and what does the quasispherical shaped distribution of planetary mass represent in this context ?
a sort of continuum of the pattern we see with the planar distribution of mass in our solar system, our galaxy and other galaxies ?
... Read more
26 July 2007
The Magdeburg hemispheres: Guericke thermodynamics and the history of flight
One of the episodes in the history of flight involves two aeronef designs that trace their inspiration to an experiment that may or may not have contributed a bit to the development of the ideal gas laws by Boyle and Hooke, which themselves led to the development of the first steam engine. In effect, the little episode , fruitless in the history of the development of flight, shows links with other episodes in the history of science and technology.
The designs in question concern first a 1709 airship proposal by a portuguese scientist named de Gusmao whose designs for aero lift involved the exploitation of lighter than air volumes that would carry the ship up. He was renouned for making a model balloon fly up to the roof. His airship design involved an apparatus or grid to to heat the air underneath a canopy that covered the airship, a conceptual predecessor of the hot air balloons. He was encouraged in his design efforts by another lighter-than-air idea, 37 years older at his time, and unfortunately impractical , by a Fransisco di Terzi, who imagined an airship relying for its buoyance on thin copper vacuum spheres .
Terzi's idea of the vacuum spheres , and the calculation of the relative weights of the air-less copper spheres and their equivalent in air, was in fact, despite the oversight quite brilliant and sensical. Yet it derives from another vacuum sphere , one that was developed twenty years earlier.
That sphere, as it turns out, was a much more famous sphere, that in fact was not a sphere but consisted of two hemispheres named after the town where they were conceived , Magdeburg.
The two hemispheres of copper , about a foot in diameter, were made in 1650 and demonstrated repeatedly at royal courts through the following dozen years by the german scientist and public servant, Otto von Guericke who set out to demonstrate the power of the pressure of gazes like the air and fluids like the atmosphere. In so doing, he wanted to disprove a long held notion , originating with Aristotle, on the reason why solids were held together so tightly , what made substance, utterly divisible into dust particles, be able to hold itself.
Artistotle's proposition stipulated that nature abhors a vacuum, and in the same way , earth is attracted downward and fire is attracted upward, there was a natural disposition to fill in in gaps in space causing matter to condensed in its solid forms. This interpretation of his thus came to be known , by Guericke's time as "horror vacui".
Guericke seemed to believe that it was rather the pressure of the air , a force of our atmosphere that held solids together. An erroneous notion that can be more than forgiven for the ingenuity with which he set out to prove it.
The hemispheres were to be brought and held firmly together after covering their rims with a layer of grease or naphta oil. They were then to be emptied of their air content by means of an air pump von Guericke had developed specifically for the experiment. Once devoid of air, the hemispheres became so tightly held together that no amount of available force could do the work of displacing them apart. To demonstrate this fact each hemisphere was tied to a team of horses , both facing opposite directions. Both teams would then be made to pull the hemispheres in opposite directions, but no matter how hard the horses pulled the hemispheres held tightly. the enormous force of atmosphere pressure on the vacuum inside the sphere held its hemispheres together.
In setting up this experiment Guericke demonstrates some fine details.
- The experiment was a success and was even popular , making it part of popular knowledge not just insular recondite science.
- The experiment's apparatus was the world's first artificially (human) made vacuum enclosure. This particular activity, creating a vacuum , is very important to the advancement of modern chemistry, and later electronics.
- The design of the air pump to create the vacuum went on to contribute to Robert Hooke and Robert Boyle's work and consequently to the prolegomena of modern chemistry and thermodynamics that they both have laid down. Other chemistry researchers followed Boyle and Hooke's example and made use of Guericke's pumps to enable to examine chemical propertie and reactions in a vacuum, greatly aiding the advancement of chemical science. Vacuum flasks and tubes later carried electrical research through the invention of incandescent and fluorescent light , the radiotelegraph and the radio , and the vacuum tubes of the television and the computer.
The graph below happens to capture some of the threads of this short historical episode,
but moreover it looks like a useful tool for rendering (and variously compressing, analyzing visualizing and summmarizing text such as those from which the information in this note was gathered.
The texts used were largely en.wikipedia articles, plus the illustr. ...
- more - ... Read more
15 July 2007
الخان و الخاقان و القان و القانون
ملاحظة لغوية
كلتا الكلمتان خان و خاقان تعدان مترادفتان بحيث أن معناهما واحد و هو حاكم أو ملك فى حين أن لفظ خاقان فيه تعاظم على لفظ خان حيث يشابه فى معناه اللقب الفارسى شاهنشاه و معناه ملك الملوك ، و يكتب اللفظ فى اللغات الرومانسية هكذا Khâgan
و اللفظ خان أو قان من أصول مغولية أو تركية و الأغلب من أصل مشترك حيث تتشابه اللغتان الى حد بعيد فى أغلب مفرداتهما. و لدى الصينيون تحوير ثالث للقب خان و تعريبه هان، و تكتب كلمة خان هكذا بالصينية
可汗 .
