KRAEPELIN (1899/1921) identified five characteristics of sad speech: (1) low overall pitch, (2) small pitch movement, (3) quieter, (4) mumbled articulation, and (5) slower speaking rate. Over the past century, Kraepelin's clinical observations have been confirmed through controlled experimental studies. With regard to small pitch movement, sad vocal prosody is more "monotone" compared with normal voice (Banse & Scherer, 1996; Bergmann, Goldbeck & Scherer, 1988; Breitenstein, van Lancker, & Daum, 2001; Davitz, 1964; Eldred & Price, 1958; Fairbanks & Pronovost, 1939; Huttar, 1968; Skinner, 1935; Sobin & Alpert, 1999; Williams & Stevens, 1972). Wide pitch excursions are associated with high physiological arousal, such as occurs in joy or anger. By contrast, low variability of the fundamental pitch (F0) is characteristic of low arousal, including both sad voice and sleepy voice.

In historical and cross-cultural studies, music-related sadness is one of the most commonly described affects. In his volume De Medicina, the first century Roman physician Aulus Celsus described how "playing soft music" might be used to treat the mental stupor thought to be caused by an excess of black bile—a condition Celsus described by its literal Latin term, melancholia. Similar descriptions of music's ability to evoke or temper sadness can be found in many historical texts spanning many cultures, including ancient Egyptian, Chinese, Hebrew, Persian, Arabic, and Sanskrit sources. Apart from historical sources, there also exist both ethnographic and empirical descriptions of grief- or sadness-related musical experiences in many cultures. Laments, sorrow songs, dirges, elegies, and mourning-song traditions are evident around the world, especially in eastern Europe (e.g., Mazo, 1994; Seremetakis, 1991; Wilce, 2009), Africa (e.g., Anyumba, 1964; Nketia, 1975), the Middle East and Asia (e.g., Naroditskaya, 2000; Racy, 1986; Wilce, 2002), and Oceania and Australia (e.g., Feld, 1982/1990; Magowan, 2007; Moyle, 1987).

Sadness has been one of the most commonly studied affects in research on music and emotion. At least in the case of Western-enculturated listeners, both adults and children readily identify particular melodies or passages as sounding "sad" (e.g., Dolgin & Adelson, 1990; Terwogt & Grinsven, 1991). The ability of music to evoke or portray sadness or grief does not appear to be limited to Western music. Anthropologists are not easily given to claims of universality, however, in the case of music-related grief, a number of scholars have pointed to an apparent commonality. For example, writing about grief expressions and situations in non-Western cultures, ethnomusicologist Greg Urban has noted that the experiences are "transparently understandable, not in need of detailed ethnographic description." (Urban, 2000, p. 151).

For Western-enculturated listeners, sadness has a long association with the minor mode. The association of the minor third and minor triad with sadness was already described in the sixteenth century by Zarlino (1558). Experimental studies by Heinlein (1928) and Hevner (1935) show that the minor mode continues to evoke sad, dejected, or serious connotations for Western-enculturated listeners.

It is important to note that the minor mode is not solely associated with sadness. For Western-enculturated listeners, the minor mode is also associated with exoticism (especially "orientalism"; Said, 1978), as well as passion and seriousness (Hevner, 1935). When the minor mode is linked to Kraepelin's cluster of acoustic cues for sadness (low pitch, small pitch movement, quiet, slow, mumbled articulation), the resulting music has a strong tendency to exhibit a sad character. "Exceptions" to the minor↔sadness association appear to confirm the need for this cluster of features. For example, W.A. Mozart's popular "Rondo Alla Turca" can hardly be described as "sad" despite the prevalence of the minor mode. Similarly, the aria "He was Despised" from G.F. Handel's Messiah is widely regarded as very sad, despite the use of the major mode. However, the "Rondo Alla Turca" is fast-paced with relatively detached articulation; whereas "He was Despised" is slow and quiet. In short, it is difficult to identify exceptions to the minor↔sad association unless the music also violates one or more of the other acoustic features identified by Kraepelin as characteristic of sad speech prosody. Other challenges to the minor↔sad association can be found in the ethnomusicological literature. For example, scales similar to the Western harmonic minor can be found in traditional Balkan music and in various North African and Middle Eastern musics, without any accompanying association with sadness (Rice, 2004).

Most music scholars now reject the notion that the minor scale is inherently sad, and attribute its sad connotations to learned associations. An early proponent of this view was Valentine (1913/1914), who proposed that Ivan Pavlov's recently-formulated concept of the conditioned reflex might account for the sad connotations evoked by the minor mode:

The general significance of the minor key for modern European ears is not due to an effect inherent in the relation of the notes in a minor interval, but is more probably the effect of association…with the custom of setting sad songs to minor keys (Valentine, 1913/1914, p. 197-8).

