Global Music Theory

Tag: music theory

  • Investigating How Environments Shape What Music Was Created And Performed

    Investigating How Environments Shape What Music Was Created And Performed

    As a composer, I often find myself captivated by the ways in which the environment shapes the music that is created and performed around the globe. From some of the more traditional societies of Africa and Asia to the modern metropolises of the West, the music of the world reflects the unique characteristics of the places and times in which it is born.

    • Physical environment
    • Social environment
    • Religious environment
    • Political environment

    Physical environment and music

    From the harsh and unforgiving landscapes of Siberia to the lush and tropical jungles of South America, the music of the world reflects the unique characteristics of the places it is born. And nowhere is this truer than in the way in which the physical environment shapes the music that is created and performed.

    During a composition festival, we had composers from all over the US visit the deserts of New Mexico. After I had presented my piece in a master class setting, one of the visiting composers declared there was a “desert school of composition here.” My fellow composers and I had noticed that much music coming from composers that live in much more dense and metropolitan areas had a very different feel to their music. The “desert composition school” had a lot of space in the textures. The rhythms were open and harmonically the pieces were “vast.” Our physical environment was influencing the sounds we were creating. Even though we all composed in very different styles, there was a common thread. Let’s move on to other examples.

    One of the most striking examples of this can be found in the traditional music of the Tuvan people of Siberia. Their music, known as Khöömei, is a form of throat singing that is characterized by deep, resonant, and sustained notes that seem to echo the vast expanses of the surrounding steppe. This music reflects the people’s close relationship with nature and their deep respect for the land they inhabit. The harsh and unforgiving environment of Siberia has given rise to a unique form of music that reflects the strength and resilience of the people who call it home.

    Another example of how the physical environment shapes music can be found in the traditional music of the Andean people of South America. In the high altitudes of the Andes, the thin air and extreme weather conditions have given rise to a distinctive form of music that is characterized by the use of panpipes and other wind instruments. These instruments reflect the wind and air of the mountains, and the music itself reflects the people’s deep connection to the land and their environment.

    The physical environment plays a notable role in shaping the music of nomadic cultures around the world. This can be observed among groups such as the Bedouin of the Middle East and the Mongols of Central Asia, who have developed musical traditions that are closely tied to their nomadic way of life and the landscapes they traverse. In order to accommodate their need for mobility, these cultures often rely on instruments that are portable and able to be played in outdoor settings. Such instruments include the lute and the flute. The music that is produced by these cultures is influenced by the rhythms of the land, and often evokes the sense of constant movement and change that is an integral part of the nomadic lifestyle. The music can also serve as a reflection of the spiritual practices and social customs of the people, which could be marked by celebrations, rituals or even daily routines.

    Even today, in a world where many of us live in urban environments, the physical environment continues to shape the music that is created and performed. For example, in the modern era, many urban musicians have been inspired by the energy and chaos of the city, and the music they create reflects this energy and reflects the hustle and bustle of the urban landscape.

    The land shapes the notes. I’ve seen it firsthand, from the bitter cold of Siberia to the sticky heat of Thailand. Each place breeds its own tune. As a composer, I draw inspiration from traveling the globe and studying the music of different regions and eras. The world is my muse, and through my compositions, I strive to capture its essence.

    Social environment and music

    The music of the world mirrors the societies that birth it, from ancient Africa and Asia to the bustling cities of the West. Nowhere is this connection clearer than in the way music is employed to commemorate life’s important moments. From celebrations to ceremonies, music gives voice to the culture’s norms and values.

    West African Societies

    West Africa’s traditional societies offer a prime example of how music can be used to mark significant moments in life. From birth to death, music is an integral part of daily rituals, serving not only as an art form, but also as a medium to strengthen community ties and convey cultural heritage. The beats and harmonies of the music reflect the lively atmosphere of these events, while the lyrics communicate the reverence for family, community, and tradition. In Ghana, for example, the Akan people use music and dance as part of naming ceremonies and funeral rites.

    The Yoruba people of Nigeria have a rich and diverse musical tradition that is closely tied to their culture and way of life. Among other things, traditional music is used to mark important life events such as births, marriages, and deaths.

    For instance, when a child is born, the Yoruba people celebrate with music, dance and other rituals. The arrival of a new baby is considered a significant event in the community, and music plays a central role in the celebrations. The mother and baby are serenaded with songs, and traditional instruments such as the talking drum and the shekere, an instrument made from a gourd, are played to announce the arrival of the new child to the community. The drumming and singing are believed to usher in the new life and bring good luck and blessings to the child and the family.

    Here’s a short example of the talking drum:

    Here’s an explanation of the shekere:

    In addition, the music and lyrics of the songs performed at these events often contain important cultural and social messages. They may express congratulations and well wishes for the new family, convey moral and ethical values, or offer advice and guidance for raising the child. The lyrics can also contain spiritual and religious elements, such as invoking the blessings of the ancestors and the gods. Music is not only a celebration, but it also a medium to transmit cultural and spiritual knowledge and practices.

    The rhythms of the traditional music of these societies, such as the Ghanaian Highlife and Nigerian Afrobeats, are deeply rooted in the West African rhythms and drums, giving a sense of energy and joy to these events.
    Also, the prominent musicians and singers such as Osibisa, E.T. Mensah, and King Sunny Ade from these regions, have taken traditional music to new heights and popularized it globally.

    North American Indigenous Society and Music

    The music of North American Indigenous peoples is a reflection of their culture and surroundings. Ceremonies and community gatherings are where their music shines. Take for example, healing rituals, where music plays a central role. Traditional songs passed down from one generation to another, serve to anchor the community to their heritage. The rhythms and melodies reflect the close connection of these people to the land. Lyrics often speak of the importance of living in harmony with the natural world, of being one with the earth.

    A case in point, the Navajo Nation in Southwest of America, where the traditional healing ceremony “Sing” is performed by a medicine man and his apprentice, using the power of song and chant to heal the patient. Or the Lakota people, who use the drum and singing in the healing ceremony “Sweat Lodge” for both physical and spiritual purification.
    The traditional music of these societies not only provides comfort and healing but also a connection to the spiritual realm.

    Urban Societies and Music

    Urban social environments shape the music that is created and performed. In the modern era, many urban musicians have been inspired by the social issues and challenges of the day, and the music they create reflects this. For example, in the United States, the music of the Civil Rights Movement was a powerful tool for expressing dissent and resistance, and in many parts of the world, the music of protest movements reflects the political and social issues of the day.

    Political environment and music

    From the revolutionary songs of Cuba to the protest anthems of South Africa, the music of the world reflects the political issues and struggles of the people who create and perform it.

    One of the most striking examples of this can be found in the traditional music of Cuba. During the revolutionary period of the 1950s and 60s, a new style of music emerged in Cuba, known as Nueva Trova. This genre of music reflected the political and social changes taking place in Cuba at the time and was used as a means of expressing dissent and resistance. The lyrics of Nueva Trova songs often dealt with issues of poverty, injustice, and the struggle for freedom, and the music itself reflected the energy and passion of the revolution.

    One example of a Nueva Trova song is “Volver a los 17” (Going back to 17) by Silvio Rodríguez. The song was written in 1972 and was released on his album “Dulce y amargo” (Sweet and Sour). The song is widely considered one of the most popular and enduring songs of the Nueva Trova movement.

    The lyrics of the song are nostalgic and reflect on the innocence and idealism of youth, and the passing of time. The lyrics are poetic and metaphorical, expressing the longing for the past and the sense of loss and regret.

    Here is a translation of the first verse and the chorus:

    Verse 1: I’m going back to 17, with my guitar, to sing to the girls in the plaza, to sing to the stars that shone on the nights of my youth

    Chorus: Going back to 17, with the same illusions, with the same songs, with the same love.

