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Relative Pitch

An Octave Is Not Always Twelve Half Notes and A-sharp is Not Quite B-flat

Maurice E. Reagan in collaboration with Deac Martin

Barbershop harmony is the most exact type of music because the three voices which accompany the lead in a Grade A quartet vary the tone level to give the right pitch on each tone. Believe it or not, those accompanying voices MUST vary the pitch of various tones depending upon their voice position in the chord. This may seem confusing to those who consider that a piano in perfect tune is an exact instrument. Actually four voices can produce much closer and more perfect harmony than four notes on a piano. That is one reason why we thrill to the effect of a perfectly blended quartet as we do to no other form of music.

 

Introduction to Tone Blending

What follows is based upon the assumption that readers have to some extent familiarized themselves with the “Mechanics of Barbershop Harmony” presented some years back in the Harmonizer. Take the last three words in the first phrase in the chorus of “Let Me Call You Sweetheart.” The sequence of chords on “love with you” is 11 o’clock major, 3 o’clock seventh and 2 o’clock seventh. The Lead has the same melody tone-LA-on all three words. The tenor sings FA-SaL-fl., the Baritone DO-di-DO and the Bass F A-MI-RE. It is surprising to discover that the Baritone, in order to get good blend on the third chord must drop the pitch of DO below the first one. This is the concept of relative pitch.

Harmonizing Relative Pitch

Some years ago when making the first “mechanical man” talk, the real reason for this variation developed in my mind. In this illustration, the BARITONE MUST DROP THE PITCH OF HIS SECOND DO ALMOST ONE QUARTER OF A TONE BELOW THE FIRST DO TO MAKE SATISFACTORY HARMONY.

Other harmony parts must also adjust their tones or relative pitch at times but usually not to such a great degree. Here, the Lead has established the level of the melody tone, and thru the harmony parts must line up with it. In Barbershop quartet singing, it is only the true ear of the Lead that keeps them from changing pitch as they progress from chord to chord. 

The Mathematics Behind Harmony

Here is the arithmetic necessary to explain this example and achieve relative pitch: Suppose we as­ sign 400 cycles to the first Bass tone FA. Don’t worry about that word cycle as it just a measure of pitch like a POUND of butter or a DOZEN eggs. Likewise, the term frequency is just another way of saying the NUMBER of cycles, (A 400 cycle tone has a frequency of 400). A seventh chord based on 400 cycles consists of 400-500-600-700 (1 – 1 ¼ – 1 ½ – 1 ¾ times the root). The 400 cycle root is chosen here to simplify the arithmetic.



TENOR
LEAD
BARITONE
BASS

(11-T)
LOVE
FA’ = 800
LA = 500
DO’ = 600
FA = 400

(3-7)
WITH
SOL’ = 875
LA = 500
di’ = 625
MI = 375

(2-7)
YOU
fi’ = 822-2/3
LA = 500
DO’ = 583-1/3
RE = 333-1/3

The First Chord

The root of the first (11 o’clock) chord is FA and, being a Tonic or Major chord the tones are FA-LA-DO-FA. Then Tenor sings an 800 cycle tone (FA) or an octave above the Bass. The Lead has the third tone of the chord (LA) which is 1 ¼ times 400 or a 500 cycle tone. Likewise, the Baritone, who has the fifth of the chord (DO), sings a (1 ½ times 400) 600 cycle tone.

The Second Chord

As we move on to the second chord, the Lead maintains his 500 cycle pitch because it is the same tone. This means that all other voices must line up with his tone. The chord is the three o’clock structure and is based on LA-the Lead’s tone. To repeat, the three O’Clock chord is LA-di-MI-SOL. The Baritone has the third of the chord-di-which is a (1 ¼ times 500) 625 cycle tone. The Tenor tone -SOL’- is the seventh or a (1 ¾ times 500) 875 cycle tone. The Bass, with the fifth tone of the chord would have a (1 ¼ times 500) 750 cycle note except for the fact that he is singing an octave lower. This gives him a (½ of 750) tone of 375 cycles.

The Third Chord

Again on the third chord, the Lead maintains his 500 cycle pitch on LA. Since this is a two o’clock seventh chord based on RE, (RE-fi-LA-DO’) the Lead has the fifth of the chord. Therefore, the Bass tone-RE-is of a pitch, which when multiplied by 1 ½, would be 500. This establishes RE as a 333-⅓ cycle note. The Baritone note-again DO’-is the seventh tone of the two o’clock chord and is therefore a (1 ¾ times 333-⅓) 583-⅓ cycle tone.

The Baritone sings a 600 cycle tone on love and must drop to a 583-⅓ note on you, a difference of 16-⅔ cycles. This represents a lowering in pitch of 2.778 percent. An evenly divided scale of twelve half-tones has approximately a six (5.9463) percent between half-tones. So we have the proven fact that the Baritone, in this case, has to vary the pitch of a given tone .47 of a half-tone or almost one quarter tone to make “solid” harmony.

What Separates Great from Good

Obviously this getting a blend that is closer than possible on a piano demands a sharp ear. Without it, it is entirely possible for four trained voices, each interested primarily in getting his own note exactly as written (without “feeling” his way into the closer harmony blend) to be “just another quartet” not completely melted together. This might apply particularly to soloists thrown together into a foursome; while four untrained voices with instinctive sense of barbershop harmony would blend like cream.

Conclusion

These tone adjustments are necessary to make perfect ringing chords aka relative pitch or close harmony. As we sing our songs, we do not think in terms of frequencies nor do we need to. But it is necessary to listen to the other voices and adjust our tone to obtain the “ring.” The more we rehearse, the more accurate we become as we first strike the tone and the less time it takes to adjust to the correct value. The main point to realize is that our tones must vary slightly to line up with, not only the melody note, but with the tone’s position in the chord structure. Our Society champions win their coveted medallions only after months and months of concentrated work in smoothing out these tonal values.

Reagan, M. Relative Pitch, The Harmonizer, Volume 6, No. 3, February 1947, pages 26-27.  Copyright by the Barbershop Harmony Society. Reprinted with permission. Note: minor adaptions made.

Click to read about The Basics of Barbershop Harmony or read about the Barbershop in Popular Culture which includes a discussion on the history and origins of the Barbershop style of a cappella music.  

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