و الخان أو الخاقان إسم مذكر ، مؤنثه ختون و خانوم و ربما يرجع اللقب المؤنث هانم الى مؤنث النطق الصينى للكلمة، هان .
و فى حين أننا نجد أن كلا الإسمان مستعملان فى الخطاب التاريخى العربى ، نود الإشارة الى إستهجاء أسيوى لنفس الللقب ألا و هو القان (هذا الى جانب المرادف الصينى هان).
تجدر الإشارة أيضا فى هذا المضمون أن الأسم الذى إشتهر به موحد أمبراطورية المغول ، جنكيز خان أو جنكيز قان ، هو فى الواقع لقب ترجمته الحرفية هى حاكم المحيط بمعنى حاكم العالم
، فى حين أن إسم هذا القائد الأصلى هو طيموجين.
مع مقارنة المرادفات الثلاث ، خان خاقان و قان ، و التفكر فى معناهم نرى أنه ربما هناك علاقة بين هذا اللقب و معناه المشتمل على الحكم و أصل كلمة القانون.
هنا نرى إمكانية القرابة بين القان الذى يسن القانون. و هى قرابة إن كان حقيقية فهى تشابه القرابة بين بين كلمة السياسة و أصلها اللغوى و هو الياسا و هى التشريعات التى وضعها جنكيز قان عند جمع قبائل المغول تحت رايته و إنتصاره على ممالك الصين الشمالية.
نود أيضا مقارنة التركيب اللفظى فى الألقاب شاهنشاه و قائمقام مع تركيب خاقان ، أما فى اللفظين السابقين فلا يخفى الأثر التركى و إن كانت شاهنشاه فارسية ، أما فى اللفظة الثالثة فربما تدل على أن قان قد يمثل الجمع للمفرد خان.
من الممكن أيضا وجود قرابة لغوية بين لفظ خاقان و كلا من اللقب اليابانى شوغان و اللقب العبرى حاخام ، و إن كان فى الأغلب تشابه عابر . حاخام تتصل بالمصدر حكم و معناها حاكم أو بالأحرى حكيم ممما يدفعنا لمقارنة الأحرف حـ كـ م و الأحرف خ / ق ن
أما الحرفان ح و خ فهما قابلين للتبادل فى علم و تاريخ أنساب الأسماء , نجد كذلك تقارب صوتى بين الحرفين ك و ق الى جانب تقارب مكانى إن صلح التعبير بين الزوج م و ن حيث نجدهم متجاورين فى معظم الأبجديات
كنت أتسائل ما اذا كانت الحروف خ و ه و ح قابلة للتبادل مع حرف أو صوت شين مثلما هو الأمر مع والحروف أو الأصوات اللاتينية c ch kh k
فربما ساعد ذلك على يشير ذلك الى أصل مشترك للقب المغولى خان و قان و مقابله الفارسى شاه ، و لكن هذا غير صحيح لأن تسمية شاه إنما ترجع الى السانسكريتية گذشته.
يجدر التساؤل أيضا عن تاريخ استعمال هذا اللقب فى أراضى السند و فارس.
كذلك أفتقر الى أصول و تاريخ غستعمال هذا اللقب، و إن كا ن هنالك إشارات تعود الى ما قبل عصر جنكيز بزمن. فعلى سبيل المثال نجد أن البلغار النازحين من القوقاز الى أراضى التراقيين فى القرن السابع الميلادى تأسست إمبراطوريتهم اﻷولى حوالى عام 632 م على يد ملكهم المسمى خان أسباروخ ابن المك خان كوبرات .
و الذى انتصر من ضمن آخرين على مملكة اﻷفار فى الغرب و التى كانت أيضا تعرف بالخاقانية.
و قد قدم اﻷفار أو اﻷواريون و البلغار من القوقاز ، و يعتقد أن اﻷفار اﻷوربيون قد يعودوا فى أصولهم للروران ( تان تان أو شيانباى) ذوى الأصل المغولى و الذين إستعملوا لقب الخاقان منذ القرن الثالث الميلادى. هذا الى جانب أن البلاد التى سكنتها الشعوب التركية فى حقبة ما بعد إنهيار إمبراطورية الرومان كانت تعج بالخانات (خانقاه) مثل الخزر و الأفار .
و ﻻ يسعنى اﻻ أن ألمح الى تقارب الخاقان و بالتحديد اللقب اﻷقدم المستعمل لدى المغوليين اﻷول ، كيهان (可寒) مع الألقاب السامية كاهن و حاكم . و من التحوير العبرى لكلمة الحكمة ، خُخمة، نجد المرادف للحاكم أو الحكيم فى العبرية هو حاخام أو خاخام و هنا نجد وضوح قى تشابه اﻷخيرة مع اللقب المغولى ثم التركى ، خاقان.
冨田勲 طوميــطـا
Isao Tomita is one of the most remarkable Japanese composers and recording artists.
His music has provided me, an amateur musician, with a certain sense of vindication in terms of an approach to
music that tends to transcend traditional forms, in terms of their accoustics, harmonies and thematics.