    Silvio Rodríguez

    The song speaks about the longing for the past, the nostalgia of youth, and how things change and how the time goes by. The metaphor of going back to 17 years old, is a way to express the idea of wanting to go back in time to relive and enjoy the moments of our youth, with its dreams, illusions, and passions. The music and lyrics of this song, like many other Nueva Trova songs, are deeply rooted in the Cuban culture and history, and they often reflect on the social and political issues of the time.

    Another example of how the political environment shapes music can be found in the traditional music of South Africa. During the apartheid era, music was used as a powerful tool for expressing dissent and resistance. The music of artists such as Miriam Makeba and Hugh Masekela reflected the struggle for freedom and equality and became the voice of the anti-apartheid movement. The lyrics of these songs often dealt with issues of injustice and inequality, and the music itself reflected the energy and determination of the people who were fighting for their rights.

    Even in parts of the world where many of us live in more politically stable environments, the political environment continues to shape the music that is created and performed. In many parts of the world, music is still used as a means of expressing dissent and resistance, and the lyrics of songs often deal with issues such as poverty, injustice, and the struggle for freedom.

    The environment shapes the music, that much is clear. From the guttural Khöömei of Siberia to the lively Nueva Trova of Cuba, each corner of the world has its own unique sound. As a composer, it’s my honor to draw inspiration from these varied places and times, to capture the essence of the world in my compositions. The political climate, social norms, religious beliefs, and physical surroundings all play a vital role in shaping the music of a place. To truly understand a culture’s music, one must understand the forces that shape it. It’s a never-ending exploration, but one that I find endlessly fascinating.

  • What is voice leading in music? a quick overview

    What is voice leading in music? a quick overview

    I learned about voice leading from a very academic angle. It was introduced to me through counterpoint and then through four-part writing. I was never a singer, except for my first year of college where I had to be in the choir, and though voice leading pertains to all instruments, it’s very clear when singing. When singing part of a choir you see/feel where your melodic line fits and moves within the music – i.e., voice leading.

    Voice leading is the way that individual parts in a musical composition move, or “lead,” between different pitches and chords. It refers to the smooth and logical progression of individual voices within a piece of music, and is an important aspect of counterpoint, which is the art of combining melodies in a way that is harmonically interesting and pleasing to the ear.

    In a piece of music that has multiple voices or parts, voice leading helps to create coherence and continuity by ensuring that the individual lines flow smoothly and logically from one chord to the next. It can involve the use of various techniques, such as smooth movement by step (minor 2nd or major 2nds), leaps (anything larger than an interval of a 3rd), or scale degree, or the use of voice exchange, where two voices swap melodic material – like the alto taking over from the soprano line.

    Good voice leading can help create a sense of forward momentum and direction in a piece of music and can also contribute to its overall structural coherence. It’s an important aspect of composition and is often considered in conjunction with other factors such as melody, harmony, and form.

    Voice leading in Baroque, Classical, and Romantic music?

    Voice leading is an important aspect of music composition in many different musical styles and periods. In Baroque music, which flourished in Europe from the late 16th to the early 18th century, voice leading was often used to create intricate and complex counterpoint (checkout my articles on counterpoint), with multiple voices interacting and interweaving with one another in a highly structured manner.

    In classical music, which emerged in the late 18th century, voice leading continued to be an important factor in composition. Classical composers such as Haydn, Mozart, and Beethoven often used voice leading to create smooth and logical progressions between chords, and to ensure that the individual voices in a piece of music moved in a cohesive and coherent manner.

    In Romantic music, which emerged in the 19th century, voice leading played a somewhat different role. Romantic composers such as Wagner, Liszt, and Chopin often used voice leading to create more expressive and emotional effects, and to create a sense of drama and tension in their music. In Romantic music, voice leading was often used to heighten the emotional impact of a piece by creating more dissonant and expressive progressions between chords, or by using larger leaps and more chromatic movement in the individual voices.

    Overall, the role of voice leading in different musical styles and periods has varied somewhat, but it has remained an important factor in the creation of well-crafted and harmonically interesting music.

    Voice leading in contemporary pop music

    Voice leading is an important aspect of music composition in many different styles and genres, including contemporary pop music. In pop music, voice leading is often used to create smooth and logical progressions between chords, and to ensure that the individual voices in a piece of music move in a cohesive and coherent manner.

    In pop music, voice leading is often used in conjunction with other techniques such as chord progressions and melodies to create a specific emotional or stylistic effect. For example, a pop song might use voice leading to create a sense of tension or resolution, or to add depth and complexity to the harmonies.

    In contemporary pop music, voice leading is often used in combination with electronic instrumentation and production techniques, such as synthesizers and drum machines. These tools allow for a wide range of creative possibilities in terms of voicing and arranging the individual parts in a piece of music, and can be used to create intricate and expressive voice leading patterns.

    Voice leading is an important aspect of contemporary pop music and is used by songwriters and producers to create harmonically interesting and emotionally impactful music.

    Voice leading and its evolution from Gregorian chant to today

    Voice leading in music has evolved significantly over time, and the ways in which it has been used and understood have varied significantly between different musical styles and periods.

    One of the earliest forms of Western music that made use of voice leading was Gregorian chant, which flourished in the Western Church from the 9th to the 12th centuries. In Gregorian chant, voice leading was often used to create a sense of unity and coherence within a piece of music, with the individual voices moving in a smooth and logical manner between different pitches and chords. Voices during this period were limited, not by any rule but by what they found to be pleasing, to a small set of intervals – unison, perfect fourths, perfect fifths, and octaves.

    As Western music developed over the centuries, the ways in which voice leading was used and understood continued to evolve. By the time we reach the 21st century all bets are off when it comes to voice leading but in pop music there are overarching trends.

    In contemporary music, voice leading continues to be an important aspect of music composition and is used in a wide range of styles and genres, including pop, rock, electronic, and more. The ways in which it is used and understood have continued to evolve over time, and today, voice leading is a vital part of the musical language. Voice leading sensibilities have been shaped by at least a thousand years of composers paying attention to how polyphonic voices interact.

    Voice leading outside the Western music tradition

    Voice leading is a concept that is relevant to many different musical traditions, and is not limited to the Western musical tradition. In fact, voice leading has been an important aspect of music composition in many different cultures and musical styles around the world.

    In non-Western musical traditions, voice leading is often used to create specific musical effects and to achieve specific musical goals. For example, in traditional Indian music, voice leading is often used to create complex and intricate melodies, and to achieve specific emotional and expressive effects.

    In African music, voice leading is often used to create a sense of unity and coherence within a piece of music, and to create a sense of group identity and collective expression. In many African musical traditions, voice leading is closely tied to the use of call and response patterns, where one voice or instrument leads and the others respond.

    Two examples of well-known voice leading

    “Canon in D” by Johann Pachelbel

    Canon in D is a piece of music that is widely known for its excellent voice leading. The piece is a canon, which means that it is built on a repeating melody that is played by different voices at different times. In “Canon in D,” the main melody is played by the first violin, while the second violin, viola, and cello provide accompanying lines that follow and respond to the main melody.

    One of the things that makes the voice leading in “Canon in D” so effective is the way that the different voices move smoothly and logically between different chords. The main melody moves by step, while the accompanying voices move in a more flowing and legato style. This creates a sense of unity and coherence within the piece and helps to give it a sense of forward momentum and direction.

    “Moonlight Sonata” by Ludwig van Beethoven

    “Moonlight Sonata” by Ludwig van Beethoven is a piece of music that is known for its excellent voice leading. The first movement of the sonata, which is the most well-known part of the piece, is built around a series of arpeggios, or broken chords, that move smoothly and logically between different chords. Logical movement means the melody and the harmony move according to long established chord progressions and utilize intervals suited to the tastes of the day.

    One of the things that makes the voice leading in “Moonlight Sonata” so effective is the way that the different voices move smoothly and logically between different chords. The main melody is played by the right hand, and moves in a flowing and legato style, while the left hand plays a series of arpeggios that provide a harmonic foundation for the piece. This creates a sense of unity and coherence within the piece and adds to its overall structure and flow.

