The Science of Music

The Science of MusicDr. David HamrickZale Library at Paul Quinn College16 November 2012- some music fundamentals (pitches, intervals, scales)- acoustical foundations of these fundamentals- discovery of these principles by various ancient cultures- connections to ancient mathematics, cosmology- are these universal? comparison of how these are applied in music of different cultures*Demonstrates connections between arts and sciences*Introduces the breadth of thinking and intercultural exchange in the ancient world*Shows universality of experience in some areas; challenges preconceptions in other areas*Illustrates influence of cultural conditioning of perception

1What is Sound?Sound is a mechanical waveIt moves through a mediumLike waves in waterOr earthquakes through the groundWe usually think of air as the mediumCan travel through other gasesCan travel through liquidsCan travel through solids (varies depending on material)Why does helium make your voice sound higher?Helium is a lower-density mediumMore on this later!

2What is Sound?Sound is a compression waveVibrating body transfers energy to mediumMedium is compressed, then releasedThe wave is really a series of high and low pressure areasIts easier to represent this as a 2-D wave

The Speed of SoundDensity of the medium determines how fast it can compress/decompressThe average density of air allows a wave to travel about 768 mphHeliums lower density allows sound to travel 3x faster!Use a slinky to demonstrate this3Measuring the WaveWave = Complete cycle of compression/decompressionIn a 2D representation, 2 points at same place in the cycleUsually measured from midpoint to midpoint

Measuring the WaveFrequency = Number of waves per secondMeasured in Herz (Hz), kiloHertz (kHz), megaHertz (mHz)In musical terms this is called pitchWe call shorter waves (high frequency) high pitchesWe call longer waves (low frequency) low pitches

Measuring the WaveAmplitude = 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 decibelsZero decibels (0 dB) is just below range of human hearingThe decibel scale is logarithmic, not linearEvery 10 decibels describes 10x power increase20 dB is not twice as loud as 10 dB, it is 10x as loud!In musicals terms this is called volume or dynamics

Measuring the Wave

Radio works by modulating either frequency or amplitudeRadio waves are electromagnetic, not mechanical, but described the sameAmplitude Modulation (AM) =Constant frequencyChanging amplitudeFrequency Modulation (FM) =Constant amplitudeChanging frequencyAlso much higher frequency than AMShorter waves make FM signal easierto bounce around corners, inside buildingsAM limited by amount of amplitude change you can forceFM carries more complex signals (stereo & quadrophonic)What We Can HearHuman hearing can detect an amazing range of amplitudeNormal conversation (about 50 dB) has an amplitude 1,000x the hearing threshold (0-1 dB)Jet engine (about 100 dB) has an amplitude 100,000x the thresholdHuman hearing can also detect a wide range of frequenciesAbout 20 Hz to 20 kHz is the typical rangeLowest note on piano (A0) is 27.5 Hz; highest (C8) is 4.2 kHzAnimal hearing can go far beyond ours!Most dogs hear about 40 Hz to 60 kHz (about 3x human range)Bats use echolocation calls at frequencies up to 150 kHz Baleen whales vocalize at about 10-30 Hz, at up to 80 decibels!Music or Noise? The Role of HarmonicsAlmost all sounds are a mix of a large number of frequenciesA sound made of a single-frequency wave sounds artificialSo what is the difference between a musical tone and noise?The musical tone has a regular frequencyThe musical tone is composed of waves that fit together easily

Music or Noise? The Role of HarmonicsHow frequencies fit together in a musical pitchWhich wave is the loudest? Which has the highest pitch?What is the ratio or proportion between the two frequencies?

Why doesnt it make two different notes?The wave with greatest amplitude will sound like the real noteThe shorter wave fits within the longer wave and reinforces itSee examples at UNSW Physclips: adding harmonics, composite tone

The Harmonic SeriesHarmonics: frequencies that naturally combine as a musical pitchDiscovered by Pythagoras in the 6th century B.C.(?)The lowest tone (longest frequency) is called the fundamentalEach harmonic is a multiple of that fundamentals frequencyFirst Five Harmonics of the Pitch A0Pitch nameFrequencyInterval above previous pitchE3 (two octaves & 5th)165 HzMinor 3rd C#3 (two octaves & major 3rd)137.5 HzMajor 3rdA2 (two octaves)110 HzPerfect 4thE1 (octave & 5th)82.5 HzPerfect 5thA1 (one octave higher)55 HzOctaveA0 (lowest A on grand piano)27.5 Hz(Fundamental)Multiply the fundamental (27.5) by 16 and you get A-440!11The Harmonic SeriesThis video shows a real-world demonstration using an oscilloscope

The Role of Harmonics in TimbreTimbre is the quality of a musical pitchWhat 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 harmonicsWhy 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 earsThrough your own head (conductive hearing)A recording device is only recording the sound in the airThe recording device is limited to the frequencies it can detectThe playback device is limited to the frequencies it can reproduceExample: telephone audio is only 300 Hz to 3.4 kHz (saves bandwidth!)What is Harmony?Combination of two or more different notes at onceDistance between two notes is the intervalCombination of intervals (3 or more notes) is a chordWhich ones sound good? Why?We tend to prefer the intervals at the beginning of the harmonic seriesSimpler ratios; harmonics of each note clash less

