Music theory Rutgers

types of melody

A melody is a "meaningful series of notes or pitches." In order to make a melody "meaningful," it must have some form of organization when it comes to pitch, beat, meter, and rhythm. A melodic motion in the pitches should be present, as well as some sort of rhythmic pattern.

accent

An accent is the stress on a beat that can be created by playing the note on that beat louder than the others. Different meters have the accent on different beats of each measure.

accidental

An accidental is a note of a pitch or pitch class that is not a member of the scale or mode indicated by the most recently applied key signature. In musical notation, the sharp , flat , and natural symbols, among others, mark such notes and those symbols are also called accidentals.

what is pitch and how does it change ?

Pitch is how high or low we hear a sound. Faster vibrations have higher frequencies, which are heard as higher pitches. Slower vibrations have low frequencies and are heard as lower pitches. The length of a plucked string can determine its pitch because shorter strings will vibrate faster than longer ones

what is pitch range ?

Pitch range is the highest and lowest pitches that an instrument can create.

must polyphony use cf?

Polyphony does not need to use a cantus firmus. Instead, by the eighteenth century, different composition procedures were used that allowed composers to create their own melodies. This gave them much more freedom with their compositions as they did not need to fashion their melodies to be agreeable with a cantus firmus. These techniques were used by Bach and other composers in the time period.

What is sound and how does it travel?

Sounds are vibrations that are created when energy is applied to an object. The vibration creates a disturbance in the air that reaches our ears and vibrates them. Our brain has the ability to interpret the sound.

spiritual and types

Spirituals commonly used the major pentatonic scale, but certain types of spirituals also utilized the minor pentatonic scale. Many of these songs used the major pentatonic scale because the slave owners wanted their slaves to be cheerful and happy. These work songs caused the slaves to work more efficiently. Minor key Spirituals such as the "sorrow song," started to appear in the mid-nineteenth-century, with the end of slavery.

whole tone scale

The whole tone scale is made of six notes that are each separated by a whole step. The earliest use of this kind of scale is found in Russian music. Whole tone scales lack a sense of key and seems tonally vague, so it often used to create a mood or atmosphere.

which instruments cross family lines?

The xylophone is an example of an instrument that crosses family lines. This is because it is played like a percussion instrument, but it has the ability to play different pitches and chords

chromatic note

a note that falls within the half step between the lines and spaces of the lines and spaces on the staff. A good visiualization of a chromatic note is to imagine the black and white keys of a piano. The black key between the C and D white keys is the black key representing C#. Chromatic notes will often be represented with the use of accidentals if the chromatic note is not found within the key.

guillame machaut

an important composer who led the Ars nova style of music. He is most known for composing the Messe de notre dame, which was the first composition that linked the separate parts of the Ordinary of the Mass together.

rest

counted silence.

enharmonic spelling

An enharmonic spelling is when a note sounds the same as another note, but it has a different name. A chromatic note can be named as either the sharp of one note or the flat of another. Which it is named depends on the direction that the alteration leads the melody. An example of an enharmonic spelling is F sharp and G flat. The two notes have different names, but when they are played, they sound the same.

what is an interval?

An interval is the distance from one pitch to another. The octave is an example of an important interval in which we hear the same note but one is higher than the other.

beat

Beat is the regular pulse that can be felt in music. Each song or movement generally has a steady beat, though the rate can change through it. Musicians can use this rate change in order to separate sections of the music.

ledger line

Because the staff has only five lines and four spaces, but there are many more possible pitches above and below the staff, ledger lines are used for notes that exceed the staff. These lines are added in, but they are only drawn as to be as long as the notes. Ledger lines help musicians to identify notes that are not on the staff itself.

church modes

Church modes include the Dorian, Phrygian, Lydian, and Mixolydian. Like the natural major scale, these church modes had 7 notes in each octave. Usually in these four modes only one notes sounds amiss from the natural major scales. the Lydian and Mixolydian modes differ by one note from the major scale, the Dorian and Phrygian differ from the minor scale by one note.

comping

Comping is considered a hybrid of homophonic a polyphonic texture heavily used in jazz in which chords are filled in on an irregular basis to accompany a main solo or melodic voice. Although the texture is mainly homophonic it will incorporate polyphonic snippets with the bass line acting as a partner in creating a secondary melody to the higher voice solo/melody.

what is a concertato?