[ It may seem that the same can be said of so-called "world" music - and as it happens Tomita has featured on recordings that are labeled "world" music or ethnic (as with Nasco Fantasy recording with the Japanese taiko drumming group Kodo) - but we're not talking about world music here ]
But Tomita's work is classical music music that departs from the traditional sounds of accoustic instruments into the vast world of synthetic sounds. Sounds that are engineered with the same ingenuity used in his music composition.
Thematically Tomita is a classical composer, most of the time, but essentially his are modern compositions that can span with ease the spectra of classical, experimental, and electronic music as also ,i daresay, even jazz.
His music has, to me, an inescapable familiarity that is felt with only the best composers like Beethoven, Debussy, McCartney, Wonder, Coltrane or Zappa. But that is also because Tomita's music includes a lot of interpretations of classical works.
Tomita recorded / interpreted / covered Debussy works (whichever your musical persuasion is) in his first album issued in 1974, Snowflakes are dancing, such as Suite Bergamasque no. 3 , better known as Clair de Lune, of which i think there 's a free excerpt at the artist's page for the album.
True to his title as a President of the Japan Synthesizer Programmers Association, the master composer provides a tally of the equipment used on his albums at his web site (at least the dot org site) together with images and samples liner notes and other information.
He has made modern classical compositions, and has been a renouned classical composer and motion picture composer through the 1950s and 1960s. as well as others more akin to the socres of Scott Bradley and Raymond Scott during the 1950s.
This familiarity in the music along with the pensive musical landscapes fashioned by both the composition and the sounds used, gives Tomita's works haunting qualities.
Perhaps those electronically induced soundscapes may not be everyone's liking now or ever, but it is certain that they are timbral territories that have only been explored for the past six decades, less than a hundred years.
In terms of centuries, the mozarts, Bachs, Davis and Coreas of these new soundscapes, may have not yet appeared. but of those, Tomita certainly gives us a more than a few hints.
-----------
Music worth checking out includes
Footprints in the snow and Passepied from the album Snowflakes are dancing; The Planets (1976), in which he reinterprets Holst's 1917 Planets Suite,
Also recommended are Cum Mortuis In Lingua Mortua from Mussorgsky: Pictures at an exhibtion (1975), which also features the unmissable Promenade: Ballet of the chicks in their shells; Peggasus from Dawn chorus (2004). ... Read more
冨田勲 طـومـيــــطــــــا
Isao Tomita is one of the most remarkable Japanese composers and recording artists.
His music has provided me, an amateur musician, with a certain sense of vindication in terms of an approach to
music that tends to transcend traditional forms, in terms of their accoustics, harmonies and thematics.
[ It may seem that the same can be said of so-called "world" music - and as it happens Tomita has featured on recordings that are labeled "world" music or ethnic (as with Nasco Fantasy recording with the Japanese taiko drumming group Kodo) - but we're not talking about world music here ]
But Tomita's work is classical music music that departs from the traditional sounds of accoustic instruments into the vast world of synthetic sounds. Sounds that are engineered with the same ingenuity used in his music composition.
Thematically Tomita is a classical composer, most of the time, but essentially his are modern compositions that can span with ease the spectra of classical, experimental, and electronic music as also ,i daresay, even jazz.
His music has, to me, an inescapable familiarity that is felt with only the best composers like Beethoven, Debussy, McCartney, Wonder, Coltrane or Zappa. But that is also because Tomita's music includes a lot of interpretations of classical works.
Tomita recorded / interpreted / covered Debussy works (whichever your musical persuasion is) in his first album issued in 1974, Snowflakes are dancing, such as Suite Bergamasque no. 3 , better known as Clair de Lune, of which i think there 's a free excerpt at the artist's page for the album.
True to his title as a President of the Japan Synthesizer Programmers Association, the master composer provides a tally of the equipment used on his albums at his web site (at least the dot org site) together with images and samples liner notes and other information.
He has made modern classical compositions, and has been a renouned classical composer and motion picture composer through the 1950s and 1960s. as well as others more akin to the socres of Scott Bradley and Raymond Scott during the 1950s.
This familiarity in the music along with the pensive musical landscapes fashioned by both the composition and the sounds used, gives Tomita's works haunting qualities.
Perhaps those electronically induced soundscapes may not be everyone's liking now or ever, but it is certain that they are timbral territories that have only been explored for the past six decades, less than a hundred years.
In terms of centuries, the mozarts, Bachs, Davis and Coreas of these new soundscapes, may have not yet appeared. but of those, Tomita certainly gives us a more than a few hints.
-----------
Music worth checking out includes
Footprints in the snow and Passepied from the album Snowflakes are dancing; The Planets (1976), in which he reinterprets Holst's 1917 Planets Suite,
Also recommended are Cum Mortuis In Lingua Mortua from Mussorgsky: Pictures at an exhibtion (1975), which also features the unmissable Promenade: Ballet of the chicks in their shells; Peggasus from Dawn chorus (2004). ... Read more
10 July 2007
beschreiben timbre
Often people try to characterize types of timbre quality as fat, deep or in terms of having colour.
but calling the sound of 3 overlapping oscillators "Fatter" just because there are more sound sources is a bit inaccurate. It seems color is naturally suited to describe differences of timbre between instruments.