  • Should you study music theory? reasons for and against

    Should you study music theory? reasons for and against

    I get asked and even ask myself sometimes, “should musicians learn music theory?” When I was completing my undergraduate work in Theory and Composition there was always this air of prestige and expectation from some of my pop-music friends. Some knew no theory and played wonderfully, but they would usually express a desire to learn music theory. Music theory is very useful up to a point. At a certain level of theory it gets pretty stuffy and impractical and unusable in the creation of music.

    In this article I go over a few reasons musicians may want to learn music theory and give a few reasons why they may not. There is a lot of grey area in this, meaning musicians usually don’t just go one way or the other but rather somewhere in between.

    Why study music theory?

    The study of music theory can be of great value to musicians, providing a more nuanced understanding of the fundamental principles of the art. It serves to facilitate communication between musicians, aiding in the creation and arrangement of musical works, as well as in the process of improvisation and interpretation. Some specific benefits of learning music theory include the ability to communicate more effectively with one’s colleagues, an enhancement of creative abilities, an improvement in one’s overall musicality, and a more refined performance. In some cases, a thorough knowledge of music theory may even be a requirement for certain musical careers, such as teaching or composition.

    A few reasons to learn music theory

    Here are a few specific ways in which learning music theory can benefit a musician:

    1. Improved communication: Music theory provides a common language that musicians can use to communicate with one another. This can be particularly useful when working in a group setting, as it allows musicians to discuss and understand the various elements of a piece of music, such as the key, harmony, and form. I used to be shy when someone would ask, “can you move that to the key of G?” And I didn’t know what they even meant. Now I know and it certainly helps with playing with others and with my confidence.
    2. Enhanced creativity: Music theory can help musicians to understand the underlying principles of music, which can in turn inspire new ideas and approaches to music-making. For instance, understanding how different chord progressions work can help a musician come up with new melodies or harmonies. (check out my article on Bach’s chord progressions)
    3. Enhanced musicality: Learning music theory can help musicians to develop a deeper understanding of the structure and organization of music, which can lead to a more refined and sophisticated musical style. Phrasing in particular can be better understood with a strong foundation in music theory.
    4. Improved performance: Understanding music theory can also be helpful for musicians when it comes to interpreting and performing a piece of music. For example, understanding the form of a piece can help a musician to better understand how to structure their performance and make musical decisions.
    5. Enhanced career opportunities: Some music-related careers, such as teaching or composing, may require a strong understanding of music theory. In these cases, learning music theory can be an important step towards achieving these goals.
    6. Crossover applications: I’ve found that the analytic principles and techniques I learned and used in music theory are applicable to other fields. I use it in my writing, art, and even business. Music theory is about patterns and understanding relationships and those skills are transferable to many other areas.

    Reasons musicians may not study music theory

    Here are a few reasons why some musicians may choose not to learn music theory:

    1. Limited time or resources: Learning music theory can be a time-consuming process, and some musicians may not have the time or resources to devote to it.
    2. Intimidation or lack of interest: Some musicians may find the subject of music theory intimidating or may simply not be interested in it. In these cases, they may choose to focus on other aspects of music-making.
    3. Preference for intuition: Some musicians may prefer to rely on their ears and intuition rather than formal theory when creating and performing music.
    4. Different learning styles: Music theory can be taught in a variety of ways, and some musicians may find that certain approaches do not work for them. In these cases, they may choose not to pursue music theory.

    It is important to note that these are just a few potential reasons why some musicians may choose not to learn music theory, and that each individual’s decision will be based on their own goals and preferences.

    Some musicians will find that they are able to create and perform music to a high standard without any formal training in the subject.

    Ultimately, the decision of whether or not to pursue the study of music theory should be based on the individual musician’s goals and preferences. While it can be of great benefit to some, others may find that a basic understanding is sufficient. There are also various approaches to the study of music theory, and what may be effective for one musician may not be as beneficial for another.

    I have found a lot of value in my music theory training, but I have also seen where the study of music theory can get far away from the music. I view music theory as a tool I can choose to employ or not. The study of music theory can be an invaluable tool for musicians, but it is not a requirement for all.

  • Writing music analysis for non-musicians & music majors

    Whether you know music or not, you may be asked to write an essay/analysis on a piece of music. If you’re a music major or thinking about studying music in college, get used to it! This task can feel a little overwhelming, especially if it is your first time writing about music. This article is tuned for people who have very little music knowledge on up to people who have some formal music theory courses under their belts. I think the tips, suggestions, and resources I provide are useful to anyone who is tasked with this kind of writing.

    Your teacher or professor gave you some direction as to what they are looking for in your work, so I’ll be addressing the topic more generally and offering my own ideas. Always refer to your specific assigned requirements.

    What should music analysis include?

    Before we get to the step-by-step, here’s what I think most music analysis essays should include:

    • Background of the music.
      • Context
      • Significant performances
    • Background of the composer(s).
    • Musical analysis
      • Timbre
      • Form
      • Harmony
      • Melody
      • Orchestration
      • Composition techniques
    • Your own ideas and conclusions

    So, how do you start analyzing music? I lay out some step to get you started below.

    Step 1: Get to know the music

    Before writing you should listen to the music many times. Each time you listen, try listening for different things. I suggest listening at least five times in five different ways.

    1. Listen then write what the music made you feel or imagine. Did it take you on a ride? Did it make you think of your childhood? Jot down a few notes. Then try to articulate why it had that effect on you. Was it the melody? Was there a rhythm or specific instrument that pulled you on a journey?
    2. Listen for instrumentation. What instruments do you hear? Are they playing all the time? What combinations of instruments did you hear? Is there any significance in the instrumentation that was chosen? Are these traditional instruments or perhaps all electronic?
    3. Listen for dynamics. You can use a line on a page to indicate the dynamic shape of the music. Did it start out quiet and stay quiet for the entire piece? Or did it go up and down?
    4. Listen for rhythm. What kind of rhythms did you hear? Were they steady throughout the piece? Did the rhythm become more complex in some places? Polyrhythms?
    5. Listen for meter and tempo. Were you able to identify the meter? Did the music speed up or slow down? If yes, where in the music?

    Once you have listened through five times with different ears on, I like to sketch what I think the music looks like visually. I use colors, shapes, figures, words, anything to attempt to capture the music on one sheet of paper.

    Finally, to get the know the music, you must get the score or written version of the music. This will help you see things in the music you may not have heard. It will also be essential if you’re going to be doing detailed music analysis (see steps 5-7). If you have a good ear, you can make your own transcription of the piece.

    Step 2: Get to know the composer

    Whether you’re writing about Adele or Bartok, you need to know some background information about the composer. Some key things to know are:

    • Full name
    • Date of birth
    • Date of death (if applicable)
    • About their musical background/career
    • Their other works
    • Musical “trademarks” they have
    • Where they live(d)

    Having this knowledge before writing will help you add colorful details to your writing. Rather than simply listing these elements as facts, you’ll be able to sprinkle these facts into your paragraphs breathing a little more life into them.

    Depending on the scope of the assignment, I wouldn’t recommend doing a deep dive into the composer but rather grab info from a few sources outside of Wikipedia.

    • Interviews on youtube can be a great place to grab quotes and get to know more about the composer in their own words.
    • Documentaries on youtube are great places to get a fast overview of the composer.
    • Composer websites is a curated experience that the composer wanted you to experience.
    • Fan websites
    • Books about the composer or by the composer (if you have the time to read an entire book about the composer, this is where you will learn the most).

    Step 3: Put the music in context

    Nothing exists in a bubble, so figure out where this music fits in. Here are three parameters you may explore.

    • Time era – When were they writing? What was the time like? Are we talking horses or Teslas? How does the time in which the composer wrote the music affect the music? Was the composer part of a particular music or art movement?
    • Geography – Where in the world did the composer live and where did they write the music in question? Was it in the French countryside? Or an island off of Australia? Austin, Texas? Does the geography influence the music and in what ways?
    • Within their works, when was this piece written?
      • Listen to the first piece of music this composer released (or the earliest one you can find), how is it similar or different?
      • Listen to the last piece of music released by this composer, how is it similar or different?
      • Was the music written during a particular phase or episode in the composer’s life? A bad breakup? The death of a child? Just won prestigious award? Was the composer overtly trying to say something?

