Learning to play scales on any instrument with velocity is an important part of developing a technique which will support anything the player wants to accomplish. It is not the only thing; there are, after all, many other aspects to a solid technique which must be learned. But learning scales is usually one of the first things taught.
It is, however, not a great idea to begin studying scales technically on an instrument unless you have a well grounded idea of how they work within music.
How scales work
Tetrachords
The definition of a major scale: two major tetrachords separated by a whole step.
Let’s face it, that mouthful is going to need some explanation.
A tetrachord is, as one can figure out from the word-roots, four (tetra) notes that are connected (chord). Though the idea of tetrachords is derived from the ancient Greeks, who apparently worked them out exclusively from top to bottom, western music since the early medieval period has worked them out from bottom to top and top to bottom, depending on the type of scale.
Even if you are not a keyboard player, it is convenient to speak of scales in terms of the keyboard because of its visual geographical layout. It is easy to visualize half- and whole-steps when using the keyboard as the template upon which scales are placed. So even if you are a trumpeter or violist, put yourself in front of some kind of keyboard to do the following investigation.
To make a major tetrachord:
Hold up your four fingers (no thumb) facing palm away. The finger farthest to the left is your “starter.” The next finger to the right is a whole-step higher; the next finger to the right is also a whole-step up; the finger all the way to the right is a half-step up.
If you have trouble with half- and whole-steps, just remember that from one key to the very next key is a half, while a whole step leaves out one key, going to the second key away from the first. This works from any key in either direction.
So back to the tetrachord. Pick a key and play it with your left hand pinky (5). That’s the “starter.” Now with 4 play the tone a whole step up; then with 3 play a whole step above your 4th finger. Now comes the most crucial key — finger 2 will be only one half step above finger 3.
Do the same thing with your right hand using 2 as the starter, followed by whole with 3, whole with 4, and half with 5.
Now you have made two major tetrachords.
To make a major scale from any key put your left hand 5 on that key, follow the tetrachord pattern up. Now make your right hand starter be a whole step above your left hand 2, and make another tetrachord with your right hand. Play the neighboring tones up and back and you will have played a major scale ascending and descending.
5 4 3 2 2 3 4 5
W W H W W W H
How scale tones are named
The steps of the scale (and the chords built upon them) are numbered using Roman numerals. This is to distinguish them at sight from intervals, which use Arabic numbers. The quality of the chord is indicated through the use of upper and lower case of the Roman numeral.
A I chord will be major and a i chord will be minor. When writing about chords with less specificity — not needing or wanting to mean major or minor — then upper-case numerals are used. So one can write “go from I to III” and it won’t matter whether either is major, it’s just generic.
In addition to a Roman numeral, each of the seven steps of the diatonic scale has a name. Here they are, but not in numerical order. Instead they appear in the order which will explain their names and function more easily:
I = Tonic. Think “tone-ic”, the home-base tone in a scale.
V = Dominant. This is because Tonic is most often defined by playing Dominant first. V-I is the most common cadential pattern because it defines the sound of I.
The reason for this is found in physics, the kind of physics that any brass player knows well. In any vibrating string or column of air there is the fundamental. If that vibration is cut in half, the resulting pitch is an octave higher, which means the number of vibrations will double. Say the fundamental is A=220hz. Cutting it in half results in A=440hz. . Now divide the fundamental vibration into 1/3. The resulting overtone is E.
Now here’s the big one — divide the original 220hz into 1/4 and the vibrations will be 880hz, yes, two octaves above the fundamental. So what we have as a pattern in nature is A, A, E, A. E-A (V-I) is so primal that it still sets up our ears to affirm I as the home pitch.
Note that V/Dominant is the “starter” of the upper tetrachord.
IV = Sub-Dominant. If the Dominant is up five, then the Sub-Dominant in down five, the lowest tone if one places a tetrachord beneath the one based on Tonic.
F G A Bb C D E F G A B C DEF#G
If C D E F is the lower tetrachord of the C major scale, note that G is the begining of the upper tetrachord. But also note that F is the beginning of the next tetrachord below C. Therefore, the Sub-dominant.
III = Mediant means central, in the middle. And sure enough the third step is half-way between I and V.
VI = Sub-Mediant, then, obviously means half-way between I and down to IV.
II = Supertonic. Super is, of course, above. So it’s the tone above Tonic.
VII = Leading Tone. This, in spite of its final place in this list, is in many respects the most important in relation to other pitches. It is only 1/2 step below Tonic, and therefore when in the context of a scale or a well established key it pulls the ear to desperately want it to resolve upward to tonic.
IV is sometimes thought of as a downward leading tone. In many contexts its relationship of being 1/2 step above the Mediant tends to pull the ear to want a resolution down to III.
Closeness
When we speak of one tonality being “close” to another, we do not mean it in the geographical sense of the physical key of D being close to the physical key of E-flat. No, what is meant is based on which tetrachords are closest to each other. So the keys closest to C are F and G, closest to D are A and G, closest to Ab are Eb and Db.
The so-called “circle of fifths”
The “circle of fifths” refers to the progression of close tonal centers. Think of the pitches in a scale as being like a genetic code. A scale with one sharp or one flat is closely related to the scale with no sharps or flats, while a scale with seven sharps or flats is quite distantly from that with none.
Let’s look at the series of tetrachords beginning on C and progressing upward until C is again reached as the lowest tone of a tetrachord.
CDEF GABC DEF#G ABC#D EF#G#A [BC#D#E F#G#A#B C#D#E#F#]
[CbDbEbFb GbAbBbCb DbEbFGb] AbBbCDb EbFGAb BbCDEb FGABb CDEF
How key signatures are derived
Please note that as the progression moves upward — an upper tetrachord is renamed as a lower tetrachord and the next tetrachord becomes the upper — the new sharp is always the seventh step of the new scale.
By the same token, when we go downward making a lower tetrachord into an upper tetrachord, the new flat is always step four of the new scale.
This is why when looking at a key signature it is in a particular order: the order in which the sharps or flats appear as one cycles through the tetrachords. This regularity is why the English language slogan “Flat-Four, Sharp-Seven” will work to tell you what major key is shown in a key signature. It means that the last flat to the right will be step four of the major key to which it refers, and that the last sharp to the right will be step seven of the scale to which it refers. In the case of flats, one soon discovers that the next to last flat is tonic, while in the case of sharps just go up a half-step from seven to one to find tonic.
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