What is Harmony?The first interval is called the octave (8va)Frequency ratio is 2:1 (top note 2x frequency of lower note)Harmonics of each note are the samesound like same noteMost universal interval in all music (men, women sing together at 8va)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 5th and 4th (2-3, 3-4 in chart)After the octave, these are the most universal intervalsMost scales split the octave with a step at this point (3 in chart)5 steps from bottom to top notes of 5th (2-3 in chart)4 steps from bottom to top notes of 4th (3-4 in chart)Many kinds of folk music use the octave, 5th, and 4th as harmony5th is a 3:2 ratio (frequency of top note is 1x that of lower note)4th is a 4:3 ratio (frequency of top note is 11/3x that of lower note)

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

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

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

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

The Major and Minor ThirdsThe next intervals up the harmonic series are the 3rdsThese come in two sizes: major (4-5 on chart) and minor (5-6 on chart)Both called 3rds because take up three notes in scale (C-D-E, E-F-G)The major 3rd has a 5:4 ratio (frequency of top note is 1x that of lower)The minor 3rd has a 6:5 ratio (frequency of top note is 11/5x that of lower)

The Major and Minor ThirdsThe major chordMajor 3rd joined with minor 3rd (4-5-6 in chart)Why do we like this sound?It occurs naturally in the harmonic seriesThe middle note splits the difference in frequencies of the outer twoJust like the 5th splits the difference in frequencies in an octave

Where to next?At this point in the harmonic series, cultures took different pathsSome notes in the harmonic series werent used in Western musicNotes marked in blue in the chart are too flat (low) to fit into our scalesThe note marked in red is too sharp (high)Obviously the intervals involving these notes wont fit either

This is a cultural preference (and matter of conditioning!)Music of Middle East, Southeast Asia has used these notes & intervalsSeveral different sizes of 3rd and 2nd, not just major and minorMost music cultures have preferred a simpler system!

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

Building ScalesWhat is a scale?Scale is from the Italian scala, and means ladderA way of climbing up and down in pitch during a melodyThe rungs of the ladder are the individual notesCan be fixed in many different positions!Modern Western music uses major and minorKarnatic (South Indian) music has 72 different melas (scales) In many musical cultures, certain scales are associated with certain moodsCommon ground across culturesEvery theory of scales uses divisions of the octave (Impossible to avoid!)Every(?) theory of scales splits the octave at the 5thAlmost every scale is either 5 or 7 different notesBuilding ScalesThe Pentatonic (5-note) ScaleFound in folk music and childrens songs around the worldAlso fundamental to blues, jazz, rock, pop musicMajor PentatonicMade of only 2 different intervals: major 2nd, minor 3rd Called major because of emphasis on major 3rd (DO-re-MI)Black keys on piano are arranged (by coincidence) in major pentatonicCommon arrangement is: maj. 2nd, maj. 2nd, min. 3rd, maj. 2nd, min. 3rd

Major Pentatonic

These men are celebrating their safe return from fighting the 2009 La Brea forest fire in California.

The Irish hymn Rop T mo Baile (Be Thou my Vision) is mostly pentatonic.

Many (Most?) childrens songs use pentatonic scales. Note that the child is most in tune on the octave & 5th (bottom, middle, and top notes of the tune).Another Form of Major PentatonicThe same intervals can be ordered: maj. 2nd, min. 3rd, maj. 2nd, maj. 2nd, min. 3rd

Arirang is a famous folk song in Korea

Minor PentatonicArranges intervals: min. 3rd, maj. 2nd, maj. 2nd, min. 3rd, maj. 2ndCalled minor because of emphasis on min. 3rd (LA-DO)

Blues Scale and the Minor PentatonicOne of the earliest forms of the blues scale probably came from adding minor 2nds to the minor pentatonic.

Big Mama Thornton, Hound Dog(the original version)Minor Pentatonic using Minor 2ndSome minor pentatonic scales use minor 3rds, major 2nds, and minor 2ndsParticularly common to folk music of Southeast AsiaA common arrangement is: maj. 2nd, min. 2nd, min. 3rd, min. 2, min. 3rd

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 ScalesEuropean music based on 7-note combinations of major, minor 2ndsFrom ancient Greece through the Western Renaissance, there were several different 7-note scales or modesIn the modern period, most Western music uses just 2: major and minorSome folk and popular music still uses the older modes

C major scaleC minor scaleMaj.2ndMin.2ndMaj.2ndMaj.2ndMin.2ndMaj.2ndMaj.2ndMaj.2ndMaj.2ndMaj.2ndMin.2ndMaj.2ndMaj.2ndMin.2ndWestern Seven-Note ScalesOne of the other modes that turns up often is called DorianLike minor, except minor 2nd moved from 5th-6th notes to 6th-7th notesCommon in folk music, rock, jazz

