Creating A Baroque/ Classical Musical Composition That Represents The Fibonacci Sequence

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The Fibonacci sequence

The Fibonacci sequence is the core structure of this composition. This artefact will not have been successful unless the mathematical concept of this sequence is followed in order to produce a musical version of the Fibonacci sequence. There is often talk of the Fibonacci sequence in nature such as in plants, however there is not much talk of the Fibonacci sequence influencing musical structures, therefore this project is exciting and unusual.

In order to create a piece of music that can resemble and express the concept of the Fibonacci sequence, it is first and most important that the structure of the Fibonacci sequence is fully researched. The sequence begins: 0, 1, 1, 2, 3, 5, 8, 13… 1 and continues where you add one number in the sequence to the number that precedes it. The equation for the sequence is x_(n+2)=x_(n+1)+x_n(2) and having learned this, starting from the 3rd term of the Fibonacci sequence, 2 themes that can be created, developed and expanded on: themes that can combine to create a new theme. There will begin theme a, followed by theme b, followed by theme c which is a combination of a and b, followed by theme d – a combination of c and b, and so on. Fragments of themes and messages will be passed through the orchestra as well as progressing through the piece if they are savoured when fragmenting the themes.

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Harmony

The harmony of a piece of music is delicate and crucial. The tonality, modulations, and progressions of the music are what contribute to the texture and satisfaction of the structure. If the harmony fits then the themes will.

Before beginning the composition, it is important that the fundamentals of harmony have been thoroughly researched, and the most important place to start is with cadences. For the work to be phrased correctly and harmonically logical, there must be a thought process of the chords and cadences within each theme, passage or phrase. The first source3 in the research of cadences broke down the importance of cadences within a piece of music – cadences are required to control the momentum and progression of a piece of music. The dominant chord will always want to fall to the tonic chord as a strong perfect cadence because this feels completed and final, and is a very common cadence one would find at the end of a large orchestral piece of music, and is a perfect cadence at the end of phrases is something that is very common in classical and baroque music, the harmonic structure that was most widely used across both periods therefore it is important research how to write these before beginning to compose. However, the perfect cadence is not only found at the end of music, and not only in orchestral music either. The perfect cadence is used widely throughout most classical music. The imperfect cadence ends on the dominant chord. It is called imperfect as one expects the tonic chord to follow but it doesn’t, leaving a dominant chord ringing and creating a suspense that is never fulfilled. Perfect and imperfect cadences are the two most significant cadences that will be used when composing music in the baroque/classical genre. The cadence occurs at the end of each phrase and marks a natural stopping point in the music. Humans can recognise when music sounds consonant (good) or uncomfortable (like in an imperfect cadence. Not dissonance) and therefore one would assume that it is easy to write cadences due to every human’s musical ear. However, the way you write each cadence differs depending on how many instruments you use, how strong the cadence should be, and how the composer wants the music to sound: Where is the phrase going? Should the music flow? Or is this cadence final? The varied use of cadences is completely down to the composer so it is important that, as the composer, one is educated of the many different cadences, cadential structures, and cadential sequences can be used and manipulated to create the foundations of the music.

After learning about the different cadences available to use, website music theory academy4 gave some great insights into learning how to properly write cadences. A cadence consists of 2 or three consecutive triads (a type of chord) at the end of a phrase. A triad consists of the 1st, 3rd, and 5th note in a chord so, in the key of C major, the tonic chord would be CEG and the dominant chord would be GBD. As all dominant chords are major, the dominant chord (chord V) of C major is G major. The relative minor of C major is A major, and the subdominant chord (chord IV) is F major. Chords I, IV, and V are the most common chords used in most classical compositions from the baroque to romantic period as well as chords II and VI. Chords III and VII are rarely used as they are unpleasant in a flowing chord progression however they may feature in an interrupted cadence, but this is not necessary for this project.

I communicated with Mrs Libby Fisher, a teacher in the music department at wellington college, and she gave advice on how to structure cadences in a similar style to Bach’s chorales. She said, “not to double the 3rd note of the triad, but also never to omit it as Bach would not”. As well as stating this, she also said it is also very important “not to have parallel 5ths when one chord progresses to another, as the chords will sound too mechanical and clunky”.

