key signatures / major tonality

So, the "F's" are actually "F#", the "C" is "C#" without extra notation, thanks to the key signature? Yep. These key signatures help to make the reading easier by eliminating the need to always notate diatonic accidentals, sharps ( # ) and flats ( b ), within the chosen key throughout an entire piece of music. Of course a musical piece can change keys. Using a different key signature within a given piece of music is very common, whatever will help to facilitate the transfer of the composers ideas to the players of the music, easing their interpretation of the written music.

There are basically 12 different key signatures, one for each of the 12 major / relative minor scales. The keys they represent are the 12 major and 12 minor keys found within the equal temperament system. One way to understand how the key signatures are created within the equal temperament system is to simply use the intervalic formula used to create the major scale and arranging the 12 keys using the cycle of fifths. Here is a chart of the intervalic formula of the major scale and the creation of the C major scale. In the following chart, the number 1 represents a whole step interval, the fraction 1/2 is a half step interval. Example 2.

See any sharps or flats attached to any of the letter names in the chart above? No. Does the key of C even have a key signature? Well, yes but if there are no sharps or flats... In a piece of written music, not seeing any accidentals at the beginning of the staff designates that the music is indeed in the key of C major. What about it's relative key A minor? Same situation, no accidentals, thus the music generally looks like this. Example 2a.

What about the other 11 major keys and their signatures? Using our intervalic formula for the major scale, lets start to add keys using the interval of a fifth and watch what happens. What is the fifth scale degree of C major? Here is the chart. Example 3.

Are the pitches of the G major scale correct? Nope. There is no leading tone. In the key of C, the 7th B is a half step below the C. What is the interval between F and G? Right, a whole step. How can we fix it? Right again, by simply raising the F by half step to F#. Example 3a.

That's better, so, what is the key signature for the key of G major? Right, one sharp. Here is the music using the key of G major, with it's one sharp F# key signature, the seventh degree. If moving up keywise by fifth adds one sharp to the major key, what about it's relative key? Same situation, moving up a fifth adds one sharp to the relative minor. So, from C major up to G major and A minor up to E minor. Thus the music generally looks like this. Example 3b.

Cool so far? What's the fifth degree of G major? From the chart above we can see it is D. Any guesses as to which scale degree we will have to alter to perfectly satisfy the intervalic formula for creating the major scale on the root D? Do we need the F# to create the D major scale? Yes we do. Here is the chart. Example 4.

Well, no wonder that it is again it is the seventh degree which is raised a half step to comply with the major scale intervalic formula. By now you can probably sense that the relative minor color is consistently created from the sixth scale degree of the major scale, same pitches, thus same key signature. Here is the music. Example 4a.

Up a fifth from D to A. Keeping the key of D's two sharps, we add a third sharp to create the key signature for A major and it's relative minor key built on it's sixth degree, F#. Example 5.

Here is the music. Example 5a.

Up a fifth from A to E. Keeping the key of A's three sharps, we add a fourth sharp to create the key signature for E major and it's relative minor key built on it's sixth degree, C#. Example 6.

Here is the music. Example 6a.

Can you begin to see how this is evolving? What about keys with flats in their signatures? Let's keep moving up in fifths and see what happens. Up a fifth from E to B. Keeping the key of E's four sharps, we add a fifth sharp to create the key signature for B major and it's relative minor key built on it's sixth degree, G#. Example 7.

Here is the music. Example 7a.

Up a fifth from B to F#. Keeping the key of B's five sharps, we add a sixth sharp to create the key signature for F# major and it's relative minor key built on it's sixth degree, D#. Example 8.

Here is the music. Example 8a.

Up a fifth from F# to C#. Keeping the key of F#'s six sharps, we add a seventh sharp to create the key signature for C# major and it's relative minor key built on it's sixth degree, A#. Example 9.

Here is the music. Example 9a.

B#? Really. I thought that was something more to do with my attitude than music theory. Is there an easier way to notate the key of C# major / A# relative minor? Yes there is, here come the flats. The key of C# major / A# relative minor, actually all pitches and keys, have what is termed their enharmonic equivalents. This is simply a second way to designate a given pitch and usually used to ease the writing, thus reading of the music. What is the enharmonic equivalent of the key of C# major? Right, Db major. Lets compare the pitches of the two keys. Example 9b.

Do they sound the same? Which key to use in notating the music is oftentimes chosen simply by which has the least number of accidentals, which hopefully will facilitate the transfer of the composers ideas. Thus in example 19 above, we see the key of C# has seven sharps while the key of Db has only five flats. Cool with this? Do these two keys sound the same? Pretty much, yes, but oftentimes in the context of the music, it is the contrast of pairing two or more keys within a given piece of music that helps determine which key signature is used. Confused? Sorry, but discussing key color is a whole other topic, which is more about "art" than the theory. For now, back to the theory.

Does the key of Db major have a relative minor key? Of course it does, but you knew that right? So instead of dealing with A# minor, a difficult key to write and read, especially given the variances of pitch within the minor tonality, we simply use Bb minor, which is still a bit cumbersome accidental wise, but easier none the less. Example 9d.

Up a fifth from Db? Right, Ab. Here is the comparison chart. Example 10.

Things are starting to simplify themselves, as we hoped they would. We move from five flats to four. The relative minor of Ab major? F minor. Here is the music. Example 10a.

Up a fifth from Ab? Right, Eb. Here is the comparison chart. Example 11.

Here is the music. Example 11a.

Up a fifth from Eb? Right, Bb. Here is the comparison chart. Example 12.

Here is the music. Example 12a.

Up a fifth from Bb? Right, F. Here is the comparison chart. Example 13.

Here is the music. Example 13a.

Up a fifth from F? Right, C. Back to where we started. Here is the comparison chart. Example 14.

Here is the music. Example 14a.

So, that's the cycle of the 12 major / relative minor keys. Musicians use a circle to help visualize the keys and the way they loop onto themselves. And since there are 12 keys, this circle looks a bit like the face of a clock, a "key clock" of you will. Theorists call it the cycle of fifths. Here are the picture cycles for the 12 major and minor keys, with the key signatures. Example 16.

Can we use different key signatures within one piece of music? Sure. When the music modulates or changes key, oftentimes the new key's signature is inserted into the music to ease the notation. The following music modulates from C major up a whole step to D major. Example 16a.

One sure way to put a key on the map so to speak, is to learn a song, or a part of which, is written in that key. Although any song can be in any key, the following choices are paired with the keys that these compositions are most commonly found in real books. All of the music in the listing which follows are recognized as jazz standards and as such, are worth a thorough reading. So, let the listing begin. Example 17.

All of these tunes listed above are basically created in the major tonal environment. Minor tonality tunes? You betcha, we got it all here. Example 17a.

Are there other types of signatures?

Where to next?

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