Appalachian hymn Wondrous loveWestern Seven-Note ScalesPhrygian mode was common in the Renaissance, and was revived in modern jazzSounds neither major nor minor(but leans toward minor)Unusual for having a minor 2nd above the key-note

Psalm tune by Thomas Tallis, 1567 Middle Eastern & Indian ScalesScales of the classical music of Middle East, India & Pakistan are based on smaller intervals than used in Western scalesTheoretically divides the octave into quarter-steps, not half-stepsIn addition to min. 2nd (half-step) and maj. 2nd (whole-step) -step-step1-stepThese intervals are also in the harmonic series, just not used in WestConcept of scale is more complicatedStill 7-note scales, but many different forms (not just major & minor)Scale includes not just series of notes, but mood, style, melody ideasScales in the Middle EastArabic maqm (Turkish makam)Made by stacking two tetrachords (four-note groups)Lowest, highest notes are octave, really just 7 different notesUpper tetrachord usually starts a perfect 5th above octaveMany maqm, but some little usedBest-known in the West is the HijazLower tetrachord is the Hijaz tuning

Scales in the Middle EastThe Bayati maqmLike a Western minor scale exceptUses two -steps at the bottom instead of whole-step, half-stepThat is, the second note from lowest sounds -step flat to WesternersIf this is not learned from childhood, difficult to hear, much less to sing!

Maj.2ndMaj.2nd stepMaj.2ndMaj.2ndMin.2nd stepScales in Indian MusicSouth 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 5th!)MA has a low position and a high positionRI, GA, DA, and NI each have a low, middle, and high positionUnlike Western music, a RI sharp is not the same as a GA flat

Scales in Indian MusicMela or thaat (Hindustani) is the foundation for a ragaRaga is not only scale, but melodic ideas, style, mood, rhythmic patternsEach raga is associated with a time of day, sometimes also with a seasonConsidered inappropriate (even unlucky!) to play a raga at thewrong timeImprovisation is essential to raga, will never be played same way twice

Tansen, the great 16th-century musician, was said to have made it rain by playing a raga for monsoon season!The 16th century pandit (master)39Scales in Indian MusicRaag KhamajBuilt on one of the scales common to the ancient Hindustani thaat and more modern Karnatic melasTo be played in the mid-eveningScale equivalent to:Major scale when ascending, but7th note flatted when descending

Performance by Ravi Shankar (sitar) and his daughter Anoushka Shankar (sitar); player of tabla unidentifiedThis flat-7 scale is called Mixolydian in Western music.

The 16th century pandit (master)40Scales in Indian MusicThis chart shows all 72 Karnatic melas (all possible combinations of note positions)

This is what Karnatic music has, as opposed to just major and minor!41From 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 ENDWorks ConsultedSound 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.htmlWhat is the frequency response of the NAPSTN? Hubtechinsider. http://hubtechinsider.wordpress.com/2009/06/03/what-is-the-frequency-response-of-the-north-american-public-switched-telephone-network/Courtney, David. Rag Khammaj (Khamaj). Indian Classical Music. http://chandrakantha.com/raga_raag/khammaj/khammaaj.html Image Creditshttp://commons.wikimedia.org/wiki/File:Ripple_effect_on_water.jpghttp://commons.wikimedia.org/w/index.php?title=File:CPT-sound-physical-manifestation.svg&page=1http://commons.wikimedia.org/wiki/File:Wave_frequency.gifhttp://commons.wikimedia.org/wiki/File:Modulation_d%27amplitude_figure_2.2.1.3.pnghttp://commons.wikimedia.org/wiki/File:Amfm3-en-de.gifhttp://images.tutorvista.com/content/waves/noise-music.gifhttp://commons.wikimedia.org/wiki/File:Aulos_player_MAR_Palermo_NI22711.jpghttp://en.wikipedia.org/wiki/File:C_major_pentatonic_scale.PNGhttp://upload.wikimedia.org/wikipedia/commons/0/08/Green_harp_flag_of_Ireland.svghttp://commons.wikimedia.org/wiki/File:C_major_scale.PNGhttp://commons.wikimedia.org/wiki/File:C_minor_pentatonic_scale.pnghttp://commons.wikimedia.org/wiki/File:Aeolian_mode_C.pnghttp://commons.wikimedia.org/wiki/File:Dorian_mode_C.pnghttp://upload.wikimedia.org/wikipedia/commons/c/ca/Hijaz_scale.pnghttp://en.wikipedia.org/wiki/File:Bayati.pnghttp://commons.wikimedia.org/wiki/File:Akbar_and_Tansen_visit_Haridas.jpg http://commons.wikimedia.org/wiki/File:Melakarta.katapayadi.sankhya.72.png

Rop T mo Baile sung by Gareth Hughes. http://en.wikipedia.org/wiki/File:Rop_tu_mo_baile.ogg

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