Intervals of a fourth, such as the interval from C to F, are common in western music, but consecutive intervals of this size are not. Quartal harmony is based on intervals of fourths, and quartal melodies use a lot of fourths, particularly consecutive fourths.
Maybe the most famous quartal melody is the opening fanfare to Star Trek (original series). Here’s a transcription of the opening line:
And here is the same music with the intervals of a fourth circled.
The theme opens with two consecutive fourths, there’s an augmented fourth in the middle, then two more consecutive fourths. There are two major thirds in the phrase above, which you could call diminished fourths.
Incidentally, there are four bell tones before the melody above begins, and the interval between the first two tones is a fourth.
Making the sheet music
Here’s the Lilypond source code I used to create the images above.
\begin{lilypond}
\score {
\relative e'{
\time 4/4
\partial 2 a4. d8 |
\tuplet 3/2 {g4~ 4 ges4} \tuplet 3/2 {d4 b4 e4} |
a2 ~ 4 ~ 8 8 |
des1
}
\end{lilypond}
This uses a few Lilypond features I hadn’t used before.
- The
\partialcommand for the two pickup notes. - The
\tuplecommand for the triples. - The shortcut of not repeating the names repeated notes.
The last point applies twice, writing g4 4 rather than g4 g4 and writing a2 4 8 8 rather than a2 a4 a8 a8.
Thank you for posting this material. It will be very useful to me.
The fourth note is idiomatically spelled as an F#, for (at least) three reasons: 1) it resolves the fourth scale degree down to the third scale degree in the D major key implied by the melody; 2) the interval from the previous note is semantically a minor second, not an augmented unison; and 3) the interval to the following note is semantically a major third, not an diminished fourth. (It is pretty rare to encounter diminished fourths in functional tonal music, and one would never take a major third and “call it a diminished fourth” unless there was a very specific reason for it. One example might be the diminished fourth of a D-Gb dyad resolving to the minor third of D-F, but nothing like that is happening here.) For analgous reasons, the final note should be spelled C#.
This is not to diminish (no pun intended) the quartal nature of the theme, which you rightly note, but it all comes from the A-D-G and B-E-A arpeggios. The intervals are, in order, P4 up, P4 up, m2 down, M3 down, m3 down, P4 up, P4 up, M3 up (P=perfect, M=major, m=minor).
Nice article.
Thank you for Greate post.
You notated the rhythm of the first half incorrectly. The first note should be at the beginning of the bar, the first two notes are not a pickup. The 3rd note note is less then half the length it should be, and the third note should be notated as a half note tied to a quarter note in the next bar, followed by the fourth note being notated as a quarter note. Everything afterwards is correct, at least in the original series rendition, though I have heard other renditions where the first and final quarter note are played as triplets.