The most important sources that contributed to the research of harmony for the project were the YouTube videos from Rick Beato5,5b that teach the importance of orchestration as well as how to orchestrate chords, the melodic range of orchestral instruments, and how to harmonise a melody so that it is interesting. These videos teach that it is important to only work on a small section at a time otherwise it is easy to get carried away and create a piece of music that is not very exciting to listen to due to too many ideas and no . For example, in one of these videos, Rick Beato talks of interlocking melodies, polyphony, staggered entries and imitation. Within the artefact there are so many techniques that are difficult to introduce and write for the first time, and even more difficult to orchestrate, that can be explored. In Rick Beato’s video on orchestrating a chord5, he discusses the importance of each note in a triad. Libby Fisher said not to double the 3rd of a triad when composing however, in a full orchestra it is difficult. Therefore, when orchestrating large chords, it is important to have more of the tonic and dominant note within the chord than the third, and often the chord will sound more correctly arranged if the 3rd is in an instrument with a soprano or alto range. These videos have been beneficial as Rick Beato taught a valuable lesson that harmonically, the structure of each chord is one of the most important aspects to consider when creating a piece of music.

Composition for orchestra

Composition for orchestra is difficult to handle. It is important to investigate the process, as well as learn how to compose for each instrument’s unique range and timbre.

A source regarding composition for orchestra6 is from a composer answering a question on an online platform. JJmusicnotes (is what he calls himself) writes of ways to structure a composition. He writes of the three primary ways to structure a composition – Piano score, Short score, and Open score. A piano score is where a composer writes the whole concept of the music out on two staves, treble and bass, like for a piano. Composers will annotate and add indications of which instrument should play which part and put in several parts on only one stave where they have several ideas. This is helpful as many composers are pianists, so the Piano score is within their comfort zone, making it an easy way to visualise their goal. Once the piano score is complete the composer orchestrates the music and adds in extra orchestral details. The 2nd way for a composer to work is with a short score: the short score is much like a piano score but there are 3-6 extra staves as well as the grand staff. This means that the composer can write out melodic lines in other instruments – there will often be a stave for upper woodwind, lower woodwind, brass, upper strings, and lower strings, plus the grand staff (piano). This leaves plenty of opportunity for the composer to begin with their orchestral details before they have to perform the full orchestration. This is probably the easiest way to compose, however there is again the case of not being able to write the music in depth right off the bat. Although some composers prefer this – it is similar to the style of composition that film composers such as John Williams and Hans Zimmer use called an orchestral sketch9. The final scoring technique is Open score, also known as Full score – the composer writes each part individually for a full-size orchestral score. This could be 24 – 60 staves depending on the instrumentation and number of parts per instrument. If a composer has many different melodies in different instruments then Open score is the best option for that.

For this project, Open Score is the greatest option as I will be using the program Sibelius, which has synthesised sounds that allow you to listen to how the instrument would sound if it were performed live. Using an Open score means that, when composing, it is possible to realise the chords, harmonies modulations etc. while writing so it is possible to quickly write ideas and then change them just as quickly

Researching the ranges of the orchestral instruments was not difficult. Website7 dedicated purely to the range of musical instruments combined everything necessary to know into one table: range as seen on a stave, written range, and any important comments about the difficulty of some notes and delicateness of some instrumental ranges. Another helpful website gave 10 really great tips on how to create a good composition. It advised speaking to instrumentalists and asking them if the part is playable, otherwise there is no point in writing something so tricky. This site also states that it is important not to make the piece too long: ‘people rarely want to sit through a long piece of music from a composer they’ve never heard of’7 and that a 30 minute sonata is not what anyone is largely interested in if you are not a famous composer.

