The Musician's Desk - Music theory resources and blog

November 14, 2011
by Alec
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Introduction to Sound and Acoustics

Sound is a constant part of our everyday lives; indeed we cannot turn off our own ears from detecting and interpreting the world of sound around us. As musicians, we constantly create sound through our various instruments. However, many musicians do not possess a full understanding of what sound is, or of how it is created and manipulated in the musical world. This post will attempt to cover the basics of sound and acoustics, particularly with respect to musicians.

What is Sound?

Sound can be defined as a vibration in the particles of a medium (typically air) that causes an auditory sensation within the ear. As an object vibrates, the vibration displaces the molecules of air around it, causing a chain reaction of motion through the air. The particles move back and forth from their point of rest in patterns of compression (particles closer together) and rarefaction (particles farther apart from each other). These high and low pressure areas shift through the air as the energy is passed from molecule to molecule.

This pressure variation hits our eardrum, causing it to move in and out in the same way as the particles move. The number of times the particles are displaced back and forth on the eardrum is interpreted by our brain as the frequency, or what we would commonly call the pitch. The more times the molecules vibrate back and forth per second, the higher the frequency of the perceived pitch. We measure this frequency using the unit Hertz (Hz), which is a measurement of cycles per second. A normal human is born with the ability to perceive sounds between 20Hz and 20,000Hz (or 20 kHz), but as we get older, our sensitivity to sound decreases due to damage to our ears and aging processes, particularly with respect to high frequency sounds. In actuality, an adult human probably is sensitive to sounds only up to 16,000Hz – 18,000Hz (16-18 kHz).

The perceived volume of a sound source is a result of how far it vibrates away from its equilibrium and how much it displaces the molecules around it. Greater amplitude of displacement will result in greater eardrum movement. Our brain interprets this as the perceived volume of a sound. Greater energy applied to the eardrum will mean louder sound in our brains.

Now that we understand how sound is created and propagated through the air, we can begin to understand how our instruments function, both in terms of in an acoustic space, and on a recording. These concepts of vibrations, coupled with the physiology of our ear, are the foundation of how we hear sounds, and how we listen to and interpret music. We will delve further into these topics in the next posts, and we will explore other aspects of sound and acoustics, in order to help both the musician and listener understand the world of sound and music.

October 26, 2011
by Taylor
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Sheet Music of the future?

When historians of the future look back on the year 2011, they will certainly point to the rise of digital content and the growth of electronic resources as important trends of our era. Smart phones, streamed content from the internet, “cloud” computing systems and social media all provide us with information in fast, exciting new ways.

I recently came across two videos online which made me wonder – how will new technology affect the sheet music of the future? Electronic screen-equipped music stands are already in use by many studio orchestras and touring groups, but will the basic format of written sheet music eventually become a thing of the past?

The first video is entitled “Animated Sheet Music: ‘Giant Steps’ by John Coltrane” and the format is exactly that – an animated version of the printed sheet music which is lined up with the music. In other words, each note appears on the staff in rhythm, as it is played. Watch it here:

This is a very interesting way to read the music – while it is obviously not practical if you are trying to play the music yourself (since sight-reading would be impossible), it could be very useful as a tool for study or learning. Seeing the notes appear exactly as they are played connects the visual and auditory aspects of the rhythms and note values, and gives a sense of the contour of the phrases (watching the notes step up or down, etc.)

The second video is in a similar vein, except instead of printed sheet music, it uses a “bar-graph score” to notate the music. A series of coloured dots connected with lines are read from left to right, and as the notes are played, the dots light up. Different colours are used to distinguish separate musical lines in the piece, which is particularly interesting and engages the listener’s ear to more than just the surface elements of the music. As well, the bar-graph is an excellent way of notating rubato and the rhythmic nuances of the performance.

While printed sheet music is likely here to stay (at least for the foreseeable future), it is certainly interesting to wonder how new and emerging technologies will shape the way we read and learn about music. Will printed notes and rhythms eventually become obsolete, replaced by bar-graph scores and visual representations?

What do you think? Your thoughts are always welcome!

October 17, 2011
by Taylor
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Arranging Basics: Getting Started

Writing or arranging your own music can be incredibly rewarding. The feeling of standing in front of an ensemble and hearing them play your music is like nothing else! While arranging, like any other skill, requires a lot of time, dedicated hard work and practice to master, for many people one of the hardest parts is just getting started.