A friend once observed that "colour" was a pretty natural choice of metaphor when describing the timbre of a sound, refering to the fact that the presence of multiple frequencies is at play both in the visible light waves we call colour and in the waves of musical tones.
In general, the timbre of a given musical sound (indeed any sound) is determined by the harmonic content of the accoustic pressure wave. OK statements like this are deceptively simple (save perhaps for the term harmonic to some readers) but they contain within a great deal of information. Let's simplify this statement and explore the concepts it encapsulates.
For starters, if the term "harmonic" sounds confusing we can do without it for now, because in any sound wave there are two components (among others) that make up / describe the qualities and characteristics of the wave: Amplitude (the loudness of the wave over time), and its frequency (the number of times the periodic waveform is repeated in a given unit of time). The latter , frequency, or rather a multitude of frequencies - combined together (added, interfering) to form the Waveform of the sound , ie the way the wave's amplitude looks during the time of a single cycle of the wave - make up the harmonic content of a wave.
I would also like to add that when I speak of waves I shouldn't only be speaking of accoustic or sound waves, which because they travel through air contracting and expanding it, I like to call by their other physical name, pressure waves.
There are also electric waves. And much of what gets said of the sound produced by material accoustic instruments , also applies to waves of electrical current, voltage waves , or electrical signals, streams of them. These are usually produced not by material accoustic instruments but by electric circuits that generate waves of different types and that modify them in different ways, (this is called synthesizing) and then drive loud speakers which convert the electric current waves into actual sounds that we hear (this is called reproduction). The electric waves themselves could also be analogs of wave information initially produced as binary data that describe all the properties of the waves produced, from waveforms to full performances. This binary data, called digital, is converted to an analog electrical wave or signal or current (stream) , using a device called DAC (Digital to Analog converter), and eventually the "analog" electric current is itself converted into accoustic sound waves or pressure waves, which are audible analogs of the electric current waves, and that travel in the air to reach our ears.
Let's simplify the earlier statement and then proceed to discuss the waves and their timbres.
In general, the timbre of a given sound is determined by the content of its wave.
The wave itself is a composite of several other waves, all added together - That is, they produced pretty much at the same time, and their intensities (loudness) combine to give the total loudness of the wave. These several other waves have different loudness values but are all considerably lower than the loudest composite wave, which has a frequency equal to the pitch of the musical note being sounded.
This loudest wave is called the fundamental, and the other less intens waves are called the overtones of the waves. The fundamental and the remaining overtones are also known as the harmonics of the wave. Each one of the overtones (aka harmonics) has a frequency that is a multiple of the frequency of hte fundamental, that is a multiple of the musical note's own pitch. I won't get into the arithmetic and trigonometrical relations between the harmonics here now because I'd like to focus on timbre now. But I'll say the easiest representation of the relationship (ratios) between the harmonics (and their frequencies) is the famous one using the length of a guitar string.
Because the overtones have frequencies that are multiples of the fundamental harmonic of the musical note (or electric signal), the harmonics of any sounds are distributed over the same values of frequency, namely, (f, 2f, 3f, 4f, 5f, ... and so on ).
What differs from sound to sound (among other things) is the relative loudnesses of the different harmonics.
There are other factors affecting timbre, such as the relative phases of the harmonics of the wave, as well as the presence or absence of other waves combined each with its own set of harmonics. But I believe the relative loudness of the overtones is the crucial factor in a sound's timbre or colour.
The harmonics of an accoustic instrument depend on the materials of which the sound generating components are made as well as the shape of the sound box of the instrument. The shape and materials of a violin's sound board, the hairs of its bow, the make of the strings, affect the harmonics of the instrument, and so despite the kinship different violin instruments sound different from one another. The same is true for most other instruments. Even playing techniques affect the tones' timbre.
Now when we want to look at a representation of the harmonics of a given wave, we have to use a diagram that plots Amplitude against (not time as in the more familiar wave diagram - called time domain diagrams but against) Frequency.
Based on the aforementioned, we should expect to see that at the the frequency of the fundamental the amplitude has the highest value, and that the other overtones appear in the graph as spikes in amplitude right where each overtone's frequency is on the horizontal axis. Here is a sample diagram of the harmonics of a wave produced on a VST synth and plotted by the FREE fre(a)koscope 0.8 spectrum analyzer plugin,
koscope.spectrum.analyzer.01.png)
The tools that let us look at a wave's harmonics in this way are called spectrum analyzer, which are desendants or cousins of the oscilloscope which plots the Amplitude of a wave (vertical axis) against the time axis (horizontal axis).
Note the name spectrum here is not used in vain. Because as you see in the picture, the graph actually shows us a spectrum of frequencies, with spikes where overtones occur in the wave. This is very much like the spectra we get when analyze chemical elements and compounds to get to see which frequencies of light they emit (or absorb i don't remember) in the visible light band of the electromagnetic spectrum. Very much in the same vain, the color of an object is also those portions of visible light that are reflected or emitted by it.
