Monday, 12 January 2009, 22:10
Today's the BIG DAY! we were getting back our olevels Higher Chinese results! it was thrilling cause every sms or call i thought was our much anticipated results. but still, we had our lesson on
HARMONICS!
And so, we were given a Guzheng, and adjusted the bridge of the longest string to the 100cm mark. Our task: Mark out ALL harmonics points of the string! To obtain the harmonic pitches, we basically need to pluck one end of the string while placing the other finger very lightly against different positions on the string. It wasn't easy listening for the harmonic pitches.
Briefly said, harmonics are basically the
relationship between frequencies of sound waves. In more complex terms, it is any of a set of partials that are whole number multiples of a common
fundamental frequency.
This set includes the
fundamental, which is a whole number multiple of itself (1 times itself).
*Pitch: pitch of a plucked string is dependent on three factors: the
length of the string, the
tension in the string, and the
mass density of the string (mass divided by string length). The pitch increase as tension increases, string shortens and mass density decreases.
-->This is no wonder the pitch of the guzheng is highest at the shortest and thinest string, where the bridge is the closet and therefore greatest tension.
Anyway, Shufen, Elaine and I worked together to figure the harmonics out and we got most of them right except for 2. not bad eh:D
The CORRECT
harmonic series/ ratio:(1/8), (1/6), (1/5), (1/4), (1/3), (2/5), (1/2), (3/5), (2/3), (3/4), (4/5), (5/6), (7/8)
Afterwhich, we were to identify the different notes of the scale along the string, taking the basic note plucked to be DOH, and calculating these harmonic ratio for each note. We were then to compare our findings with those calculated using the
pythagora's intonation.
*Pythagora's intonation: Back in Ancient Greek times, Pythagorus developed a mathematical connection between consonant tones. If a string is plucked it will play note of a certain pitch. If the string is divided in half it will play the exact same note an octave higher. Further subdivision of the string will result in an even higher pitch. An octave's pitch would be in a ratio of 2:1. If the string were divided into thirds, a new note with the ration of 3:1 would be produced by plucking the string. Pythagoras worked out a whole series of such mathematical ratio between notes, creating a scale with 8 notes A-G and 12 different pitches (including flats and sharps). Pythagoras's scale is often known as the circle of fifths. All frequencies on this scale can be produced by multiplying by 2 or 3. The scale looked good on paper, but it just didn't sound very good.
We found that F did not match as well as the other notes, and it was due to an error in calculation using pythagora's scale, starting from F# in the circle of fifths. Therefore anything after isn't as accurate.
An improved and more popular scale used predominantly worldwide now is the
equal temperament scale: octave divided into 12 equal parts, creating 12 semitones. (Chinese, dialect, Balinese music)
Other scale include
Just Temperament but is more complicated and problems occur as well.
*European divided one octave into 1200 cents (100Hz for evert semitone) for more accurate pitches.
*Indian music- 8 tones in one semitone
*
something interesting
Mr Ye teaching
Working hard on calculations kae! (iynyi-me, and nicolette)
Elaine (left) and Mag too!
Labels: Iynyi
Music, AWESOME