Concertato is an early Baroque term referring to either a genre or a style of music where the contrast of music is between different or opposite groups of voices and instruments in concert style.

consorts

Consort is a collections of instrumentalists who would play at dances. A consort is a collection of instruments of the same family playing together. A broken consort is a collections of instruments of different families playing together

what is the head ?

Curiously, playing an established song as the head somehow gives identity to all the improvisations in-between as being that song. If the improvisations are played without the head, it is, to the listener, no particular song at all.

homophony

Homophony describes a music texture in which the focus and attention is on a single voice, usually the voice with the highest pitch which is also supported by chords. The texture features more than one voice. "Treble-dominated" means the highest voice carries and "dominates" the only melody.

What is isorhythm? Discuss pitch and rhythm in isorhythmic Medieval music

Isorhythm was the mathematical process of composing which evolved in Medieval music. Isorhythm was made up of two components, the color and the talea. The color would draw from notes of the cantus firmus while the talea was a pattern that guided the rhythm of the color. The composer was free to create his/her own talea patterns and allowed for the possibilities of mathematic expansion in music.

dot

dot as increasing the value of the note it follows by 50% of the value of the note.

what is continuo ?

fattened" the sound by giving the chords behind the "front voices." We have this same situation in the rock band today with the continuo played by the rhythm guitarist.

atonality

term associated with Arnold Schoenberg, an Austrian composer. It is the use of all of the notes in the chromatic scale. This type of music lacked a tonal center, and therefore needed to be composed by using trial and error. The atonal period (1908-1914), was closely linked with the Expressionism movement in art.

ordinary of mass

the music that is sung during every mass. This includes the Kyrie (lord), Gloria (glory), Agnus Dei (lamb of God), Credo (creed), and Sanctus (holy). The advantage to composers composing music for the Ordinary of the Mass is that the music is to be sung at every mass. The Proper changes every mass and therefore is sung a lot less frequently. Protestants will recognized these items as being part of the Protestant service, and that is because this service is based upon the Mass. In Protestant usage, the Ordinary is recited so that they do not take up as much time. This leaves time for the other different item, the sermon, itself modeled on the teachings Jesus did in the field to convert followers.

sequence

the repetition of a motive or a melodic fragment, with the same intervals separating the notes, but on a different starting pitch. Sequences can occur many times in a row with the same motive or melodic fragment. Sequences might relate to isorhythm because composers might have used sequencing in isorhythm to add variety to their music.

polyphony

two or more simultaneous melodies of roughly equal interest

cadence

A cadence is a point in music where the melody and the text pause. A cadence can be a half-cadence or a full cadence. The half-cadence does not allow for closure of a thought or a piece because it does not end on a note in the tonic chord. The full cadence does land on a note in the tonic chord, which allows closure and releases tension, suitably ending the period, stanza, or the piece.

cantus firmus, cantus firmus technique, ostinato

A cantus firmus is the melody that serves as the scaffold for a polyphonic piece. These melodies were pre-existing and came from the chants used in Church masses. Cantus firmus technique is when the chant is used in the lower voice as a scaffold. Ostinato is a musical device that occurs in the present day that utilizes the principle of the cantus firmus. It involves repetition of the same musical phrases.

chord or triad

A chord (triad) is made up of three-note combinations. Chords are formed using specific notes in a key. Each note in a scale has a corresponding chord that is built upon that note. The note that the chord is built upon is called the root of the chord. Each chord contains a root, a third, and a fifth. The third of the chord is the note at the interval of a third away from the root of the chord. The third can be either a minor third (three half steps), or a major third (two full steps). The fifth of the chord is the note that is a perfect fifth away from the root of the chord.

what is a consort instrument?

A consort of instrument is a group of instruments belonging to the same family, but have different sizes. An example is the violin, viola, and cello.

flag and beam

A flag can be added to the symbols for the quarter note or the eighth-rest in order to convert it to the next shorter duration, that is half the duration of the note. Multiple flags can be added in order to further decrease the length of the note or rest. Beams are combined flags that can help to organize music. It can be hard for musicians to read multiple consecutive flagged notes so they can be beamed in order to make it easier.

half cadence

A half cadence will represent pause in the music but not completion. Any cadence landing on the V chord is considered a half cadence and will have a feel of tension for the music to continue to resolve.

whole and half step pattern of scale

A half-step is the smallest distance recognized in Western music (microtones are occasionally used in music of other cultures). A whole-step on the other hand is equal to two half-steps. In the major scale two half-steps occur naturally between notes. The first is between the third and the fourth note of the scale (E and F in a C-major scale), and the other takes place between the seventh and the octave (B and C in a C-major scale). All of the other steps in a major scale are naturally whole steps.

what is a riff ?

