What Hides Behind the Listener: Harmonic Contribution to Timbre

Pedro Javier Gómez Jaime, Global Education Magazine,Pedro Javier Gómez Jaime

Doutorado Multidisciplinar e Multi-institucional em Difusão do Conhecimento (DMMDC), Universidade Federal da Bahia (UFBA),

[email protected]


Victor Mancir da Silva Santana, Global Education MagazineVictor Mancir da Silva Santana

Doutorado em Física, Universidade Federal da Bahia (UFBA),

[email protected]


Abstract: the timbre is the more complex attribute of the sound and it is characterized by the harmonics components of a sound. In the present paper we investigate the harmonic contribution of a fragment of the song “In the times of India” by Jethro Tull band. This fragment was taken in consideration because it represents the peak point of the music, and because the execution´s flute by his leader Ian Anderson is meaningful. To study the harmonic contributions was applied Fast Fourier Transform. The curves marked contribution highlight fundamentally bands 5, 6 and 8 frequencies. In this sense, we can verify the harmonic contribution curves which featured the flute with regard to the range of harmonic frequencies for musical instruments.

Keywords: frequency, harmonics, timbre, harmonic contribution.


1. Introduction.

This article aims to analyze the harmonic behavior of a fragment of “In the Times of India,” a song by Jethro Tull, which highlights the performance on flute made ​​by its leader Ian Anderson and an approach to timbre as sound attribute. The choice of this song is given initially by the instrumental resources used by the band which are closely related to their involvement with genres such as rock, jazz, folk and classical music. So that the musical performance developed by the members of this grouping is intended to influence the musical sensibilities of several generations of listeners.

Another criteria is that the choice in this song the band wanders through rhythmic and timbral variations that underlie some of the genres mentioned above, showing the influence of typical sounds of Indian music, allowing the exploration of instrument tones own culture and the others influence not indians like alpa​​, bells, tambourines, keyboards and violins more common in Western music.

The target fragment of this study has duration of 5 seconds, a range that is subjectively considered as the point of emphasis. This point is repeated several times, always with a different dynamic excelling at each instrumentation and intention of the author to the extent that resources are exploited sound of instruments like bells, which operate in the background throughout the fragment. This theme is an instrumental and therefore allows to perform a harmonic analysis that does not consider the human voice, which would also be involved in the intentionality of the interpreter. So that although our analysis is limited to the harmonic study of this music the methodology that we use is the same as would be used for a review or timbre timbre because the harmonics are responsible for this sound quality (timbre). Speaking of this attribute with respect to scientific and acoustic involves taking into account the harmonic behavior that forms part of the sound event, but a single instrument or voice, with regard to music. That is why, in certain moments we alluded to timbre, as it is connected to the harmonic structure that has a specific sound. In this article we will study the harmonic contribution, ie, the harmonics that have greater prominence within the musical fragment object of study, without losing sight that will analyze the sound produced by a band or set of instruments. This is the reason why we can not talk about the timbre that “In the times of India”.

The argue that it is the timbre of the sound attributes, Loureiro Bastos (2006), which presents more complex because it is not linked solely to a physical dimension, therefore, it can not be specified quantitatively in musical notation system. In this sense, these authors advocate the idea of being perceived timbre due to the interaction of dynamic and static properties that influence psychological and musicals from a complex set of loved hearing.

And the experience of hearing timbre always had and still has in the works of Bartók, the function of making the “soul” vibrate inside her (…) The timbre as such features not only a reaction of the listener, but is also in itself an important stylistic element and formal Western music.

A body of sound by Calvo-Manzano (1991), namely a body that emits sound can produce various sounds in dependence on the conditions under which it vibrates. For example, a guitar string produces a sound by the bridge and other various if it were pulsed sound at the mouth of the box or above the neck of the instrument. The most serious of these sounds is called the primary and the others are called partial harmonics which can be and if they are similar to the harmonic series derived from the same fundamental frequency, are also called rates or concordant.