There’s no magic bullet to explain how to start the writing process itself (you just sort of have to take a stab at it) but here are a few things you’ll need before you begin.

1. Make sure you have the right supplies

If you’re writing your music by hand, you’ll need:

A soft lead pencil and good quality eraser
Score paper (music paper with the right number of staves for the ensemble you’re writing for)
Extra manuscript paper and/or extra lined or blank paper for notes and sketches

If you’re going to use the computer, you should have:

Music notation software (Sibelius or Finale are two of the most common)
An input device (this might be your computer keyboard/keypad, or a MIDI controller/keyboard for note entry)
Extra manuscript paper and/or extra lined or blank paper for notes and sketches

2. Set up your score

How the score pages are laid out depends on the size of group you are writing for. If you’re using computer software, there are usually many pre-made templates that you can select when you’re first creating the file (“orchestra”, “big band”, “woodwind quintet”, etc.). These will organize the score pages for you and label the staves appropriately. If you’re writing by hand, you’ll need to do this yourself.

For formatting, there is a basic set of conventions that should always be followed, to avoid confusion or ambiguity. The first page of the score needs to have a title, credits for the composer, arranger (which in this case is you), and all pertinent musical information (tempo, stylistic indication, key signature, time signature, etc.). Staves should also be labelled with the full names of all instruments used in the score. If a player uses an additional instrument later on in the score (for instance, if your alto saxophone player switches to flute later in the piece), this should also be indicated on the first page. This would be written as “Alto Saxophone, Flute” or “Alto Sax w/ Flute”.

Here is an example of a properly formatted first page of a score (in this case for big band):

A handwritten page should follow the same conventions as a typed one. With handwritten scores, ensure that you write as clearly and as legibly as possible. After the first page, the full names for the instruments don’t need to be indicated, but typically abbreviations are still used (“Fl.” for Flute, “Gtr.” for Guitar, etc.), to make the score easier to read at a glance.

3. Make a form map or plan

Arrangements usually unfold with a structure or form in mind. Because of this, many arrangers begin by making a short visual plan or framework called a “form map” on a blank sheet of paper to show the structure of the arrangement and help them plan ahead. This can be very helpful because (a) it makes you to consider the formal structure, length and design of the arrangement early in the process, so that the result is logical and well-constructed, and (b) it can keep you on task, since you can skip ahead to write bits of later sections of the piece without losing your place.

The form map does not have to be set in stone right away, and it shouldn’t “box you in” musically – the point is to aid and assist your creativity, not stifle it – but it can be a very effective and useful tool for you to use when arranging. Form maps can be written in many different ways, but a simple one might look something like this:

As well as making a form map, it can often be helpful to write down descriptive words or concepts about your arrangement before or as you start. This is why you need extra blank paper – you might get a quick musical idea, or a word might pop into your head and you need to be able to strike while the iron is hot!

OK, time to get started! There’ll be lots more posts on arranging to come, and as always, you can leave your questions or suggestions in the comments below.

October 7, 2011
by Taylor
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Can computers compose music?

Recently a friend of mine sent me the link to an article entitled “Algorithmic symphonies from one line of code — how and why?” from a blog called countercomplex. The author describes how he and others have written short computer programs (consisting of only a few lines of code) which create audio output based on algorithms. The article is quite detailed and focuses on the mathematics and detailed code used in the programs, but for the layman, accompanying the article is a great Youtube clip of the audio generated by seven of the programs:

Since I’ve always tried to listen to music with an open mind, approaching many varied genres and styles for inspiration and enjoyment, I found this video and article fascinating and thought-provoking. If the sound is merely mathematical information being generated by a computer, does it qualify as music? The patterns are not heard as simply random noise; it is clear that there is a logic and structure inherent in their design. Is that enough?

It led me to think: in this case the “music” is generated by a computer, but are we actually doing something very similar when we compose? Composers spend time arranging ideas and motives (or are they patterns and algorithms?) to generate sounds which are structured and logical – even mathematical at times. What, if anything, keeps this computer-generated output from qualifying as music? In a hundred years, will beeps and bloops and squelches be the tonal language of music?