A riff is a musical motive (a short musical idea) that is used to create a melody/head. This is commonly found in swing music.

chord function

Chord function is the differing uses that each chord in a key has. Various chords have different functions because of the differing levels of tension that they contain. The tonic chord, gives a sense of resolution to the music. This is because it is built upon the tonic, or the first note of the scale. The dominant chord, on the other hand, is built on the dominant, or the fifth note of the scale. The dominant chord is used to build the most tension possible before resolving to the tonic chord in order to releasing all of it. Notes in the dominant chord (the fifth, the seventh, and the second) are the most unstable notes in the scale, which is why they pull towards the tonic chord.

What is a Chordophone?

Chordophones are instruments that have strings stretched between two points. The three types of chordophone are keyboard instruments, the lyre, and the harp.

special instruments

Chordophones, especially the piano and the guitar, are special because they can play the most and the richest music due to the ease at which multiple notes can be played at once.

how are the chords identified in analysis

Chords in scales are identified with Roman numerals according to their root. For example the chord built on the third in a scale is labeled as III. If the Roman numeral naming the chord is upper case, it means that the chord is a major chord, or one that contains a major third rather than a minor third. If the Roman numeral naming the chord is lower case, it means that the chord is a minor chord, or one that contains a minor third. The seventh chord is a diminished chord, which contains a minor third and a diminished fifth, instead of a perfect fifth.

what are the basic instrument families

Different instrument families include bowed strings, woodwinds, brass, and percussion instruments. Bowed string instruments are all southern lyres that are bowed and not plucked. Woodwinds mostly use reeds (minus the flute), and they are all instruments that require air as the energy source. Brass instruments are made out of brass and do not use reeds. They do however still use air as their energy source. Finally, percussion instruments include trap sets and the timpani. They are primarily played with sticks, mallets, or brushes.

meter and types

Duple meter means that the meter has two-beat units with the accent on the first beat. Triple meter means that the meter has three-beat units with the accent on the first beat. Quadruple meter means that the meter has four-beat units. Here, the accent is either on the first beat only, or on both the first and third beats. This depends specifically on the music.

voice range

Every singer or instrument (aside from keyboard instruments) has a range of notes that can be sounded; that is a number of notes that can be played, bounded by its highest and lowest notes. The highest voice range is the soprano (upper female range), followed by the alto (lower female range), tenor (upper to middle male range), and the bass (lower male range). Instruments aside from the voice also use these terms to define their ranges.

chord progression

In a composition, chords are arranged so that it makes sense to the hearer. An ordering of chords in such ways is called chord progression. There are 7 different chords within a key and the way these chords have rules in which they must abide.

hybridization of textures

In music controlled by chord progressions the higher voiced melody will mostly be dictated by the accompanying chord progression. Chord tones for the most part will occur on accent beats and primary notes in the higher voice will mostly be notes of the chord. Even if the music is to become busy, the listener will most likely be able to detect chord changes.

monophony

Monophony is a single line of music, in which all notes are sung in unison. The music texture is "one layer" music. A type of chant called "plainsong" is an example where monophony occurs

new orleans band vs big band

One similarity between the Dixieland band and the big band was the instrumentation. They both contained trumpets, clarinets, trombones, and rhythm sections, which included drums, bass, guitar, and piano. However the big band generally had at least four of each non-rhythm section instrument. This is why the big bands were so large. Another similarity between the two types of band was that they both played music that used the "two-step." However, the big band also played music using the "four-beat" metric pattern.

organum

Organum was the earliest singing that did not have a monophonic texture. The different types of organum were parallel organum, organum purim, and discant. Parallel organum was the first type of organum to appear. It contained two melodic lines that moved together at either parallel fourths or parallel fifths. In the late twelfth and early thirteenth centuries, the other two types of organum emerged. Organum purim was organum that was not metered, but the upper voice was much more elaborate than the lower voice. The upper voice was considered to be the melody and yet the lower voice was still the chant. Discant, on the other hand, is the type of organum that had regular beat and meters.

what is perfect and relative pitch ?