    With this knowledge, you’ll be able to add depth to your analysis.

    Step 5: The Music’s Structure

    Every type/genre of music has its own musical structures. Here are a few types of structures your piece may be using:

    • Strophic – a specialized binary form where all verses are sung to the same music. You might see a song labeled with “A section and B section” or “verse and chorus”.
    • Ternary – a three-part form typically ABA.
    • Theme and variations
    • Through composed – the music does not repeat sections (Bohemian Rhapsody uses this form).
    • Sonata – be careful with this one, there are many variations.
    • Chance

    In tonal music (most music form the West) we have many cues to let us know the structure of the music. If there are lyrics, then there may be lyrical patterns that inform the structure of the music. Typically, it’s a combination of melodic, rhythmic, and harmonic cues that let the listener know where the end of a section is. Here is a quick example from Adele’s Hello that exemplifies three typical signs the phrase has ended.

    1. The melody moves downward and finishes on the tonic.
    2. The melodic rhythm ends on a long note.
    3. The harmony ends on the tonic.
    Example of phrase ending for music analysis

    The key to analyzing musical structure is to find the major sections of the music and determine how the composer fit these sections together – how are the various sections related? There is a lot that can go into this part of the analysis, but at the very least you should know the basic structure of the piece.

    For an in depth look at form and structure here is a book by Leon Stein, Anthology of Musical Forms — Structure & Style: The Study and Analysis of Musical Forms

    Step 6: The notes

    After the structure is understood, getting a handle on the melody, harmony, articulation, and dynamics is the next step. Once again, this can go as deep or shallow as you like. I’ll go over some of the basic elements to highlight in each area.

    Melody

    You will want to do some basic phrasal analysis, which entails understanding the smallest units of the melody that combined together to create the full melody. You are looking for how long the phrases are. How do they relate to each other? Are the phrases transposed, inverted, retrograded, etc…? But remember to keep in mind why it matters in the first place to understand this. I look at analysis as the practice of figuring out what “works” in music. What makes music communicate so powerfully? It’s easy to get lost in the minutia of the music and then not say anything important. How are the melodic phrases and structures related and how and why do you think this contributed to the music? Here is a brief example of how I’d start a melodic analysis. This is from MINUET No 1, in G Major by Mozart. This example is by no means exhaustive of how deep you can go analyzing melody.

    • The pink dashed box shows the prime melodic unit – two eighth notes descending to a quarter note all slurred together.
    • There are two short phrases that make up the red “phrase #1”. These two phrases are a descending sequence.
    • The blue phrase #2 uses the prime melodic unit but shortens it by using it back to back.
    • Phrase #2 in measure 8 ends on the dominant five chord – a half cadence.
    • Phrase #1b begins with the prime melodic idea just transposed down a 6th from measure 1.
    • Phrase #2b begins like phrase #2a but transposed down by a perfect 5th.
    • The green arrows indicate a change in melodic direction at the same point in the phrase.
    • Phrase #2b ends on a tonic – a perfect cadence. This type of cadence completes the section before it moves onto the a B section.
    Brief melodic analysis of Mozart

    Harmony

    If you’re a music student, you should probably go ahead and do a full roman numeral analysis. In some music, harmony will reveal many structures and patterns that hold the piece together. But be aware that many types of music place little to no importance on harmony. For example, one time I was analyzing a piece of traditional Thai music and very quickly found that there were only two harmonies used throughout the entire piece. It just went back and forth between a I (tonic) and a V (dominant). In a way the Roman numerals did their job by showing the harmony was not an element that the composer was used to hold the piece together. In most tonal music, the harmony is very important, but be careful to point out areas of harmonic interest rather than just rattle off the chords. Here are a few things to look for in harmony:

    • harmonic rhythm
    • cadences
    • repetitions in progressions and how the repetitions are varied
    • sequences
    • modulations
    • key changes
    • how expectations may have been played with (did the composer end on a surprising chord? and why?)

    articulation

    It can be useful to pay attention to some of the less structural elements in the music, like articulation. Articulation is one of those aspects of the music that is riding on the surface playing a significant role in the experience of the music.

    • legato: note are performed smooth and connected
    • staccato: notes are shorter than their written rhythmic value
    • tenuto: hold the note for the entire rhythmic value
    • marcato: louder and more forceful
    • accent: play the note with a little bite at the beginning of the note

    dynamics

    Dynamics are an important way for the composer to communicate. The very quiet sections can get an audience on the edge of their seats just as much as a loud section. Here are some basic dynamics volume terms:

    • fortissimo = very loud
    • forte = loud
    • mezzo forte = kind of loud
    • mezzo piano = kind of soft
    • piano = quiet
    • pianissimo = very quiet

    Here are some terms to describe changing dynamics:

    • crescendo = slowly get louder
    • decrescendo = slowly get quieter
    • diminuendo = slowly get quieter
    • subito piano = suddenly perform at the piano volume level
    • sforzando = suddenly loud

    Step 7: Compositional techniques

    Whether it’s Bon Iver or Bach, composers use compositional techniques to express themselves through the music. Every genre, composer, time period, geographic location, has their own unique set of established compositional techniques. I’m providing just the smallest sample of a few common techniques, but there are way to many to cover here.

    • chance: a set of rules is created and the composer plays a game to generate musical ideas and content. For example, I have some dice. Every time I roll a “1” I write the tonic of my key. I roll again to determine the rhythmic value. And I roll again to determine the articulation. And this can go on and on. If you did this, then you’d be able to generate a piece by the roll of the dice – chance.
    • repetition: self explanatory, just repeat a section.
    • sequence: take a melody or piece of the music and repeat it but alter it by transposing it up or down. Usually, do this three or more times.
    • pedal tones and bell tones: a pedal tone is a low pitch that is repeated over and over while the other parts change. A bell tone is a high pitch that is repeated over and over while the other parts change.
    • textures: think of complex vs simple.
    • counterpoint: layered melodic lines that follow carefully thought out rules of voice leading.
    • range: low vs high and everything in between.

    Step 8: Outline the essay

    Now that you know the music, the composer, the context, and the specific musical elements of the piece, it’s time to start outlining what you’re going to say about this music. One common method for presenting music is to start wide and zoom in with every paragraph. Think of it like an opening shot of a movie. The camera is pulled out (an establishing shot) to give the viewer context. So maybe imagine a setup with something as big as a planet, a continent, country, or city. Then the camera moves in to a neighborhood or high rise, or field. Then we get in closer to the home where we find our protagonist. We can do the same thing throughout the musical essay. Here is an example outline I did for the essay I wrote on Alfred Schnittke – Concerto Grosso no. 1.

    Five-paragraph essay outline

    Introduction – zoomed out look at the context of the composer, time, location, performance, etc

    Establish polystylism the compositional technique as my “protagonist.” Start zoomed out and discuss what polystylism is and other examples of this technique in use. Introduce Schnittke and his personal context. Get down to the piece and list a few of the styles that will be encountered in the music. Finally, deliver the thesis of the essay (the problem of the story), an examination of how to successfully deploy polystylism through consonance and dissonance.

    Body paragraph #1- looking at polystylism across the entire piece and form

    Discuss how many time styles are changed. Maybe present a chart showing the combinations of styles. Where’s the climax of the piece and what happens there?

    Body paragraph #2 – zoom in a bit more and look at an entire section of a stylistic change

    Give examples from a few different sections that show the stylistic writing of the various styles. For example, during a baroque section, show the counterpoint involved. Show the extended piano technique in the “contemporary” sections.

    Body paragraph #3 – zoom in and look at the notes, articulations, orchestration, voice leading of the moment of change

    Discuss what is happening in the music at one of the shifts from one style to another. What orchestration, textures, dynamics, and harmonic language is being used?

