule 21.

Three images of Hindemith's rule 21:

https://www.flickr.com/photos/198448552@N03/52948432808/in/dateposted-public/

https://www.flickr.com/photos/198448552@N03/52947377277/in/dateposted-public/

https://www.flickr.com/photos/198448552@N03/52947377262/in/dateposted-public/

Question 1: How do you suppose Hindemith would have defined tritone chords?

Question 2: Does Hindemith have in mind tertial chords only (chords built in thirds)? For example, the stack of seconds f - g - a - b involves a tritone (namely f - b), but would Hindemith call such a stack of seconds a chord?

Question 3: What is distinctive about example 48a? Hindemith uses the words such as these to point at this example, but what about them is he trying to point out?

Question 4: Augmented triad formations of this kind are entirely prohibited, says Hindemith. Does the word triad exclude, for example, the augmented seventh chord (e.g., A-C#-E#-G)?

Question 5: How can I tell what counts as a triad formation?

Question 6: By tetrad does Hindemith mean any chord using four distinct pitch classes?

• This should be six distinct questions Commented Jun 5, 2023 at 11:28
• Point taken. However, I figured someone curious about one would be curious about all, and someone able to answer one of them would be able to answer all of them, so that dividing them would only be inconvenient for askers and answerers alike; and in a way they are one question, namely, "What does Rule 21 mean?" Commented Jun 5, 2023 at 14:42

### Question 1: How do you suppose Hindemith would have defined tritone chords?

Hindemith is referring to diminished, diminished seventh, dominant seventh, and, probably, half-diminished seventh chords.

### Question 2: Does Hindemith have in mind tertial chords only (chords built in thirds)? For example, the stack of seconds f - g - a - b involves a tritone (namely f - b), but would Hindemith call such a stack of seconds a chord?

Hindemith addresses this indirectly in the final paragraph and example 48b. He's saying that any chord outside the usual tertial formations (i.e., basic triads and seventh chords) "may be used with impunity". The example of a quartal chord clarifies his meaning in this regard.

In the specific example of f - g - a - b, it's entirely possible that Hindemith would regard that as an inverted ninth chord (g - b - f - a). But since this still falls under the umbrella of "more complicated tetrads", the rule would not apply, despite the tritone.

### Question 3: What is distinctive about example 48a? Hindemith uses the words "such as these" to point at this example, but what about them is he trying to point out?

Here he's referring to any seventh chords other than those containing a tritone: so, a minor seventh and major seventh (as shown in the example) and perhaps a minor-major seventh.

### Question 4: Augmented triad formations of this kind are entirely prohibited, says Hindemith. Does the word triad exclude, for example, the augmented seventh chord (e.g., A-C#-E#-G)?

He's referring specifically to augmented triads. Seventh chords containing an augmented triad would fall under the category of "more complicated tetrads."

### Question 5: How can I tell what counts as a triad formation?

Hindemith uses the standard definition for the four basic triads: diminished, minor, major, and augmented.

Yes.