7 / 5 / 12

Wow, 7 / 5 / 12 ... a numerical formula! Who said we are not scientists! Let's sus this out. So if the 7 in the formula represents the number of pitches we use to create the major and relative minor tonalities, such as C major scale and A minor etc., and the 5 represents the blue notes, so loved by the creators of the American blue sounds, that by adding 7 and 5 together, is the number 12 representative of the number of pitches that one octave is divided into? Are these the 12 pitches of the chromatic scale, thus the basis for the multi key system of equal temperament? And bingo was his name oh! But wait theres more ...

So, the chromatic scale ( 12 pitches ) contains both sets of pitches to establish either a major or minor tonal center ( 7 pitches ) with chords and the blue notes ( 5 pitches ) to color it? Yep. Minor or major? Yep. Together? Absolutely. Did the Eurocat's know this when they created equal temper?

And it must follow that from any of the 12 pitches of the chromatic scale we can project the 12 major and 12 minor key centers? Yep. Any color? For sure. Anything from anywhere? Exactly. And in modulating between tonal centers, do any of the original 12 pitches ever change? Naaa ... that's the beauty of equal temper. But what about these blue notes?

7 / 5 / 12 ... perhaps all the theory a person ever needs, ya just never know.

Thinking major tonality, here is a chart using C as the tonic pitch which outlines the above ideas. Example 1.

See any pattern to the orange grouping of pitches? Thinking relative minor to C major, the minor tonality based on the root pitch A emerges. Example 1a.

So, where might this way of viewing the resource come in handy? Well, potentially it's an awfully easy way to understand all of the pitches available in regards to an established tonal center. With the vast majority of music within all of the American styles written in either the major or minor tonalities ( 7 pitches ), we can simply utilize the blue notes ( 5 pitches ) as "off key" colors to enhance our lines. Melodies and chords? you bet. Thus, if a player has the major scale / natural minor scale ( 7 pitches ) under their fingers, exploring the blue notes ( 5 pitches ) in relation to the tonality created by the grouping of 7 can begin to open up a new vista of colors for the creative artist of any style, adding coolness to their palettes and creating bridges between the various American musical styles we love to play and listen to. Using a piano illustration, here are the pitches from the chart above. Example 2.

7 white keys

5 "other" keys

thus 7 + 5 become 12 pitches

Cool with this? Nice graphic huh? Look familiar? We are simply pairing up the 7 pitches of the major scale and the 5 pitches of the pentatonic scale and combining them together to create the chromatic scale.

With so much of the discussions within this text devoted to the major scale, let's look at each of the 5 pitches, place them into the major tonality and see what sort of coolness we can come up. Here is a chart of the pitches from example 1 above, here we include the interval of each pitch as measured from the root C and span one perfect octave of pitches. Example 3.

Here is an old time American idea created from the major scale grouping of pitches. Example 3a.

# 1 / b2. The first of the non diatonic pitches C# / Db, is commonly known within the diatonic major tonality as the # 1 ( sharp One ) degree when the bass line is ascending, as in the following idea, or b2 when descending. Jazz players often build a fully diminished passing chord on this pitch to accelerate the motion towards the Two chord. We take advantage of the new harmonic scheme to create a variation of our original melodic idea. Example 4.

Lot's and lot's of jazz players love the # 1 diminished 7th chord. As an integral part of the rhythm changes form first made popular during the 30's, the sharp one diminished color is just about somewhere in every nook and cranny of the American sounds. In brighter tempos, the excitement of the acceleration of tonal gravity created by #1 dim 7 is priceless to the those who dig it. Oftentimes a first step for the newly emerging jazz artist, the # 1 position is an ideal placement for the diminished color, thus perhaps a good vehicle to introduce the diminished scale color, whose sound, theory and applications has created dramatic implications in the direction of the music we love.

As a blue note, the # 1 is often heard as an "off key" tonic. Try this color in the blues by simply bending the tonic pitch up a little, make it sharp, maybe not a full half step, in between somewhere? Might sound a bit weird at first, but in experienced hands, the # 1 as a blue note color is very powerful. Guitar players often come to love this pitch. Horn players and singers too. But how does a piano player get there? Good question. You'll have to experience this # 1 blue note first hand, as my music software just won't do it any aural justice.

b2. So, in thinking of converging towards the tonic pitch from a half step above, we often see this pitch supporting chords rather than as a melodic device when heading in this direction. Perhaps the most common ways of voicing chords on this pitch is known to theorists as the tritone substitute. Go there and explore it's potentially essential color.

b3. The next blue note pitch in the chromatic sequence above is the minor 3rd, perhaps the quickest way to blusify any lick, line or phrase. Here is the original line blusified in the digital world. Written here as a grace note, this type of half step melodic treatment of minor to major 3rd is all over the American sound. Check out it's digital coolness. Example 5.