    Conclusion – draw conclusions and say something interesting

    Discuss the specific techniques Schnittke employed to transition between styles. What other contextual elements supported this music? If a composer wanted to use this as a case study, how would you distill down the polystylistic technique of Schnittke?

  • 3rd Species Counterpoint – (audio ex) rules and steps

    If you do not know about cantus firmus, 1st species counterpoint, or 2nd species counterpoint, check out the following articles first:

    In 3rd species counterpoint the counterpoint moves in quarter note durations against the cantus firmus in whole notes.

    Rules of 3rd Species Counterpoint

    • If 5 quarter notes are ascending or descending the following must be observed:
      • The first note must be consonant
      • The second note may be dissonant
      • The third note must be consonant
      • The fourth note may be dissonant if the fifth is consonant

    Consonant and dissonant beats

    Here is an example of having the 1st and 3rd beats consonant and the 2nd and 4th can be either consonant or dissonant. Remember perfect 4th (perfect 11ths) are considered dissonant.

    Here is an example where the 3rd beat is allowed to be dissonant as long as the other beats are consonant.

    Another acceptable consonant dissonant movement is the cambiata or “exchanged note.” This is where the 2nd beat is dissonant and then you leap away to a consonant and resolve the leap in the opposite direction.

    The next to last measure in 3rd Species Counterpoint

    If the cantus firmus is in the lower part, then the second to last note must be an interval of a Major 6th that then moves by contrary motion to the octave.

    If the cantus firmus is in the upper part, place a minor 3rd at the second to last note and resolve to a unison. Alternatively, you can use a minor 10th and resolve to the octave.

    Using sharps and flats and examples

    Sometimes it is necessary to use sharps and flats in order to avoid tritones (augmented 4th/diminished 5th). Here are some examples from Joseph Fux. Even in these examples there are issues that might be flagged as “less good” or “incorrect”. In my experience, writing counterpoint (or any composition) there is no “perfect” answer. You should try to learn the principles behind the theory or exercise but don’t be bound by them. Use your ear. And if something just sounds strange or breaks the rules, don’t fret. One of the beauties of music is that you can always write more.

    From The Study of Counterpoint trans. Alfred Mann pg. 54

    The two issues I flagged in the example above are “too many notes going in the same direction in a row” and “large repetitive leaps”. The first issue of too many notes going in the same direction also outlines a major 9th (d to e) which is dissonant. The second issue is the octave leap of c to c and back to c again. And then the leaps of a to d repeated. Typically, in counterpoint we try to avoid repeated patterns and sequences (at least for now). Is the above example “wrong”? No. There are countless ways this example could have been written, and in the end if it sounds good, it is good. Here is what this short counterpoint sounds like.

    Here is an example of using flats and sharps in the same exercise.

    From The Study of Counterpoint trans. Alfred Mann pg. 54

    Here is what this example sounds like. I love the mixing of B and B-flat.

    Lastly, here is an example where Fux accepts lots of leaps. Usually, counterpoint favors smooth voice leading – meaning steps are preferred to skips. But as you can see in the example below, there are many leaps and some are “unresolved” by stepping back in the opposite direction.

    3 species counterpoint audio example #8

    It’s easy to get wrapped up in all the rules of counterpoint, but examples like the one above shows that you can be lenient and to just enjoy writing rather than being so strict.

  • 7 Music Scales Beyond Major & Minor You Should Know

    As you know there are plenty of scales throughout the world, and I want to highlight a few here. Whether as a classical style composer or someone just interested in creating music, being exposed to more types of scales will broaden the music you create. In order to get the most out of this article, you will need to understand intervals.

    The seven scales you should know are:

    1. Whole-tone scale
    2. Chromatic scale
    3. Hemitonic – pentatonic scale
    4. Anhemitonic – pentatonic scale
    5. Hexatonic scales
    6. Tetratonic scale
    7. Octatonic scale

    Of course, there are many more scales to explore – from microtone scales to the scales found in nature! But hopefully, this will be a nice look at scales you don’t typically encounter.

    Here is an image of all the scales I talk about in this article:

    I find improvising with these scales helps to unlock new ideas and sounds.

    I’ve written a short book for composers that explores how music is organized and the roles it can play across the globe. The book is called Formative Forces in Sound. If you are interested, it’s available on Amazon here for $0.99 www.amazon.com/formativeforcesinsound

    What is the whole-tone scale?

    This is a simple scale to understand. It consists purely of whole tones, no half-steps. You can find many examples of composers using this scale. Since this scale consists of 6 notes, it’s actually under the Hexatonic scale category but I thought it could use its own example because it has been used in many pieces of Western classical music such as Debussy’s Prélude à l’après-midi d’un faune.

    The whole-tone scale is commonly used to create a “dreamy” sound.

    There are only two versions of this scale, one starting on C and the other starting on D♭.

    c – d – e – f# – g# – a# – c

    d♭ – e♭ – f – g – a – b – d♭

    Whole-tone scales sound less driven toward a goal because they lack a leading tone. Every interval is equal so composers either playing with the fact that the music does not demand to go anywhere, or they find other ways to create a “tonic” note.

    A whole-tone scale can temper expectations and just let the music breath in a different way than a typical major or minor scale can.

    I’m sure music from other musical traditions have used the whole-tone scale, but I’m ignorant to those that do. I’ll keep my ears out for some examples to place here.

    Chromatic Scale

    In the equal temperament tuning system, the chromatic scale consists of 12 pitches equally spaced by half-steps (semitones). Of course, not all tuning systems are tuned to be a series of 12 equal half-steps. Some traditions, such as Indian music, tune using just intonation (just intonation is a tuning system that uses simple ratios rather than the complex ratios required to cut an octave into 12 equal pieces). A chromatic scale in just intonation will not have equal half-steps but it will still contain 12 pitches.

    Like a whole-tone scale, the chromatic scale has a difficult time establishing a “tonic” pitch because all intervals are the same (no leading tone). The chromatic scale in its entirety is rarely used, except in 12-tone music where it is exploited to the fullest degree. This is not to be confused with chromaticism which has been a feature of music since the beginning, it just may not have been called that. Chromaticism is when a composer introduces pitches that are outside the key. Since the voice can easily slip around pitches, human surely sang with “chromatic” inflections whether intentionally or not. To me, the difference between using the chromatic scale and chromaticism is that if a piece uses the chromatic scale, it actively uses all 12 pitches with no key center. Whereas chromaticism has a key center and notes are going in and out of the key. Highly chromatic music might use all twelve tones, but if it is still using the language of a key, then it is chromaticism not using the 12-tone scale.

    For a fantastic example of early chromaticism, here is Carlo Gesualdo’s Sesto libro di madrigali. Just look at all the accidentals and lines moving by half-step. This is a great example of a composer not using triadic harmony but using counterpoint voice leading and their ear.

    Hemitonic – pentatonic scale

    Pentatonic scales are awesome! They seem to be an almost universal of human musical expression – they are found everywhere and at all times. According to Michael Spitzer (his book The Musical Human is very interesting) a bone flute dated around 40,000 BC was found and it has five finger holes to play a pentatonic scale! Here is Wulf Hein playing a reconstructed bone flute.

    Pentatonic means there are five pitches that make up the scale within an octave. Pentatonic scales come in a variety of flavors so here is but one large group – hemitonic scales contain one or more half-step (semitone).

    d – e♭ – g – a – b♭

    Japanese pentatonic. (I hear a bit of OK Computer in this)

    Of course, you can place the half step(s) anywhere you like.

    d – f# – g – a – b♭

    d – f# – g – a – b

    Anhemitonic – pentatonic scale

    Another flavor of pentatonic scales are those with no half-steps – anhemitonic. Here are a couple of examples:

    c – d – e – g – a = major pentatonic

    c – e♭ – f – g – b♭ = minor pentatonic

    major pentatonic
    minor pentatonic

    These can be grouped into major and minor. These scales are commonly used in rock and blues music. A blues scale just needs the “blue” note – the g♭ in the example below.

    c – e♭ – f – g♭ – g – b♭

    As long as you know the intervals used in the scale, you can transpose these to any starting pitch.

