Sound Design of Machines from a Musical Perspective

In this paper, relations between musical acoustics and sound quality engineering are displayed. First, the concept of musical consonance proposed by Terhardt, based on the seminal classic work of Helmholtz is discussed. In particular, the view of Helmholtz on modern psychoacoustic magnitudes important in sound quality design like fluctuation strength and roughness is illustrated. The application of Terhardt's concept of sensory pleasantness in sound quality engineering is discussed, and advantages and disadvantages are shown. The concept of virtual pitch, i.e. a pitch sensation which has no direct correspondence in the spectrum, is traced back to the concept of "basse fondamentale" put forward by Rameau in the 18 century. Characteristics of musical keys as advocated by Kirnberger and Schubart are displayed in view of the sound quality of the interior sound of passenger cars. Musical dynamics from ppp to fff are contrasted to current category scales for loudness scaling and the relations of loudness and tone color. Finally, examples of audio-visual interactions in speech and music as well as sound quality rating are given. CONCEPT OF MUSICAL CONSONANCE The concept of musical consonance as advocated by Terhardt (1984) is illustrated in figure 1. Musical consonance depends on two features, namely harmony and sensory consonance. Figure 1: Concept of musical consonance according to Terhardt (1984). sound quality and music Fastl The concept of harmony was developed for musical sounds, whereas the concept of sensory consonance can be applied not only to musical sounds, but to all categories of sounds, e.g. sounds usual in sound quality engineering. Nevertheless, the concept of harmony also can have an impact with respect to sound quality. A basic result of the work of Helmholtz (1863) was his discovery that the hearing sensation roughness strongly influences sensory consonance. In modern terminology (e.g. Zwicker and Fastl 1999), the concept of Helmholtz would read that fluctuation strength and roughness are mainly based on interactions of spectral components of sounds. Figure 2 gives an illustration of the concept of Helmholtz in musical notation. Figure 2: Interaction of spectral components in musical notation according to Helmholtz (1863). In figure 2, the unfilled notes represent the sounds played e.g. on a piano. The filled notes indicate harmonics. In example 1, the musical interval of an octave is displayed. The sounds played are c2 and c3 as indicated by unfilled notes. In addition to c2 the harmonic c3 (filled note) is audible, which gives a perfect match to the presented note c3. This means that in the musical concept, the octave c2-c3 represents a perfect consonance without beats, because the second harmonic of c2 (c3) is identical to the higher note c3. In contrast, example 2, which consists of the notes c2 and b2 represents a dissonance, because the presented note b2 is a semitone apart from the second harmonic c3 of the note c2. A similar argument holds for example 3. Examples 4 and 5 of Helmholtz again show consonant intervals which is easily seen in example 5: the notes played are d4 and a4 which form the musical interval of a fifth. The second harmonic of d4 is d5 and the third harmonic a5, whereas the second harmonic of a4 is a5. Since the second harmonic of a4 and the third harmonic of d4 coincide, the interval of a fifth is considered to be a consonance. This reasoning is described in more detail in figure 3 from Helmholtz, where he illustrates the roughness of different musical intervals. Figure 3: Roughness of different musical intervals according to Helmholtz (1863). The intervals considered always start with c4, and the magnitude of the peaks indicates the magnitude of the roughness of the respective interval. As is easily seen in figure 3, the octave namely the interval c4-c5 represents a perfect consonance and no roughness is visible. Also for the fifth c4-g4, Helmholtz displays no roughness values. On the contrary, the roughness of Musical perspectives. Fastl musical intervals reaches according to Helmholtz a maximum for one musical semitone (c4-cis4) or for eleven semitones (c4-b4). The results displayed in figure 3 clearly show that the concept of musical consonance is based on the absence of the psychoacoustic magnitude roughness, which we use these days in sound quality engineering. In line with classic music theory dating back to 500 BC of Pythagoras, the musical intervals of octave, fifth and fourth with frequency ratios of 1:2, 2:3, and 3:4 are considered as perfect consonances because they show no fluctuation strength or roughness. Based on the classic findings by Helmholtz (1863), Terhardt and Stoll (1981) proposed the concept of sensory pleasantness which is illustrated in figure 4. Figure 4: Concept of sensory pleasantness according to Terhardt and Stoll (1981). As expected from the classic works of music theory, sensory pleasantness decreases with increasing roughness (figure 4a). Also in line with data from Helmholtz (1863), figure 4b shows that sensory pleasantness decreases with increasing sharpness. Panels 4d and 4c indicate that sensory pleasantness decreases with increasing loudness, but increases with increasing tonality. sound quality and music Fastl While the results displayed in panels 4a, 4b, and 4d are well known in sound engineering and sound quality design, the results displayed in panel 4c have to be considered in more detail. It is clear that in a musical context, as displayed in figure 1, sensory consonance and hence sensory pleasantness