The Science of Music Dr David Hamrick Zale

The Science of Music Dr. David Hamrick Zale Library at Paul Quinn College 16 November 2012

What is Sound? Sound is a mechanical wave • It moves through a medium • Like waves in water • Or earthquakes through the ground • We usually think of air as the medium • Can travel through other gases • Can travel through liquids • Can travel through solids (varies depending on material) • Why does helium make your voice sound higher? • Helium is a lower-density medium • More on this later!

What is Sound? Sound is a compression wave • • Vibrating body transfers energy to medium Medium is compressed, then released The “wave” is really a series of high and low pressure areas It’s easier to represent this as a 2 -D wave The Speed of Sound • Density of the medium determines how fast it can compress/decompress • The average density of air allows a wave to travel about 768 mph • Helium’s lower density allows sound to travel 3 x faster!

Measuring the Wave = Complete cycle of compression/decompression • In a 2 D representation, 2 points at same place in the cycle • Usually measured from midpoint to midpoint

Measuring the Wave Frequency = Number of waves per second • • Measured in “Herz” (Hz), “kilo. Hertz” (k. Hz), mega. Hertz (m. Hz) In musical terms this is called “pitch” We call shorter waves (high frequency) “high” pitches We call longer waves (low frequency) “low” pitches

Measuring the Wave Amplitude = Intensity of each wave (power exerted) • In the image below, the frequency (pitch) remains the same while the amplitude (volume) increases and decreases • Measured in “decibels” • Zero decibels (0 d. B) is just below range of human hearing • The decibel scale is logarithmic, not linear • Every 10 decibels describes 10 x power increase • 20 d. B is not twice as loud as 10 d. B, it is 10 x as loud! • In musicals terms this is called volume or dynamics

Measuring the Wave Radio works by modulating either frequency or amplitude • Radio waves are electromagnetic, not mechanical, but described the same • Amplitude Modulation (AM) = • Constant frequency • Changing amplitude • Frequency Modulation (FM) = • Constant amplitude • Changing frequency • Also much higher frequency than AM • Shorter waves make FM signal easier to bounce around corners, inside buildings • AM limited by amount of amplitude change you can force • FM carries more complex signals (stereo & quadrophonic)

What We Can Hear • Human hearing can detect an amazing range of amplitude • Normal conversation (about 50 d. B) has an amplitude 1, 000 x the hearing threshold (0 -1 d. B) • Jet engine (about 100 d. B) has an amplitude 100, 000 x the threshold • Human hearing can also detect a wide range of frequencies • About 20 Hz to 20 k. Hz is the typical range • Lowest note on piano (A 0) is 27. 5 Hz; highest (C 8) is 4. 2 k. Hz • Animal hearing can go far beyond ours! • Most dogs hear about 40 Hz to 60 k. Hz (about 3 x human range) • Bats use echolocation calls at frequencies up to 150 k. Hz • Baleen whales vocalize at about 10 -30 Hz, at up to 80 decibels!

Music or Noise? The Role of Harmonics • Almost all sounds are a mix of a large number of frequencies • A sound made of a single-frequency wave sounds artificial • So what is the difference between a musical tone and noise? • The musical tone has a regular frequency • The musical tone is composed of waves that fit together easily

Music or Noise? The Role of Harmonics • How frequencies fit together in a musical pitch • Which wave is the loudest? Which has the highest pitch? • What is the ratio or proportion between the two frequencies? • Why doesn’t it make two different notes? • The wave with greatest amplitude will sound like the “real” note • The shorter wave fits within the longer wave and reinforces it • See examples at UNSW Physclips: adding harmonics, composite tone

The Harmonic Series Harmonics: frequencies that naturally combine as a musical pitch • Discovered by Pythagoras in the 6 th century B. C. (? ) • The lowest tone (longest frequency) is called the “fundamental” • Each harmonic is a multiple of that fundamental’s frequency First Five Harmonics of the Pitch A 0 Pitch name Frequenc y Interval above previous pitch E 3 (two octaves & 5 th) 165 Hz Minor 3 rd C#3 (two octaves & major 3 rd) 137. 5 Hz Major 3 rd A 2 (two octaves) 110 Hz Perfect 4 th E 1 (octave & 5 th) 82. 5 Hz Perfect 5 th A 1 (one octave higher) 55 Hz Octave A 0 (lowest A on grand 27. 5 Hz (Fundamental)

