The Sound page. Paragraphs in this page are: Sound physics The sense of hearing Sound parameters Musical instrument families Harmonics The Well Tempered tuning The Cents Sound physics Well, this page will not dive deep in this issue, but it would be perfect to intrigue the readers curiosity to search and know further. Sound is a wave. A wave is a method for transferring energy, in which the transfered energy does not follow the carrier's direction. For example, when we see sea waves, water follows a vertical close-to-ellipse motion, while the wave itself moves horizontally. Another phenomenon, electricity, has similar interesting issues. When we apply 2 volts in a metal tube, the elecrons move from the negative to the positive pole transferring energy, but seeing this in our dimensions, a single electron moves really a very small distance, while the wave itself moves in the speed of light! The electrone that was first "moved" will never be the same with the last one that reaches the other pole 1/100000000 sec later. So, what really carries the wave? In the elecromagnetic research in physics, 1 century ago, a strange "substance" was assumed to exist that would carry the light, which is an elecromagnetic wave from a point of view, called "Ether". This fictionary "Ether" had to be thick enough to allow light to travel for billions of years, while thin enough for planets and suns to move inside it. Needless to say, that the assumpsion of Ether was later abandoned, since physics develloped enough to get rid of it. Light is an electromagnetic wave that travels in the void. Sound however is not. In the void, the sound wave stops. Sound needs matter as a carrier. The vibration of matter helps the sound wave move in it. think of this vibration as instant pressing-depressing between molecules. the next molecule does this vibration in a very small lag, so that in our dimensions we see the vibration itself "move". So, the sound wave moves in a certain speed. The speed is relevant to the matter thickness. Sound moves faster using the ground than the air. In the past, warriors connected an ear to the ground to hear enemy cavalry presence much earlier than seeing them or hearing them by air. In the air close to ground, sound moves 340 m/sec. It takes approximetly 3 secs to travel a km. Bass waves last longer than tremble. Photo by: aethro-kinematics.com The Sinus sound wave, a single harmonic, is like the above picture. The wave has parameters like: Speed, Wavelength, Period, Frequency, Speed is easy to understand, Frequency is 1/period, meaning simply how many waves pass the spot per sec. Period is the time a single wave travels through a single point, Wavelenght is the length of a single wave. But the wave is both the compression and decompression, not just the half. So, Speed is Wavelenght/Period therefore Speed=Wavelength*Frequency. The Tone A (La) 440 hz has a Wavelength of 340/440=0.77m If a 20cm brickwall seems thin to a middle tone like this, imagine the relation to a really bass tone! The y axis inticates the intensity of the wave and therefore the energy that it carries. So, a quieter sound would be more in the x axis and would appear more "horizontal", a louder sound takes space in the y axis and appears more vertical than the quieter sound. I hope you got more curious already. The sense of hearing Our goal is music theory, not sound physics. If sound is generated and noone is to hear it, it is just if there was no sound at all. Music is not all about sound. Our hearing is a large part of it. For example, when we hear a sound and then another of a double frequency, we understand this as an octave. This ability makes us understand tones repetively as the same but higher by octaves. Furthermore, a sound is nearly never a single harmonic (sinus) wave. But despite all the complexities inside the wave, we understand a basic frequency, therefore tone, and we merge all complexity in what we call "timbre", which is the quality that differs e.g. the sound of a violin to the one of the clarinet. If a base frequency doesn't exist, then we hear 'noise", but despite that, we can still feel noise differences. The human ear frequency range is about 20hz - 20khz (20 thousand herz). A very bass (subsonic) sound could indeed escape the ear, but our body would feel it. The ear can respond to a wide energy range. The mosquito buss we hear is a millionth of a Watt! 60 million buzzes would be able to light our bedroom lamp. After we marvel at the pic below, let's get to the next paragraph. Photo by: www.tutor.com.my Sound parameters Being logical beings, we surely can distinguish differences between sounds in an abstract way. There are 5 parameters: Intensity quiet or loud Duration short or long Frequency bass or tremble Timbre the distinged sound uniqness Clarity tone or noise The clarity is the most obscure, but we see it in everyday life. A sound without tonal clarity is not a tone; it may be noise or clatter. Hitting a drum cymbal, produces a sound without too much clarity while