Find the triad common only to the following keys:
1. A major, F# minor, A minor
2. Db major, Bb minor, Cb major, F minor, Ab major
To find the triad common only to the given keys, we need to identify the notes present in the given keys and determine which three notes form a triad that is common to both sets of keys.
1. A major, F# minor, A minor:
- A major: A, B, C#, D, E, F#, G#
- F# minor: F#, G#, A, B, C#, D, E
To find the common triad, we need to find the common notes between these two key signatures. The common notes are A, B, C#, D, and E.
2. Db major, Bb minor, Cb major, F minor, Ab major:
- Db major: Db, Eb, F, Gb, Ab, Bb, C
- Bb minor: Bb, C, Db, Eb, F, Gb, Ab
- Cb major: Cb, Db, Eb, Fb, Gb, Ab, Bb
- F minor: F, G, Ab, Bb, C, Db, Eb
- Ab major: Ab, Bb, C, Db, Eb, F, G
To find the common triad, we need to find the common notes between these five key signatures. The common notes are Db, Eb, Ab, and Bb.
Now, let's determine the triad common only to these two sets of keys.
The common notes between the two sets are A, B, C#, D, E, Db, Eb, Ab, and Bb. From these notes, we can form several triads; however, let's look for the triad that appears in both sets of keys, but not in any other key signatures.
The triad that satisfies this condition is a triad with the notes A, B, and E.
Therefore, the common triad only to the given keys is A major (A, C#, E).
To verify this, you can use a music theory reference, such as a chord calculator or a keyboard, to analyze the notes and confirm the common triad.