Estimated reading time 7 minutes
Table of Contents
Introduction
Want to sing in tune? Knowledge is power. The following post talks about how singers group pitches as they perform. Read more to find out how the fact that a note contains many pitches can impact singing in tune.
Today’s post expands upon the second section of the post 10 Elements that Impact Singing in Tune.
- It surprises many musicians when I tell them that a note can have more than one pitch.
- You get used to looking at an instrument like the piano and thinking that one note contains one pitch.
- Indeed, on fixed pitch instruments (such as the piano, organ, guitar, and xylophone) it does work that way.
On instruments with flexible pitch (such as the voice, violin, flute, and trumpet) a range of pitches remain available. However, this brings up many questions, such as:
- How many pitches can a note encompass?
- What pitches can be considered to be in tune, and which will be out of tune.
- How can we apply this to singing or playing in tune?
When a Note Contains Many Pitches, We Call Them Pitch Clusters
Robert Jourdain
In Music, the Brain, and Ecstasy, Robert Jourdain explains how a note can contain many pitches. He says that though your brain can discriminate hundreds of pitches, it does not have the capacity to label that many frequencies.
Then, he goes into how this impacts tuning. “When we listen to musical tones, we divide the range of pitches in an octave (its pitch space) into only a dozen positions or ‘categories.’ Although under laboratory conditions we can distinguish perhaps thirty shades of pitch within a category, in the rough and tumble of music performance we hear most such pitches as being the same note.
“When a note comes in dead center, we deem it to be perfectly in tune. But even when the tone’s frequency is somewhat higher or lower, our brains still categorize it as being an instance of that note. Only at the borders between the divisions of pitch space can a note waver between categories. Such ‘out of tune’ notes leave our brains in a state of consternation and even agony” (64 – 65).
The quote above states that when a singer has a pitch fall inside a note category it will be in tune. However, if it falls outside the pitch category it will be out of tune. How would this look on a chart?
Charles Shackford and Paul C. Greene’s Intonation Studies: Interval Sizes
Below I have provided two charts, one derived from a study by Charles Shackford and another derived from a study by Paul C. Greene. Both scientists studied violin intonation.
The black typeface shows the equal tempered (the piano’s tuning) cent values. (For a review of cents click here.) The blue typeface shows each note category. Namely, the range of pitches for each interval class.
Shackford states, “It can be seen that in spite of size range, the intervals are all distinct entities, separated from each other by an absolute abyss ranging from a little over a quarter tone to a little under; all, that is to say, except the two tritones which overlap into each other’s territories.
“The pitch gap between interval sizes, perhaps the significant aspect of Example 1, is, of course, a distinct feature of Western harmonic music” (3: 299).
In other words, the note D (200 cents above C on the piano) on Shackford’s chart has a range of 56 cents (235 – 179 = 56). This means that the note D can potentially have 56 pitches. Indeed, a note can contain many pitches!
However, big gaps separate it from its neighbors.
Mobile users: for best results reading the music, tilt your screen 90o to the right.
Charles Shackford and Paul C. Greene’s Intonation Studies: The Pitch Void
So, the interval classes have a definite range of pitches that sound in tune. In addition, Shackford remarks on the distinct gaps that exist between the intervals. I call these gaps the pitch void. I added the pitch void numbers (red typeface) to Shackford’s and Greene’s charts. This means that a note can contain many pitches that may be considered to be in tune, but not an infinite number.
Shackford’s and Greene’s charts look remarkably similar. This implies that musicians (at least within the same culture) will tune similarly.
On the other hand, the interval classes do differ somewhat between Shackford’s and Greene’s charts. This implies that the tuning will vary from performer to performer.
I’ve spent a lot of time studying guitar open tunings, where the guitarists tuned without using frets. I found that the same open tuning varied from player to player. Also, it varied when the same player tuned at different times. Nonetheless, all of the tunings fell within similar parameters.
Notice that the range for each note is surprisingly wide. Most of the intervals have a range of around a quarter step (50 cents). A quarter step is kind of big. Does this mean that almost any pitch will be acceptable?
In both studies they used professional musicians and paid particular attention to the tuning, going for the best intonation they could. It turns out that the interval variance’s outermost range is only part of the story.