hitting a note in a vibraphone produces a fine tone with its own timbre quality. "Clear" or not, every sound can be used to produce music, but sound itself is not sufficient, as we will see in other areas of theory. Musical instrument families We will put aside elecronic methods for producing a sound, as the simple ones (oscillators, filters, resonance etc.) are simple enough to understand, yet already too old, therefore useless for knowledge as for producing music in the present time. Technology itself goes so fast that 10 years from now usually appears as history. The natural sound initialization is spread among many methods, making whole musical instrument families. Percussion Possibly the oldest method - apart from using voice itself of course, to hit a piece with another and produce the desirable (hopefully) event. Percussion instruments vary from single piece (sticks or metal) to complex instruments (drum) or even combination of simple ones, like the xylophone. Percussion instruments can produce clear sounds as well as non-clear ones. Using percussion, the first aquaintance to music is rhythm itself and because of the simplicity of use, percussion is the most direct to understand and manipulate. Percussion training should be a must for any child that starts learning music. In older times, music teaching tended to overload children with theory information that in this age appears as stale, way before making music a fun activity, which is definetly wrong for one of the simple reasons that theory itself may be detested and this is bad in the long run. Gracefully, modern teaching usually corrects this error. The sound of the percussion instruments derives from the piece itself that is hit. Smaller mass generates higher pitch. Woodwind The first pneumatic instrument family and possibly the second oldest method, simple enough for crude instruments, but requiring much effort for producing a satisfactory sound for the requirements of our times. This method can be passive also. A Big shell that we find in the seashore produces a beautiful sound just by the wind but it can be heard only if we put it close to the ear. Flutes and clarinets are examples of modern woodwinds. Wood was a fine material for a long time for woodwind making, but the saxophone family and the modern flute are bright exceptions to this rule. Sound is always produced with the help of a mouthpiece. Even in flute, the lips have to be in a special position against the mouthpiece in order to produce sound. in other words, sound is not produced directly. The mouthpiece can have a hole (flute), single reed (clarinet) or double reed (oboe). These types are the most common ones. The sound  of the woodwind instruments derives from the air itself inside it. By opening and closing holes, the air mass and length is altered, therefore different pitch is produced. But controlling the air speed blown inside the instrument is another way of changing tone. This is a very common and required technique for the flute and can alter the sound at least an octave. Brass The second pneumatic instrument family differs from the first in the way sound is generated. Unlike woodwind, sound in brass instruments is generated directly by the lips "vibrating" on a rim connected to the tube. Trumpets, trombones etc. are among the brass family. The sound of the brass derives always from the whole air inside the tube. No holes are used and because of the length of such a tube, it is a tradition over the years for it to be made of metal (with exceptions of course) in order to "fold around" and save length. Pitch can be changed in two ways in brass instruments: 1) Lip stretch: Here the lips produce other frequencies. Worth mentioning is that the tones follow the harmonic pattern: tone, octave, perfect fifth perfect fourth, major 3rd, minor third, minor small third, big tone, small tone etc. Because not all of these tones are always in the modal system of various eras, certain harmonic positions are more common and fine tuning as well as transposed instruments may be needed. 2) Altering the tube length: ... but still not with holes. Tube inside tube (trombone) or valves adding various lengths (trumpet) are used to change the length. It appears that by crafting experience over the centuries, holes and non metal material have been abandoned because the sound would not be clear or bright enough, or the instrument itself would not be very practical for use. Imagine a 4m straight wood made "brass" instrument... Strings A streched string can be "unbalanced" in 3 ways: hit (dulcimer), plucked (violin), pulled (guitar). Using the bow, the plucked sound is stable, while hitting and pulling a string is almost instantaneus and sound starts fading right away. The sound of the strings derives from the string itself. However, a bare string simply can not "arouse" many air molecules around it and a resonator (void curved shape) must be connected to the strings to produce a satisfactory sound. The quality of the sound is directly affected by