What do you think? Add your thoughts in the comments below!

October 5, 2011
by Taylor
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Understanding Chord Symbols, Part Three

In part three of this series, we will look at chords with alterations, extended chords, chords with added notes and alternate bass notes, and the chord symbols used to display these more complex chords.

Chords with Alterations

A note within a chord may be altered by adding a flat or sharp. We have already looked at an example of this in Part Two – the minor seventh chord with a flat 5th – m7(b5). This basic format is used to indicate a basic chord with an altered note: the note name, followed by the basic chord suffix, followed by the alteration(s) indicated in brackets. Here are some examples of how these chords are notated:

The dominant seventh with a suspended fourth occurs frequently in many styles of music, and because of this, the chord symbol shown above is often abbreviated to simply F7sus (i.e. omitting the “4″ from “sus4″).

Extended Dominant Chords

If you continue to “stack” notes in thirds, a variety of extended chords are possible. With dominant chords especially, notes can continue to be added and altered to produce a wide variety of chords. Musicians enjoy these chords because they are very interesting and colourful. Chord symbols for some of the basic types of extended chords are shown below:

Chord symbols for extended dominant chords replace the normal dominant seventh suffix “7″ with the highest extension found in the chord. An important note, however: the eleventh chord shown above is rarely found in this form because this vertical stacking can produce unwanted dissonant intervals. To illustrate this, try playing the third and eleventh of this chord on the piano – you will hear a fairly strident dissonance. Most of the time, the dominant eleventh chord is played without a third, and the thirteenth chord usually omits the 11th from the voicing.

Additional Extended Chords

The same principle of “stacking” can be applied to the other basic chord types as well. Their chord symbols are structured the same way, with the highest extension being added to the basic suffix. Here are some examples:

Note that the minor eleventh chord is not as problematic in its stacked form, because the dissonance between the minor third and eleventh is less harsh.

Extended Chords with Alterations

An extended chord which contains altered notes is notated using the same basic principle: the note name, followed by the suffix for the basic chord type up to the highest extension and the alterations in brackets. Brackets are used in order to distinguish the altered notes from the basic chord type. Since there are a great many possibilities, here are six examples:

These chord symbols will seem less confusing if you remember the basic rules for how they are constructed: the note name, the suffix for chord type, and any additional information or alterations indicated in brackets.

Chords with Added Notes

A chord can also have a single note added to it. The most common added-note chords are the major sixth chord, major sixth/ninth chord and the add-2 chord. They are indicated like this:

The add-2 chord is often indicated as add-9. The “add” suffix is necessary to differentiate this chord symbol from that of a dominant ninth chord.

Chords with Alternate Bass Notes

All of the chord symbols we have looked at so far have been in root position (in other words, the note name in the chord symbol is also the note in the bass – the lowest note of the chord). To indicate an inversion or a different bass note, a slash symbol is used. The basic chord symbol is written first and the alternate bass note follows. Some examples:

Hybrid Chords

Hybrid chords or composite chords are constructions which are made up of two chords at once. They differ from added-note and extended chords because they are usually voiced as two distinct chords, one above the other. These are indicated as fractions, with the higher chord indicated above the lower chord, like so:

In Summary

This completes our three-part series on chords. Chord symbols will seem much less complicated if you just remember the basic format of the symbols and the guidelines for how they are put together.

Remember to post questions or thoughts in the comments below!

October 4, 2011
by Taylor
1 Comment

Understanding Chord Symbols, Part Two

In Part One, we covered the chord symbols for major triads, minor triads, diminished chords and augmented triads. In today’s post, we will look at how the basic types of seventh chords are represented with chord symbols.

Dominant Seventh Chords

The most common form of seventh chord is the dominant seventh. To review, a dominant seventh chord is a major chord with a flattened seventh added above it – in other words: C-E-G-Bb.

The chord symbol used to represent a dominant seventh is simply the note name and then a superscript “7“ following the note name:

Minor Seventh Chords

A minor seventh chord consists of a minor triad with a flattened seventh added above it – in other words: C-Eb-G-Bb. It is represented by the note name and lower case “m” used to indicate the minor triad, and the superscript 7.

In the same way that a minor triad is sometimes represented by a minus (-) sign, a minor seventh chord can sometimes be written as C-7. For reasons of legibility and to minimize confusion, the lowercase “m” is preferable.