Each object has its own spectrum (ie, collection of frequencies that make up its color) In the case of material objects , the frequency is that of electromagnetic waves, in teh case of sounds, the frequencies are those of accoustic pressure waves in the air, and in the case of synthesized sounds, they are frequencies of an electrical current signal.
Therefore, as my friend has noted, it does make perfect sense to use colour when describing a musical sound.
The images that follows as the one above, are of the same synth preset, but the harmonics look different , the peaks more or less are the same but the all sorts of amplitude changes occur to different frequencies,
koscope.spectrum.analyzer.02.png)
koscope.spectrum.analyzer.03.png)
This is because, the harmonics , and therefore the timbre of a sound vary with time, as the instrument is used to play a melody.
The images below show the frequency spectrum for a software electric piano playing C3 and C4 respectively,
koscope.spectrum.analyzer.05.png)
In the latter figure the resolution of the sampling window was increased adding sharpness to the frequency spectrum graph, (chalk one up for the software designers and engineers),
koscope.spectrum.analyzer.06.epiano.c4.png)
This image is of a software organ playing a C4 (Do 4) note ,
koscope.spectrum.analyzer.07.sworgan.c4.png)
The images used here are screenshots of the free fre(a)koscope 0.8 FFT-based realtime spectrum analyzer plugin, available on the FFT tools page at smartelectronix.com , a collective of quality-friendly audio and music software developers. ... Read more
but calling the sound of 3 overlapping oscillators "Fatter" just because there are more sound sources is a bit inaccurate. It seems color is naturally suited to describe differences of timbre between instruments.
A friend once observed that "colour" was a pretty natural choice of metaphor when describing the timbre of a sound, refering to the fact that the presence of multiple frequencies is at play both in the visible light waves we call colour and in the waves of musical tones.
In general, the timbre of a given musical sound (indeed any sound) is determined by the harmonic content of the accoustic pressure wave. OK statements like this are deceptively simple (save perhaps for the term harmonic to some readers) but they contain within a great deal of information. Let's simplify this statement and explore the concepts it encapsulates.
For starters, if the term "harmonic" sounds confusing we can do without it for now, because in any sound wave there are two components (among others) that make up / describe the qualities and characteristics of the wave: Amplitude (the loudness of the wave over time), and its frequency (the number of times the periodic waveform is repeated in a given unit of time). The latter , frequency, or rather a multitude of frequencies - combined together (added, interfering) to form the Waveform of the sound , ie the way the wave's amplitude looks during the time of a single cycle of the wave - make up the harmonic content of a wave.
I would also like to add that when I speak of waves I shouldn't only be speaking of accoustic or sound waves, which because they travel through air contracting and expanding it, I like to call by their other physical name, pressure waves.
There are also electric waves. And much of what gets said of the sound produced by material accoustic instruments , also applies to waves of electrical current, voltage waves , or electrical signals, streams of them. These are usually produced not by material accoustic instruments but by electric circuits that generate waves of different types and that modify them in different ways, (this is called synthesizing) and then drive loud speakers which convert the electric current waves into actual sounds that we hear (this is called reproduction). The electric waves themselves could also be analogs of wave information initially produced as binary data that describe all the properties of the waves produced, from waveforms to full performances. This binary data, called digital, is converted to an analog electrical wave or signal or current (stream) , using a device called DAC (Digital to Analog converter), and eventually the "analog" electric current is itself converted into accoustic sound waves or pressure waves, which are audible analogs of the electric current waves, and that travel in the air to reach our ears.
Let's simplify the earlier statement and then proceed to discuss the waves and their timbres.
In general, the timbre of a given sound is determined by the content of its wave.
The wave itself is a composite of several other waves, all added together - That is, they produced pretty much at the same time, and their intensities (loudness) combine to give the total loudness of the wave. These several other waves have different loudness values but are all considerably lower than the loudest composite wave, which has a frequency equal to the pitch of the musical note being sounded.
This loudest wave is called the fundamental, and the other less intens waves are called the overtones of the waves. The fundamental and the remaining overtones are also known as the harmonics of the wave. Each one of the overtones (aka harmonics) has a frequency that is a multiple of the frequency of hte fundamental, that is a multiple of the musical note's own pitch. I won't get into the arithmetic and trigonometrical relations between the harmonics here now because I'd like to focus on timbre now. But I'll say the easiest representation of the relationship (ratios) between the harmonics (and their frequencies) is the famous one using the length of a guitar string.
Because the overtones have frequencies that are multiples of the fundamental harmonic of the musical note (or electric signal), the harmonics of any sounds are distributed over the same values of frequency, namely, (f, 2f, 3f, 4f, 5f, ... and so on ).
What differs from sound to sound (among other things) is the relative loudnesses of the different harmonics.
There are other factors affecting timbre, such as the relative phases of the harmonics of the wave, as well as the presence or absence of other waves combined each with its own set of harmonics. But I believe the relative loudness of the overtones is the crucial factor in a sound's timbre or colour.