the quality of the resonator. Sound will be produced if the string is stretched enough. A "dead" string will produce no sound, as a minimum tension is needed for the string to vibrate. The pitch is reverse to the string mass: Lower mass produces higher pitch. So: If in a tensioned string we: shorten the string length then mass is diminished and pitch goes higher add to the string tension then mass is diminished and pitch goes higher The length is used primarily when playing and the tension is used for tuning the instrument. String instruments usually have many strings tuned to certain intervals between them. The violin is one example. With four strings (perfect 5th steps) all tones are produced in a fretless (not tone-specific) neck. The guitar in the contrary, is tuned in another way and uses a fret neck. The fretless quitar is not uncommon though. The harp is one string instrument though that use many strings, one for a diatonic (not chromatic) tone, repeating in octaves. The tone's in-all-octaves pitch is controlled via pedals. String instruments come with families. The violin family etc. Strings are mainly "inside" instruments, while percussion and woodwinds are used very effectively in the open. Keyboards We are not talking about electronic keyboards of course. The first keyboard recorded in history is the Hydraulis, invented by Ktesibios in 300 B.C in Alexandria. Link: http://www.archaeologychannel.org/hydraulisint.html Keyboards generate sound just like the other instrument families. The presence of the keyboard mechanism makes the actual sound production easier while in the same time "loads" the player with more complicated tasks due to the augmented capabilities of the instrument. The main capability is the completely separated full-note polyphony. String keyboards are the piano (pianoforte) and the harpsichord. The piano uses a string-hit mechanism capable of producing quiet (piano) and loud (forte) sounds. The harpsichord uses a string "pulling" mechanism that does not alter sound volume. Interesting issue is the sound quality of a piano, though. Not only the strings or the resonator alter the sound, but also the hardness or softness of the hammer tips. Hard hammer tips produce a brighter sound, while softer ones favour a darker sound. The piano age can be determined by this brightness, because the velvet overlay additions on the hammer tips get pressured and harden as years pass. Pneumatic keyboards are the various pipe organs. The mechanism though was hydraulic or mechanic in nature. Originating from their ancestor, the hydraulis, they were greatly developed in Western Europe and their just auxiliary or perculiar initial role became a full time one in music playing and composing. Read: http://panther.bsc.edu/~jhcook/OrgHist/begin.htm The sound of the pipe organs can vary greatly. Using knobs, tubes can be activated-deactivated , altering the harmonic quality, thus changing the sound timber very effectively. Organs often have 2 or 3 keyboards and pedals to produce sound, taking great advantage of different timbres and volume levels. The big ones were specifically designed to fit in the chamber they were planned for (e.g. church) therefore unmovable. There is also a percussion keyboard: the celesta. This instrument uses small metal pre-manifactured pieces that get hit by a hard hammer. Although percussion, the sound is far away from loud. Harmonics Let's now take a tentioned string and pull it to make sound. The most easy experiment is to practice on a guitar. The half of a string produces the same tone an octave higher, the 1 third produces a perfect fifth and an octave, which leads to the fact that a 2/3 of the string will produce the same as in 1/3 but an octave down, therefore a simple perfect fifth. But for the string ratios to vibrate, we do not have to put our fingers. They do vibrate by their own! In other words, as the whole of the string vibrates, the 1/2, 2/3 do too and so on. They just do not have the intensity of the whole, so their "tones" are merged in our acoustic hearing as an internal quality of the sound, the one that distinguishes it between two different musical instruments that play the same tone, the "timbre". Harmonics is a wide issue applying also to electrical and elecronic study in Physics. The 1 to 16 harmonics order. The timbre of a sound is depended on the intensity ratio the harmonics have among them, and it is better to calculate this against the first harmonic. So, when all the ratio is stable and the base harmonic is quieter, the same sound is just in a lower intensity. The 1st harmonic is the base tone frequency and the one that is giving the pitch of the tone. The multiples of 2 are the same tones octaves up. Because this means 2,4,8,16,32, more and more tones "fit" between them. All beyond the 15/16 ratio are less than the so called "semitone" as defined in our musical system. tones with + are a little higher. tones with - are a little lower. Why is that? As the ratio "shrinks", the intervals do also. So, not