Intro / Op-Ed
As the parenthesized number in the title suggests, 4ths are the main focus of this post. However, before we take a look at them, I want to say a few words about major scales. The scope of my comments is limited to the 1-octave span of the scale (major scale steps 1-8 only).
If you’re unsure about what you’re doing when you’re writing or playing major scales, you might try working from a “blueprint” that details a system for placing the scale’s notes in their proper sequential order. This helps minimize or eliminate mistakes in construction and/or execution. The “blueprint” I suggest you use contains numeric and intervalic information about the scale.
The numeric information gives you an outlined overview of the scale steps. Counting each step, as you move along (1-2-3-4-5-6-7-8), helps with keeping you aware of exactly where you are at each step of the construction process.
The intervalic information places the notes in order by measuring intervals: whole, whole, half, whole, whole, whole, half. This tells you the exact spacing required between each scale step.
The bone structure of a major scale is a string of major and minor 2nds, mostly whole steps between each note with the exceptions of steps 3 to 4, and 7 to 8.
The construction crew discusses the major scale specifications
1-8 = scale steps
w = whole step (major 2nd)
1/2= half step (minor 2nd)
1 w 2 w 3 1/2 4 w 5 w 6 w 7 1/2 8
If you start with C and follow the schematic’s instructions, step-by-step, the C major scale will reveal itself on the white keys of your piano. Play the scale in the keys of G, D, A and E also.
Use this onscreen piano keyboard to play the scale in these 5 keys or go for all 12 if you like!
Our musical alphabet uses only the 1st seven letters of our Arabic alphabet, A B C D E F G. However, for the reasons I mentioned in AC #10, I’ll use the same letter sequence but I’ll have the string start with C.
Now, to make a 4th, simply follow theses steps.
C D E F G A B
1. Select any letter from the 7-letter sequence.
(In doing that you’ve established the interval’s letter name and root… think of it as scale step “1″.)
2. Skip over the next 2 scale steps.
(In doing that you’re skipping over scale steps 2 and 3 because your mission is to make a 4th.)
3. Now, having skipped over scale steps 2 and 3, select the very next letter in the sequence.
(In doing that, you’ve selected scale step “4″ as the interval’s upper note and then you extract scales steps 1 and 4.)
That’s it! You’ve constructed a 4th… a generic 4th*.
*(All accidentals are omitted or ignored In generic intervals. Only staff position matters.)
4ths – These intervals may be identified by their letter names because both letter names are the 1st and 4th letters of an alphabetically sequenced 4-letter string.
When written in standard music notation, 4ths will have exactly 2 unoccupied staff steps in between the interval’s lower and upper notes–a line and a space, OR, a space and a line–two alphabetically sequenced letters.
Keep the following points in mind:
1. The staff, by itself, represents a piano’s white keys only. Black keys are notated by accidentals. (Staff steps, unmodified by accidentals, are whole steps, except for the half steps at E to F and B to C)
2. Every staff line and every staff space correlates to a specific white key on the piano.
(This point applies to all ledger lines and ledger spaces.)
3. If two consecutive staff steps are skipped over, both correlating piano keys are also skipped! (One staff step = the distance from any staff line to the very next space or vice versa–up or down)
Perfect 4ths are formed by extracting the 1st and 4th notes of any major scale.
What are they? Why are they called “perfect”?
Part of the answer to both questions has to do with the overtones and harmonics that only this particular class of intervals produce. Many piano tuners rely on perfect intervals in their craft. However, since the details that explain overtones and harmonics go far beyond the scope of this post, I’ll simply tell you which intervals are “perfect” and I’ll mention a distinguishing and affirming “key” characteristic of perfect intervals, (“Key” pun intended).
Which intervals are perfect?
There are only 4 of ‘em! They come directly out of the major scale. Memorize ‘em!
1-1 Perfect 1st or Perfect Unison
1-4 Perfect 4th
1-5 Perfect 5th
1-8 Perfect 8th or Perfect Octave
Here’s an optional verification process you can use to confirm an interval’s “perfect” status.
Perfect Interval Evaluative Characteristics Affirmation Test (P.I.E.C.A.T.)
(OK! I just made-up this tongue-in-cheek acronym but here’s how the test works…)
A perfect interval is affirmed when the upper note of any given interval is also found in the major scale that begins on that interval’s lower note, AND, the lower note of that interval is also found in the major scale that begins on that interval’s upper note. Here’s another way to say it…
If your interval’s top note is present in its bottom note’s major scale, AND, its bottom note is present in its top note’s major scale, voilà! You’ve affirmed a perfect interval via “P.I.E.C.A.T.“!
The most commonly used accidentals are shown in the lineup just below followed by examples of the most common occurrences of 4ths in the key of C.
♮ = natural
♯ = sharp
X = double sharp
♭ = flat
♭♭ = double flat
Perfect 4th = C to F (The 4th note of a major scale remains unmodified)
Augmented 4th = C to F♯ (The 4th note of a major scale is sharped once)
Minor 1st *(N/A)
*(Minor functionality isn’t allowed on any perfect interval.)
Diminished 4th = C to F♭ **(The 4th note of a major scale is flatted once)
**(Perfect intervals become diminished with only one flat)
This link will open an Acrobat/Adobe flash type of applet where you’ll be asked to correctly match ten intervals via a drag-n-drop process. Doing the exercise at least 4 or 5 times will give you an introductory workout on identifying and matching the intervals in C and other keys.
Study well and have fun,
See you next post,