The number of harmonics that make up the pitch of each sound directly from applicant’s body produces and how the instrument is run. The same note can be produced in different instruments and yet can always distinguish one from another. For example, the same music produced by different instruments, say, harpsichord, violin and piano feature a distinctive feature is that the timbre. And this distinction is given by the harmonics that can be heard each instrument or any other that we have not mentioned here, because the sounds we hear are different while the intensity and energy distribution. The sounds in this case have the same harmonics at frequencies, but their distribution is different intensities. See Figure 1.

Victor Mancir da Silva Santana, Global Education Magazine

On the other hand, there are two limitations Calvo-Manzano (1991) which makes it impossible for human beings, in theory, infinite perception of harmonics produced by a complex sound according to the Fourier theorem. Those harmonics whose frequency is at the upper limit of human hearing, ie, above 20 k are not perceptible to our ears, and neither are those whose intensity level is below the audible threshold for this frequency. These limitations mean that the number of harmonics that the human ear perceives is relatively small and are called harmonics present.

1.1 Acoustic Spectrum.

As stated above, the quality of the timbre of a sound is not measurable as with the height and intensity of this, due to the dependence of the pitch with the complexity of the vibratory movement that originated it is impossible to establish a unit of measurement or scale to enable comparison sound with respect to its character timbre. In this regard, with respect to the timbre of a sound analysis that can be achieved is an acoustic spectrum. In this article, the use of the acoustic spectrum has been instrumental in getting the harmonic analysis of the fragment chosen “In the times of India” because this (the spectrum) offers to obtain graphs with the distribution of harmonics with their relative values frequencies and intensities. This is a spectrum diagram of overtone frequencies of which are part of the sound, depending on the extent of each. See Figures 1 and 2.

The ridges on the graph to define each of the harmonics that make up the sound and its relative frequency is plotted on the X axis and its intensity is measured on the Y axis (see figure 2).

the harmonic on the fundamental frequency, Global education magazine

In the study we make, the presence of several instruments, has a characteristic spectrum. Likewise, each instrument has a typical spectrum which identifies the harmonic component in dependence on the complexity of the acoustic pulse in question. Both situations differ in the concrete form of the wave that would adopt an instrument that emits a pure sound. In this last case, the sound will have a single frequency, also called the fundamental. This does not happen with the flute performed by Ian Anderson, the music that we analyze. In this case, the flute is heard in “In the Times of India” so with all other instruments that participate in music, showed various harmonics in the sound spectrum, analogous to those that can be seen in the figures presented above. The most serious is the harmonic on the fundamental frequency and other frequency values ​​correspond to the other harmonics that in turn also differ in their relative amplitudes. In the presence of harmonics with their respective frequencies and amplitudes are the musical instruments and even the human voice, with regard to music, his distinctive timbre.

1.2 General aspects of timbre.

The specification of musical timbre appears when in the system is considered its complexity and the contribution of other sound attributes, among which is the height (frequency), rhythm (time) and volume (intensity). In this sense, the tone has been widely used for the recognition of different instruments as well as the recognition of multidimensional scaling techniques which are determined by small variations along three dimensions which are called: attack time, spectral centroid, and spectral flux . An example of the hitherto said can be reflected in changes (indications) of the intensity score and combinations of heights that induce the listener psychological manifestations related to variations in timbre. For authors like Le Groux and Verschure (2010) sounds can be described mainly by perceptual five components, four of which have been mentioned above and add these spatialization. This due to the relationship of these elements in the timbre space, manifesting so, too, its multidimensionality. Other studies, according to these same authors have reported the perceptual dimensions of sound through acoustic descriptions. Such descriptions may take into account the element spectral, temporal and spectral element-time and thus generate a timbre space. The timbre space is determined using multidimensional analysis derived from experiments in which listeners estimate the disparity between pairs of sounds with different timbre characteristics.