    Intervals of a minor blues scale: m3 – M2 – m2 – m2 – m3

    Hexatonic Scales

    These are six note scales. As with any scale it just means a collection of pitches with certain interval relationships. So, any six notes within an octave can be a hexatonic scale. With that said, it should be clear there are many hexatonic scales (including the whole-tone scale mentioned above). Below are just a few of the more common ones.

    Blues scales

    Blues scales can be viewed as a pentatonic scale with an added “blue” note. If you are a guitar player, check out this fantastic article with tons of examples https://www.jazzguitar.be/blog/blues-scales/

    Here are the minor and major blues scales.

    Many of the hexatonic scales can be made by placing mutually exclusive triads (triads that don’t share pitches in common) on top of each other. For example, two major triads would be:

    c – e – g + d – f# – a = c – d – e – f# – g – a

    You can do the same with minor triads:

    c – e♭ – g + b – d – g♭ = c – d – e♭ – g♭ – g – b

    Or augmented triads:

    c – e – g# + d – f# – a# = c – d – e – f# – g# – a#

    Or diminished triads:

    c – e♭ – g♭ + d – f – a♭ = c – d – e♭ – f – g♭ – a♭

    Tetratonic Scales

    These scales only have four notes to the octave. As with the other scales there are many possible scales that can be built on just four notes. These scales are not as common in modern day music. Four-note scales were more commonly found in ancient humans, though not as widely spread as pentatonic scales. Michael Spitzer writes about the importance of tetrachords in how early musicians organized and built the seven note scales that came to dominate Western music. The ancient Greeks used the interval of the perfect fourth as a building block for their music. A tetrachord is filling in the gaps of a fourth. For example, the following tetrachord spans the interval of a perfect 4th (c to f):

    c – d – e – f

    The Greeks would then layer on the next tetrachord:

    g – a – b – c

    And that gives us the C major scale.

    Spitzer goes on to express the importance of the interval of the 4th up until changing tastes preferred thirds.

    Here is an example of a tetratonic scale:

    c – e♭ – f – g – c

    tetratonic scale

    When playing around with these intervals, I inevitably end up with an “old” sound.

    Octatonic scale: Alternating half-steps and whole-steps

    This one is pretty self-explanatory, just pick a pitch and decide to begin with a half-step (semitone) or a whole-step (whole-tone) and keep alternating until you reach an octave. For example:

    c – d♭ – e♭ – e – g♭ – g – a – b♭ – c

    half-step whole-step octatonic scale

    c – d – e♭ – f – g♭ – a♭ – a – b – c

    These are members of the octatonic scale family because they have eight notes.

    There are many more scales to explore and when you add in the variable of different tuning systems and microtones the number of possibilities explodes!

  • What is music analysis? What’s it good for?

    During my undergrad, I heard the performance majors’ groans percolate through the theory classes: “Why do we need to learn what a Neapolitan chord is?” “Who cares about the rules of counterpoint?” Typically, when the performers fell asleep, that’s when I sat up.

    Music analysis is a powerful tool used to understand how and why music works. Analysis can be used for a variety of reasons by musicians of any genre. Using classical music theory and/or other techniques, music around the world can be better understood.

    In this brief article, I’ll cover some of the most common analysis techniques.

    What can be learned from music analysis?

    In a grandiose way, music analysis is trying to grasp why the particular rhythms and pitch configurations move us humans the way they do. Music theory and analysis investigate the power of frequencies and sound waves and how humans have learned to manipulate them and in turn manipulate ourselves. Sound waves are part of the very essence of the universe, so it seems appropriate to spend some time on this topic.

    Back down on Earth, what music analysis aims to do is uncover patterns and reasons for what we hear and experience. It asks questions like: “How was this piece structured? Why is that structure successful?” or “Why does this rhythm move us?” Or “How are the pitches related throughout the piece?” These are just a few of the most basic questions music analysis has asked over the years.

    Like music theory, analysis searches to explain why music is such a powerful force!

    Aural music analysis

    An often-overlooked form of music analysis is to use your ears! Though this may not be as “rigorous” as other types of analysis, it’s an important part of any analysis. Aural analysis is critically listening to the music – active and careful listening. Our ears are able to process many micro and macro elements of the music that may or may not be apparent when looking at the music written out on a staff. Key musical elements you may want to listen for are:

    • instrumentation
    • scale type or “pitch world”
    • tempo and meter
    • form
    • melodic shape
    • articulation
    • dynamics
    • music and lyric relationships
    • who is performing
    • surprising moments
    • emotional response (mood)

    The output of this type of analysis is typically a descriptive response. Whether written or spoken, the description aims to examine and explain the music in a way that increases our understanding of it. It should help the audience hear the music in a more nuanced and, hopefully, appreciative way.

    I believe this type of analysis should be a common addition to all types of analysis. At times when studying music theory, I got so deep into the “paper relationships” that I lost what it meant to the piece as a whole. Using our ears, rather than our eyes to investigate music is something every musician should be able to do.

    Roman numeral analysis

    Roman numeral analysis, a technique all music majors must learn, is all about harmony and structure. This analysis fundamentally explores the “vertical” nature of music (I’m using vertical to mean if you are looking at a staff the notes stacked on top of each other). This form of analysis works very well for music that was written with key signatures and written in the major and minor modes (this analysis doesn’t work well on modes such as Dorian, Phrygian, etc.).

    Roman numerals help show the harmonic relationships of tonal music. The roman numerals themselves come from scale degrees.

    Uppercase numerals indicate a major chord, lowercase indicates a minor chord. Figured base notation is typically added to give more information about the interval structures from the bass note up. See my article here that talks about figured bass.

    One of the fantastic uses of this analysis is it cuts through the note-to-note intricacies to reveal deeper structures. It can show more plainly what the ear is hearing when you strip away some of the complexity of the ornamentation.

    Another use is to show the cadential moments in the music. Cadences are typically important structures in the music and roman numerals help define the different types of cadences.

    Roman numeral analysis works well for the common practice period (Baroque, Classical, and Romantic periods) but is not so useful for earlier Renaissance or Middle Ages music or music form the 20th century onward. However, there are plenty of 20th and 21st century composers working in neo-baroque, neoclassical, and neo-romantic idioms that lend themselves to roman numeral analysis.

    Roman numeral analysis many not (probably doesn’t) work well on music outside of the Western music tradition. Music from other traditions has different, perhaps non-harmonic, organizational structures. Many times, they use scales in a different manner. Western music during the common practice period organized scale degrees and chords into a hierarchy of importance. Other music most likely doesn’t employ the same hierarchy. For example, some Thai music if analyzed through the lens of roman numerals looks like it just oscillates between I and V over and over. By this standard the music appears boring and repetitive, but this is because roman numerals are only able to show unimportant relationships in the music.

    Roman numeral analysis can work well on pop music, but a LOT of pop music regularly breaks the “rules” of classical chord progressions and voice leading as you can see in this example from Linkin Park. A chord progression of i – vii – VI is not your “standard” classical progression. And look at the “non-chord tones” in the melody! This is a perfect example where roman numerals do not help all that much to tell the story of this music.

    Shenkarian Analysis

    Shenkarian analysis takes roman numerals to their limits when it comes to showing the most fundamental structures of the music. The goal is to distill melodic and harmonic movements down to the most essential components of the music. Typically, Shenkarian analysis shows the bass and harmonic structure moving from I to V and back to I. There are usually small departures noted but most common practice music does fall into this large-scale structure. This analysis also shows the main outline of the melody by especially pointing out the moments in the music that establish a melodic progression moving from scale degrees 3-2-1.