In effect, Valentine proposed that the sad connotations of the minor mode originated in an early accidental pairing of sad lyrics with the minor scale. This association then provided a bootstrap for a self-sustaining cultural practice unique to Western European music-making.

This view implies that the association of the minor mode with sadness is arbitrary or random. For example, the view implies that, with a different history, it might well have been the major mode that formed a learned association with sadness whereas the minor mode formed a learned association with happiness. Without suggesting that there is anything inherent about either the major or minor modes, and without suggesting that the connotations of the minor mode are anything other than culture-bound, in the study that follows, our data will suggest that the relationship between the major and minor modes may not be arbitrary.

If the minor mode tends to be used to express or represent sadness for some listeners, then we might expect to observe an association between the minor mode and those acoustic characteristics of sad speech prosody identified by Kraepelin. That is, if the minor mode is commonly involved in the expression of sadness, we might expect that, compared with major-mode music, music in the minor mode is typically: (1) lower in overall pitch, (2) employs small pitch movements, (3) is quieter, (4) entails "mumbled" articulation (e.g., legato), and (5) exhibits a slower tempo.

The results of several correlational studies are consistent with these conjectured associations. For example, Huron (2008) calculated the average melodic interval size for nearly 10,000 Western classical instrumental themes and found that the average interval size is slightly smaller for themes written in the minor mode compared with themes written in the major mode. As small pitch movements are found in sad speech prosody, one might speculate that small melodic interval sizes might also contribute to the perception of sadness—at least for Western-enculturated listeners.

One might suppose that many factors contribute to the size of melodic intervals in music. One factor is the scale itself. A pentatonic scale, for example, might encourage larger average melodic intervals than the major scale merely because there are fewer scale tones per octave. Consider, by way of illustration, the pentatonic scale consisting of the pitch classes C, D, E, G and A. For each pitch-class pairing, we might calculate the minimum interval size in semitones (e.g., C↔D = 2, C↔E = 4, C↔G = 5, C↔A = 3, D↔E = 2, etc.). 1 If all pitch transitions were equally probable, then the average interval class for random pitch sequences in the common pentatonic mode would be 3.60 semitones. By contrast, if all pitch-class transitions were equally probable, then the average interval class for random pitch sequences in the major mode would be 3.43 semitones. Of course, in real music, not all pitch transitions are equally probable, so the actual average interval size will depend on the nature of the melodic organization.

Rather than presuming that all pitch transitions are equally likely, in this study, we employ the pitch transitions found in actual melodies. We will then explore the influence of scale structure on average interval size. Specifically, we will begin with the major scale and make systematic pitch modifications; for each modification we determine its effect on the average interval size for a sample of melodies. Our goal is to determine which scale modifications most reduce the average melodic interval size. If smaller interval sizes are robust acoustic cues for sadness, one might expect that the scale modification that results in the smallest average interval size would also tend to most contribute to the perceived sadness of a melody.

To anticipate our results, we will see that among the optimum modifications to the major scale, lowering the third and sixth scale tones—as in the harmonic minor scale—provides one of the best means for reducing the average melodic interval size. That is, the results are consistent with the idea that transposing a major-mode melody to the harmonic minor scale is among the very best pitch-related transformations that can be done to modify a major-mode melody in order to render a sad affect. Skeptics are likely to view this result as too good to be true. Accordingly, in the final Discussion, we will consider and identify the statistical properties of Western major-mode melodies that are the proximal cause of this striking result.

METHOD

In brief, our method can be best understood by describing the following hypothetical scenario. Suppose a composer has created several melodies in the major mode, and wants to transform these melodies so that they sound sadder. Research in speech prosody suggests that making the melodic intervals smaller will contribute to the perceived sadness. Rather than merely compressing all of the melodic intervals, our composer wishes to achieve a smaller average interval size by modifying the pitches of the major scale. Are there pitch modifications that can be made to the major scale that will, on average, transform most melodies so that the average melodic interval is smaller?

Our method involved assembling three contrasting samples of melodies in the major mode, calculating the average melodic interval size for each melody, and then determining whether the average interval size increases or decreases for different scale modifications. In this study, we will limit ourselves to modifications of the Western diatonic major scale. In principle, the same method could be applied to any scale from any culture—and so the potential cross-cultural generality of the hypothesis might be tested.

