The Scale Illusion was discovered by Deutsch in 1973, first reported at a meeting of the Acoustical Society of America (1974)1 and first published in the Journal of the Acoustical Society of America (1975)2. The pattern that produces the Scale Illusion is shown in Figure 1A. This consists of a major scale with successive tones alternating from ear to ear. The scale is played simultaneously in both ascending and descending form; however when a tone from the ascending scale is in the right ear a tone from the descending scale is in the left ear, and vice versa. (Figure 1B shows these ascending and descending scales separately, and you can see that the pattern shown in Figure A is produced by the superposition of the patterns shown in Figure 1B). The tones are equal-amplitude sine waves, and the sequence is played repeatedly without pause at a rate of four tones per second.
Figure 1. The pattern that produces Deutsch’s Scale Illusion (a) and a way it is often perceived when listening through headphones (c). The notation in (b) shows how the pattern is composed of ascending and descending scales.
The Scale Illusion is best heard through stereo headphones. Make sure that the loudspeakers on your sound system are turned off, and that the left and right channels are balanced for loudness. Then readjust the settings on your amplifier so that the sounds, as heard through the headphones, are somewhat on the soft side.
Now listen to this pattern. If you hear higher tones in one ear and lower tones in the other ear, decide which ear is hearing the higher tones. Then reverse the earphone positions and listen to the pattern again. Decide again which ear is hearing the higher tones.
An illusion that many people experience when listening to the Scale Illusion through headphones is shown in Figure 1C. A melody corresponding to the higher tones appears to be coming from one earphone, and a melody corresponding to the lower tones from the other one. When the earphone positions are reversed, the ear that had heard the higher tones often continues to hear the higher tones, and the ear that had heard the lower tones often continues to hear the lower tones.
Right-handers and left-handers tend to differ in how they hear this pattern. Right-handers tend to hear the higher melody on the right and the lower melody on the left, whereas left-handers vary considerably as to where the higher and lower tones appear to be coming from.
People have also described a number of different percepts on listening to the Scale Illusion though headphones. Some of these are illustrated in Figure 2.
Figure 2. Some other ways in which Deutsch’s Scale Illusion is perceived.
It is also interesting to listen to the Scale Illusion through stereo loudspeakers that are placed in front of you, with one to your left and the other to your right. Before you begin, make sure that the left and right channels are balanced for loudness. Then listen to the pattern first with the channels playing simultaneously. You will most probably hear a higher melody and a lower melody in contrary motion. Then play each channel separately – you will then hear entirely different patterns, in which the tones leap around in pitch. Then play the two channels together again, and the two smooth melodies will probably return. Since similar sounds are likely to be coming from the same source, and different sounds from different sources, the brain rejects the improbable, jerky patterns that are coming from each loudspeaker, and instead reorganizes the tones perceptually so that two smooth melodies are heard instead.
Figure 3. The beginning of the final movement of Tchaikovsky’s Sixth Symphony - The Pathetique. The upper part of the figure shows the passage as it is played by the two violin sections, and the lowerpart of the figure shows how it is generally perceived.
Perceptual illusions such as in the Scale Illusion also occur in the classical music repertoire. For example, at the start of the second movement of Tchaikovsky’s Sixth Symphony – The Pathetique – the notes from the theme alternate between the first and second violin parts, and the notes from the accompaniment alternate reciprocally, as shown in Figure 3(a). However the passage is not perceived as it is performed: one violin part is heard as producing the theme and the other as producing the accompaniment, as in Figure 3(b). This effect occurs even when the orchestra is arranged in 19th Century fashion, with the first violins to the left of the audience and the second violins to the right. This was demonstrated by the UCSD symphony orchestra conducted by Tom Nee, as shown in the video below.
Diana Deutsch plays her Scale Illusion to a subject in her laboratory. From “NOVA” What Is Music? (1989), produced by WGBH Boston for PBS.
The perceptual reorganization into higher and lower melodic lines that occurs with the Scale Illusion even occurs in a very informal setting. The video below shows two fifth graders playing the illusion pattern on Orff instruments. The two parts are played separately and then together, and the illusion emerges clearly in the combined version.
Deutsch's Scale Illusion performed and experienced by the fifth graders at Atwater School, Shorewood, Wisconsin. The video was created by their music teacher Walt Boyer, and is posted with permission.
The Scale Illusion, as presented through headphones, is an example of an illusory conjunction of pitch and location. We can take a listener who hears the higher tones in his right ear and the lower tones in his left ear. For this listener, when a higher tone is presented to the left, it is perceptually linked to the right-sided location. Analogously, when a lower tone is presented to the right, it is perceptually linked to the left-sided location. Illusory conjunctions such as these also occur for other patterns, such as the Chromatic Illusion and the Cambiata Illusion.
Why does the Scale Illusion occur? The pattern is creates from tones that are in overlapping pitch ranges. In everyday life, sounds that are similar in pitch are likely to be coming from the same source, and sounds that are different are likely to be coming from different sources. So the most likely interpretation of this sound pattern is that one source is producing the higher tones and another source is producing the lower tones. The brain therefore reorganizes the tones in accordance with the most plausible interpretation, even though it is incorrect; this illustrates the power of unconscious inference in perception 3.
Similar examples of spatial reorganization occur in vision. Figure 4 shows a picture of a hollow mold, taken from the inside. We perceive the features as projecting outward while in reality they are projecting inward. Our knowledge and expectations that faces project outward are so strong that we perceive this image quite incorrectly. The Scale Illusion and the hollow mask illusion both illustrate the importance of unconscious inference in perception (see also references 4-7).
Figure 4. Picture of a hollow mold of a face. We perceive the features of the face to be projecting outward, even though they are projecting inward. This, as the Scale Illusion, provides an example of the strong influence of unconscious inference in perception.3
References:
1. Deutsch, D. An illusion with musical scales. Journal of the Acoustical Society of America, 1974, 56, s25. [Web Link]
2. Deutsch, D. Two-channel listening to musical scales. Journal of the Acoustical Society of America, 1975, 57, 1156-1160. [PDF Document]
4. Deutsch, D. Auditory illusions, handedness, and the spatial environment. Journal of the Audio Engineering Society, 1983, 31, 607-618. [PDF Document]
5. Deutsch, D. Illusions for stereo headphones. Audio Magazine, 1987, March, 36-48. [PDF Document]
6. Deutsch, D. Hearing music in ensembles. Physics Today, 2010, February, 40-45, [PDF Document]
7. Deutsch, D. Grouping mechanisms in music. In D. Deutsch (Ed.). The Psychology of Music, 3rd Edition, 2013, 183-248, San Diego: Elsevier. [PDF Document] [Web Link]
8. Deutsch, D. Musical Illusions and Phantom Words: How Music and Speech Unlock Mysteries of the Brain, 2019, Oxford University Press. [Web Link]
9. Deutsch, D. (Ed.). Grouping mechanisms in music. Chapter 6 in The Psychology of Music, 3rd Edition, San Diego: Elsevier, 2013.
10. Deutsch, D. Some musical illusions are discovered. Chapter 2 in Musical Illusions and Phantom Words: How Music and Speech Unlock Mysteries of the Brain, Oxford University Press. 2019.
11. Deutsch, D. Musical Illusions and Phantom Words: How Music and Speech Unlock Mysteries of the Brain, Korean translation, 2023, Eidos Publishing Group
12. Deutsch, D. Musical Illusions and Phantom Words: How Music and Speech Unlock Mysteries of the Brain, Chinese translation, Guangxi Normal University Press, Group Co, Ltd., 2024.
