_May I introduce myself?
__Oh! My name is Trazom, or Wolfgang Amadeus Mozart.
___Zealously I wanted to be appointed as a composer to the distinguished court of Vienna.
____As you know, my musical talents, my works and my skill in composition are well known in foreign countries,
_____Respectfully my name is treated everywhere.
______Thirty three years old I am now. Still young. Call me Amade.

---

The Burgtheater by Google The Burgtheater internal view

I composed and finished this Quintet for Clarinet and Strings A Major on 29 September this year in 1789 for my friend Mr. Anton Stadler, an excellent clarinettist. He is three years older than me. Now he is 36. I put him a nickname "Red-currant Face". On the day December 22, 1789 this work was premiered at the Burgtheater in Vienna. It was my contribution to the annual Christmas benefit concert for widows of Viennese musicians. A clarinet quintet is a work for one clarinet and a string quartet, two violins, a viola and a cello. Mr. Anton Stodla, ah!, non Stadler, played the clarinet part and I played the viola. Because the viola is the only instrument I like more than the clarinet. How I wish you all could have heard it! And how beautifully it was performed! But the concert was beneficial, then my income was very little from it. The Burgtheater is the place where my opera "Le nozze di Figaro" was performed in May, 1786. It was three years ago. Those days were good. And it was revived here during this summer. "Cosi fan tutte" will be performed on January 26th, next year. I am inviting Mr. Haydn and a special friend Mr. Michael Puchberg, who will rescue me from my present horrible financial situation, to hear a short rehearsal of my opera.

---

Arundo donax is Reed. And here are a mouthpiece and a reed.

I don't like French people of recent years. Because my second visit to Paris was horrible. But in the old days they were different. And about a hundred years ago, one French philosopher wrote, "L'homme n'est qu'un roseau, le plus faible de la nature, mais c'est un roseau pensant." In short, "Man is a thinking reed." Then I changed it to "Clarinet is a singing reed." How beautiful the sound is from low to high! It is strong and unwavering. "A Treatise on the Fundamental Principles of Violin Playing", in german "Versuch einer gründlichen Violinschule ", is a textbook written by my father Leopold Mozart in 1756 and even now so popular that it was reprinted two years ago. In this book my father conceded that "there are performers who tremble consistently on each note as if they had the permanent fever", condemning the practice, and suggesting instead that vibrato should be used only on sustained notes and at the ends of phrases when used as an ornament. I feel exactly the same way about it. Clarinet players rarely play with vibrato. So I like this instrument. A coming Riddle over Vibrato of Clarinet According to the analysis by Mr. Iori Fujita of 2011, because the tone of clarinet is produced by its cylindrical pipe closed at one end, clarinet can make a low tone of one octave lower than flute with the same length. (W.A.M. I love this low tone. ) On the fundamental frequency, the first overtone is the third harmonic, and the second overtone is the fifth harmonic. Basically it has only odd numbered harmonics. Then the wave has the rectangular or square shape. Though violin or flute keeps the same timbre with vibrato, clarinet changes its own timber in case with vibrato. If you add vibrato while playing your clarinet, there will emerge overtones vibratos with amplitude waves, which sound strange like the sounds from outer space, "Waw, waw, waw..... ( not Wam, wam, wam....)" If you like the tone like this, you can use it. But the timber of clarinet with vibrato is not original for clarinet. It is different. ( W.A.M. I don't like it. ) An additional comment by Mr. Iori Fujita of 2011: Frequency Spectrum of Frequency Modulated Sound Wave sin(2πf0 t - m cos(2πfb t)) = J0(m) sin(2πf0) t - J1(m) (cos(2πf0 + 2πfb) t + cos(2πf0 - 2πfb) t) - J2(m) (sin(2πf0 + 2·2πfb) t + sin(2πf0 - 2·2πfb) t) - J3(m) (cos(2πf0 + 3·2πfb) t + cos(2πf0 - 3·2πfb) t) - · · · m = Δf / fb : modulation index Δf : half of bandwidth of vibrato, fb : vibrato frequency Jn (m) : Bessel functions of the first kind

Vibrato is a kind of frequency modulation, which will made sideband effects because "m" (modulation index) is about 1 or bigger than 1. It can be said to be "a wide-band frequency modulation". These sideband effects are not familiar in classic music. The bigger the modulation index, the stronger sideband effects. In case when Δf is more than 20Hz, you will hear other sounds which are not of vibrato. They sound like "waw waw"produced by sidebands.

Deviation of Δfactual / fb

---

Even harmonics are blended of course depending on the dynamics and/or the tone range. Many excellent clarinets produce the second harmonic overtone which makes very good sound. But basically the absence of even harmonics is the distinctive characteristic of the clarinet sound, which makes clarinet sound just like clarinet.

Then usually clarinet sound is assumed to be modeled with a Square Wave.

ClarinetSimulatedSquareWave(t)
= sin(2πf t) + (1/3)·sin(3·2πf t) + (1/5)·sin(5·2πf t) + (1/7)·sin(7·2πf t) + (1/9)·sin(9·2πf t) + (1/11)·sin(11·2π t) + (1/13)·sin(13·2πf t) + · ·
These overtones are very strong in their amplitude.

And one of the reserchers made a simulation based on an acutual clarinet sound, then got this.

