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4 Pitch and range in language and music

4.1 Average and range of pitch in spoken language and song

4.1.1 Average and range of pitch in language

Fant (1956) determined the average values for fundamental frequency in conversational

speech in European languages were approximately 120 Hz for men and 220 Hz for

women, and the typical range exploited by a single speaker within one utterance is

normally within one octave.1 The maximum overall range of fundamental frequency (F0)

in ordinary conversation is about 50–250 Hz for men, and about 120–480 Hz for women.2

Whereas Fant’s average Hz values are for European languages in general, Campione and

Véronis’ (1998) study of five languages (English, French, German, Italian, and Spanish)

demonstrated that there is a significant difference in the average spoken pitch across

languages. Their study used a large corpus of read speech in each of the five languages

by both male and female native speakers and determined the fundamental frequency of

what they termed individual pitch target points, or points of pitch which “represent the

macromelodic movements of the utterance.”3 The results of their study of the mean

frequency for each language are reproduced in Example 4.1; in both male and female

speakers, the average fundamental frequency for spoken French was the highest of the

1 Fant 1956. 2 Laver, p. 451. 3 Campione and Véronis, p. 1.

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languages in the study, while the average for German was the lowest of the studied

languages.4

Example 4.1: Campione and Véronis (1998), Figure 2: Mean frequency per language and sex

The y-axis of the graph illustrates pitch represented by ST (semitones), indicating pitch as

a number of semitones above a logarithmic frequency baseline of 1 Hz.5 Example 4.2

converts Campione and Véronis’ results for French and German from the semitone

notation into Hz, and compares the resulting value to the Hz value associated with equal-

tempered pitches.

4 French was also found to have a higher average overall pitch than Spanish in Brosnahan and Malmberg, Introduction to Phonetics, Cambridge University Press, 1970. 5 An application capable of converting between semitones and Hz can be found online at http://users.utu.fi/jyrtuoma/speech/semitone.html.

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Example 4.2: Campione and Véronis’ values for French and German.

Average in semitones

F M

Average in Hz

F M

Closest approximate pitch in equal temperament F M

French 96.5 86.0 263 143 C4 = 261.63 D3 = 146.83 German 91.7 81.3 199 109.5 G3 = 196.0 A2 = 110.0

Campione and Véronis’ average pitches for spoken French (263 Hz for females, 143 Hz

for males) are slightly above Fant’s averages of 220 Hz for females and 120 Hz for

males, and the average pitches for spoken German (199 Hz for females, 109.5 Hz for

males) are slightly below Fant’s averages for both genders. The closest approximation to

Campione and Véronis’ measured averages in equal tempered pitch is C4, or middle C,

for French females, and for German females is G3, or the G below middle C. For males,

the closest equal-tempered pitches to their measured averages are D3 for French and A2

for German.

Thus for both French and German, the difference between the average pitch of male and

female speakers is approximately ten semitones. In addition, the average pitch is also

consistent within gender; for both males and females, the average spoken pitch for

spoken French is roughly seven semitones above the average pitch for spoken German.

These results are significant because linguistic pitch is generally considered a relative

phenomenon – that is, it is impossible to tell if a given pitch is high or low without the

pitch being put in some kind of context. A pitch of 240 Hz, for example, is in the middle

of the typical female’s speaking range, but is near the high end of the typical male’s

range; an utterance at that pitch will carry a different paralinguistic meaning based on the

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context in which it appears. The fact that French speakers tend to speak at a higher

average pitch than German speakers consistently enough to cause the average pitch of

spoken French to be measurably higher is significant.

Campione and Véronis also noted that compared to the other languages in the study, both

French and German speakers had relatively small ranges (the distance between the

highest measured pitch target point and the lowest) and relatively small standard

deviations from the range, as illustrated in Example 4.3.

Example 4.3: Campione and Véronis’ Figure 3: Standard deviation vs. range per language and sex

For each of five speakers for both male and female, the range size is plotted on the y-axis

measured in semitones, and the standard deviation is plotted on the x-axis. The graphs

show that French and German speakers had ranges comparable to or smaller than the

other languages in the study, and that the speakers of both languages tended to be

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consistent within-language; in contrast, Spanish shows much more range variability

across speaker.