In modifying the pitch of a scale tone, one consideration is the amount of modification. In the case of the Western equally-tempered pitch set, the smallest modification would be a semitone. Larger modifications are possible, but they risk potential perceptual confusions. Obviously, if we were to raise the second scale degree (supertonic) by 2 semitones the resulting scale tone would be indistinguishable from the third scale degree (mediant). It is therefore unlikely that the resulting pitch would be heard as a "modified supertonic." In the major scale, any modification greater than one semitone will lead to such confusions. Moreover, even in the case of semitone modifications, there are four changes that will also lead to similar scale-degree confusions: raising the third scale tone, lowering the fourth scale tone, raising the seventh scale tone, and lowering the tonic. A further restriction is that the tonic pitch remains fixed: one might reasonably argue that changing the tonic will cause the scale to be perceived as an entirely different scale rather than as a modified version of some original. For similar reasons, we will avoid modifying more than half of the scale tones at a time. That is, we will consider only modifying up to three scale tones. We conjecture that listeners would tend to hear four or more modified pitches as an entirely different scale—rather than a modified major scale. Accordingly, we will limit ourselves to one, two or three pitch modifications of just one semitone; we will avoid modifying the tonic, and we will exclude from consideration those semitone modifications that result in pitches equivalent to other scale tones.

Intuitively, one might suppose that lowering one or another scale tone might tend to result in smaller melodic intervals. However, this is not necessarily the case. Lowering a scale tone might well result in larger average melodic intervals. If, in some hypothetical culture, all of the scale tones occurred with equal probability and the successions of different scale tones were randomly ordered, then modifying one of the scale tones would have no effect on the average interval size. Figure 1 illustrates this effect for a hypothetical five-note scale. In this case, the third tone has been lowered. Notice that intervals such as 1-3 and 2-3 will be smaller; however, the intervals 3-4 and 3-5 will be larger in size. In this case, it is not clear that lowering the third scale tone would have any effect whatsoever on the average interval size for melodies employing this scale.

	Original Scale         Modified Scale (3rd tone lowered)
Smaller Intervals           Larger Intervals

Fig. 1. Effect of pitch modification for a hypothetical five-note scale. Lowering the third scale tone (lower image) causes intervals such as 1-3 and 2-3 to be smaller, whereas intervals 3-4 and 3-5 are larger. If all pitches occur with equivalent frequency and all pitch transitions are equally likely, then modifying a scale tone should have no overall effect on the average interval size.

In real music, however, scale tones are not equally common, and some tone successions occur much more frequently than others. Figure 2 shows the probability of different scale-tone successions for a large sample of Germanic folk melodies in the major mode (from Huron, 2006). The width of each arrow is proportional to the probability that one tone is followed by another. Pitch transitions whose probabilities are less than 0.015 are not indicated. Notice that there is considerable variability in the likelihood of different tone successions. For example, the third and fourth scale tones are closely linked. In the case of the seventh scale tone, there is a much stronger connection to the first scale tone (7-1) than to the sixth tone (6-7). In fact, there is so little movement between 6 and 7 that the probability falls below the 0.015 threshold needed to draw a line connecting them. In the major scale, if we were to lower the seventh scale tone by one semitone, the distance between 6 and 7 would be reduced, but the distance between 7 and 1 would be increased. Since alternations between 7 and 1 are more common than between 6 and 7, the likely consequence of lowering the seventh scale tone would be to increase the average melodic interval size.

Given the fact that some scale tones are more common than others, and that some successions between scale-tones occur more frequently, modifying the pitch of a given tone might well be expected to influence the average melodic interval size for common melodies, unlike the neutral situation illustrated in Figure 1. Accordingly, we will systematically modify the different scale tones and measure the effect on the average interval size for samples of real major-mode melodies. In order to pursue this approach, we must first identify a suitable sample of melodies.

Fig. 2. The probability of different scale tone successions for a very large sample of melodies in the major mode. Frequency of occurrence is proportional to the width of connecting lines. Lines are drawn only for those transitions with a probability of 0.015 or greater (Huron 2006).

SAMPLE

Since we are interested in melodic intervals, we restricted our musical sample to single-line melodies and themes. For this study, only melodies in the major mode were used. Creating a "representative" sample of music in the major mode raises significant challenges. Instead of attempting to create a broadly representative sample, we proposed to examine three subsamples, each exhibiting a different set of stylistic properties and biases. Specifically, our three subsamples included:

1) 151 major-mode national anthems including countries such as Albania, Colombia, North Korea, Palau and Zimbabwe. Although the anthems originate from different cultures, they all share a basically Western-European musical template which includes the tendency to employ the major scale. This sample was selected from a longer list of 195 national anthems. Roughly 20 anthems were deemed to be not clearly in the major mode and so were excluded from the sample. In addition, in order to minimize the potentially confounding effect of modulation, anthems longer than 50 measures in length were excluded. According to this latter criterion another 20-odd anthems were eliminated.