Perfect pitch, which is fairly uncommon, is the ability to name notes without having reference to others. People with relative pitch, which is more common, can name other notes based on a given reference note.

pentatonic scale

Pentatonic scales can be found in many cultures and American pop music has a lot of it. There are two types: the major and minor pentatonic scales. The both scales are gapped scales that omit the second and sixth notes.

phrase

Phrases in music are short bursts of ideas. They are important because they allow the player or singer to take quick breaks between them in order to breathe or rest. The breaks between phrases also give the listener time to absorb and understand the music contained within the phrase.

melodic symmetry

Phrases in music have two levels of musical symmetry in order to convey similar ideas between phrases. The first level is that rhythms can be re-used in phrases or altered very slightly from one phrase to the next. The other level is that the melodic motion contained in a phrase, or the exact pitches in a phrase, can be repeated in later phrases.

tempo

Presto = very fast Allegro = fast Moderato = moderately fast Andante = medium speed Adagio = slow Lento = slower Largo = very slow

rhythm

Rhythm is the arrangement of the durations of events in a musical structure in order to form specific patterns. Rhythm is not independent of the meter. In music that has more than one part playing at once, each of the parts can have a different rhythm.

dodecaphony

Schoenberg's systematization of atonal music. It was mainly used by Schoenberg and his students, Alban Berg and Anton Webern. Dodecaphonic music was created by creating a "tone row." A tone row was any sequence of the twelve chromatic notes in which no note is repeated. Once the tone row is formed, the composers used techniques such as using the row in retrograde, inverting the tone row, or even using the retrograde of the inversion. Using these techniques, the composers were able to form unique phrases and chords that had distinct sounds.

what are swing and sweet ?

Sweet was a music heavily influenced by European traditions that came into the United States during the wave of immigration. It often used the "two-step" and was safe and predictable and quickly established itself as a dominant force in commercial music. On the other hand, Swing used "four-beat" and often had "walking basses."

arpeggio

The arpeggio is a homophonic device that is used to create interest in a piece of music. It is created when the notes of a chord are plucked individually rather than played together. The sequential plucking of these notes permits the tension of the individual notes to become increasingly audible rather than becoming submerged in the sound the chord creates when all the notes played simultaneously

what is a chamber orchestra?

The chamber orchestra originated in the Baroque era to provide the instrumentation for large scale compositions. The chamber orchestra is similar to the symphony orchestra in instrumentation having sections of strings, woodwinds, brass, and percussive instruments. Chamber orchestras are often smaller in size than symphony orchestras. Sometimes chamber orchestras will only have stringed instruments represented and will then be called stringed orchestas. The two major categories of concerti are concerto and concerto grosso. The concerto will feature a solo performer while the orchestra serves as accompaniment. It is possible for a concerto feature more than one musician such as Vivaldi's Double Violin Concerto which features two violin soloists. The concerto grosso will feature sections of the orchestra rather than a specific soloist. The concerto grosso demonstrates the full possibilities and capabilities of the orchestra rather than featuring one specific soloist or instrument.

cleff

The clef is used to define the pitches a staff is to represent. The clef will define range since it is not practical to include all the possible pitches on one single staff. Commonly used clefs include treble, bass, alto, and tennor clefs.

instrumentation of a rockband

The instrumentation of the rock band is generally two guitars, an electric bass guitar, drums, and occasionally the piano and/or a harmonica. The instrumentation was drawn mostly from the blues genre. However, the energy that rock bands have was drawn from "jump bands," which were cut down swing bands.

The harp and the lyre ? diff

The location of the resonating chamber is different in harps than it is in lyres. The lyre's resonating chamber is located next to the strings (to the side) and the harp's resonating chamber is located perpendicular to the strings

organization of the orchestra

The louder the instrument, the further from the front it is placed. This is a really basic way to create a balance, that is, to equalize the dynamic differences among different instrument types.

why were the lute and guitar so important ?