Campione and Véronis’ chart does illustrate a possible gender-based distinction. As the

graphs show, the overall range for French speakers is similar across gender; the range

varies between approximately 16–24 semitones for both male and female speakers.

However, the range for German speakers is markedly different across gender: the range

of individual male speakers of German varies from approximately 14–20 semitones,

whereas the range for individual female speakers of German varies from approximately

20–27 semitones. Thus it appears female German speakers use a larger overall range in

speech than male German speakers, while gender does not appear to be a factor in

French.

The standard deviation, measured on the x-axis in Example 4.3, indicates the linguistic

range, or the “range within which the phonologically relevant pitch of the speaker’s voice

habitually varies in paralinguistically unmarked, attitudinally neutral conversation.”6

Typically, 95% of the pitch values used by a speaker will occur within two standard

deviations of the average pitch; that is, the pitch target points in the middle of a speaker’s

range occur with more frequency than those at the extreme of the range. This distribution

of pitch target points approximates a normal distribution within–speaker, as illustrated by

Campione and Véronis’ Figure 4, reproduced in Example 4.4.

6 Laver, p. 457-8.

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Example 4.4: Campione and Véronis’ Figure 4: Distribution of pitch target points for French male speaker bf

This graph illustrates the distribution of pitch target points for a male French speaker.

The pitch target points are plotted along the x-axis in the linguistic semitone

representation,7 and the number of occurrences of each point is plotted on the y-axis.

Campione and Véronis’ example superimposes a normal distribution curve over the data

to illustrate that while the distribution of pitch target points does not match the normal

distribution curve exactly, the higher rate of occurrence of the pitch target points in the

approximate middle of the individual speaker’s range approximates a distribution

expected by the normal distribution curve.8

4.1.2 Hypotheses and expectations regarding average pitch and range

Based on these observations from Campione and Véronis (1998), as well as other

information about the behavior of the spoken French and German language, we can

create and study some hypotheses to determine to what degree the average pitch and

range of spoken language has an effect on musical melody in the current study.

7 The range of 75–97 semitones converts to approximately 76–271 Hz. 8 Campione and Véronis point out that most of their speakers do not fit the strict statistical definition of normal distribution, but rather approximate it.

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From the data in Campione and Véronis, we can hypothesize that if the higher average

pitch of spoken French has an effect on song, the overall average pitch of French song

should be higher than the average pitch of German song. Based on the similarity of the

ranges of the spoken languages, we can hypothesize that there should not be major

differences in the average range of individual songs either within or across languages,

and that few songs will have extremely large or small ranges. We can also expect the

songs in each language to contain a distribution of pitches approximating a normal

distribution curve.

4.1.3 Average and range of pitch in French and German song

4.1.3.1 Average and distribution of pitch in song

Example 4.5 illustrates the average pitch and the range of the French and German songs

in the current study based on the editions encoded. The pitch is shown in Hz on the y–

axis.

Contrary to the results for the average pitch and ranges for spoken languages, there is

virtually no difference in the average pitch and range for songs across languages. In the

equal tempered tuning system, both 475.16 Hz and 481.10 Hz lie in between the B-flat

and B-natural (466.16 Hz and 493.88 Hz, respectively) above middle C; therefore, a

cross-language comparison is not likely to provide interesting results. Both of these

average pitch values are also at the top end of the normal speaking range for women,

illustrating that the results likely are not the result of any effect of the spoken language.

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Example 4.5: Average pitch of French and German songs

Studying the average pitch of a large number of songs is clearly problematic, as songs

were (and are) frequently transposed to fit various singers and voice types.9 In addition,

publishers often print songs with the vocal part notated in treble clef regardless of the

actual range of the intended performer, which leads to an apparent emphasis on the

pitches easily represented within the treble clef. As a result, studying the average pitch of

a large number of songs will likely reflect more on the notational practice than on any

effect of the spoken language.

Example 4.6 confirms this notational confound by showing the distribution of pitches for

both the French and German songs represented in the study. The x-axis indicates the

pitch name and octave designation; the y-axis indicates the percentage of occurrences of

each pitch.

9 Many songs in the existing database were encoded from a source that transposed the songs from their original pitch level.