Major Seventh Chords

A major seventh chord consists of a major triad with the natural seventh above it – for example, C-E-G-B.

There are several chord symbols which are used to represent the major seventh chord. The clearest of these is the suffix “maj7″, which follows the note name, however an uppercase “M” is sometimes used (appearing as “M7“), and on occasion, a triangle following the note name is used. The uppercase M is problematic, especially in handwritten music, since differences in case are not always easy to spot (and so confusion about major and minor chords can easily result), and the use of the triangle just further complicates the system of chord symbols.

It is important to know that these symbols exist, since they do appear in printed music, however the diagram above gives a good example of how they might be confusing or unclear.

Half Diminished Chords (Minor 7-flat 5)

A half diminished chord consists of a diminished triad plus the flattened seventh above the root - C-Eb-Gb-Bb. This type of chord is typically found in a minor tonality, and is very common in jazz.

The chord symbol for a half diminished chord consists of the note name followed by the suffix “m7(b5)“. Other symbols used for this chord are the small circle (like a diminished chord) with a line through it, or the words “half-dim7” as the suffix. These look like this:

The “m7(b5)” symbol is an example of how almost all “extended” chord symbols are written – the note name, then the first part of the suffix showing the basic type of chord, and the material in the bracket showing the extra information or alterations.

This is what will be covered in the next post – part three, so stay tuned! And as always, post comments, questions, and/or additional insight in the comments below.

September 30, 2011
by Taylor
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Understanding Chord Symbols, Part One

Chord symbols are a clear and concise way of indicating the harmony in a bar of music – a kind of musical shorthand that can be quickly read while still providing all of the information you need to know.

Major Chords

The simplest chord symbols are the symbols which represent major chords. These consist of only a single letter, and look like this:

The letter represents the name of the note that is the root of the chord, and because nothing follows the letter, this implies that a major chord (in other words, a major triad) should be played over that root.

Minor Chords

The symbol for a minor chord includes the single letter to indicate the root, and also a lowercase “m” following the note name to indicate that it is a minor chord:

Sometimes a minor chord is indicated with a minus sign (-) instead of the lowercase “m”, however this is not always the best visual indicator, especially if the music is handwritten.

Diminished Chords

A diminished chord is a minor chord with a flattened fifth. There are two different chord symbols which can be used to indicate this structure: a small circle following the note name, or the abbreviation “dim” following the note name. The circle is usually favoured because it is a visually distinct symbol, making it easy to spot and identify, however both are used.

Note: the same chord symbols are used to indicate a three-note or four-note diminished chord – in other words, the chord symbol Cdim represents both C-Eb-Gb or C-Eb-Gb-A.

Augmented Chords

An augmented chord is a major chord with a sharp fifth. Again, there are two different symbols which are commonly used: a plus sign following the note name, or the abbreviation “aug” following the note name. The use of the plus sign may create confusion or ambiguity however, since +/- may incorrectly be interpreted as indicating major and minor. For this reason, the abbreviation “aug” may be more clear.

To Be Continued…

The next post will examine four-note chords and their chord symbols. As always, post questions, suggestions or thoughts in the comments below!

September 28, 2011
by Taylor
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Arranging Basics: Instrumental Ranges

Writing music One of the most basic skills necessary to start writing your own music is an awareness and familiarity with the ranges of common instruments. Without this knowledge, you might write a passage of music that is unintentionally difficult or tricky or worse, impossible to play.

With only a few exceptions, most instruments have a defined range of notes which they are technically able to produce, and also a “comfortable range” – the range which most players of the instrument are able to play with facility and ease. If you write music which stays within these comfortable ranges, it will almost always sound good!

While you shouldn’t feel artistically limited or constrained by these guidelines, when you’re first learning it is probably a good idea to write conservatively for the instruments you are writing for – until you get a better grasp and familiarity with doing it.

Below is a chart of the ranges of many common instruments with complete and comfortable ranges indicated. You may find it useful to download and keep this, for study and reference.

Note that even these ranges can vary depending on the skill level of your ensemble – student groups may have trouble with the “comfortable” ranges written here, especially with regard to intonation and control. Brass players may also have trouble staying in a high register for a long period of time, since the instruments are physically taxing to play.