The Harmonic Series This video shows a real-world demonstration using an oscilloscope

The Role of Harmonics in Timbre • “Timbre” is the quality of a musical pitch • What is the difference between a middle “C” played on a piano, or sung by a woman, or sung by a man? • Same fundamental pitch, different combination of harmonics • Why does your own voice sound funny in a recording? • You are used to hearing your voice through two media: • Through the surrounding air, into your ears • Through your own head (conductive hearing) • A recording device is only recording the sound in the air • The recording device is limited to the frequencies it can detect • The playback device is limited to the frequencies it can reproduce • Example: telephone audio is only 300 Hz to 3. 4 k. Hz (saves bandwidth!)

What is Harmony? Combination of two or more different notes at once • • Distance between two notes is the “interval” Combination of intervals (3 or more notes) is a chord Which ones sound good? Why? We tend to prefer the intervals at the beginning of the harmonic series • Simpler ratios; harmonics of each note clash less

What is Harmony? The first interval is called the octave (8 va) • Frequency ratio is 2: 1 (top note 2 x frequency of lower note) • Harmonics of each note are the same—sound like same note • Most universal interval in all music (men, women sing together at 8 va) • Scales repeat at the octave (start the series of notes over again) • In letter notation, each note of an octave is same letter (low C, high C)

What is Harmony? The next two intervals are the 5 th and 4 th (2 -3, 3 -4 in chart) • After the octave, these are the most universal intervals • Most scales split the octave with a step at this point (3 in chart) • 5 steps from bottom to top notes of 5 th (2 -3 in chart) • 4 steps from bottom to top notes of 4 th (3 -4 in chart) • Many kinds of folk music use the octave, 5 th, and 4 th as harmony • 5 th is a 3: 2 ratio (frequency of top note is 1½x that of lower note) • 4 th is a 4: 3 ratio (frequency of top note is 11/3 x that of lower note)

The Octave, Fifth, and Fourth Instruments using this combination go back to ancient times!

The Octave, Fifth, and Fourth The drone pipes on bagpipes are tuned to make this combination:

The Octave, Fifth, and Fourth In Indian raga music the tambura plays this combination as accompaniment to the sitar soloist

The Octave, Fifth, and Fourth The Western tradition of harmony began during the Middle Ages with the use of these intervals:

The Major and Minor Thirds The next intervals up the harmonic series are the 3 rds • These come in two sizes: major (4 -5 on chart) and minor (5 -6 on chart) • Both called 3 rds because take up three notes in scale (C-D-E, E-F -G) • The major 3 rd has a 5: 4 ratio (frequency of top note is 1¼x that of lower) • The minor 3 rd has a 6: 5 ratio (frequency of top note is 11/5 x that of lower)

The Major and Minor Thirds The major chord • • Major 3 rd joined with minor 3 rd (4 -5 -6 in chart) Why do we like this sound? It occurs naturally in the harmonic series The middle note splits the difference in frequencies of the outer two… • Just like the 5 th splits the difference in frequencies in an octave

Where to next? At this point in the harmonic series, cultures took different paths • Some notes in the harmonic series weren’t used in Western music • Notes marked in blue in the chart are too flat (low) to fit into our scales • The note marked in red is too sharp (high) • Obviously the intervals involving these notes won’t fit either This is a cultural preference (and matter of conditioning!) • Music of Middle East, Southeast Asia has used these notes & intervals • Several different sizes of 3 rd and 2 nd, not just major and minor

The Major and Minor Seconds Last two intervals we need are the seconds (two adjacent notes) • Western music uses sizes most common in upper end of the harmonic series • Major 2 nd (8 -9 on chart) • Commonly called a “whole step” • Interval 9 -10 is almost a major 2 nd but is a little flat • Minor 2 nd (15 -16, 16 -17, 17 -18, 18 -19) • Commonly called a “half step” • Intervals on high end of the series are actually successively smaller, but the differences are within the threshold of our ability to detect