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Example 4.6: Pitch distribution as percentage of total in French and German song

Pitch distribution as percentage of total, French and German songs

0.00

0.01

0.00

0.00

0.00

0.01

0.02

0.13

0.09

0.06

0.12

0.09

0.20

0.32

0.18

0.21

0.25

0.46

1.00

0.80

2.13

2.03

3.35

4.62

3.85

8.60

6.33

10.04

8.67

8.90

10.54

5.95

7.96

4.44

3.67

2.53

1.06

0.90

0.28

0.14

0.04

0.02

0.00

0.00

0.00

0.00

0.00

0.00

0.03

0.01

0.08

0.01

0.11

0.10

0.06

0.11

0.10

0.23

0.26

0.38

0.87

0.92

2.11

2.03

3.37

4.25

5.54

7.52

6.15

9.17

7.80

9.96

8.38

7.53

8.48

4.41

4.53

2.53

1.62

0.85

0.31

0.14

0.03

0.02

0

2

4

6

8

10

12

F2

F#2

G2

A2

A#2

B2

C3

C#3

D3

D#3

E3

F3

F#3

G3

G#3

A3

A#3

B3

C4

C#4

D4

D#4

E4

F4

F#4

G4

G#4

A4

A#4

B4

C5

C#5

D5

D#5

E5

F5

F#5

G5

G#5

A5

A#5

B5

Pitch

% o

f to

tal

French German

The vast majority of notated pitches in songs in both languages fall in the range typically

represented by notation in treble clef, or C4–G5 (97.3% and 98.0%, French and German

respectively). This is obviously not an accurate representation of the average sung pitch,

and instead is a reflection on notational practice for the genre.

4.1.3.2 Range of pitch in individual songs

Based on the observed ranges of the spoken languages in Campione and Véronis

illustrated in Example 4.1, as well as the very similar overall ranges of French and

German song exhibited in Example 4.3, it is reasonable to expect that individual French

and German songs will exhibit similar ranges and that extremely small or large ranges for

individual songs will be rare. Example 4.7 illustrates the overall range by song for both

French and German songs; the distance between the highest and lowest pitch in the song

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is measured in semitones and plotted on the x-axis, and the percentage of songs with each

range is plotted on the y-axis.

Example 4.7: Overall range distribution, French and German songs

Song range distribution as a percentage of total, French and German songs

0.34

0.68

1.02

0.68

11.53

6.78

15.25

10.17

8.81

17.63

5.08

8.81

6.78

3.05

1.02

0.68

1.02

0.00

0.34

0.341.24

0.31 1.24

2.48

4.33

6.19

11.15

11.46

9.29

19.50

6.81

9.60

6.81

5.88

2.17

0.62

0.62

0.00

0.00

0.31

0

2

4

6

8

10

12

14

16

18

20

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

song range in semitones

% o

f to

tal

French German

The average overall range for French songs is 15.98 semitones, compared to a slightly

larger range of 16.42 semitones for German songs; the standard deviation for both is

σ=3.07. The chart illustrates a very rough normal distribution of song ranges for both

languages. As is typical of a normal distribution, the majority of song ranges – 94.9% of

the French song and 93.1% of the German – fall at or near the middle of the distribution,

here represented by the ranges between 12–22 semitones inclusive, and a small number

of extremely large and small ranges populate the outsides of the distribution.

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The charts for both French and German song demonstrate a dramatic peak at the range of

17 semitones. This range is in the middle of the distribution of song ranges and would be

expected to be the most frequently occurring value according to the laws of normal

distribution. However, there is likely another reason for the frequent occurrence of the

range of seventeen semitones; it is the equivalent of the interval of a P11, which allows a

composer an octave range plus a fourth below to reach the dominant. The frequency of

occurrence of this range, therefore, is likely a result of the influence of the tonal system.

The dramatic peak in both French and German song on this particular range probably

arises from a combination of these two factors.

The chart in Example 4.7 also shows a higher rate of occurrence for the ranges of twelve

and fourteen semitones in French song. The higher rate of occurrence of these ranges in

French song is again due at least in part to the influence of the tonal system, as the ranges

are equivalent to the intervals of an octave and a major ninth. However, if the tonal

system was the primary influence on the range distribution, German songs would also be

expected to show a higher rate of occurrence of those ranges; German does not show

peaks on these or any other individual ranges other than the peak on 17 semitones.