2) 935 randomly selected major-mode instrumental themes from the Barlow and Morgenstern Dictionary of Musical Themes (Barlow & Morgenstern, 1948). This collection includes themes from the period-of-common-practice Western art-music literature with a bias towards orchestral works from the 19^th century.

3) 103 major-mode works from a collection of songs most well-known to residents of the United States, including such songs as "Jingle Bells," "Happy Birthday," "Three Blind Mice," "Frosty the Snowman," "Yankee Doodle," "Mary Had a Little Lamb," and "Auld Lang Syne."

Although we would not claim that our sample of major-mode melodies is representative of Western music-making in general, our three samples includes both instrumental and vocal works, music of European and American origin, art-music and popular styles, music spanning a period of roughly four centuries, and instances of music from a genre that spans many countries. The sample also includes whole melodies and shorter thematic statements. It should be noted that the average passage lengths differ for the three samples. For the national anthems, the average length was 104 notes; for the American songs, the average length was 53 notes; and for the Barlow and Morgenstern instrumental themes, the average length was 20 notes. In general, effect sizes are likely to be smaller for the shorter sampled passages.

All of the musical materials were encoded in a computer database and were processed using the Humdrum Toolkit (Huron, 1995). In total, our sample represents passages from some 1,189 individual works involving roughly 40,000 notes. In carrying out our analyses, we will report separate results for each of the three samples.

PROCEDURE

For each work in the three samples, the average melodic interval size was measured only for immediately consecutive tones. No intervals were calculated for tones separated by a rest. Figure 3 illustrates the measurement method for the beginning of "Mary Had a Little Lamb." Figure 3a shows the original (unmodified) song in C major. The overall average interval size is indicated below each example. Figure 3b shows what happens when the third scale tone (E) is lowered by one semitone. Five intervals are affected, and the overall average interval size is reduced slightly.

Fig. 3. The effect of lowering the third scale tone (E) for the beginning of "Mary Had a Little Lamb."
Fig. 3a shows the original (unmodified) song in C major. The overall average interval size is indicated below each example. Fig. 3b shows what happens when the third scale tone (E) is lowered by one semitone.

In interpreting the results, readers should bear in mind the four restrictions imposed in our simulations:
(1) pitch modifications of only one semitone, (2) tonic remains unmodified, (3) modifications that result in pitches equivalent to other scale tones are avoided, (4) no more than three pitch modifications.

RESULTS

One-Pitch Manipulations

In our first simulation, we modified a single scale-tone by either raising or lowering it by one semitone. With seven scale tones there would nominally be 14 possible up/down modifications, however, with our imposed restrictions that number drops to 9. Once again, we avoided modifying the tonic, raising the 3^rd or 7^th scale tones, and lowering the 4^th scale tone. After making the appropriate scale modification, we re-calculated the average melodic interval size for each of the 1,189 passages in our musical sample. For each sampled passage, the average interval size for the modified scale was compared with the average interval size for the original major-mode version. The modified passage can then be classified as exhibiting either a smaller average interval size, a larger average interval size, or no change in interval size. We could have amalgamated all of the melodies together and compared the means of the interval distributions for the modified and unmodified melodies. However, we a priori elected to treat each melody as a single observation in order to maximize data independence.

Table 1 identifies the effect on average interval size for each of the scale modifications according to the three different musical samples. Numerical values represent the percentage of melodies exhibiting smaller average interval size for the given scale modification—excluding those melodies for which the modification had no effect on the average interval size. For example, suppose that a given modification produced 35 melodies whose average interval size decreased, 65 melodies whose average interval size increased, and 25 melodies whose average interval size did not change. Discarding the unchanged melodies, 35% of the remaining melodies exhibited a decrease in the average melodic interval. Values around 50% suggest that the modification has little appreciable effect on interval sizes. Values larger than 50% suggest that the modification tends to cause melodies to have a smaller average interval size than the unmodified major-mode version. The right-most column (Average) provides a summary result for all three samples, where all samples are weighted equally. As can be seen in Table 1, the greatest decrease in average interval size occurs when scale degree 6 is lowered by one semitone: 68.0% of major-mode passages exhibit smaller average interval sizes when this scale modification is made. The second greatest decrease (60.3%) occurs when scale degree 3 is lowered.