ClarinetSoundWave(t)
= sin(2πf t) + 0.75·sin(3·2πf t) + 0.5·sin(5·2πf t) + 0.14·sin(7·2πf t) + 0.5·sin(9·2πf t) + 0.12·sin(11·2πf t) + 0.17·sin(13·2πf t)

This formula above is by Physics of Music; B. H. Suits, Physics Department, Michigan Technological University
The overtones are much stronger than those of ClarinetSimulatedSquareWave in this case.
For third 1/3=0.333 vs 0.75 ; For fifth 1/5=0.200 vs 0.50 ; For ninth 1/9=0.111 vs 0.50 etc.

clarinet / violin / flute ; sample of real and actual sound analysis upper:log and lower:liner for amplitude
I could not get the same tone samples for clarinet, violin and flute. But the overtone relationships are the same.

clarinet	violin	flute

Look at the frequency/amplitude(log) graphs. You can see that each sound contains many and rich overtones. But it is rather difficult to say the characteristic differences among them. Then turn to the frequency/amplitude(liner) graphs. Now the differences are obvious. For violin and flute the second overtones are strong. For violin the second overtone is 25% of the basetone in amplitude. For flute the second overtone is 38% of the basetone in amplitude. The third and fourth overtones are weak. The fifth overtones are almost zero.
On the contrary, for clarinet the third and fifth overtones are remarkably strong. This is the distinctive characteristic of the clarinet sound. We love it.

Let's think about the vibrato and sidetones by Bessel functions of the first kind. If you make a vibrato on 440Hz basetone with modulation frequency 6Hz and half of bandwidth of vibrato 6Hz. Arround 400Hz, 100cent is about 26Hz. ±6Hz of vivrato is 12Hz wide and about 50cent. This is very usual assumption.

base / overtone		f0		Δf		fb		Δf = half of bandwidth of vibrato fb = vibrato frequency m = modulation index = Δf / fb
the basetone		440Hz		Δf = _6Hz		fb =6Hz	→	m = 1 → almost no sideband effect
the second harmonic		880Hz		Δf = 12Hz		fb =6Hz	→	m = 2 → sideband effect : negligible
the third harmonic		1320Hz		Δf = 18Hz		fb =6Hz	→	m = 3 → sideband effect : significant
the fourth harmonic		1760Hz		Δf = 24Hz		fb =6Hz	→	m = 4 → sideband effect : significant
the fifth harmonic		2200Hz		Δf = 30Hz		fb =6Hz	→	m = 5 → sideband effect : significant
upper harmonic		2640Hz		Δf ≥ 36Hz		fb =6Hz	→	m ≥ 6 → sideband effect : less by smaller amplitude

For clarinet on the third and the fifth harmonic overtone, sideband effects are so significant that you can hear them. And the reverberation of overtones are unbearable, because strong two high tones with about 20 or 30Hz differencials ring which are two peaks of the overtone. So it should be avoided to make a long, strong and flatly sustained note. This is the problem for clarinet vibrato. I listened to a beautiful jazz clarinet play with vibraro. Then I analyzed its wave by FFT. This jazz clarinet player was making vibrato in a special way. From the center tone, he goes down in pitch with a little more strength, returns to the center tone losing additional strengh and then goes up in pitch slightly weakening its power. Again he climbs back to the center. This is a combination of frequency and amplitude modulation, which can avoid the strange "waw waw" and make a mellow sound. But it will not fit to the Mozart Clarinet Quintet.

the third harmonic overtone of the 440Hz basetone which has the almost half amplitude of the basetone.

In doing vibrato, there are some tips useful.

1	--	Combine amplitude modulation carefully to frequency modulation to avoid sideband effects.	one method
2	--	When you add vibrato to a high tone note, increase your vibrato speed. For example, from 6Hz to 10Hz. (Arround 400Hz, 100cent is about 26Hz. Arround 800Hz, one octave up, 100cent is about 52Hz. It means doubled.)
3	--	When you add vibrato to a high tone note, make bandwidth of vibrato narrower.

Benny Goodman's short G3 vibrato : There is no twin-peaks.

---

Thank you, Mr. Fujita. I appreciate your effort to describe something scientific. But it's not to my taste. I love my wife, Constanze. Many days we are separated, so I sent letters to her, saying for example; I kiss and squeeze you 1095060437082 times (now you can practise your pronunciation) and am ever your most faithful husband and friend. or Dear little wife, I have a number of requests to make. I beg you (1) not to be melancholy, (2) to take care of your health and to beware of the spring breezes, (3) not to go out walking alone and preferably not to go out walking at all, (4) to feel absolutely assured of my love. Up to the present I have not written a single letter to you without placing your dear portrait before me. (6) and lastly I beg you to send me more details in your letters, I should very much like to know whether our brother-in-law Hofer came to see us the day after my departure? Whether he comes very often, as he promised me he would? Whether the Langes come sometimes? Whether progress is being made with the portrait? 1 What sort of life you are leading? All these things are naturally of great interest to me. (5) I beg you in your conduct not only to be careful of your honour and mine, but also to consider appearances. Do not be angry with me for asking this. You ought to love me even more for thus valuing our honour. By mistake, I put (6) before (5).

portrait of Constanze Mozart with vibrato originally by her brother-in-law Joseph Lange Does vibrato make her better looking?

---

listen midi ** 1.Allegro * 2.Larghetto ** 3.Menuetto * 4.Allegretto con Variazioni ** listen midi

These are made on midi by Iori Fujita.
A=440Hz for midi.

---