For authors such as Grey (1977); Risset (1991) and Loureiro and Bastos (2006) it is clear that the perception of timbre participating elements as the evolution of the overall intensity. Named for the latter two researchers as amplitude envelope, other factors such as fluctuations in volume and height, the spectral distribution (amplitudes of the frequencies of the spectral components) and the evolution time involved in timbre perception not only of musical instruments, but also voice human. So that the analysis that makes this music is imbued with the use of a quantitative methodology that allows to analyze and interpret the behavior of the same harmonic.

1.3 Effects of frequencies.

The following is a description of the psychological effects caused by frequency values ​​during the execution of musical instruments and voice. In this sense, we have 31-63 Hz are the fundamental frequencies of bass, tuba, 6-string basses and pedal organ. These frequencies give the sound sense of “power”. If emphasized, make the sound get “plastered”. Voice, gives sense of power range of exceptional singers (bass). 80 to 125 Hz, the enhancement of these frequencies because the effect of “boom” pronounced. The cut of 120 Hz helps in noise rejection grid (1st harmonic). Of 160-250 Hz fundamental frequencies are located drums and low (basic voice, too). If enforced, can cause the “boom”. The cut at 180 Hz helps eliminate noise grid (2nd harmonic). 315 to 500 Hz fundamental frequencies of strings and percussion in general and constitute an important frequency range for the vocal quality. Of 630-1000 Hz are the fundamental frequencies and harmonic strings, keyboards and percussion. Although we have previously stated that our study is deprived of the consideration of the human voice, it is worth noting that this range is important for the “naturalness” of speech, ie, the time in which there are no tonal variations or other whatever are the causes of change. The excessive reinforcement because the instruments the sound of “tin horn” and voice the sound of “telephone”. 1.25 to 4K Hz are found the fundamental drums, guitar, accenting vocals, strings and bass. Excess strengthening these frequencies also causes “noise fatigue,” which the listener tired after about 30 min.

Vocals can have more shine enhancing frequencies around 3 kHz, but it is necessary to simultaneously mitigate somewhat the same range for the instruments.

Of 5-8 kHz frequencies that we emphasize the percussion, such as cymbals and snare drum, accenting feminine voice and falsetto. Reductions from 5 kHz make the sound more “distant and transparent”, because it disperses in place. Attenuation in this range help to reduce hiss.

  The range of 1.25 kHz to 8 kHz governs the clarity and definition of sound for both voice and instrument. 10 to 16 kHz are the dishes and treble frequencies in general. Based on the information given above, it was possible to determine the harmonic contribution, which is presented in the following section.

2. Methodology.

Once defined the music target of our study was done in recognition that fragment that emphasizes the intentionality of the author. The passage that identifies this state peak is used in several occasions marking a different dynamic in each of the replicates, thereby insisting on arrival from music to its climax. The fragment “In the team the India”, which is the time to highlight which drove our study, was identified as Test 1” and understands the range of 2:21 to 2:26 s original music. This was segmented into three other moments which call tests, in order to facilitate the study and the large number of data associated with each point in analyzing the music in question. The first test is called Test 1” _Frag 1_1 until the third named them Test 1” _Frag 1_3. In turn, these were subjected to a segmentation now considering the second periodic passages, although they may vary from one test to another, but this threading allowed a periodic same passage were not analyzed twice by these occur more than once in different segments.

music harmonic analysis from the Fast Fourier Transform, global education magazine

Figure 3.

This fragmentation process enabled the implementation of the music harmonic analysis from the Fast Fourier Transform (FFT – Fast Fourier Transform) in order to identify the harmonics associated to specific points (discrete) for each test and study in correspondence of each them (points) with values ​​of frequency and amplitude. The Fast Fourier Transform allows a signal that is put in the time domain frequency domain, the use of this in our study finds subsidy because our hearing sensitivity has a clear relationship between the frequency and implicit in time. The transform was applied to different fragments, ie taking into account the frequency spectrum and equalization for musical instruments and audio.