Another common placement for the blue 3rd in the major tonality finds the color located within the cadencing of the line. When added into a dominant 7th chord, it's triad becomes augmented and we create a cool, melodic passing tone melodically. Again minor to major 3rd, stepwise upward by half step. Feel the tonal pull of the augmented triad on beat 3 of bar 20. Example 5a.

Sound familiar? Nice way to spice up the diatonic realm of things n'est pas?

# 4 / b5. Based on the interval from the root, theorists often call the  # 4 / b 5 simply the tritone. I have begun to call it the blue 4th, but it's taken me a long time to come to and accept this understanding. However labeled, it's unique sound is not quickly forgotten once our ear has come to terms with it. Used everywhere, from the the pep band's "chants of impending doom" for opponents at high school sporting events to safety sirens in European movies, the tritone enjoys great popularity in the blues and jazz realms, some in rock and usually avoided at all possible costs in traditional folk music, excepting when encapsulated within the V 7 chord of course. Here we borrow a bit from the Mozart library located in Vienna and simply enjoy the half step motion into the fifth degree of the C major scale, the pitch G, in bars 24 and 25. Example 6.

As a blue note, the tritone always evokes a bit of the jungle to my way of interpreting the color. Example 6a.

Not much left of the original line eh? The major scale color gives it up pretty quick when the blue notes are sounded. Goes away pretty fast, thus the historical and intuitive strength of the blue colors for the creative musician.

A rather common place for the b5 pitch harmonically is in Bossa Nova music, the sensual, Brazilian flavored pop music of the 60's. Most often used within the dominant family, by altering the 5th downward by half step we create the cool V 7b5 chord. Here we use the b5 / dominant color on Two, creating a Five / of Five motion within the C major tonality. The tritone / b5 interval is created here between the root of the Two chord D and it's flatted 5th Ab. Example 6b.

Are you hip to the origins of the tritone within equal temper? Hip to the tritone sub? In the jazz style known as Bebop, the flatted fifth is often an essential component of the line.

# 5 / + 5 / b6. The interval of the augmented 5th / minor 6th above the root is perhaps the least "blue" of 5 non diatonic pitches when associated with the major tonality. So where do we commonly find this pitch spicing up the major tonal environment? Well, in a couple of places. In perhaps it's widest application through the various styles of American music, we often find the # 5 / b 6 pitch creating the minor Four chord, normally a major triad in diatonic harmony created from the major scale. The minor Four usually follows the diatonic major Four chord, before returning by various ways to the major tonic. Here we place it in the second half of our chosen illustrative theme. Do you remember this line? Example 7.

Now, slipping in the minor Four chord. Example 7a.

So, Four, minor Four, Three, Two and Five. Cool huh? Pretty common harmonic motion in all of the American styles.

A second placement for this # 5 / b 6 color is to add this pitch to a vanilla V 7 chord creating the V 7b9 color, potentially an essential color for the emerging jazz artist. Here the color emerges in bar 48 of the following idea. Example 7b.

So, is there a fully diminished chord in the upper structure of the V 7 b9 chord? So, we are using the diminished color twice in one, four bar phrase? Exactly. Ain't nothin, just something a jazz player might do at any given moment, in any given tune.

b 7. Using the flat 7 in the major tonality is oftentimes like the b3, used to invoke a bit of blues flavor into the line. Here we use it both melodically and harmonically, recoloring our tonic chord to dominant as well as in the diatonic Five chord in measure 53, to add a bit of the blues in an otherwise pretty vanilla line in the major tonality. Ah, the # 9 color emerges, so essential to the blues artist. Example 8.

Pretty basic huh? Well, have to start somewhere. The V 7 #9 is a blues, rock and jazz favorite. Folk players beware!

Review. So, do you have a sense of how the 7 pitches of the major tonality can be spiced up by adding any of the 5 non diatonic bluer notes, which when combined together create the 12 pitches of the chromatic scale? Thus the formula of 7 / 5 / 12? Did you ever figure out the name of the group of pitches created from the 5 non diatonic pitches? Are there other possibilities for these 5 pitches within the major tonality? Gillions upon gillions. What about the minor tonality? The same for sure.

The idea at this juncture might be that in your shedding, to run your explorations of this formula from one key as done above, then when a cool idea emerges, run this coolness from within each of the tonics as created by the 12 pitches of the chromatic scale, each of which can function as the tonic pitch of either the major or minor tonalities right? Advanced players often use the 12 bar blues format for just such explorations. Oh, does this 7 / 5 / 12 way of theoretically understanding the resource lead to the important idea of anything from anywhere? Just might.

Where to next?

review new ideas

"Where words fail, music speaks." Hans Christian Andersen