Which of the following is a compound interval of a fourth?

Question

BlackTom AI · Accepted Answer

A compound interval is any interval greater than an octave; a compound fourth is therefore an octave plus a simple fourth. Interval numbers are counted inclusively (both start and end notes count), and adding an octave effectively increases the simple interval number by seven.

Relevant concepts:
- Simple intervals: unison (1), second (2), third (3), fourth (4), fifth (5), sixth (6), seventh (7), octave (8).
- Compound interval = simple interval + an octave. In numbering, that adds 7 (because inclusive counting makes an octave span 8 scale degrees, so adding an octave to a simple interval increases the numeric name by 7).

Step-by-step reasoning and calculation:
1. Start with the simple interval: fourth = 4.
2. Add one octave: 4 + 7 = 11.
3. Therefore a compound fourth is called an eleventh.

Concrete example (showing inclusive counting):
- Take C up to F (within one octave): C(1)–D(2)–E(3)–F(4) = a fourth.
- Take C up to the F an octave higher: C(1)–D(2)–E(3)–F(4)–G(5)–A(6)–B(7)–C(8)–D(9)–E(10)–F(11) = an eleventh.

Why the other choices are incorrect:
- Ninth = octave + second (2 + 7 = 9), not a fourth.
- Tenth = octave + third (3 + 7 = 10), not a fourth.
- Twelfth = octave + fifth (5 + 7 = 12), not a fourth.

Conclusion: Using the rule compound = simple + 7, a fourth becomes an eleventh when made compound. The correct answer is an eleventh, matching the provided answer.

Which of the following is a compound interval of a fourth? 单项选择题

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