Overall, the range distribution for French songs is positively skewed (skew = .40,

kurtosis = .27), which indicates that the data trend towards the smaller ranges in the

center cluster of 12–22 semitones; this is clearly illustrated in Example 4.8, where the

ranges are divided into categories. The smallest and largest ranges have been grouped

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together, and the remaining ranges have been grouped symmetrically around the peak

range of 17 semitones, which marks the midpoint of the distribution.

Example 4.8: Categories of song range distribution as a percentage of total

As is clear from Example 4.8, the overall frequency of occurrence decreases as the range

increases for both French and German songs, indicating some trend in both languages

towards smaller ranges. However, German songs show a smoothly decreasing frequency

of occurrence as the range increases; French songs exhibit a strong trend towards ranges

in the smaller half of the distribution of 12–22 semitones, and specifically in the category

of ranges from 12–14 semitones inclusive. In fact, in every other category with sufficient

data, German exhibits a higher percentage of songs with ranges in each category than

French. 10

10 The small amount of data for the extreme ranges makes the results for those categories unreliable; the range of 8–11 consists of 9 French and 17 German songs, and the range of 23–27 consists of only 6 French and 5 German songs.

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In contrast to the positive skew for the distribution of ranges for French songs, the

distribution of ranges for German songs are very slightly negatively skewed (skew = -.05,

kurtosis = .16), indicating that the distribution for German more closely approximates a

normal distribution than the distribution for French, but that German does have a slight

trend towards larger ranges while French trends towards the smaller ranges. Thus,

contrary to the expectation that French and German songs would have similar overall

ranges, it appears French songs have a strong tendency towards smaller overall ranges

than German songs.

As with rhythm, averages within languages can mask data trends for individual

composers. Example 4.9 illustrates the range of pitch ranges and average range for songs

for individual French and German composers.

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Example 4.9: Range of ranges and average range for individual French and German composers

The bars indicate the range of ranges for that composer; for example, the smallest overall

range for a Strauss song is 14 semitones and the largest is 24 semitones. The marker

indicates the overall average range for songs by that composer; the overall average range

for all Strauss songs is 18.64 semitones. Visually, it is notable that several French

composers use a smaller range of ranges than the German composers: David, Massenet,

Reyer, and Saint-Saëns in particular use a very narrow range of ranges in their songs.

However, there is no clear trend for the average range by composer visible from this

graph for either French or German songs.

Example 4.10 further explores the observation regarding the size of the range of ranges

for the individual composers. This graph plots the range of ranges for each composer on

the x-axis against the composer’s overall average range on the y-axis. For example, the

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range of ranges for Strauss is equal to the largest range for an individual song minus the

smallest range for an individual song, or 24–14=10 semitones. Thus Strauss is

represented in Example 4.10 at the intersection of 10 semitones on the x-axis and 18.64 –

his overall average range size – on the y-axis. Composers who use a smaller overall range

of ranges are thus represented on the left-hand side of the graph, and those who use a

larger range of ranges are plotted on the right-hand side. In addition, the composers with

smaller average ranges are plotted lower on the graph, while those with higher average

ranges are plotted higher on the graph.

Example 4.10: Range of ranges and average ranges for individual composers,

scatter plot

As in Example 4.9, there is no trend regarding the average range of songs for either

French or German composers (t(17) = -.36, p = .36); the average range is spread across

the spectrum from 14-19 semitones for both languages. However, there is a trend

involving the range of ranges used across songs; French composers tend to fall on the left

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side of the graph, indicating a smaller range of ranges, while the German composers tend

to fall on the right side of the graph, indicating a larger range of ranges. This difference is

significant (t(17) = -2.34, p = .01).

Strauss, Lalo, and Bizet are visible exceptions to this trend. However, the measure of

“range of ranges” is very sensitive to extreme events in the data; one extremely large or

small range can create what appears to be a much larger overall range than is actually

typical for that composer. This is the case for both Lalo and Bizet; the large range of

ranges for both of these French composers are due to one unusually large value in their

dataset. The database contains one Lalo song with a large range of 24 semitones,

resulting in a range of ranges spanning from 8 to 24 semitones, or 16 semitones. The data

point of 24 semitones is an outlier; removing that data point, Lalo’s range of ranges drops

to 9 semitones (from 8 to the next largest range at 17 semitones). Similarly, Bizet has one

song with a range of 27 semitones, which is also a statistical outlier, reducing Bizet’s

range of ranges to 9 semitones. The same criteria identify one large range by Duparc (26

semitones) and Wolf (27 semitones) as outliers, so these datapoints have been eliminated

as well and the composers’ range of ranges reduced accordingly. A graph of the revised

data is shown in Example 4.11; removing the outlying datapoints from the data for Lalo,

Bizet, Wolf and Duparc provides a more accurate reflection of their typical ranges than

the graph in Example 4.10, in which the data for each composer was influenced by one

extremely large song range in their dataset.

