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AU / Music / MUSI 2750 / How many half steps is a perfect 4th?

How many half steps is a perfect 4th?

How many half steps is a perfect 4th?


School: Auburn University
Department: Music
Course: Music and Science
Professor: Ann knipschild
Term: Summer 2015
Tags: Music and science, Music, and Science
Cost: 50
Name: Music and Sciences STUDY GUIDE #2
Description: Music and science quiz #2 study guide Dr. Knipschild
Uploaded: 03/05/2016
9 Pages 144 Views 3 Unlocks

Music and Science Quiz #2 Study Guide

How many half steps is a perfect 4th?

Music and Math 

Scales and Intervals 

∙ Scale – ordering of pitches

∙ Note names use the alphabet (originating in Ancient Greece)

o The first note in a scale is what the key is

∙ Scale types – major, minor, others

∙ Interval – a distance between any 2 notes

∙ In a major scale, intervals are either perfect (P4, P5, P8) or major (M2, M3, M6, M7) Circle of Fifths 

∙ Created by stacking 5ths (fifth of C is G, fifth of G is D, fifth of D is A, etc.)

∙ This is how we got the non-perfect notes in scales and music

Figured Bass 

What is the fifth of g?

∙ Baroque Period keyboard instrument notation

∙ Also called “thorough bass”

∙ The harpsichord (keyboard instrument for accompanying) would only be given the bass line and  the figured bass

∙ The numbers under the baseline represent intervals between notes above the bass line ∙ It’s a numerical language to a keyboard player We also discuss several other topics like How do you find a tangent line?

o Numbers and symbols (accidentals i.e sharps, flats, naturals) to the bass line o It indicates intervals and chords to be played 

o Often improvised and embellished Don't forget about the age old question of What are the four levels of protein structure?
We also discuss several other topics like When does the filipino war happen?
If you want to learn more check out What are the three parts of parties?

Rhythm and Counting 

∙ Numbers and fractions are used for beat, rhythm, and counting 

Why is the accompaniment played by the harpsichord called a figured bass?

o Time signatures – Ex: 4/4 quarter note gets the beat, 4 beats per measure 

o Measures 

o Meter – duple/triple; beats divided by twos or threes 

o Division within the beat: whole note, half, quarter, eighth, sixteenth, etc. 

∙ Use of patterns

∙ Hemiola – when in 3/4, you group notes to feel like a big 2/4  

∙ Polyrhythms – 2 against 3; i.e. eighth note and triplet eighths OR 3 against 4; triplet eighths  against sixteenth notes

Form and Symmetry  

∙ Balanced forms:

o Sonata allegro: exposition, development, recapitulation  

o Ternary: A B A  

o Binary: A B  

o Rounded binary: A B A’ If you want to learn more check out In microeconomics what does bf stand for?

Transformation Treat these terms like vocab, just kinda know what they mean. She might do a T/F or  matching thing with them.  

∙ How to vary a theme mathematically

∙ Transposition – play theme up or down a certain note distance (half step up, whole step down,  third up, etc.)

∙ Retrograde – play the theme backwards 

∙ Inversion – notes move opposite of the theme, looks upside down 

o Contrary motion is usually a type of inversion

∙ Augmentation – half speed (ex: every quarter note becomes a half note)

∙ Diminution – twice as fast (ex: every quarter note becomes an eighth note) ∙ Transformations can also be combined, as in using more than one at the same time o Ex: retrograde inversion – backwards and upside down Don't forget about the age old question of What happened in the neolithic revolution?

∙ * Fun Fact: Mozart loved using math when writing to create perfect mathematical balance and  relationships

∙ Other composers such as Bach and Haydn used these various transformations to make songs  that could be played backwards and upside down, or would have 2 instruments play the same  line in a different direction

Music by Chance I don’t know why, but she said to know this and that there would be questions on it

∙ Also known as Aleatoric music

∙ Mozart Dice Game – certain numbers represented notes or motives that would make up a  random piece

∙ Terry Riley’s “In C” She spent a good bit of class time on this so just know that it was a song o All performers play the piece in order, but players change to the next motive at different  time

o Usually lasts about 45+ minutes

Listening (Use this for your concert report!) This is pretty much just a guideline for concert reports

∙ Your thoughts and reactions

∙ Tempo (fast or slow) – What tempo words would you use?

∙ Is it duple or triple?

∙ What’s the melody? Who plays it? Describe it.  

∙ What’s the instrumentation?