The harmonics of an accoustic instrument depend on the materials of which the sound generating components are made as well as the shape of the sound box of the instrument. The shape and materials of a violin's sound board, the hairs of its bow, the make of the strings, affect the harmonics of the instrument, and so despite the kinship different violin instruments sound different from one another. The same is true for most other instruments. Even playing techniques affect the tones' timbre.
Now when we want to look at a representation of the harmonics of a given wave, we have to use a diagram that plots Amplitude against (not time as in the more familiar wave diagram - called time domain diagrams but against) Frequency.
Based on the aforementioned, we should expect to see that at the the frequency of the fundamental the amplitude has the highest value, and that the other overtones appear in the graph as spikes in amplitude right where each overtone's frequency is on the horizontal axis. Here is a sample diagram of the harmonics of a wave produced on a VST synth and plotted by the FREE fre(a)koscope 0.8 spectrum analyzer plugin,
The tools that let us look at a wave's harmonics in this way are called spectrum analyzer, which are desendants or cousins of the oscilloscope which plots the Amplitude of a wave (vertical axis) against the time axis (horizontal axis).
Note the name spectrum here is not used in vain. Because as you see in the picture, the graph actually shows us a spectrum of frequencies, with spikes where overtones occur in the wave. This is very much like the spectra we get when analyze chemical elements and compounds to get to see which frequencies of light they emit (or absorb i don't remember) in the visible light band of the electromagnetic spectrum. Very much in the same vain, the color of an object is also those portions of visible light that are reflected or emitted by it.
Each object has its own spectrum (ie, collection of frequencies that make up its color) In the case of material objects , the frequency is that of electromagnetic waves, in teh case of sounds, the frequencies are those of accoustic pressure waves in the air, and in the case of synthesized sounds, they are frequencies of an electrical current signal.
Therefore, as my friend has noted, it does make perfect sense to use colour when describing a musical sound.
The images that follows as the one above, are of the same synth preset, but the harmonics look different , the peaks more or less are the same but the all sorts of amplitude changes occur to different frequencies,
This is because, the harmonics , and therefore the timbre of a sound vary with time, as the instrument is used to play a melody.
The images below show the frequency spectrum for a software electric piano playing C3 and C4 respectively,
In the latter figure the resolution of the sampling window was increased adding sharpness to the frequency spectrum graph, (chalk one up for the software designers and engineers),
This image is of a software organ playing a C4 (Do 4) note ,
The images used here are screenshots of the free fre(a)koscope 0.8 FFT-based realtime spectrum analyzer plugin, available on the FFT tools page at smartelectronix.com , a collective of quality-friendly audio and music software developers. ... Read more
beschreiben timbre
Often people try to characterize types of timbre quality as fat, deep or in terms of having colour.
but calling the sound of 3 overlapping oscillators "Fatter" just because there are more sound sources is a bit inaccurate. It seems color is naturally suited to describe differences of timbre between instruments.
A friend once observed that "colour" was a pretty natural choice of metaphor when describing the timbre of a sound, refering to the fact that the presence of multiple frequencies is at play both in the visible light waves we call colour and in the waves of musical tones.
In general, the timbre of a given musical sound (indeed any sound) is determined by the harmonic content of the accoustic pressure wave. OK statements like this are deceptively simple (save perhaps for the term harmonic to some readers) but they contain within a great deal of information. Let's simplify this statement and explore the concepts it encapsulates.
For starters, if the term "harmonic" sounds confusing we can do without it for now, because in any sound wave there are two components (among others) that make up / describe the qualities and characteristics of the wave: Amplitude (the loudness of the wave over time), and its frequency (the number of times the periodic waveform is repeated in a given unit of time). The latter , frequency, or rather a multitude of frequencies - combined together (added, interfering) to form the Waveform of the sound , ie the way the wave's amplitude looks during the time of a single cycle of the wave - make up the harmonic content of a wave.
I would also like to add that when I speak of waves I shouldn't only be speaking of accoustic or sound waves, which because they travel through air contracting and expanding it, I like to call by their other physical name, pressure waves.
There are also electric waves. And much of what gets said of the sound produced by material accoustic instruments , also applies to waves of electrical current, voltage waves , or electrical signals, streams of them. These are usually produced not by material accoustic instruments but by electric circuits that generate waves of different types and that modify them in different ways, (this is called synthesizing) and then drive loud speakers which convert the electric current waves into actual sounds that we hear (this is called reproduction). The electric waves themselves could also be analogs of wave information initially produced as binary data that describe all the properties of the waves produced, from waveforms to full performances. This binary data, called digital, is converted to an analog electrical wave or signal or current (stream) , using a device called DAC (Digital to Analog converter), and eventually the "analog" electric current is itself converted into accoustic sound waves or pressure waves, which are audible analogs of the electric current waves, and that travel in the air to reach our ears.
Let's simplify the earlier statement and then proceed to discuss the waves and their timbres.
In general, the timbre of a given sound is determined by the content of its wave.