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Example 4.11: Range of ranges and average range, with outliers removed

With the outliers removed, the difference between the average range is still not

significant (t(17) = -.5, p = .31), but the difference between the range of ranges for

French composers and the range of ranges of German composers is even more

significantly different (t(17) = -3.59, p = .001); the average range of ranges for French

composers is 9.3 semitones and 13.3 semitones for German composers. The trend

towards a smaller range of ranges for French composers indicates less variability in range

across songs; in other words, French composers tend to be more consistent about the

range they use in individual songs, whereas German composers tend to have more

variability in range measured across songs.

The exception for this trend for German composers is Strauss. The location of the data

point for Strauss – a relatively small range of ranges (14-24 semitones, for a range of

ranges of 10 semitones) but a high average range (18.6 semitones) – indicates he tends to

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consistently write songs with large ranges. Since all of his songs have relatively high

ranges, the range of ranges is necessarily smaller than it would be if he wrote songs with

a wider variety of ranges.

As the Strauss data illustrates, the average range size is related but not directly correlated

to the range of ranges; for example, Reyer’s average range is one of the smallest at 14.4

semitones and Saint-Saëns’ average range is one of the higher averages at 18 semitones,

but they both have a small range of ranges (five and six semitones, respectively). Reber’s

smaller average range is because his songs remain within the relatively small ranges of

12–17 semitones, and trend towards the smaller ranges within that range of ranges, while

Saint-Saëns tended to write songs with larger ranges, varying between 14–20 semitones

and trending towards the larger ranges within that range of ranges.

Example 4.12 represents each composers’ skew within their range of ranges. The y-axis

represents their range of ranges, and the x-axis indicates the degree of skew within that

range of ranges. A result falling on the positive side of the x-axis indicates that overall,

the range of ranges is positively skewed, indicating the composer trended towards the

smaller ranges in his range of ranges. If the data falls on the negative side of the x-axis,

the range of ranges is negatively skewed, indicating the composer trended towards larger

ranges. If the skew is at or near 0, it indicates the composers’ average range is an accurate

reflection of their distribution of ranges.

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Example 4.12: Skew and range of ranges by composer

For example, as described above, Saint-Saëns is negatively skewed (skew = -1.1),

indicating that within his range of ranges of 6 semitones, he tended to use the larger

ranges more frequently than the smaller. There is no trend across languages for the

amount of skew (t(17) = -.33, p = .36).

4.1.3.3 Range of pitch in phrases

The values in Example 4.11 and 4.12 represent the ranges, averages, and range of ranges

for entire songs. However, as with the rhythmic characteristics discussed in Chapter 3,

pitch and pitch range is a linguistic characteristic that “resets” at the level of the

intonational phrase. Within an utterance, a speaker organizes relative values of pitch such

as pitch height, pitch range, and pitch slope11 for prosodic purposes, and these values tend

to be reset across phrase or group boundaries. Therefore, as with the nPVI calculations in

11 Fox 2000, p. 309.

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Chapter 3, it is more appropriate to look at individual phrases within songs than at songs

as a whole. In addition, studying the phrase level of songs lines up more evenly with the

study done by Campione and Véronis (1998), as that study focused on the pitch range for

sentence-length utterances. Example 4.13 shows the distribution of ranges at the phrase

level for both French and German songs; the range of the individual phrase is measured

in semitones along the x-axis and the percentage of occurrences of each range for each

language is measured along the y-axis.

