What does Hindemith's Rule 20 mean? (The Craft of Musical Composition, book 1: Exercises in two-part writing)

Question

Paul Hindemith's Rule 20 in his The craft of musical composition: Book 2: Exercises in two-part writing has two paragraphs:

Paragraph One:

If the last tone of the model is approached from a fifth above or a fourth below, [then] the [second] voice must move into its last tone by a [major or minor second] progression. Conversely, the [second] voice may use the final progressions given in Rule 15e only if the model moves into the last tone by a [major or minor second] progression.

Paragraph Two:

If we are certain that a [major or minor second] step may be used in the [second] voice between the next-to-the-last and the last tone, then the closing tone of the model may be approached by a skip of a fourth from above or by the skip of a fifth, a major third, or a minor third from below. ... Condensed and in a simpler form: If one of the two voices reaches its final tone by skip, [then] the other voice must reach its final tone by step.

For reference, Rule 15e reads:

In addition to the approaches to the last tone permitted by Rule 5, [the second voice may approach the last tone] also [by] the skip of a fifth from below and that of a fourth from above.

I have two questions:

1 Is the following a fair paraphrase of Paragraph One? If the last interval of the model is a downward fifth or an upward fourth, then the second voice's last interval must be a step. If the second voice's last interval is an upward fifth or a downward fourth, then the model's last interval must be a step.

2 Could someone please explain or paraphrase the entirety of Paragraph Two? Namely:

(a) How do we know that a major or minor second may be used as the final interval of the second voice? Are the relevant rules to be obeyed just these: Rule 3, if the second voice is the lower voice; Rule 18; and part of the first paragraph of Rule 20, namely, the model's last interval must be a downward fifth or an upward fourth?

(b) When Hindemith says that ``then the closing tone of the model may be approached by a skip of a fourth from above or by the skip of a fifth, a major third, or a minor third from below,'' does he mean that these intervals are permitted, or does he mean that they are in this case obligatory?

(c) By the final sentence (``Condensed and in simpler form: ...'') does Hindemith mean to replace both paragraphs of Rule 20 or merely the second one?

Thanks!

Answer 1

1. Your paraphrase of Paragraph One is generally accurate. If the final interval of the model is a downward fifth or an upward fourth, then the second voice's final interval must be a step. Conversely, if the second voice's final interval is an upward fifth or a downward fourth, then the model's final interval must be a step.

2. Here's an explanation of the entirety of Paragraph Two:

(a) The determination of whether a major or minor second can be used as the final interval of the second voice depends on the rules mentioned: Rule 3 (if the second voice is the lower voice), Rule 18, and part of the first paragraph of Rule 20 (which states that the model's final interval must be a downward fifth or an upward fourth).

(b) When Hindemith says that "then the closing tone of the model may be approached by a skip of a fourth from above or by the skip of a fifth, a major third, or a minor third from below," he means that these intervals are permitted options. In this case, they are not obligatory but are allowed as possible approaches to the closing tone.

(c) The final sentence of "Condensed and in simpler form" does not mean to replace both paragraphs of Rule 20. It is an attempt to summarize the rule in a more concise and straightforward manner. It provides a simplified version of the rule, emphasizing that if one voice reaches its final tone by skip, the other voice must reach its final tone by step.

Note: It's important to refer to the original text and consult any accompanying explanations or commentaries provided by Hindemith in his book for a more comprehensive understanding of his rules and their applications.