FAMILIA DOS CLARINETES

A família completa dos clarinetes fabricados pela Leblanc, desde o sopranino até o raríssimo octo contra baixo, o mais alto no centro da foto, que segundo informações devem existir quatro ou cinco instrumentos destes no mundo. Os mais utilizados atualmente são os clarinetes em sistema Bohem dos tipos sopranino em Mib também conhecido como requinta, o soprano  em Sib, o alto em Mib e o baixo em Sib, sendo estes dois últimos conhecidos mais pelo nome de clarones. Futuramente serão adicionados exemplos de sons e alguns solos em arquivos MP3  dos tipos mais comuns de clarinetes.   

                     Curiosidade

                Clarinete Buffet Crampon R13 com chaves banhadas em ouro 18K

Madeira utilizada na construção de clarinetes, Mpingo ou Grenadilla

Esta madeira é uma das mais densas existentes, chegando a 1 tonelada por metro cúbico.Comercialmente muito se fala em clarinetes de Ébano,o que não é verdade pelo fato que esta madeira está praticamente extinta mundialmente, pois no passado foi muito utilizada na fabricação de assoalhos,móveis, estátuas, altares de igrejas, portas e batentes e com isto florestas inteiras foram devastadas.  

Artigos

O artigo abaixo faz uma análise física do espectro de harmônicos emitidos por uma nota do clarinete, justificando o intervalo de 12ª quando da abertura da chave de registro realçando a emissão do 3º harmônico diferentemente do saxofone onde a abertura da chave realça a emissão do segundo harmônico. Esta característica física se deve ao fato do clarinete ser um tubo cilíndrico internamente  e o saxofone cônico. Na medida do possível estaremos traduzindo e comentando  este e os demais atigos para o idioma português para facilitar o entedimento.

Clarinet

A clarinet is an example of a cylindrical bore instrument closed at one end. Hence, the normal resonant modes must have a pressure maximum at the closed end (the mouthpiece) and a pressure minimum near the first open key (or the bell). These conditions result in the presence of only odd harmonics in the sound. This contrasts to the saxophone or oboe, which have a conical bore and hence include the even harmonics.

A snapshot of the sound of a clarinet (playing Bb) is shown below:



and the absence of the even harmonics in the spectrum is clearly evident.


The absence is even harmonics is (part of) what is responsible for the "warm" or "dark" sound of a clarinet compared to the "bright" sound of a saxophone.

Click here for more information on the difference between cylindrical and conical bores, or see
"The conical bore in musical acoustics," by R. D. Ayers, L. J. Eliason, and D. Mahgerefteh, American Journal of Physics, Vol 53, No. 6, pgs 528-537, (1985).

Here is a WAV file with a recorded clarinet sound: Clarinet.

You can create your own simulated clarinet sound s(t) as follows:

with w₁ = frequency of fundamental (in Hz) times 2 pi, the simulated clarinet waveform as a function of time, t (in seconds) is:

s(t) = sin(w₁t) + 0.75*sin(3*w₁t) + 0.5*sin(5*w₁t) + 0.14*sin(7*w₁t) + 0.5*sin(9*w₁t) + 0.12*sin(11*w₁t) + 0.17*sin(13*w₁t)

and then multiply s(t) by a constant to change the amplitude. The waveform for the simulated clarinet will look a little different than that of the recorded clarinet since no phase shifts are included (e.g. only sine functions are used, and no cosine functions), but it sounds remarkably similar.
Check it out: Simulated Clarinet WAV file (fundamental = 235.5 Hz).

Questions/Comments to: suits@mtu.edu
To Physics of Music Notes
To MTU Physics Dept Home Page  

Conical vs Cylindrical Bores

Why do they sound different?

For a cylindrical bore, the amplitude of the pressure variations for resonant modes are well described by sine waves. At the ends of an open finite cylinder (neglecting end effects), the pressure variations should be zero (i.e. the ends are a pressure node). At a closed end, the pressure variations should be a maximum (i.e. an "anti-node").

For a conical bore, the amplitude of the pressure variations are not simple sine waves, but are described by sin(x)/x, where x represents a distance (in appropriate units) along the cone, and x = 0 is the apex. As is the case for the closed cylinder, a pressure anti-node must be present at the closed end of the cone, which occurs automatically for the function sin(x)/x, and a pressure node should be present at the open end.