A Note Contains Many Pitches: Core Clusters
Can Akkoc also detected a similar pattern of clustered pitches surrounded by “empty zones” in the music of Turkish maqam. Using cluster analysis to further study pitch groupings, he found smaller clusters within the extreme cent ranges of each interval class. In other words, there would often be tighter groupings of pitches, which he called the core cluster. “We are going to refer to such concentration zones close to the mean (medoid) as the ‘core’ of the cluster” (288).
Similarly, Ternstrom and Sundberg found this type of pattern in Western choirs, having a core cluster range of around 30 cents. (Not that they referred to them as core clusters.)
This means that the bulk of the pitches fell within a fairly tight range of about a third of a semitone. Conversely, fewer and fewer pitches occurred the farther they got from the center of the pitch cluster. A note may contain many pitches, but most of the pitches will fall close to the central pitch.
So, how can we use this to sing in tune?
A Note Contains Many Pitches: How We Can Help Singers
The Practical Application
Here is the practical application part of A Note Contains Many Pitches. Since all the violinists tuned similarly, this implies that culture will play a role in learning accurate tuning. This in turn means that including intonation exercises into your daily practice will help you learn to sing (or play) in tune.
How can you best do this? By having an intonation “flight simulator.”
The Intonation “Flight Simulator”
A note may contain many pitches, but these posts will help you to sing the best ones. The links below have sing-along song tracks that will help you learn how to sing in tune. They work like the singing equivalent of a flight simulator, distilling the essential elements you need to work on to improve. The posts:
- Singing Exercises with Harmony: This post introduces the Singing in Tune series, giving a lot of basic advice. It also exhorts you to breathe between phrases.
- Harmonize with Sing-Along Songs: It works on harmonic and melodic intonation in the same exercise. Also, it discusses good vowel production and performing with a high soft palate.
- Ear Training Exercises for Harmonizing in Tune: This post is the heart of the training method. It works on intervals in combination with well-tuned harmonies. Also, it talks about singing with a free and open tone.
- Harmony Singing Examples for Children: It covers the same basic material as the last post, but in a more compact, maintenance-oriented exercise.
- How to Hear the Notes When Harmonizing: This post does not have sing-along song tracks per se. Its song tracks provide the listening material so the post can show you how to listen for harmony parts.
- Singing Major and Minor Harmonies in Tune: Earlier posts focused on singing notes against well-tuned major chords. This post mixes in minor harmonies as well.
- How to Harmonize in Minor Keys: It builds on the material in the last post, taking the next step: singing in the harmonic minor mode.
The Intonation "Flight Simulator" Part II
Here’s the second group of Intonation Flight Simulator posts for A Note Contains Many Pitches.
- How to Sing Key Changes in Tune: Up to now, all of the examples have stayed in one key. This post works on a commonly used pivot modulation.
- Singing 7th Chords in Tune: Most vocalists find seventh chords hard to sing, because they tune differently than thirds, fifths, and octaves. Don’t worry, the song tracks will help.
- Sing in Tune Like a Rock Star: This post focuses less on vocal tuning, and more on critical listening skills. These skills in turn help with learning good vocal intonation.
- Singing Schwa Vowels: The post introduces the vowels series of posts. It teaches how to sing schwas vowels and “singing into the mask.”
- Singing Tongue Vowels: This post in the vowels series shows you how to fine tune your tongue vowels to best fit the melody note and harmony.
- Singing Lip Vowels: This post is similar to the last one. It shows you how to fine tune your lip vowels to best fit the melody note and harmony.
- How Can I Tell When I’m Singing in Key: The name pretty much says it all.
More Tips
These don’t really have anything to do with the main topic of A Note Contains Many Pitches. Nevertheless, they provide useful singing tips that you’ll find helpful.
- Singing with power
- Phrasing with your breathing
- Singing without vibrato
- Singing from down low
- Fine-tuning your notes until any beating fades away
- As you harmonize, listen to how the shifting tone color of each chord change effects the sound of your part.
Concluding Thoughts About Notes Containing Many Pitches
The fact that a note can contain many pitches has a huge impact on how you view singing in tune. When singing, instead of having one note to hit, you have a cluster of pitches that you can shoot for. Like an archer, you aim for the target. You don’t necessarily need to hit the “bullseye” to sing in tune, but you do need to hit the target.
The sing-along song tracks will help you learn how to do just that. See you next time and have fun singing!
© 2022 Geoffrey Keith
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