Intro / Op-Ed
Sixths are consonant intervals that add stability to many situations where stability is desired. They’re beautiful sounding intervals that add richness to the music in which they are used. Things like block chords, melodic passages, and improvisations are enhanced with their use.
Hopefully, the mechanics of transforming major intervals into their other states of modification is “old hat” 
to you by now. With that said, we’ll quickly move through this post and the rest of this series starting from here. If you have any questions, just sign-up for a few lessons.
Construction of Major 6ths from the numerical scale steps of Hexachords
Hexachords are 6-note scales. The Major Hexachord is a major scale subgroup that’s comprised of major scale notes 1 thru 6. Extracting the 1st and 6th notes make a major 6th.
Major Hexachord Legend
1-6 = 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
If you start with C and follow the schematic’s instructions, step-by-step, the C major hexachord will reveal itself on your piano’s white keys. Play the hexachord in the keys of G, D, A and E too.
Construction of Generic 6ths from the 7-Letter Musical Alphabet
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 3 scale steps.
(In doing that you’re skipping over scale steps 2, 3, 4, and 5 because your mission is to make a 6th.)
3. Having skipped over scale steps 2, 3, 4, and 5, select the very next letter in the sequence.
(In doing that, you’ve selected scale step “6” as the interval’s upper note and then you extract scale steps 1 and 6.)
That’s it! You’ve constructed a 6th… a generic 6th*.
*(All accidentals are excluded In generic intervals. Only letter names and staff position matters.)
6ths – These intervals may be identified by their letter names because both letter names are the 1st and 6th letters of an alphabetically sequenced 6-letter string (hexachord).
When written in standard music notation, 6ths will have exactly 4 unoccupied staff steps in between the interval’s lower and upper notes–a space/line/space/line, OR, a line/space/line/space. Also, four alphabetically sequenced letters will be skipped over.
Keep the following points in mind:
1. The staff represents a piano’s white keys only. The 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) (One staff step = the distance from any staff line to the very next staff space or vice versa, up or down)
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 4 consecutive staff steps are skipped over, 4 correlating piano keys are also skipped over! (This “skip-over/fly-over” concept and analogy is illustrated in the key of C in the photos just below.) (Your eyes skip-over the 4 staff steps while your fingers “fly-over” the 4 correlating piano keys.)
(The video below shows 6ths being used in block chords and descending scale passages.)
The most commonly used accidentals are shown in the lineup just below followed by examples of the most common occurrences of 6ths in the key of C.
♮ = natural
♯ = sharp
X = double sharp
♭ = flat
♭♭ = double flat
Major 6th = C to A (The major 6th is unmodified)
Augmented 6th = C to A♯ (The major 6th is sharped once)
Minor 6th = C to A♭ (The major 6th is flatted once)
Diminished 6th = C to A♭♭ (The major 6th is flatted twice)
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,