I’m fairly certain that if I asked a room full of music teachers to tell me what a key signature is, nearly everyone would tell me something akin to “it is an indication of which pitches will be sharped or flatted throughout the piece of music.” As accurate as that is, it is also simplistic enough to allow us to overlook some details about performing and listening to music, and about musical tonality. When a person listens to a musical work, they are unlikely to be concerned with a key signature. Most times, if the music is from the Western art music tradition, a keyality (Gordon’s term) and tonality will be included in the title, such as with Beethoven’s Symphony No. 3 in E-flat major. But the technicality of how many flats are involved is more a concern of the orchestral players than the audience. For the audience’s part, it will audiate the tonality as major upon hearing a few chords and a few notes of the melody, and will know that the tonic is E-flat from the designation, or from having perfect pitch. The key signature in the musicians’ music keeps all of the pitches in the correct relationship with each other. There is a perfect fifth ^1 to ^5, a a minor third from ^4 to ^6 and so forth. There is also a major tonic, subdominant and dominant chord, and a minor supertonic, and submediant. As long as all of this is in order, the audience is satisfied that both the orchestra and Beethoven knew what they were doing, and that the music is indeed in E-flat major.
The key signature, then, provides instructions for the performer on how to play in the intended tonality (major) and keyality (E-flat). What about music that is not written down? Does it also have a key signature? Does it need to have a key signature? I know a song that my mother used to sing to me at bedtime. She learned it from her father, who sang it to her at her bedtimes. I sang it to my children at their bedtimes. I have never played this song on a musical instrument, only sung it and heard it sung. Clearly I have heard it and sung it in a keyality and tonality, and depending on what keyality I heard or sung, there were none to seven flatted or sharped notes used. But because the song is part of an oral tradition, no instructions on what notes were to be sharped or flatted were needed; they were just sung because that’s how the song goes. No one needed to know which notes were sharped or flatted, and likely no one did or cared. All that mattered was singing the beautiful melody correctly and well.
Of course, there is no need for any element of musical notation in an oral tradition. But key signatures are different. Key signatures are not like notes that indicate pitch and duration, or articulation markings, or dynamic markings. Unlike all of these, you cannot hear a key signature, only the notes to which it applies. Even when a musician makes a mistake in performance, you never hear someone say, “he played the wrong key signature.” You may hear “he played in the wrong key” (though what was meant was the wrong tonality), or “he played wrong notes.” The key signature was not followed, resulting in the errors, but it is the wrong notes we hear, not the key signature itself.
Lest you think all of this is merely academic nonsense, let me ground this in reality. When a student is taught to sing or play notated music, he or she must be taught to audiate the music using the pitches as they are notated. The key signature must direct the students to hear the correct intervals and harmonic implications in the melody or harmony part they are playing or singing. It must not be mistaken for instructions on what key to press on an instrument, or what individual pitch to sing. The key signature is there to help the musician produce exact relationships between pitches so that the listener will audiate the intended keyality and tonality. If the musician is not auditing these, then he or she cannot possibly be doing anything with musicality or musicianship, and isn’t that the high ground of music performance, and the priority of music education? Singing or playing arpeggios or scales by ear on a variety of starting pitches, and requiring the student to make the necessary adjustments from the all-natural scale is much more beneficial than having him or her memorize the key signatures. Those can be memorized after the scale and chord are learned by ear, and after the student understands where the major and minor intervals are.
For example, students should perform a D major and a D minor arpeggio, and learn the difference before they learn the key signature of two sharps and one flat. They should also learn that a D major chord is not just the tonic in D major, but also the dominant in G major and G harmonic minor, the subdominant in A major, the mediant in B natural minor, and so forth. It is important that students audiate different chord functions for the same chord, so they can play or sing it correctly in all tonalities. They should also learn D Dorian, D Mixolydian, and D Lydian by ear, so that when they learn those key signatures, they will realize that two sharps is not just the key signature for D major, but also for B minor, E dorian, G Lydian, and A Mixolydian.
When we consider all of this, we realize that key signatures are much more than just “indications of which notes will be sharped or flatted,” and highly unreliable indicators of keyality. For any key signature to be fully understood, the music to which it has been attached must be audiated, and that just doesn’t happen if a student’s knowledge ends with memorizing how many sharps or flats are in each major and minor key.