Building Scales What is a scale? • • “Scale” is from the Italian “scala, ” and means “ladder” A way of climbing up and down in pitch during a melody The “rungs” of the ladder are the individual notes Can be fixed in many different positions! • Modern Western music uses major and minor • Karnatic (South Indian) music has 72 different melas (scales) • In many musical cultures, certain scales are associated with certain moods • Common ground across cultures • Every theory of scales uses divisions of the octave (Impossible to avoid!) • Every(? ) theory of scales splits the octave at the 5 th • Almost every scale is either 5 or 7 different notes

Building Scales • The Pentatonic (5 -note) Scale • Found in folk music and children’s songs around the world • Also fundamental to blues, jazz, rock, pop music • Major Pentatonic • Made of only 2 different intervals: major 2 nd, minor 3 rd • Called “major” because of emphasis on major 3 rd (DO-re-MI) • Black keys on piano are arranged (by coincidence) in major pentatonic • Common arrangement is: maj. 2 nd, min. 3 rd, maj. 2 nd, min. 3 rd

Major Pentatonic Many (Most? ) children’s songs use pentatonic scales. Note that the child is most in tune on the octave & 5 th (bottom, middle, and top notes of the tune). These men are celebrating their safe return from fighting the 2009 La Brea forest fire in California. The Irish hymn “Rop Tú mo Baile” (“Be Thou my Vision”) is mostly pentatonic.

Another Form of Major Pentatonic The same intervals can be ordered: maj. 2 nd, min. 3 rd, maj. 2 nd, min. 3 rd “Arirang” is a famous folk song in Korea

Minor Pentatonic • Arranges intervals: min. 3 rd, maj. 2 nd, min. 3 rd, maj. 2 nd • Called “minor” because of emphasis on min. 3 rd (LA-DO)

Blues Scale and the Minor Pentatonic One of the earliest forms of the blues scale probably came from adding minor 2 nds to the minor pentatonic. Big Mama Thornton, “Hound Dog” (the original version)

Minor Pentatonic using Minor 2 nd • Some minor pentatonic scales use minor 3 rds, major 2 nds, and minor 2 nds • Particularly common to folk music of Southeast Asia • A common arrangement is: maj. 2 nd, min. 3 rd, min. 2, min. 3 rd One form of the Japanese hirajoshi scale This tune is “Sakura” or “Cherry blossom. ” The cherry tree is a national symbol of Japan.

Western Seven-Note Scales • European music based on 7 -note combinations of major, minor 2 nds • From ancient Greece through the Western Renaissance, there were several different 7 -note scales or “modes” • In the modern period, most Western music uses just 2: major and minor • Some folk and popular music still uses the older modes Maj. Min. Maj. 2 nd 2 nd Min. Maj. nd 2 nd 2 C major scale Min. Maj. 2 nd 2 nd Maj. nd nd 2 2 2 nd C minor scale

Western Seven-Note Scales One of the other modes that turns up often is called “Dorian” • Like minor, except minor 2 nd moved from 5 th-6 th notes to 6 th 7 th notes • Common in folk music, rock, jazz Appalachian hymn “Wondrous love”

Western Seven-Note Scales Phrygian mode was common in the Renaissance, and was revived in modern jazz • Sounds neither major nor minor (but leans toward minor) • Unusual for having a minor 2 nd above the key-note Psalm tune by Thomas Tallis, 1567

Middle Eastern & Indian Scales • Scales of the classical music of Middle East, India & Pakistan are based on smaller intervals than used in Western scales • Theoretically divides the octave into quarter-steps, not half-steps • In addition to min. 2 nd (half-step) and maj. 2 nd (whole-step) … • ¼-step • ¾-step • 1¼-step • These intervals are also in the harmonic series, just not used in West • Concept of “scale” is more complicated • Still 7 -note scales, but many different forms (not just major & minor) • Scale includes not just series of notes, but mood, style, melody

Scales in the Middle East Arabic maqām (Turkish makam) • Made by stacking two tetrachords (four-note groups) • Lowest, highest notes are octave, really just 7 different notes • Upper tetrachord usually starts a perfect 5 th above octave Many maqām, but some little used • Best-known in the West is the “Hijaz” • Lower tetrachord is the “Hijaz” tuning

Scales in the Middle East The “Bayati” maqām • Like a Western minor scale except… • Uses two ¾-steps at the bottom instead of whole-step, half-step • That is, the second note from lowest sounds ¼-step flat to Westerners • If this is not learned from childhood, difficult to hear, Maj. much. Maj. ¾ ¾ less to sing! 2 nd step Min. 2 nd Maj. 2 nd