∙ Ex: Vivaldi’s “Four Seasons” (1725)

o It describes the four seasons, includes poems

o Consists of 4 violin concerti (solo violin with orchestra)

o Concerto No. 1 – Primavera, 3 movements

o Good example of early program music

Music and Physics 


∙ Pythagoras Just know a lot about this dude. He’s kind of a big deal. Know why. o Weight and string length

o Ratios and musical intervals

▪ Octave 2:1

▪ Fifth 3:2

▪ Fourth 4:3

o He stretched strings over a “monochord” with a movable bridge

∙ It took scientists over 2000 years to figure out that these ratios and intervals were related to  frequency This is a good relative time frame item to remember

∙ Early scientists Just know the order NOT the exact years. Know who came before who and that  Galileo wasn’t alive in the 1800s and stuff

o Galilei (1584-1642) – described resonance and pendulum vibrations

o Mersanne (1588-1648) – pitch is based on frequency

o Hooke (1635-1703) – frequency associated with pitch

o Saveur (1653-1716) – foundation for concept of overtones

o Fourier (1768-1830)

o Helmholtz (1821-1894) – modern acoustics


∙ Originates from a vibrating physical body or object

∙ Sound: A regular pattern of changes in air pressure (also sound waves)

∙ Sound waves cause the ear drum to flex in and out, then the brain interprets those waves as  pitch

∙ Musical notes are waves patterns that repeat 

∙ Faster vibration = higher pitch; slower vibration = lower pitch 

∙ Pitch is based on frequency or the number of pulses that arrive at the ear in a certain time Frequency and Pitch

∙ Frequency – the rate of vibration measured in cycles per second (cps) aka Hertz (Hz) ∙ Frequency is interpreted as pitch BUT frequency ≠ pitch 

∙ Frequency ratios and intervals are the same as the string intervals 

o Again, took scientists over 2000 years to realize this 

∙ Mersanne found that string lengths inversely relate to frequency

o Doubling the string length halves the frequency She will probably ask something about  this. Remember that they are INVERSELY related.

∙ Range of Hearing Maybe know this ordering, not specific numbers.  

o Humans: 20 – 20,000 Hz

o Dogs: 50 – 45,000 Hz

o Cats: 45 – 64,000 Hz

o Bats: up to 120,000 Hz

o Dolphins: up to 200,000 Hz

Overtone Series This is a little confusing, but pretty much just ignore the confusing parts and know that  notes have other notes that ring above them when played and that overtones are what make different  voices and instruments have a different timbre

∙ Most sounds are made up of complex vibrations

o Frequency is simply integers of 1, 2, 3, …

∙ Fundamental – corresponds to the number (1st harmonic)

∙ 2x Frequency = 2nd harmonic or 1st overtone

∙ 3x frequency = 3rd harmonic or 2nd overtone

∙ There is an infinite number of overtones for each pitch 

∙ Overtone series = harmonic series; both names are used 

∙ Terms to know: harmonic, overtone, partial 

o Every note has a fundamental not and overtones above it 

o Harmonic, overtone, and partial are different names for the same thing 


∙ (pronounced “Tamber” FYI)

∙ Why some instruments have characteristic sounds

∙ Same note – different sound or quality 

∙ Instruments have different proportions of various harmonics

o They have a different overtone profile Organize overtones and timbre together o The various harmonics layered are what create different timbres for each instrument

Instruments and Sound Production Be able to give examples for a cylindrical vs. conical instrument. If  she asks which one a clarinet is, know that it’s cylindrical, etc.  

∙ Wind instrument bores are either cylindrical or conical

∙ Cylindrical – constant diameter 

o Woodwinds include flute and clarinet

o Brass include trumpet and trombone

∙ Conical – diameter varies, not constant 

o Woodwinds include oboe, bassoon, and saxophones

o Brass includes French horn, euphonium, and tuba


∙ Amplitude of a tone

∙ How much energy an instrument creates and how much air is displaced

o NOT how fast vibrations are; it’s the height and how tall the vibrations are 

∙ Measured in decibels (dB) – compares relative loudness

∙ Double the volume = +10 dB, so 80 dB is twice as loud as 70 dB Don’t let this confuse you! Resonance  

∙ A sound of vibration produced in on object that is caused by the sound or vibration in another  object Know that this is what happens when you play a tuning fork or wine glass ∙ Ex: tuning fork struck, you hear the tone when you place the end on another object ∙ Ex: water in a wine glass


∙ Sound reflection, absorption, and reverberation time in a performance space ∙ Reverb times: cathedrals 5-10 sec, outdoors 0 sec

∙ Reverberation – the time that it takes for sound from a source to reach inaudibility; the time it  takes for the sound to go away

Music and Technology

∙ Music printing and technology allowed for musical works to be preserved and shared Early Music Notation

∙ Ancient Greeks printed songs onto papyrus

∙ Most music was not written down, but passed through oral tradition

∙ Later, only clergy and the church were literate for the most part, so they had control over how  music was written and distributed (and pretty much only their sacred music was written down)

o They made manuscripts very decorative

∙ Neume was used to show direction of the melody instead of exact notes

∙ Later, lines and note heads were added to more explicitly show the melody ∙ Most early notations are from the middle ages, but the earliest ones are from Ancient Greece

Okay, be able to tell the difference between these different early notations, and know their order. Don’t focus on all the details of each of them, just specifically what made them different from previous ones

Woodblock Printing

∙ Woodblock printing began during the Renaissance period

∙ You draw music backwards onto a flat piece of wood, carve around the lines and notes, then ink  and press it; similar to a big stamp