all the "appearing" 3rd minors are the same, and not all the 2nd Majors. Most harmonics are "out of scale" and in reality, there are only some ratios that "suit" for mode or scale production. The use differs between different musical systems. The semitone is thankfully not of much concern. It is 15/16 and we were all happy till till the end of the Modal System. The tone, though gave a headache considering mode-scale usage and tuning even in the Modal System age. There are simply 2 tones. The "big" 8/9 and the "small" 9/10. Using both, created a very difficult issue considering transposition and tuning keyboard instruments, until Werkmeister proposed the "Well Tempered tuning" that equalized all intervals as multiples of the one and only semitone interval. This issue will be mentioned later. Here is a 2nd example of the scale - harmonic incompatibilities that are never met only in theory. In this example, the E created by perfect 5th steps is a little higher than the one created in the harmonic order. Trumpet playing always considers this issue. Lower sounds are richer than high ones. We can see this trying low piano tones and compare them to the higher. This happens because in low sounds, more harmonics are within the hearing range. Considering all sound produced in non elecronic instruments, the lower harmonics, and primarily the first, have greater intensity than the upper ones. A sound produced in an electronic instrument defying that rule, would seem "strange". The above is valid to pipe organs too. Additionally, the pipe organs do not just add plain harmonics (1/3, 1/4) but also "complicated" ones i.e. 2/3 3/4 that are more close to the base tone. Thinking now about sound generation, string cords are more close to lines, woodwind and brass are close to cylinders and cones and percussion can be much more complicated (circle areas, cubes etc.). When we hit a drum cymbal, so many areas of it vibrate, that we can not speak of simple harmonics any more. The Well Tempered tuning In 1600, from the western Modal System emerged the Tonal Music System. Being as economic as this page needs, the new system brought new ways of creating music, and mainly the "modulation", where not only the mode changes, but also the central tone, allowing ideas to cyrcle freely inside the note range. Because of this, older tuning was put in question; when changing tone, the big and small whole tones had to change in order for the new tonality to be correctly heard. Instruments like the violin did not have much problem because they are tuned by perfect 5ths and are fretless, so the alteration could be easily done. Woodwinds and Brass could also alter the tuning and use different fingerings in order to alter the tone. But fretneck strings and fixed tuning instruments like the Harpsichord had a hard time following the othe instruments. Werkmeister then tried to "fix" the 5ths: 12 fifths cyrcle the 12 notes: C G D A E B F# C# Ab Eb Bb F C. 2/3 perfect 5ths resulted to the top C to be slightly "higher" than the base one. So, the difference was spread among all the 5ths fixing the steps alltogether. Then, the semitones got all equal, a little lower than 16/15, and all whole tones equaled to 2 semitones. The formula is this: If a tone has a freq. of a, then an octave up is 2a. a semitone from a is 2^(1/12) "12th square root of 2". All intervals are generated based on the chromatic distance. A perfect 5th (7 semitones) instead of being 3/2, now is 2^(1/12*7) "the 7th power of the 12th square root of 2". This tuning, although completely artificial considering harmonics, allowed total freedom to explore the new capabilities of the Tonal Music System, because it allowed to transpose everywhere (meaning 24 keys - 12 major and 12 minor). See also: http://www.answers.com/topic/well-tempered-clavier The Cents By the 20 century, Western European Music met all other cultures and the affection in music was bidirectional. What emerged from the mixing was a need to analyse the different music "materials" and primarily the ways of tuning. The interesting part is that all tuning is artificial in all cultures, although not the same necessarily. imagine (and hear) 57 tones per octave, or quartertones, or pentatonics based on perfect 5ths and so on. The fact that we may not like the tuning of others is of no concern, they may not like ours anyway. The evolution of electronics opened more flexible ways to structure a new material from bottom up and try it. how to categorize this material though? For this reason, a climax was created that divided a single well-tempered semitone in 100 tones, the so called cents. Imagine now: If For C, C# is 100, D is 200, etc. G is 700, etc. C is 1200. The impression that frequencies are added instead of multiplied is because this climax is logarithmic. C, C1200, C2400 C3600: freq. of C3600 is not 3 times freq. of C1200. The cents provide a "digital" way of measuring, though very efficient because the 100 steps division inside a semitone produces a very dense resolution.