In another educational video from YouTube9, Rick Beato talks about how to create an orchestral sketch. It is a way of creating a larger composition in a way that simplifies the instrumentation from around 24 parts to roughly 8 staves of parts. This is so that the composer can stay on track and visualise the music in a smaller structure before adding in more parts and more orchestral details. A lot of the time, bass instruments such as bassoons, ‘cellos, and trombones will play very similar parts (sometimes identical) so it is not necessary to write that out 3 different times in the orchestral sketch. This really simplifies the large, complex ideas into a more structured and simpler visual concept. In this video, Rick Beato analyses Krypton from John Williams 1978 Superman film score. Although this is film music, it is helpful to know how a great composer such as John Williams manages to break down his ideas and structure them so that he has the fundamentals before expanding to create the bigger, more impressive project. However, a significant limitation of orchestral sketches is that there is a possibility of writing the sketch and then orchestrating it without adding any delicate details or ornamentation, without which the music would be simple and unappealing.

Structuring a composition

When considering the Fibonacci sequence it is important to notice musical structures that have been used and discovered by the very first composers: tertiary form (ABA) consists of 2 contrasting themes; Rondo (ABACADAEA) consists of several different themes with a repeated a theme; and sonata form (Exposition, Development, Recapitulation. It is also necessary to investigate fugal themes and learn how to write in this way, even if it might not be used in the project, so it is necessary to investigate the structure and laws of writing a fugue.

The Composition won’t be a fugue, but the style will be fugal and polyphonic, therefore it will be necessary to study how a fugue works in order to successfully achieve a piece of fugal writing. Upon beginning this investigation, a website from Classic FM10 was helpful. It is a short crash course on the basics of writing a fugue: Begin with a Subject – a short passage of around 8 bars, and then harmonise it as it is likely you will need it later. Next compose a counter subject that is a different melody but has the same key and harmonic structure (so they can be played simultaneously without sounding dissonant) – you may want to harmonise the countersubject too. Next you play the subject and counter subject, staggering it in different parts, sometimes with staggered entries and harmonisations of the melody. You can use stretto, a musical device where the subject tumbles over itself more rapidly than it did at the beginning, and end the fugue with a tonic pedal note in the bass, preparing the harmonic direction for a return to the tonic chord (often a perfect cadence).

To help learn by example, a pdf11 from composerfocus gives a simple fugue for four parts with detailed annotations such as the structure, areas to place/notice dissonance and resolutions, places where you might want to modulate, and the effectiveness of some simple imitation. And to finally gain a proper grasp on the signature fugal devices, a website shows the techniques12 that you may use in a fugue: Stretto is when the subject is played, and the countersubject begins before the original subject has ended. It can make music sound complex and exciting to listen to. Augmentation of the subject is when the original note lengths of the subject are of greater value, usually double. Diminution of the subject is when the original note lengths of the subject are of smaller value, usually half. This technique can be helpful in a development section where there are lots of modulations. Finally, inverse movement means that the melodic line of the subject is upside down, but the note lengths are the same. This links to the symmetry and mathematics of fugal writing as the upward intervals become downward and vice versa. Composers will often play the changed subject simultaneously with the original subject as well as two devices in combination such as augmented and inverse. Polyphony13 is when there are two or more independent lines of melody playing simultaneously. Polyphonic writing has rules so that the melodies do not sound too similar: avoid (where possible) melodies that move in parallel perfect 5ths, parallel octaves, and parallel melodic direction – contrary motion is the best way to go when it comes to polyphony as the melodies will sound more distinct. Also, it is not necessary to use all instruments all the time – sometimes it is easier for the player to have a few bars rest. As well as this, many fugues feature sequencing and fragmentation. This is when a part of a phrase is repeated at rising or falling intervals, sometimes a circle of fifths or scalic and creates a sense of anticipation and tension that builds throughout the piece towards a new modulation.

Although the structure of the composition hasn’t been decided, an informative YouTube14 video describes the fundamentals of sonata form: Introduction, Exposition (part 1 in the tonic key, bridge passage where the music modulates to the dominant key for a major tonic and mediant key for a minor tonic, part 2 in the dominant or mediant key), Development (many modulations), Recapitulation (part 1 in the tonic key, bridge, part 2 in the dominant key) and finishing with a virtuosic coda. Another YouTube15 video explains at length these structures, accompanied by a step by step walkthrough of how to compose a piece in sonata form with detailed explanations of how to create an effective transition and how to prepare a modulation.

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