    This book by Heinrich Schenker is a great way to see his analysis in action:

    Five Graphic Music Analyses (Dover Books On Music: Analysis) Paperback – Illustrated, May 17, 2012
    by Heinrich Schenker

    Centric Analysis

    Centric analysis can pull elements from roman numeral tonal analysis but also must approach music with a more atonal ear. Roman numerals may be useful but be careful because they may not have the same type of hierarchy associated with them in tonal music. Centric music is music that has a “most important pitch” that the music continually returns to, but it does not have all the expectations tonal music has. This is different than atonal music in that it typically works within some sort of scale or key signature but values different interval relationships than typical tonal music. For example, some modal music falls into the centric music category. Folk songs can exhibit more of these qualities where there is a chord progression happening it just does not fit tonal norms. Early music and music from non-Western traditions should be approached in this manner.

    You might be able to use roman numerals, but you will probably have to adjust expectations – meaning if you are looking for a I – V – I progression you may not find it. Other ways to approach this music is to investigate the melodic and bass patterns (as you would with pretty much any analysis method!). Examine how the pitches move toward the “center” note. You have to examine the piece of music on its own terms with its own musical vocabulary, you can’t rely as much on tonal crutches.

    An interesting book I like that looks at a transitional figure and has some great analysis is Bela Bartok: An Analysis of His Music by Erno Lendvai.

    Atonal (post-tonal) Analysis

    Atonal music is a wide-ranging term that can apply to many kinds of music. Where centric and tonal music have a “center”, atonal music usually does not. Atonal music does not have a key and can break other tonal norms such as form and structure. Atonality was the natural progression from the intensely chromatic music of the late romantic period to abandoning tonal structures.

    Atonal analysis, in my opinion, takes a lot of creative and critical thinking on the part of the analyst. When approaching an atonal piece, it is like a puzzle with no rules. With atonal music you will usually use set theory. Set theory is where each pitch is assigned a number (see below). By converting notes on the page to numbers it’s easier to see relationships and ways in which the composer manipulated the musical material. I have an article that goes into the relationship of numbers and music analysis here: Music theory and math – understanding connections – Global Music Theory

    Set theory is one tool to use when investigating an atonal piece but you should also examine the phrase and formal structure of the piece. With atonality I find that investigating texture, dynamics, range, articulation, rhythmic manipulations, can expose a lot about how the piece was constructed. Many composers use these non-harmonic elements of music as structural – meaning perhaps instead of a V – I cadence, the texture goes from thin to dense to signify a breathing point in the music.

    There are many fantastic books exploring the different approaches to post-tonal music, but a couple of approachable books to start with are:

    Introduction to Post-Tonal Theory Fourth Edition by Joseph N. Straus

    The Structure of Atonal Music by Allen Forte

    12-tone Analysis

    Here’s 12-tone music by Alban Berg: https://www.youtube.com/watch?v=P0GzNmf_AUw

    Where atonal music has no preconceived rules or expectations, 12-tone music has a strict ideology behind it. The idea in 12-tone music is to play all twelve pitches in a specific order. Then the composer manipulates the order, texture, orchestration, dynamics etc. of the music. Some music follows this absolutely and some is a little more relaxed so be aware that there is some gray area. Once the prime row of a 12-tone piece is found and the manipulations of the row are pretty well laid out I find it is more interesting to not look so much at the pitches but all the other elements of the music to form a better picture of what makes the music work.

    A good book exploring this topic is Twelve-Tone Tonality, by George Perle

    Spectrum Analysis

    To be honest, I’m not entirely sure what the formal name of this kind of analysis is, but it is where we capture a recording of the music and analyze the sound waves rather than only notes on a page. This method is great for music that can’t really be transcribed into staff notation. Or for music where a notated version offers no insights.

    For example, for an ethnomusicology class I was assigned a Buddhist chant to analyze. In my naivety I started to write the chanting down. Needless to say, I quickly realized that was the wrong approach to the music. The shifts in pitch were too subtle to be captured on a staff. There was no discernable rhythmic pattern. The “melody” was non-existent. There was a lot to say about the context of the chanting (i.e. location of the chant, who was chanting, what were the words and intent behind the chanting, etc.) but I needed to comment on the musical quality of the chant as well. I took the recording and loaded it in some basic audio editing software and was able to more clearly identify the phrasing, the rise and fall of pitch over longer periods. Since this was chant, rhythmic patterns were mostly connected to the text of the chant but there were large scale sections where the music moved at a faster meter. Through the lens of the sound waves, I was able to line up the text and make more insightful connections between all the layers of the chant.

    Approaching music outside of the Western tradition

    Some music just can’t be approached using the tools of Western music theory. Well, let me take that back a bit, you certainly can try to use the tools developed by Western music theory and you may find something interesting, but you are more likely to miss the larger point of the music.

    Many cultures don’t conceive of music as the West does. For example, there is a type of music that is more akin to a game. There is a loose set of rules, and the game is different every time it is played. Just like every soccer game is the same but different, that’s how this music is “performed.” More than that, the performers may not even really be identified. The people just join in and stop whenever they please on whatever pitch they please in whatever time and meter they please. The idea of writing down this music would make virtually no sense. This is where a contextual understanding of the music will tell a more interesting story than a detail note-by-note analysis.

    With all that being said, I think the tools of Western music theory can be used to understand in broad strokes the music of other traditions, care just has to be taken to not miss what is really happening. There are many musical traditions that don’t lend themselves to being written down, so trying to forcefully write them onto a staff just butchers the music leaving most analysis tasteless and uninspiring.

    https://www.youtube.com/watch?v=j9aV1547Lic

    Thoughts on the utility of analysis

    There were, heck there still are times when I’m doing an analysis and I have to take a step back and ask myself, “what is the point?” Music theory can become so obsessed with the minutia of a piece of music – how does this 32nd note relate with a whole note two hundred measures later? – maybe the analysis does discover something interesting, but it can often beg the question, “who cares?” This is where the musicologist side of me comes out and I try to examine the music within the context of the composer, time period, location, basically, how does the music impact people!

    I’ve written a short book for composers that explores how music is organized and the roles it can play across the globe. The book is called Formative Forces in Sound. If you are interested, it’s available on Amazon here for $0.99 www.amazon.com/formativeforcesinsound

  • Music theory and math – understanding connections

    This idea that music is math or at least mathematical, is one that I encountered often at the university. To be fair, virtually anything can or does involve numbers and math. But music shares a famous truism with math, they’re both “universal languages”. Whether both deserve that “universal” status could be debated but there must be something to this idea that music and math are bonded in some way, right?

    In general, music theory maps well to mathematical concepts. Notable sub-areas of music theory that work particularly well are: set theory, twelve-tone theory, scales, and tunings. Music did not come from math, but numeric notation and mathematic operations work well to describe music.

    In this article, I’ll look at some of the ways math and numeric notation have been incorporated into music theory. There are mountains of books written on each of these topics, so please keep in mind I’m just scratching the surface of the surface here.

    I’ve written a short book for composers that explores how music is organized and the roles it can play across the globe. The book is called Formative Forces in Sound. If you are interested, it’s available on Amazon here for $0.99 www.amazon.com/formativeforcesinsound

    Numeric notation

    In this case, I’m talking about when numbers are used for performance purposes, meaning the music was at least partially written down in a numeric form.

    Figured bass music notation

    The first example comes from the Baroque era (about 1600) called figured bass or thoroughbass. This system of notation is interesting because it uses both typical staff notation alongside a numeric notation underneath. Figured bass was used for accompaniment parts and was widely practiced up through the classical era. But musicians as late as Arnold Schoenberg noted that he may have been part of the last generation to use figured bass, showing this was a long-lasting form of notation (I learned figured bass in school, but never had to play from it).

    Tablature music notation

    Tablature style of notation is where numbers represent finger positions but do indicate other performance instructions. For example, tablature does not notate rhythm, articulation, or dynamics. This style of notation was popular for keyboards and lutes starting in the 1400s and is still used today! If you are a guitar player, then you have more than likely played from a tab at one time or another. I learned to play guitar by reading tabs. In many guitar books one will find tabs and standard music notation on the same page.