The wave itself is a composite of several other waves, all added together - That is, they produced pretty much at the same time, and their intensities (loudness) combine to give the total loudness of the wave. These several other waves have different loudness values but are all considerably lower than the loudest composite wave, which has a frequency equal to the pitch of the musical note being sounded.
This loudest wave is called the fundamental, and the other less intens waves are called the overtones of the waves. The fundamental and the remaining overtones are also known as the harmonics of the wave. Each one of the overtones (aka harmonics) has a frequency that is a multiple of the frequency of hte fundamental, that is a multiple of the musical note's own pitch. I won't get into the arithmetic and trigonometrical relations between the harmonics here now because I'd like to focus on timbre now. But I'll say the easiest representation of the relationship (ratios) between the harmonics (and their frequencies) is the famous one using the length of a guitar string.
Because the overtones have frequencies that are multiples of the fundamental harmonic of the musical note (or electric signal), the harmonics of any sounds are distributed over the same values of frequency, namely, (f, 2f, 3f, 4f, 5f, ... and so on ).
What differs from sound to sound (among other things) is the relative loudnesses of the different harmonics.
There are other factors affecting timbre, such as the relative phases of the harmonics of the wave, as well as the presence or absence of other waves combined each with its own set of harmonics. But I believe the relative loudness of the overtones is the crucial factor in a sound's timbre or colour.
The harmonics of an accoustic instrument depend on the materials of which the sound generating components are made as well as the shape of the sound box of the instrument. The shape and materials of a violin's sound board, the hairs of its bow, the make of the strings, affect the harmonics of the instrument, and so despite the kinship different violin instruments sound different from one another. The same is true for most other instruments. Even playing techniques affect the tones' timbre.
Now when we want to look at a representation of the harmonics of a given wave, we have to use a diagram that plots Amplitude against (not time as in the more familiar wave diagram - called time domain diagrams but against) Frequency.
Based on the aforementioned, we should expect to see that at the the frequency of the fundamental the amplitude has the highest value, and that the other overtones appear in the graph as spikes in amplitude right where each overtone's frequency is on the horizontal axis. Here is a sample diagram of the harmonics of a wave produced on a VST synth and plotted by the FREE fre(a)koscope 0.8 spectrum analyzer plugin,
The tools that let us look at a wave's harmonics in this way are called spectrum analyzer, which are desendants or cousins of the oscilloscope which plots the Amplitude of a wave (vertical axis) against the time axis (horizontal axis).
Note the name spectrum here is not used in vain. Because as you see in the picture, the graph actually shows us a spectrum of frequencies, with spikes where overtones occur in the wave. This is very much like the spectra we get when analyze chemical elements and compounds to get to see which frequencies of light they emit (or absorb i don't remember) in the visible light band of the electromagnetic spectrum. Very much in the same vain, the color of an object is also those portions of visible light that are reflected or emitted by it.
Each object has its own spectrum (ie, collection of frequencies that make up its color) In the case of material objects , the frequency is that of electromagnetic waves, in teh case of sounds, the frequencies are those of accoustic pressure waves in the air, and in the case of synthesized sounds, they are frequencies of an electrical current signal.
Therefore, as my friend has noted, it does make perfect sense to use colour when describing a musical sound.
The images that follows as the one above, are of the same synth preset, but the harmonics look different , the peaks more or less are the same but the all sorts of amplitude changes occur to different frequencies,
This is because, the harmonics , and therefore the timbre of a sound vary with time, as the instrument is used to play a melody.
The images below show the frequency spectrum for a software electric piano playing C3 and C4 respectively,
In the latter figure the resolution of the sampling window was increased adding sharpness to the frequency spectrum graph, (chalk one up for the software designers and engineers),
This image is of a software organ playing a C4 (Do 4) note ,
The images used here are screenshots of the free fre(a)koscope 0.8 FFT-based realtime spectrum analyzer plugin, available on the FFT tools page at smartelectronix.com , a collective of quality-friendly audio and music software developers. ... Read more
but calling the sound of 3 overlapping oscillators "Fatter" just because there are more sound sources is a bit inaccurate. It seems color is naturally suited to describe differences of timbre between instruments.
A friend once observed that "colour" was a pretty natural choice of metaphor when describing the timbre of a sound, refering to the fact that the presence of multiple frequencies is at play both in the visible light waves we call colour and in the waves of musical tones.
In general, the timbre of a given musical sound (indeed any sound) is determined by the harmonic content of the accoustic pressure wave. OK statements like this are deceptively simple (save perhaps for the term harmonic to some readers) but they contain within a great deal of information. Let's simplify this statement and explore the concepts it encapsulates.
For starters, if the term "harmonic" sounds confusing we can do without it for now, because in any sound wave there are two components (among others) that make up / describe the qualities and characteristics of the wave: Amplitude (the loudness of the wave over time), and its frequency (the number of times the periodic waveform is repeated in a given unit of time). The latter , frequency, or rather a multitude of frequencies - combined together (added, interfering) to form the Waveform of the sound , ie the way the wave's amplitude looks during the time of a single cycle of the wave - make up the harmonic content of a wave.