∙ Each page of a piece of music would have to have its own woodblock

Printing Press and Movable Type *Note that movable type is part of the printing press and NOT a  separate printing contraption. It’s just what’s used to organize the symbols before you press it.*

∙ Invented in the mid-15th century

∙ Made multiple identical copies of pieces possible as the woodblock did

∙ Movable type would be configured (move pieces with music notations in the desired order) and  then attached it to the printing press

∙ Movable types made of metal, so they were more durable, lasted longer, and produced a clearer  image that the wood

∙ Music publishing businesses were established which helped composers become more well known and more popular


∙ Began mid-16th century

∙ Metal tools were used to etch the music onto a flat metal plate

o Still had to write in reverse

o You could also hammer in fixed symbols like staff lines to save time

o Ink the plate then press paper with a printing press

∙ This was used by major publishing companies who continued to engrave by hand until about 15  years ago

Lithographic Printing 

∙ Invented late 1700s by a playwright who couldn’t afford engraving tools

∙ Draw the music with oil-based ink onto a smooth piece of limestone

o Acid is poured on the stone to burn the image

o Then pour water soluble solution that sticks to non-oil surfaces

∙ This did NOT replace engraving, but it was a cheaper alternative

New Technologies 

∙ Stencils – place over paper/material and draw notes and other musical symbols o This was consistent but slow

∙ Notaset – dry transfers of music symbols, rub onto blank staff paper

∙ Music typewriter – invented in 19th century, became popular in the 20th century ∙ Hand writeen was always the most common and has been used the longest o By late 20th century it could be photocopied

∙ 1960s introduced computers – music keyboards were used

o Punch cards were loaded into the computers

∙ Musicomp – similar to the music typewriter; had two keyboards

o The left one set the pitch, the right one had the musical symbols

∙ Finale and Sibelius – made in the 80s, worked best on Mac computers at the time These two  programs are important because they are still very popular today. I would assume that she would be more likely to ask about these for the new technologies.  

o Like word processors for music, but they had much more complicated symbols;  computers were programed to do the complex processing and the user just had to type  the notes

o You could also plug in a mini keyboard (as in piano keyboard) and the program would  notate what you play

o These are still widely used today

Technology and Instrument Development

∙ We know that there is evidence of flutes being made 40,000+ years ago

∙ Mosaics from 2nd century AD show early brass and pipe organ-like instruments

∙ Middle Ages – mining for metals became more common; we could mold metals into instruments  or instrument parts Middle ages = mining = metal instruments

o Alloys made it easier to bend metals

∙ Weaving loom constructions were used for early pipe pedal boards

∙ The invention of the lathe helped in construction of woodwind instruments (rotating  woodworking contraption, helps make round shapes in wood) 

∙ As manufacturing became more uniform, instruments became more reliable

∙ The more people and composers demanded of changes, the more technology was used to meet  those demands

∙ Steam engine technology in the early 1800s was used to make brass valve instruments Music “Machines”

∙ Mechanical instruments  

o Ex: Music box, player piano, Etc.  

∙ Table top clock with mini pipe organ inside; Mozart wrote “Fantasy in F minor” for musical clock ∙ Music boxes were invented about 300 years ago

∙ Ben Franklin invented the glass armonica (NOT harmonica) in the mid-1700s

o He heard someone making notes from wine glasses and wanted to create the same  sound

∙ Electronic Musical Intruments 

o The Theremin – used heterodimy (wave infrequencies) to create pitches with fixed  hand/arm positions; used by the Beach Boys in “Good Vibrations” and in old movies for  sound effects 

o Ondes martenot – based off of Theremin’s work; was an important stepping stone to  synthesizers; had the same oscillators as the theremin but was controlled with a ring  attached to a string and control panels that changed the volume and timbre; used by  Radio Head

o Hammond Organ B-3 – uses sliding drawbars (wired, electrical stops like on an organ);  used by Jimmie Smith in “Midnight Special”

∙ Edgar Varèse – wanted to free music and “liberate sounds”, made “Poeme Electronique” for the  1958 World’s Fair, made it in a tape studio, used recordings of various sounds that were then  electronically processed into altered sounds She might ask like one question about this dude.  

Just know that he wrote Poeme Electronique for the Worlds Fair, it was made from prerecorded  random sounds.  

∙ Electronic music synthesizer produced musical notes synthetically (no musical vibrations); it  used ripple patterns and speakers

o Uses overtone series to replicate instrument timbres 

o Moog 1960s/70s (inventor, brand, company)

Recording and Technology

∙ Allows us to play back, preserve, distribute, sell, etc.  

∙ First used wax cylinders, (Alexander Graham Bell, Gramophone), then tapes, tracks, CDs, etc. Overall, remember to know general orders of events and inventions and NOT specific dates.  

The test will have multiple choice and possibly T/F, matching (like terms to definitions), and fill in the  blank type stuff. Think about what questions she would ask while reading over notes.

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