The frequency ranges are presented below for the characteristic instruments and the likely effects that can induce in the listener, in view of the description given in section 1.5. It was from this characterization we have fixed values ​​of frequency (frequency bands) on which contributions were certain harmonics of each segment (fragment) Music: 32, 64, 125, 200, 500, 1k25, 2k55, 10k, 20kHz.

3. Results.

In this item we show the results from the analysis of the different fragments. Table 1 represents the areas which were determined for each fragment regarding the frequency intervals previously established. For this we consider the effects of frequency-treated prior.

It was from Table 1 that were ploteadas areas of each fragment one by one. Because of this process we obtained curves for fragment contributions which are presented below in table 1.

table I, music, global education magazine,

 Analysis of results, global education magazine

3.1 Analysis of results.

In the analysis of the results was considered the highlight of the frequency bands in which it has the largest contribution from the harmonic fragments studied. Thus, it was possible to identify the fragments frag1_1a, frag1_1b, frag1_1c, frag1_1b” 2 (b2), which are related to the track 6 which corresponds to the frequency range between 500 Hz-1k25 (see Table 1). Considering Table 2, which show below shows the ranges of frequencies associated with the fundamental and harmonics of a set of musical instruments. Among these are cited bassoon, trumpet, trombone, tuba, acoustic and electric bass, tenor sax, guitars, guitars, cymbals, drums and bass drum whose harmonics are located from the upper limit of the frequency range that we reviewed (6).

In turn, the fragments frag1_2b, frag1_3” a,” frag1_3 a’b and frag1_3 a’a” which correspond to 8 range frequencies lying between 2k55-6kHz onwards until about 10k, whose harmonics according to table 2 respond to the range of 3-8kHz, flute. This interval were identified harmonics other instruments that are present in the fragment of music chosen. Among them we also have the piano or keyboard (5-8kHz) and cello (1 to 6.5 kHz) to Table 2.






3-8 KHz



2-12 KHz



2-10 KHz



1-7 KHz



1-7,5 KHz



1-4 KHz



1-4 KHz



1-20 KHz



1-6 KHz



1-15 KHz



4-15 KHz



2-8,5 KHz



1-6,5 KHz

Bajo Acústico


1-5 KHz

Bajo Eléctrico


1-7 KHz

Guitarra Acústica


1-15 KHz

Guitarra Eléctrica


1-3,5 KHz



5-8 KHz

Saxo Soprano


2-12 KHz

Saxo Alto


2-12 KHz

Saxo Tenor


1-12 KHz



1-12 KHz

4. Final considerations.

Figures 1a, 1b and 1c which correspond to fragments analyzed for harpsichord, piano and violin respectively amostram the complexity of the sound emitted by these instruments, which in confrontation between themselves and with the figure 2 let you see the difference between each taking into account the fundamental frequencies the values ​​of their respective amplitude (intensity). In the case of the violin realize that for lower values ​​of fundamental frequency harmonics are also associated with the sonic pulse. Likewise, we find that for the piano close to 500 Hz there is a sudden peak which characterizes the fundamental frequency while the insofar as it increases there is a decrease in this amplitude spectrum. If we verify with Table 2, we found that multiple instruments can have their fundamental frequency ranges to which this point belongs. Hence it is difficult to identify, as stated above, specific instruments in the band (5).

In the fragments Frag1_3”, Frag1_2b, Frag1_3” a’a, a’b” Frag1_3 happens a breach of inaccuracies in the identification of instruments, although this is not the main goal, but we believe it would be a point to take into consideration for further research. But the undermining of bands harmonic frequencies, see table 2, to some extent hinder the identification of specific instruments such as percussion, which have conferred linked to several of the harmonic frequency bands analyzed before.

In particular we found that these fragments happens the highlight of the eighth frequency band in the corresponding spectra. According to the methodology we obtained results consistent with the range of harmonic frequencies for the flute. Instrument as said at other times this work is more prominent throughout the song. The harmonic contributions obtained in these fragments clearly reveal that the execution of the flute is remarkable.



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This article was published on September 15th: International Day of Democracy, in Global Education Magazine.

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