Estimated reading time 4 minutes
Table of Contents
Introduction
Do you have a harder time singing certain harmonic intervals? Knowledge is power! This post expands on the third element from the post 10 Elements that Impact Singing in Tune – section #3: The Difficulty of the Harmony Impacts Singing in Tune. Read more to understand how intervals affect singing in tune.
Today’s post discusses research about how intervals affect singing in tune. For practical examples on how to sing in tune:
Barbershop Quartet Video
How Intervals Affect Singing in Tune: The Easiest Intervals
Science has confirmed what vocalists already knew about how intervals affect singing in tune. Namely, singers find consonant intervals easier to tune than dissonant intervals.
In their barbershop quartet intonation study, Hagerman and Sundberg compared the standard deviations of each interval class. Then, they charted the relative tuning difficulty. They state, “The magnitude of the standard deviation for an interval is an indication of the difficulty to tune this interval… The smallest values appear as a function of the interval width.
“The smallest values appear for the fourth, the fifth, and the octave, i.e. for the ‘simplest’ intervals, if we by simplicity mean the number of partials, which, within a given frequency range, are common to the tones constituting the interval” (34).
Standard deviation formulas get used to measure statistical spread. In this study, the spread shows how closely the various interval widths within each interval class cluster around a center cent value. A smaller standard deviation shows that the singers found a particular interval easier to tune. Conversely, a bigger standard deviation indicates a harder to tune interval.
Discussion of How Intervals Affect Singing in Tune
The chart Figure II-A-3 appears on PDF p. 10 of “Fundamental Frequency Adjustment in Barbershop Singing.”
Hagerman and Sundberg’s chart plots the standard deviation for different intervals classes (in cents). Here are some conclusions drawn from the chart (at the link above) about how intervals affect singing in tune:
- The minor third has the greatest standard deviation, even larger than the major second.
- As noted by Hagerman and Sundberg, the perfect fourth, fifth, and octave have the smallest standard deviations.
- After the perfect intervals, the major third seems to be the easiest to tune. Sometimes it tuned up even more easily than the perfect fourths, fifths, and octaves.
- The tritone seems to be on par with the other intervals. In some cases, it tunes even more easily to than the major second and the minor third. However, the singers never got the standard deviation as small as the best tuned minor and major thirds, perfect fourths and fifths, major sixths, or octaves.
- The minor sevenths tune somewhat on par with the major seconds and the tritone.
- Hands down, the major third tunes up the most consistently of any interval class.
The List of Intervals that Affect Singing in Tune
From points number 4 and 5 above, it seems obvious that dissonant intervals are harder to tune. This matches the experience of practicing musicians.
Thus, it seems reasonable to say that the acceptable tuning range will be greater for the minor third and dissonant intervals. Conversely, the major third and sixth and the perfect intervals will tend to have a smaller acceptable range of pitches that would be considered to be in tune.
Therefore, the order in which teachers might wish to introduce harmonic intervals would then be:
- unisons
- octaves
- perfect fifths
- perfect fourths
- major thirds
- major sixths
- minor sixths
- minor thirds
- major seconds
- minor sevenths
- tritones
As you can see from this list, no big surprises here. However, it’s mildly surprising that the singers found the minor third so hard to tune.
If you’re a seasoned vocalist, the list shows you about what you’d expect for how intervals affect singing in tune. Hence science confirms what musicians have suspected all along.
For a practical application, this post has a sing-along soundtrack that will train you to sing in tune:
The sing-along tracks use synth voices rather than actual voices. Science has shown that this helps you, the vocalist, to identify and perform absolute pitch information. For more info:
How Intervals Affect Singing in Tune: Consonant Harmony
We’ve seen how intervals affect singing in tune. Namely, how vocalists find it easier to tune some harmonic intervals than others. Likewise, singers find some chords easier to tune than others. Shackford studied the effects of tuning complex and dissonant chords. Not surprisingly, he found that vocalists tuned the consonant chords more accurately. He asserts:
In the case of the intervals used [within a chord] in the dissonant style a comparison of Examples 3 and 4 does not show the same degree of consistency as in the case of the intervals used [within a chord] in the consonant style.” (Shackford 3:302)
Concluding Thoughts on How Intervals Affect Singing in Tune
The list in section five shows the order of the intervals that affect singing in tune. This list suggests that teachers should start with the simpler intervals first. After the intervals have been mastered, vocal students should work on consonant triadic harmonies before trying more complex chords.
© 2022 Geoffrey Keith
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