Beats&

Balinese Gamelan Orchestras

Caroline Cullinan"INDONESIAN TRADITIONAL MUSIC." Hz36s Blog. N.p., 18 Feb. 2012. Web. 15 Mar. 2015.

When two plane waves with the same wavelength propagate in slightly different directions, their relative phase varies with position. At points where the two waves are exactly in phase, the amplitudes add, resulting in constructive interference. At points where the two waves are exactly out of phase, the result is destructive interference. The regions of constructive and destructive interference are separated by intervals of space and also intervals of time.

Beating by

Wave Interference

Hawkes, Robert, Javed Iqbal, Firas Mansour, Marina Milner-Bolotin, and Peter William. Physics for Scientists and Engineers: An Interactive Approach. Vol. 1. N.p.: Nelson Education, 2013. Print. Revised Custom.

When we listen to the two sound waves that have slightly different frequencies, the alternating constructive and destructive interference caused by the increasing an decreasing amplitude as a function of time produces a beat. The sound alternates between soft and loud.

The rate at which the amplitude varies is proportional to the frequency difference. However, when the frequency difference is large, the sound can be heard as two distinct tones, instead of one tone with a varying intensity.

Hawkes, Robert, Javed Iqbal, Firas Mansour, Marina Milner-Bolotin, and Peter William. Physics for Scientists and Engineers: An Interactive Approach. Vol. 1. N.p.: Nelson Education, 2013. Print. Revised Custom.

In the previous slide, the sound waves interfere constructively at first. Then, halfway across the graph, the waves are out of phase and interfere destructively because the red wave has completed two full cycles and the blue wave has only completed one and a half cycles. After two more red wave cycles, the waves are back in phase. The varying amplitude of the resultant wave (green wave) creates the beating sound.

When the two waves are close in frequency, the resulting tone has the mean frequency and the amplitude varies by the difference in angular frequency.

Hawkes, Robert, Javed Iqbal, Firas Mansour, Marina Milner-Bolotin, and Peter William. Physics for Scientists and Engineers: An Interactive Approach. Vol. 1. N.p.: Nelson Education, 2013. Print. Revised Custom.

Hawkes, Robert, Javed Iqbal, Firas Mansour, Marina Milner-Bolotin, and Peter William. Physics for Scientists and Engineers: An Interactive Approach. Vol. 1. N.p.: Nelson Education, 2013. Print. Revised Custom.

Beats are utilized by musicians when determining whether or not an instrument is out of tune. When musicians adjust the frequencies of their notes, they aim to stop the beating sound associated with an out of tune instrument. In doing this, musical ensembles ensure that all of the sounds produced by each instrument are agreeable.

Balinese Gamelan groups are unique from typical ensembles. Unlike most musical groups, a Balinese gamelan orchestra does not use the standard pitch (in Western classical music A is tuned to a frequency of 440 Hz). Balinese gamelan groups instead use a majority of bronze percussive instruments that are intentionally out of tune from each other. Instruments utilized include xylophone-like metallophones that vary in size and pitch, tuned gong chimes, large pitched gongs, and drums. Instruments in a Balinese gamelan ensemble are tuned in pairs, with one instrument tuned higher in pitch than its partner. The intentional detuning of notes produced by pairs of instruments results in a “shimmering” effect in the music.

Beats and Balinese Gamelan Orchestras

Frequencies of the tones of several gamelan orchestras in Bali

"Gamelan Bali." Pitch and Tuning of Balinese Gamelan Orchestras. N.p., n.d. Web. 15 Mar. 2015.

*Remember: Balinese gamelan orchestra music is intentionally out of tune

Question

One day,

*Hint: If two instruments are simultaneously played and produce detectable beats, then the frequencies are not identical. Instruments that are perfectly tuned to each other will reduce and produce a beat frequency of 0 Hz.

• First, find the the beat frequencies heard for each combination of bronze percussion instruments

Solution- Instrument 1 (350 Hz) & Instrument 4 (425 Hz)

Now, look for the combination of two instruments that has the greatest beat frequency. This combination of the two most detuned instruments produces the most out of tune sound. Thus, anyone listening to the 6 combinations of beat frequencies would be able to identify the most out of tune instrument combination (that with the largest beat frequency) as the combination that best resembles Balinese gamelan music.

Works Cited

"Description Of The Music Of The Balinese Gamelan." « Gamelan Tunas Mekar. N.p., n.d.Web. 15 Mar. 2015."Gamelan Bali." Pitch and Tuning of Balinese Gamelan Orchestras. N.p., n.d. Web. 15 Mar. 2015.Hawkes, Robert, Javed Iqbal, Firas Mansour, Marina Milner-Bolotin, and Peter William. Physics for Scientists and Engineers: An Interactive Approach. Vol. 1. N.p.: Nelson Education, 2013. Print. Revised Custom."INDONESIAN TRADITIONAL MUSIC." Hz36s Blog. N.p., 18 Feb. 2012. Web. 15 Mar. 2015."Review of Soniccouture Balinese Gamelan, a Sample Library for Kontakt Featuring a Semara Dana Gamelan." Rekkerdorg RSS. N.p., 14 Apr. 2008. Web. 15 Mar. 2015.