The lute was popular in the renaissance through the beginning of the Baroque period because of its bright but gentle sound. They were also chordal instruments that were much more lightweight and portable than keyboard instruments. The guitar gained popularity because of its ability to play very sophisticated chords, but became one of the most important instruments because of its electrification. This allowed the guitar to be one of the loudest instruments.

duet possibilities

The most common type of duet is with a musician playing or singing a melody, accompanied by a chordophone. However there are other possibilities for duets. Two melodic instruments can duet but the result would have a thinner texture. Two chordophones could also play duets. A duet does not always require two musicians because a singer can accompany himself with another musical instrument.

impetus to lean a musical instrument

The new idea of "Humanism" in the early 1500s was one force that made Western culture in general more musical. Humanism was a shift from medieval barbarism to a culture focused more on education, and a level of musical proficiency was part of this education. The other force was the printing press, which made music scores very inexpensive and quite available. Early on, the piano and the guitar were favored instruments because they were chordophones with extensive and rich literatures of music.

origins of symphony orchestra

The origin of the symphony orchestras is from the smaller chamber orchestras and opera orchestras from the eighteenth century. It was however, most popular in the nineteenth century. The first composer that began to develop it was Haydn. However Mozart and Beethoven who were considered some of the finest composers of symphony orchestra music continued Haydn's work.

primary and secondary chords

The primary chords are the tonic chord (I), the dominant chord (V), and the subdominant chord (IV). They are important because between the three of them, they contain all of the notes in a scale. They can therefore support any note of a melody. When they support a note in a melody, they are harmonizing it. The primary chords can harmonize any note in a melody. Secondary chords are the chords that are left over (ii, iii, vi, and vii diminished). The secondary chords create musical interest and variety in the song apart from the primary chords. They can substitute for the primary chords in harmonizing with a melody.

common ratio of not duration

The ratio of note durations is 2:1. This 2:1 ratio means that each note duration is one-half the duration of the next longer note duration. This ratio makes it quite easy to notate the length of different notes.

staff

The staff is a series of 5 lines and 4 spaces where pitches are notated. The staff will have a clef which will determine the what notes the lines and spaces represent. For example the lowest space on the staff with a treble cleff will represent an F but on a staff with a bass clef this same space will represent an A. Notes are not restricted to the staff alone, and pitches that extend beyond the staff can be represented through the use of ledger lines.

origins of clef signs

The symbols used as clefs evolved from the medieval letters, "G," "F," and "C," for the treble, bass, and alto/tenor clefs respectively. These clefs are significant because they define ranges of instruments and voices. Different voices and instruments have different ranges (soprano, alto, tenor, bass), so different clefs are used to save space and to simplify reading of sheet music for musicians playing various instruments.

symphony vs string quartet

The symphony has a broader range of instruments, but it is the strings that do all the heavy lifting. The winds, brasses, and percussion instruments chime in from time to time and their primary purpose is to create contrast in timbre.If these are stripped away, the symphony is essentially an overgrown string quartet. At the core of the symphony IS the string quartet, though instead of having one person on a part you might instead have twenty.

consonance, dissonance, and resolution

The term consonance describes pleasing and stable sounds, while the term dissonance describes sounds that are unstable. Chords in which the notes have corresponding sound waves create consonance. On the other hand, chords in which the notes have sound waves that collide create dissonance. Both consonance and dissonance are used together in order to tell stories through music. The tension and the release of tension allow listeners to hear music in a more story-like way. The return to consonant note combinations from dissonant ones is called resolution. This serves as a great release of tension.

blue notes

The third of the minor pentatonic scale which is used in its major pentatonic scale is called "blue note".

which instruments have military origin

The trumpet is the primary instrument today but would have been preceded by the bugle. Practically speaking, the bugle has not moving parts and hence could withstand rough treatment resulting from being carried around in the theater. The saxophone, trombone, tuba, and snare drum were all well suited to military bands because they were/are loud. The timpani also stems from military origins, but obviously not in its current form, in a smaller more portable form.

two-step

The two step originated in American music from musicians discontent simply playing only the root note of the chord throughout the whole measure. With the two step bass lines could alternate between different chord notes such as the root on the 1st beat and the fifth on the third beat. The two step can be considered a variation of arpeggiation. The two step is heard in American jazz, marching band, and american popular music. First appearing in country music.

what is the two step and what is its origin?

The two-step is the 2/2 time signature. It is similar to music in 4/4 but it has accents on beats 1 and 3. It was created because some marching band music was too fast to step on every beat. The two-step allowed the members of the band to march every other beat.

types of melodic motion

There are a few different ways to create melodic motion. A step motion is when a note moves to the next note in a scale and can go either up or down in pitch. A note can also leap to a different non-adjacent note in the scale. The distance between notes in a leap that can occur depends on the instrumentation. It is much more difficult for singers to make large leaps than it is for instruments such as the guitar or keyboard. Finally, a single pitch can be repeated consecutively in a melody.

american instruments with origins outside of Europe ?