Scales in Indian Music South Indian Karnatic tradition (other is Hindustani) • Octave divided into 22 shruti (smallest perceptible difference in pitch? ) • Scale (mela) made of combining two tetrachords (as in Middle East) • “SA” and “PA” stay the same (octave and 5 th!) • “MA” has a low position and a high position • “RI, ” “GA, ” “DA, ” and “NI” each have a low, middle, and high position

Scales in Indian Music Mela or thaat (Hindustani) is the foundation for a raga • Raga is not only scale, but melodic ideas, style, mood, rhythmic patterns • Each raga is associated with a time of day, sometimes also with a season • Considered inappropriate (even unlucky!) to play a raga at the wrong time • Improvisation is essential to raga, will never be played same way twice Tansen, the great 16 th-century musician, was said to have made it rain by playing a raga for monsoon season!

Scales in Indian Music Raag Khamaj • Built on one of the scales common to the ancient Hindustani thaat and more modern Karnatic melas • To be played in the mid-evening • Scale equivalent to: • Major scale when ascending, but… • 7 th note flatted when descending Performance by Ravi Shankar (sitar) and his daughter Anoushka Shankar (sitar); player of tabla unidentified This flat-7 scale is called “Mixolydian” in Western music.

Scales in Indian Music This chart shows all 72 Karnatic melas (all possible combinations of note positions)

From the simplest drone harmony to the most complex jazz chords, from the pentatonic scale to the 72 Karnatic melas, everything comes back to the harmonic series. As different as our music is, it all has elements in common. THE END

Works Consulted • • • Sound waves and music. The Physics Classroom. http: //www. physicsclassroom. com/class/sound/ Music acoustics. University of New South Wales. http: //www. phys. unsw. edu. au/jw/basics. html “Hearing range. ” Wikipedia. http: //en. wikipedia. org/wiki/Hearing_range Physics of music notes: Frequencies for equal-tempered scale. http: //www. phy. mtu. edu/~suits/notefreqs. html “What is the frequency response of the NAPSTN? ” Hubtechinsider. http: //hubtechinsider. wordpress. com/2009/06/03/what-is-the-frequency-response-of-the-northamerican-public-switched-telephone-network/ Courtney, David. “Rag Khammaj (Khamaj). ” Indian Classical Music. http: //chandrakantha. com/raga_raag/khammaj/khammaaj. html

Image Credits • • • • • http: //commons. wikimedia. org/wiki/File: Ripple_effect_on_water. jpg http: //commons. wikimedia. org/w/index. php? title=File: CPT-sound-physicalmanifestation. svg&page=1 http: //commons. wikimedia. org/wiki/File: Wave_frequency. gif http: //commons. wikimedia. org/wiki/File: Modulation_d%27 amplitude_figure_2. 2. 1. 3. png http: //commons. wikimedia. org/wiki/File: Amfm 3 -en-de. gif http: //images. tutorvista. com/content/waves/noise-music. gif http: //commons. wikimedia. org/wiki/File: Aulos_player_MAR_Palermo_NI 22711. jpg http: //en. wikipedia. org/wiki/File: C_major_pentatonic_scale. PNG http: //upload. wikimedia. org/wikipedia/commons/0/08/Green_harp_flag_of_Ireland. svg http: //commons. wikimedia. org/wiki/File: C_major_scale. PNG http: //commons. wikimedia. org/wiki/File: C_minor_pentatonic_scale. png http: //commons. wikimedia. org/wiki/File: Aeolian_mode_C. png http: //commons. wikimedia. org/wiki/File: Dorian_mode_C. png http: //upload. wikimedia. org/wikipedia/commons/c/ca/Hijaz_scale. png http: //en. wikipedia. org/wiki/File: Bayati. png http: //commons. wikimedia. org/wiki/File: Akbar_and_Tansen_visit_Haridas. jpg http: //commons. wikimedia. org/wiki/File: Melakarta. katapayadi. sankhya. 72. png “Rop Tú mo Baile” sung by Gareth Hughes. http: //en. wikipedia. org/wiki/File: Rop_tu_mo_baile. ogg