    Musical scales and tuning

    Scales and tuning from ancient times until the present all use ratios and proportions to create a series of pitches. The earliest evidence of standardized tunings was transmitted in cuneiform, a writing system from around 3200 B.C. in Mesopotamia and Persia. Surely, by the time the tunings could be written down, some basic measurements and mathematical principles were used by the musicians when creating the tunings. However, most tunings and scales began by humans using their ears, not by calculations – their ears were making calculations that would later be codified by math. Math helped bring an aural tradition to a written notation by being able to more accurately convey scales and tunings across instruments, time, and cultures.

    Pythagoras and modes

    One of the most well-known stories of math intersecting with music is when Pythagoras was working out ratios of the overtone series on a single string. He was investigating the pitches created when shortening a string. Pythagoras was also a mathematician (the Pythagorean theorem), so math was a core piece of his work. The Greeks codified the musical modes of Western music:

    1. Ionian
    2. Dorian
    3. Phrygian
    4. Lydian
    5. Mixolydian
    6. Aeolian
    7. Locrian

    Each mode is a different permutation of intervals containing seven notes.

    Mode permutations of intervals described by number of half steps between each note.

    ModeInterval Pattern
    Ionian2212221
    Dorian2122212
    Phrygian1222122
    Lydian2221221
    Mixolydian2212212
    Aeolian2122122
    Locrian1221222

    Tunings and scales both came about through different paths depending on the culture devising the systems. Many musical cultures may not be able to describe their systems in mathematical terms because that is not at all how they think of them. Perhaps precise tunings and intervals are not necessary pieces of the music, but rather performing the intent of the music is all that is required.

    Twelve-tone equal temperament tuning

    The Western tuning system eventually landed on twelve-tone equal temperament. Zhu Zaiyu, a Chinese mathematician and music theorist developed the system around 1580 CE. If you look at a guitar you will count twelve frets that go from the open string to the octave. Moving from one fret to the next are equal half steps. Math was imperative to precisely achieve this tuning. Here is the equation:

    {\displaystyle {\sqrt[{12}]{2}}=2^{\frac {1}{12}}\approx 1.059463}

    Many have experimented with tunings and scales throughout musical history. Some used their ears, and some relied more on math. Harry Partch, the 20th century American composers, created many microtonal scales. His most used scale is the 43-tone scale. Without going too far down the microtonal rabbit hole, Partch wanted to explore sounds that were foreign to Western ears. He based his scale on the 11th limit – the 11th partial in the overtone series. He believed this was the natural next step for music.

    Analysis and composition

    Finally, let’s look at how math has been used in analysis and composition.

    Set theory

    Set theory assigns each pitch a number. From there mathematical operations can be performed. With this theory you can easily analyze intervallic relationship and transformations that happen across the piece that may have been obscured by standard music notation.

    Here is an example of transposition using pitch class notation:

    A C major chord in pitch class notation is 047. Let’s say we want to transpose it up by four half steps. Just add 4 to each of the pitches:

    • 0+4 = 4,
    • 4+4 = 8,
    • 7+4 = 11(E)

    Our new chord is 48E or EG#B an E major triad.

    Set theory enables analysis of both tonal and nontonal music. It can also handle scales that are in different modulos. The diatonic system is in “mod 12”. This means you count 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 2… But you can also have mod 5 (1, 2, 3, 4, 1, 2…).

    Set theory in music is obviously heavily mathematical. In my undergraduate days, I took a math and music class that was taught by Jack Douthett, a PhD Mathematician. As a composer, set theory and mathematical operators can be used as a basis for compositions or ways to generate material – moving from explanatory theory to being an engine for creation.

    Twelve-tone analysis

    Twelve-tone music is usually analyzed by using set theory but with one additional condition, ordered sets. In twelve-tone music there is the prime “row” which is a fixed order of the twelve equal tempered notes.

    Once the prime row has been identified one can determine how subsequent rows have been transformed. Common transformations (operators) in twelve-tone music are:

    • transposition
    • retrograde
    • reflection
    • complementation
    • multiplication
    • permutation

    All those operators maintain specific relationships with the prime row. From the example above the following chart can be created that shows many of these transformations. It’s called a 12-tone matrix.

    I-4I-7I-6I-3I-9I-TI-2I-0I-8I-5I-1I-E
    P-447639T20851ER-4
    P-1143067E952T7R-1
    P-22541780T63E8R-2
    P-55874TE319620R-5
    P-EE21T45973086R-E
    P-TT10934862E75R-T
    P-66985E042T731R-6
    P-88ET712640953R-8
    P-0032E56T84197R-0
    P-33652891E7409R-3
    P-77T960153E842R-7
    P-990E823751T64R-9
    RI-4RI-7RI-6RI-3RI-9RI-TRI-2RI-0RI-8RI-5RI-1RI-E

    There’s a lot to explain about this matrix, but I’ll leave it here for now. If you are curious, I recommend the following books.

    Here is an example of some twelve-tone music by one of my favorite composers in this style, Anton Webern.

    At this point, some may ask if music is math or art? Music is an art that can be described by using numbers and mathematical operators. Do you need math in order to create music? Absolutely not! Even when composers use numbers and mathematics to generate ideas and form pieces, including the extreme serialism of Milton Babbitt, it is a work of art. There is intent of expression beyond the notes on a page.

    Roman numeral analysis

    Roman numeral analysis is one of the basic foundations of an education in music theory. This analysis opens a way to see the relationships of harmony. By ascribing chords a number, theorists can more easily examine key elements of the music such as form, phrasing, cadences, and function. This type of analysis is designed for tonal music. Using it on pre-tonal or post-tonal music has very limited application.

    Some important ideas to know about this type of analysis is that you must be working with a piece of music that has a key. You will also have to know the names of the notes of the scale being used. The notes of the scale are called scale degrees and each scale degree corresponds to a name. Roman numerals come in capital letters for major quality triads and lower-case letters for minor quality triads.

    Scale DegreeNameRoman Numeral
    1TonicI/i
    2SupertonicII/ii
    3MediantIII/iii
    4SubdominantIV/iv
    5DominantV/v
    6SubmediantVI/vi
    7Leading toneVII/vii

    Roman numeral analysis is combined with a kind of figured base notation to indicate the intervals up from the bass note. This shows more detail and helps cut through what might be obscured by the notes on the page. I won’t go into what all the notation means but the fact that we are using numerals to better analyze and describe the music is the point.

    One of the most powerful insights that can come from this analysis is understanding the function of the harmony in relation to the entire piece. In tonal music there is a hierarchy of importance: tonic is the most important, dominant is next most important, etc… Heinrich Schenker, (1868–1935), took this concept to its extreme by breaking down large scale works to their most principal relationships – that of the tonic and dominant. Here is what one of his analyses may look like. The example is an analysis of 62 measures. As you can see it is highly condensed and the roman numerals and numbers above show the major structures of the music. The numbers above indicate the scale degree decent from 3 to 1.

    Like I said in the beginning of this article, I’m only scratching the surface of the surface. There are countless books on this topic, and I certainly won’t do it justice here. If you are interested in learning more about this kind of analysis, I recommend these books or this course.

    AI compositions

    Lastly, I wanted to include music that comes exclusively from numbers – compositions by artificial intelligence. The very “nature” in which these compositions are achieved are by ones and zeros. Even though the programs were trained and taught patterns in music, they create new and novel pieces. In my opinion this is the deepest level of numbers and music that is currently happening. Here is a video exploring a few pieces composed by AI and humans side by side.

    Math and rhythm?

    The extent of my knowledge on this topic is limited to compositional explorations. For example, exploring time signatures (expressed as fractions – hello math!), polyrhythms, and metric modulation. Unfortunately, I do not know any of the “theory” behind these techniques, so I did not discuss them above. I did not include math and rhythm because I’m unfamiliar with rhythmic theory. I know there has been a lot of work in this area but I need to read up on it. So forgive me for excluding this important part of music, it is due to ignorance not interest.