There were two that I was fishing for, the banjo and the xylophone. You all covered the banjo well so I'll talk only about the xylophone.The balafo found use in slave music and is a variant of the xylophone. This does not mean that one evolved in the US from the other. The xylophone and its variants are found in nearly all cultures and most appearances date to prehistory. It is one of those "fundamental" instruments.What the balafo did for the xylophone in the US is prime the public to not view it as exotic and be willing to easily accept it. Consequently, the xylophone is found in quite a lot of music in the 20th century, first in its acoustic form and, starting in the 1940s, in the vibraphone, the electric version of it. The "vibes" today are common in jazz music.

emotional characteristic of major and minor

These characteristics were ascribed to these scales by theorists in the 16th century as these two scales, themselves modes though not church modes, gained general popularity.

What is a timbre and what causes it ?

Timbre is a quality of sound that makes voices and instruments sound different. Different instruments produce different sets of overtones, which in turn cause them to have tone color. Timbre is useful because it allows us to identify variety in music (such as different voices, instruments, and other sounds)

time signature

Time signature is the set of numbers at the beginning of a piece of music that give the meter of the music. The top number tells us how many beats are in each measure and the bottom number tells us which type of note is given the beat. For example, a piece can have a time signature of 6/8. The top number means that there are six beats in every measure. The bottom number means that the eighth note gets the beat. In 2/4, there are two notes in each measure and the quarter note gets the beat.

differences between eastern and western modes

Western modes have fixed pitches. This means that the notes in Western modes have been predetermined by measurements and do not vary. Cultures in the Near East, on the other hand, use modes that contain microtones.

pythagoras

a man who had a cult following in the sixth century B.C.E. He was a huge contributor to the study of music. Pythagoras also performed the first scientific study of sound with the goal of quantifying these different sounds in some way. To do this, he used a monochord, which is a string that is stretched across a board. The string on the monochord could be lengthened and shortened. By lengthening and shortening the string, Pythagoras was able to determine ratios of string lengths that yielded different intervals. 2:1 yielded an octave, 3:2 yielded the fifth, and 4:3 yielded the fourth.

polytonality

occurs when a piece of music is simultaneously in two separate keys. It sounds as if polytonal music would sound messy, but the music blends together well at the chordal level which makes this type of music work. Generally different instruments are the parts playing in the different keys. Igor Stravinsky, a twentieth-century composer, used polytonality in his music very frequently.

centonization

oldest method of building melodies in Western and Eastern music. It involves using a set of already created motives in order to form different melodies. These motives can be changed in order to fit various texts. It was commonly used to form melodies in early religious chants, but sees much use in American blues and jazz music.

types of settings

re ways in which the melody and rhythm of the music can relate to the words of the text in vocal music. There are three types of text settings that can occur; syllabic, neumatic, and melismatic. In the syllabic setting, one syllable is assigned to just one note. In the neumatic setting, several notes are given to one syllable or word. Finally in the melismatic setting, many notes are given to a single word or syllable. Many times, the melismatic setting is used to end a section of music because it heightens musical tension, before the resolution releases it.

What is a resonating Chamber ?

resonating chamber is one of the components necessary to produce sound. It is where the disturbance is created and it also helps to amplify the sound wave. there are many types of resonating chambers throughout different families of instruments. Woodwinds use metal tubes, brass instruments use a metal tube, and string instruments and keyboards use wooden boxes

syncopation

syncopation occurs when a beat within a certain meter is accented that would not usually be accented. For example, for a piece in triple meter, if an accent occurs on beat two then syncopation is present

paraphrase and thematic transformation

techniques to compose a melody using a single motive. Said motive is modified by adding a note or two, subtracting a note or two, or by changing the rhythm of the motive. These techniques can be used to create themes for multi-movement pieces. An example of this is Beethoven's Symphony No. 5 in C Minor. Paraphrase and thematic transformation were developed and perfected by the members of the First Viennese School, beginning with Joseph Haydn, followed by Mozart, and finally Beethoven.

harmonia

the idea that Pythagoras and his cult believed. Basically, it was the belief that ratios could be used to explain natural phenomena of the universe. I believe that harmonia does have some validity because whilst not everything in the universe can be explained using proportions, ratios are used very often to explain mathematics, physics, and even music.