I would also like to add that when I speak of waves I shouldn't only be speaking of accoustic or sound waves, which because they travel through air contracting and expanding it, I like to call by their other physical name, pressure waves.
There are also electric waves. And much of what gets said of the sound produced by material accoustic instruments , also applies to waves of electrical current, voltage waves , or electrical signals, streams of them. These are usually produced not by material accoustic instruments but by electric circuits that generate waves of different types and that modify them in different ways, (this is called synthesizing) and then drive loud speakers which convert the electric current waves into actual sounds that we hear (this is called reproduction). The electric waves themselves could also be analogs of wave information initially produced as binary data that describe all the properties of the waves produced, from waveforms to full performances. This binary data, called digital, is converted to an analog electrical wave or signal or current (stream) , using a device called DAC (Digital to Analog converter), and eventually the "analog" electric current is itself converted into accoustic sound waves or pressure waves, which are audible analogs of the electric current waves, and that travel in the air to reach our ears.
Let's simplify the earlier statement and then proceed to discuss the waves and their timbres.
In general, the timbre of a given sound is determined by the content of its wave.
The wave itself is a composite of several other waves, all added together - That is, they produced pretty much at the same time, and their intensities (loudness) combine to give the total loudness of the wave. These several other waves have different loudness values but are all considerably lower than the loudest composite wave, which has a frequency equal to the pitch of the musical note being sounded.
This loudest wave is called the fundamental, and the other less intens waves are called the overtones of the waves. The fundamental and the remaining overtones are also known as the harmonics of the wave. Each one of the overtones (aka harmonics) has a frequency that is a multiple of the frequency of hte fundamental, that is a multiple of the musical note's own pitch. I won't get into the arithmetic and trigonometrical relations between the harmonics here now because I'd like to focus on timbre now. But I'll say the easiest representation of the relationship (ratios) between the harmonics (and their frequencies) is the famous one using the length of a guitar string.
Because the overtones have frequencies that are multiples of the fundamental harmonic of the musical note (or electric signal), the harmonics of any sounds are distributed over the same values of frequency, namely, (f, 2f, 3f, 4f, 5f, ... and so on ).
What differs from sound to sound (among other things) is the relative loudnesses of the different harmonics.
There are other factors affecting timbre, such as the relative phases of the harmonics of the wave, as well as the presence or absence of other waves combined each with its own set of harmonics. But I believe the relative loudness of the overtones is the crucial factor in a sound's timbre or colour.
The harmonics of an accoustic instrument depend on the materials of which the sound generating components are made as well as the shape of the sound box of the instrument. The shape and materials of a violin's sound board, the hairs of its bow, the make of the strings, affect the harmonics of the instrument, and so despite the kinship different violin instruments sound different from one another. The same is true for most other instruments. Even playing techniques affect the tones' timbre.
Now when we want to look at a representation of the harmonics of a given wave, we have to use a diagram that plots Amplitude against (not time as in the more familiar wave diagram - called time domain diagrams but against) Frequency.
Based on the aforementioned, we should expect to see that at the the frequency of the fundamental the amplitude has the highest value, and that the other overtones appear in the graph as spikes in amplitude right where each overtone's frequency is on the horizontal axis. Here is a sample diagram of the harmonics of a wave produced on a VST synth and plotted by the FREE fre(a)koscope 0.8 spectrum analyzer plugin,
The tools that let us look at a wave's harmonics in this way are called spectrum analyzer, which are desendants or cousins of the oscilloscope which plots the Amplitude of a wave (vertical axis) against the time axis (horizontal axis).
Note the name spectrum here is not used in vain. Because as you see in the picture, the graph actually shows us a spectrum of frequencies, with spikes where overtones occur in the wave. This is very much like the spectra we get when analyze chemical elements and compounds to get to see which frequencies of light they emit (or absorb i don't remember) in the visible light band of the electromagnetic spectrum. Very much in the same vain, the color of an object is also those portions of visible light that are reflected or emitted by it.
Each object has its own spectrum (ie, collection of frequencies that make up its color) In the case of material objects , the frequency is that of electromagnetic waves, in teh case of sounds, the frequencies are those of accoustic pressure waves in the air, and in the case of synthesized sounds, they are frequencies of an electrical current signal.
Therefore, as my friend has noted, it does make perfect sense to use colour when describing a musical sound.
The images that follows as the one above, are of the same synth preset, but the harmonics look different , the peaks more or less are the same but the all sorts of amplitude changes occur to different frequencies,
This is because, the harmonics , and therefore the timbre of a sound vary with time, as the instrument is used to play a melody.
The images below show the frequency spectrum for a software electric piano playing C3 and C4 respectively,
In the latter figure the resolution of the sampling window was increased adding sharpness to the frequency spectrum graph, (chalk one up for the software designers and engineers),
This image is of a software organ playing a C4 (Do 4) note ,
The images used here are screenshots of the free fre(a)koscope 0.8 FFT-based realtime spectrum analyzer plugin, available on the FFT tools page at smartelectronix.com , a collective of quality-friendly audio and music software developers. ... Read more