Download this document as a PDF here:

What do you think? As always, suggestions, thoughts and questions are welcome in the comments below!

September 27, 2011
by Taylor
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The Circle of Fifths Explained

The circle of fifths is a visual representation of all twelve notes of the chromatic scale arranged in a circle (similar to a clock face). You may have seen the circle of fifths (or “cycle of fifths” as it is sometimes called) before, but you may not be aware of exactly how it is structured or what its use is.

Basic Chord Relationships

If you proceed around the circle in a clockwise direction, you will find that each successive note is a fifth higher than the last one. Starting at C, the note a fifth above is G, then a fifth above that D, and so forth. And, going counter-clockwise, each note is a fifth below (or a fourth above).

Some of the most common chord progressions in music can be found by moving clockwise or counter-clockwise around the circle of fifths. One step to the right is I – V and one step to the left is I – IV (or V – I). This means, any set of three adjacent notes on the circle of fifths makes up I – IV and V in that key (for example, C, F and G in the key of C). This is pretty useful if you want to learn the blues!

If you continue moving counter-clockwise, you will find a common progression in many jazz standards or popular “tin pan alley” songs – take, for example, the root motion of the first four chords in Autumn Leaves:

This is exactly four steps going counter-clockwise on the circle (the bass moves by a descending fifth or ascending fourth). An even longer example (a series of eight counter-clockwise steps), is found in the bridge of the song:

Because these kinds of chord progressions occur so frequently in many styles of music, being comfortable moving around the circle of fifths and developing a good working knowledge of these relationships are both very useful skills.

Key Signature Relationships

In addition to learning chords and chord progressions, you can use the circle of fifths to help understand key signatures and how they are related. As you move clockwise around the circle of fifths starting at C, one sharp is added to the key signature each time. Moving counter-clockwise, flats are added. Eventually, at the bottom of the key signature, you arrive at F# major (six sharps) or Gb major (six flats).

Knowing this can aid in memorization of the key signatures and also help you grasp how the keys are related. Keys which are in close proximity on the circle of fifths have similar key signatures and have many notes in common.

Minor Key Relationships

The minor keys are related in the circle of fifths in the same way that the major keys are. The minor keys are indicated on the diagram above in the centre of the circle, matched with their relative major (as in, A minor and C major are together). This can be very useful in identifying and memorizing relative minor keys and minor key signatures.

In Summary

The circle of fifths is jam-packed with musical information and can be a very useful learning tool and memory aid, because it visually represents many important relationships in music. Relationships between keys, chords and key signatures are often easier to see when displayed visually, like they are in the circle of fifths, and the diagram can be an important tool in learning basic chord progressions and memorization of theory concepts.

What do you think? Do you have your own tricks with the circle of fifths? Are you still confused? Post in the comments below!

September 26, 2011
by Taylor
2 Comments

12 Songs to Help You Learn Intervals

Musical Confusion Learning intervals can be tricky. Even though there are only twelve possibilities within an octave, when you’re first trying to learn it can seem as if the notes blur together into a soup of indistinguishable muck. Minor 3rds, major 6ths, minor 6ths – after a while everything can sound alike and you may need to go lie down for a while!

While you should be careful not to rely exclusively on this process every time you try to identify an interval, this simple trick can be a big help when you’re first learning: associating each ascending interval with the beginning of a well-known song.

Here is the list of songs and the interval with which they are associated:

Minor 2nd – Theme from “Jaws”

Major 2nd – The opening two notes of “Do, Re, Mi” or “Doe, a deer”

Minor 3rd - “O Canada”

Major 3rd – “Morning Has Broken”

Perfect 4th - “Amazing Grace”

Augmented 4th (Tritone) – Theme from “The Simpsons”

Perfect 5th - Theme from “Star Wars”

Minor 6th - “The Entertainer” (after the pick-up – the 3rd & 4th notes)

Major 6th – “My Bonnie Lies Over The Ocean”

Minor 7th - Theme from “Star Trek” (the original series)

Major 7th - Second phrase of the theme from “Superman”

Octave – “Over The Rainbow”

Here are some recorded intervals, for you to practice with. Each interval is played twice and there are four different intervals in each set.

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Do you have other songs which you use to identify intervals? Or advice for students of music theory? Post in the comments below!