Example 4.13: Phrase range size as a percentage of the total number of phrases, French and German

Phrase range size as a percentage of the total number of phrases, French and German

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

range size in semitones

% o

f to

tal

phra

ses

French German

The distribution of phrase ranges for each language is similar to a normal distribution,

with the majority of the distribution occurring in the middle of the range of phrase ranges,

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and a small percentage of occurrences for the extremely small and extremely large phrase

ranges. (The standard deviation for French is σ=3.71, and for German is σ=3.49.)

Both languages have peaks at five, seven, and twelve semitones; these ranges represent

the interval of a fourth, fifth, and octave respectively. Similarly, both languages have a

small percentage of phrases with ranges of six and eleven semitones, which form the

dissonant intervals of a tritone and a major seventh, respectively. These distribution

trends are likely a result of the influence of the tonal system.

As discussed above, French exhibited a trend towards smaller ranges than German at the

song level; the overall range of French songs, the range of ranges, and the individual

average range were smaller for French composers than for German.12 Example 4.13

illustrates that the trend towards smaller ranges in French is consistent at the phrase level.

For every phrase range from 0–7 semitones, French has a higher percentage of phrases

with that phrase range; from a phrase range of 8 semitones and larger, the German songs

exhibit a higher percentage of phrases with those ranges. This illustrates that phrases in

French songs have a tendency to use a smaller range than phrases in German songs.

Example 4.14 illustrates this categorically, similar to the categorical graph for song

ranges shown in Example 4.8. French has a higher percentage of ranges in the smaller

categories, and an approximately equivalent percentage of phrases with the range of 7

semitones (a perfect fifth). German has a higher percentage of phrases with ranges above

12 The sole exception is the individual song range average for Debussy, which, as shown in Example 4.11, was the highest average song range (18.7 semitones) of any composer represented in the current study.

105

that of a perfect fifth until the extreme values of a phrase range of more than 17

semitones, at which point the languages have an approximately equal distribution again.

Example 4.14: Categorical distribution of phrase range sizes

The average range for French songs was 15.98 semitones, whereas the average phrase

range for French is 7.46 semitones; the average range for German songs was 16.42

semitones and the average phrase range for German songs is 8.38 semitones. The

difference between the average phrase ranges is statistically significant across languages

(t(17) = 2.46, p = .01). Therefore, in both song ranges and individual phrase ranges,

French composers have a tendency to use smaller ranges than German composers.

The phrase range distributions for both French and German are positively skewed, with

French more skewed than German (French skew = .299, German skew = .226). This

indicates that overall, both languages trend toward the smaller phrase ranges. This result

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is different than at the song level, where French was positively skewed and German was

slightly negatively skewed; in the case of phrase ranges, both French and German are

positively skewed because of the extremely large ranges (≥17 semitones). If phrase

ranges of 17+ semitones are omitted, the distribution for each language very closely

approximates a flattened normal distribution (French skew = .06, kurtosis = -.43; German

skew = .02, kurtosis = -.49).

Example 4.15 illustrates the range of phrase ranges and average phrase range for

individual French and German composers.

Example 4.15: Range of phrase ranges and average phrase range for individual French and German composers

The bars indicate the range of ranges and the marker indicates the overall average phrase

range graph for each composer. This graph illustrates that, as expected, both French and

German composers used a much larger range of ranges on the phrase level than on the

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song level. Phrases ranges can be as small as 0 semitones, and can be as large as the

largest song range used by a given composer; in fact, Bizet’s largest song range of 25

semitones happens within one phrase, and so is his largest phrase range as well.

Example 4.16 plots the range of phrase ranges on the x-axis and the average phrase range

on the y-axis for each composer, similar to Example 4.10 above for song ranges.

Example 4.16: Range of phrase ranges and average phrase ranges for individual composers, scatter plot

Unlike the results for the average range for songs, where there was no clear trend across

languages, this graph demonstrates that the French composers tend to have a smaller

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average phrase range than the German composers.13 Also in contrast to the results for the

range of ranges across languages, which was significant for songs, the difference between

the range of phrase ranges is not significant (t(17) = -.53, p = .30).