increases with the tonal character of a sound. However, in sound engineering, exactly the opposite behavior may occur! In many standards, tonal components of sounds are "punished" by tone penalties. For example, in the German standard for noise immissions from industrial noise (TA Lärm), for sounds with clearly audible tonal components, a tone correction of up to 6 dB is added to the measured A-weighted level, and calculations for the tone corrections are proposed in the German standard DIN 45681. This means that in a musical context, tonal components usually have a positive impact, whereas in sound engineering generally tonal components should be avoided. An interesting example in this context comes from Japan: A manufacturer of needle printers controlled the sequence of the needles in such a way that the printer played well known tunes. In the beginning, when this feature was introduced, it was very welcome by the users because of its novelty. However, after few days it can be pretty annoying, if a printer plays the same tunes over and over again. ROOTS OF MUSICAL CHORDS AND VIRTUAL PITCH It is well known in music theory, that musical chords represent a specific tonality, frequently called the "root" of the chord. This means that the "root" represents a suitable bass note and further can be responsible for the tonality of a piece of music, e.g. that a tune is written in Cmajor. As displayed in figure 1, this relationship belongs to the concept of harmony. It dates back to the 18 century and is described in great detail by the famous French music theorist Rameau (1750). In musical terms, the notes displayed in figure 5 illustrate that the chord g c e has the "meaning" of C-major. In music theory, this is explained that the notes g4, c5, and e5 are considered to be the third, fourth, and fifth harmonic of a common root. As displayed in figure 5, the first harmonic which fits the chord displayed by filled notes is the unfilled note c3, and the second harmonic is the unfilled note c4. The frequencies of these notes form the ratio 1:2:3:4:5 and hence correspond to the musical intervals octave, fifth, fourth, and major third. Figure 5: Illustration of the concept of “basse fondamentale” of Rameau (1750) As we have seen, up to the fourth, since ancient times these intervals are considered to be consonant. However, the major third got more and more acceptance as a consonant interval in the 17 century, but was a little suspect to older music theorists like Pythagoras. Rameau's (1750) concept of "basse fondamentale" has its modern counterpart in the virtual pitch theory of Terhardt (1974) which is illustrated in figure 6. In the example displayed in figure 6, a harmonic complex tone with a basic frequency of 200 Hz is considered, from which the first two harmonics (200 Hz and 400 Hz) are removed. In essence, the concept of virtual pitch predicts that from the spectral pitches of each harmonic, Musical perspectives. Fastl subharmonics are calculated by integer ratios (1:1, 1:2, 1:3, 1:4, and so forth). The amount of coincident calculated subharmonics gives an indication of the virtual pitch perceived. As becomes clear from the example given in figure 6, virtual pitch has some ambiguity: Terhardt's model calculates the virtual pitch of the incomplete complex harmonic tone near 200 Hz. But also pitches one octave lower or one octave higher are candidates. This ambiguity is in line with the musical concept shown in figure 5, because the "root" of the chord displayed is represented by c3, but c4 is also possible. Figure 6: Illustration of the concept of virtual pitch of Terhardt (1974). For sound quality engineering the concept of virtual pitch which is based on the musical concept of harmony plays an important role: the sound of a product can produce a pitch sensation in a frequency region where no spectral components are present! When assessing sound quality by physical means like spectral analysis, it always has to be kept in mind that audible tonal components can be virtual pitches, which show up in the spectrum only by higher harmonics. CHARACTER OF MUSICAL KEYS It is a long standing debate, whether musical keys can represent a specific character. In particular Kirnberger (1782) and Schubart (1806) related different keys to different emotions or moods. Experiments by Kunkel (1877) as well as our own experience showed that with equal temperament it is more or less impossible to correlate different emotions with different musical keys. However, in well tempered intonations, i.e. a tuning put forward in particular by Werckmeister (1702) and used by the famous composer Johann Sebastian Bach, characteristics of musical keys may be perceived by experts. Since a famous German manufacturer of passenger cars insists that a luxury car has to be tuned in minor and not in major, figure 7 gives (more as curiosity) the characteristics of minor keys in the original language German. To cut a long story short, from all the keys given in figure 7, only the first two namely a-minor and e-minor may be useful for sound design because all the other keys represent feelings of sadness and despair. However, according to the results displayed in figure 7, a-minor should have a religious, feminine character, and e-minor should be related to the love of a naive girl. sound quality and music Fastl Although this author has studied music, it is not easy to detect the character of these keys in minor, and in particular it seems to be the secret of the German car manufacturer, how to tune the interior sound of a car in a minor key, and whether this is then a-minor or e-minor.