The figure below illustrates (schematically) the pressure variations for a cylinder open at both ends, an open cone, and a cylinder closed at one end. The end conditions for the cylinder closed at one end can only be met by the odd harmonics, and hence all even harmonics are missing from the sound. On the other hand, the cone and the cylinder open at both ends contain both the odd and even harmonics and when the same length, will have the same resonant frequencies.

The frequency for the nth harmonic is f_n = n*f₁.

In addition, note that to obtain the same fundamental frequency, f₁, the cylinder closed at one end is 1/2 the length of the cylinder open at both ends. Hence, if the two were the same length, the closed cylinder would play an octave lower than the open cylinder.

To a first approximation, the clarinet can be considered as having a cylindrical bore closed at one end (by the reed/mouthpiece), whereas a saxophone has a (truncated) conical bore (with the apex near the mouthpiece).

For more detail, including the case of a partial cone with openings at both ends, see:
"The conical bore in musical acoustics," R. D. Ayers, L. J. Eliason, and D. Mahgerefteh, American Journal of Physics, Vol 53, No. 6, pgs 528-537, (1985).

Just vs Equal Temperament

The "Just Scale" (sometimes referred to as "harmonic tuning") occurs naturally as a result of the overtone series for simple systems such as vibrating strings or air columns. All the notes in the scale are related by rational numbers. Unfortunately, with Just tuning, the tuning depends on the scale you are using - the tuning for C Major is not the same as for D Major, for example. Just tuning is often used by ensembles (such as for choral or orchestra works) as the players match pitch with each other "by ear."

The "equal tempered scale" was developed for keyboard instruments, such as the piano, so that they could be played equally well (or badly) in any key. It is a compromise tuning scheme. The equal tempered system uses a constant frequency multiple between the notes of the chromatic scale. Hence, playing in any key sounds equally good (or bad, depending on your point of view).

There are other temperaments which have been put forth over the years, such as the Pythagorean scale, the Mean-tone scale, and the Werckmeister scale. For more information on these you might consult "The Physics of Sound," by R. E. Berg and D. G. Stork (Prentice Hall, NJ, 1995).

The table below shows the frequency ratios for notes tuned in the Just and Equal temperament scales. For the equal temperament scale, the frequency of each note in the chromatic scale is related to the frequency of the notes next to it by a factor of the twelfth root of 2 (1.0594630944....). For the Just scale, the notes are related to the fundamental by rational numbers and the semitones are not equally spaced. The most pleasing sounds to the ear are usually combinations of notes related by ratios of small integers, such as the fifth (3/2) or third (5/4).

You will note that the most "pleasing" musical intervals above are those which have a frequency ratio of relatively small integers. Some authors have slightly different ratios for some of these intervals, and the Just scale actually defines more notes than we usually use. For example, the "augmented fourth" and "diminished fifth," which are assumed to be the same in the table, are actually not the same.

The set of 12 notes above (plus all notes related by octaves) form the chromatic scale. The Pentatonic (5-note) scales are formed using a subset of five of these notes. The common western scales include seven of these notes, and Chords are formed using combinations of these notes.

As an example, the chart below shows the frequencies of the notes (in Hz) for C Major, starting on middle C (C4), for just and equal temperament. For the purposes of this chart, it is assumed that C4 = 261.63 Hz is used for both (this gives A4 = 440 Hz for the equal tempered scale).

Since your ear can easily hear a difference of less than 1 Hz for sustained notes, differences of several Hz can be quite significant!

Listen to the difference:
The first second of this WAV file contains a major triad starting on F# (F# - A# - C#) using the Just scale appropriate for C Major. The last part of the file contains the same triad but using the Just scale appropriate for F# Major. (This is one of the worst case situations).
Tuning Shift WAV file.

Here's another example to test your ears. The following WAV file has two "players" playing a C major scale. One of the players is using the Just Scale, the other the Equal Tempered scale. Both start on exactly the same pitch. See if you can here the notes which are different.
Major scales in different temperaments

Equal Tempered Scale - Table of frequencies

Um solo bem conhecido.....

Matérias e fotos obtidas da internet

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Prof Edu.

Reforma de clarinetes

Restaurando um clarinete antigo.....

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