As with the discussion of song ranges above, the range of phrase range measurement is

very sensitive to outliers. Example 4.17 represents the data after removing outliers.14

Example 4.17: Range of phrase ranges and average phrase ranges, with outliers removed

The removal of outliers reduces the range of phrase ranges for many of the composers,

some quite significantly. For example, in Example 4.16, Lalo’s phrase range is 22

semitones; after the ranges of 22 and 17 semitones are flagged as outliers, the next largest

phrase range is 14 semitones, so Lalo’s range of phrase ranges is shown in Example 4.17 13 Schumann is a notable exception to this trend; he also had the lowest average song range of the German composers at 14.8 semitones. 14 Outliers were determined via a nonparametric test from David Sheskin, Parametric and Nonparametric Statistical Procedures 3rd edition, (Boca Raton, FL: Chapman and Hall, 2004), pp. 400-401.

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as 14 semitones. In contrast, Saint-Saëns range of phrase ranges remains exactly the

same; no ranges were identified as outliers. The difference between the average phrase

ranges of French and German composers is still statistically significant (t(17) = -2.44, p =

.01) and the difference between the range of ranges between French and German

composers is still not statistically significant (t(17) = -.6, p = .27).

Example 4.18 represents the degree of skew present in the range of phrase ranges used by

an individual composer. Just as in Example 4.12, skew is represented on the x-axis, while

the range of ranges is represented on the y-axis. A positive skew value indicates that the

data trends towards the smaller values in the range of phrase ranges, while a negative

skew value indicates that the data trends towards the larger values.

Example 4.18: Skew and range of phrase ranges, individual composers, outliers removed

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A few interesting stylistic elements can be determined from the song range graphs in

Examples 4.11 and 4.12 and the phrase range graphs above. For example, Example 4.11

shows that Saint-Saëns has a relatively high average song range of 18 semitones, and a

relatively small range of song ranges of 6 semitones. The negative skew of -1.11 in

Example 4.12 shows that within that range of ranges, Saint-Saëns tended to use the larger

ranges more often than the smaller. However, Example 4.17 and 4.18 illustrate that Saint-

Saëns has an average phrase range size of 7.6 semitones and a range of phrase ranges of

17 semitones, with a positive skew of .33, indicating that within his range of phrase

ranges, he tends to use smaller phrase ranges. In other words, Saint-Saëns’ large song

ranges are a result of him combining individual phrases with relatively small ranges to

create a large overall song range.

In contrast, Examples 4.11 and 4.12 show that Strauss has a high overall song range

average of 18.6 semitones, a range of ranges of 10 semitones, and a positive skew of .34,

indicating that within his small range of ranges (made up of songs with large ranges), he

tends to use the smaller of the large ranges more frequently. Examples 4.17 and 4.18

describe his phrases with a phrase range average of 8.9 semitones, a range of phrase

ranges of 16 semitones, and a negative skew of -.17 illustrating that within his range of

phrase ranges, Strauss has a slight tendency to use larger phrase ranges. Therefore

Strauss’s large overall song ranges are made up from individual phrases that themselves

span relatively large ranges.

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4.1.4 Results and discussion

The hypothesis that the overall higher average pitch of French speech would influence

the overall pitch of French song is impossible to study with the current data. The results

indicate that the average pitch of the encoded repertory is very similar across languages,

seemingly contradicting the hypothesis. However, transposition and representation issues

make it impossible to accurately determine the average pitch of a large number of songs,

so the results from this study cannot be compared to the results from Campione and

Véronis. A more carefully controlled study taking transposition and vocal register into

account would need to be done to determine if the difference in the average pitch of the

spoken languages has any effect on composition across languages.

The results of the study of the range of entire songs illustrated a trend for German to have

larger ranges overall: the average overall range for songs was higher for German songs

than for French although the result was not statistically significant, and individual

German composers tended to use a wider range of ranges than did individual French

composers, which did prove to be statistically significant.

The results of the study of the range of individual phrases supported this finding; the

difference between the average range for French phrases and the average range of

German phrases was statistically significant, with French phrases having a smaller

average size. However, unlike at the song level, there was not a significant difference

between the range of ranges used by French composers and German composers at the

phrase level. The languages exhibited some similarities in the distribution of range size

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that were clearly a result of musical considerations and not linguistic ones, including a

lack of phrases with a range that constitutes a dissonance according to the tonal system.

An unanticipated result of these tests was the ability to discern portraits of individual

composer’s melodic practice. For example, Saint-Saëns and Strauss can be distinguished

from one another by significant trends in internal phrase compass vs. external song

ranges. A further investigation into this could inform us about an individual composer’s

compositional style.