Everything has intervals. Runners measure their success by the interval between their start and finish time. In math, an interval is the distance between two numbers (integers for you math wizzes). Although music is often seen as artsy and not based on anything concrete, music is actually very much based on math and today we’re going to look at an example of that.

In music, an interval is the distance between two notes and is expressed based on scale degrees. Let’s look at how to identify the basic intervals.

Let’s start with identifying the interval between C and E. If we count up from C (count C as #1) there are three scale degrees between C and E (C,D,E equals 3). For this reason, the interval between C and E is a third (3rd). What is the interval between D and A? If you count D as #1 and count up to A, there are 5 scale degrees between D and A which makes the interval a fifth (5th)

Nothing in music is that simple, though. There are different types of these intervals. There are Major 3rds, minor 3rds, Perfect 4ths, and minor 6ths to name a few but it’s not as complicated as it sounds. The amount of half steps between each interval defines the specific type of interval. Let’s look at a few.
What is the interval between C and Eb? Let’s count the half steps (C to Db, Db to D, D to Eb equals 3 half steps) 3 half steps equals a minor 3rd. Try this one on your own. What is the interval between D and A? Remember to count the half steps. The easiest way to do that is to count them on a piano. Then figure out the name: (“m” equals minor, “M” equals Major, “P” equals Perfect)

Did you say that the interval was a Perfect 5th? If you did, you got it right! Good job!
Before we call this lesson complete, two more quick facts: The reason that the fourths and fifths are called Perfect has to do with some advanced concepts grounded in acoustics but the short answer is that a perfect interval is more pure and stable than major intervals.

There are also diminished and augmented intervals as well as tritones. All of these advanced intervals will be addressed in later articles. For now, practice identifying the basic intervals and you will be well on your way to understanding the important points.

All music theory (the study of how music is constructed) is based on identifying intervals so put some work in to this lesson before moving on to more advanced topics.

For more musical knowledge, come on over to Play Piano Catalog and browse the many courses in music.

One note played alone is termed a“unison.” Two notes played simultaneously (or adjacent to one another) are termed an “interval.” Intervals are named by the distance between them, so there can be intervals of 2nds, 3rds, 4ths, 5^th, etc.  Chords are three or more notes (or pitch classes; strictly speaking, notes are the written form of pitches) played together. But these notes don’t necessarily have to be played simultaneously. Broken chords, or arpeggios, are three or more notes that aren’t played at the same time but closely enough to be heard as a group or whole. Sometimes in rock music the term “power chord” is used, meaning that the 3^rd is left out of a 3 note chord leaving just the root and 5^th.

Chords are most often named based on their number of notes or the type of intervals involved. Chords classified by note number are given names such as trichord (three notes), tetrachord (five notes), and hexachord (six notes). Chords classified by interval are given names such as tertian (third chords), secundal (second chords), and quartal (fourth chords). Sometimes chords are named based on both qualities. Tertian trichords, for example, are chords with three notes, each a third above each other. These type of chords are actually the most common in western music, found frequently in rock and pop.

These chords aren’t the only chords possible, however. There are several specialized chord types that seem to defy strict categorization. Inverted chords are created by turning any root position chord upside down. Seventh chords can be made by adding a fourth note to a triad — a third above the chord’s fifth — which makes the highest note a seventh from the root. Extended chords are those with notes that extend above a seventh, such as a ninth or an eleventh. But it’s important to mention that no extended chord can go above a thirteenth. By that point, the notes included will have already been played somewhere in the chord, taking it back down to an eleventh or thirteenth.

 A “slash chord” is a chord where the root of the chord is not the lowest note, which would include inversions, but also might include non-chordal notes. An example might be C/B.

 A “sus chord” – short for “suspension” – is a chord where the 3^rd of the chord is replaced by the 4^th.

The Nomenclature of Music: Unisons, Intervals, Chords from chordman on Vimeo.

Musical consonance and dissonance are the exact opposite of each other, like day and night. Though both refer to the type of sound achieved by playing a chord or interval, they produce radically different tonal types. Musical consonance is typically thought of as a pleasing or resolved sound; it is achieved by two notes that clearly complement each other and produce a comfortable chord or interval. Musical consonance is at the very heart of composition. Most songs consistently contain some level of musical consonance, whether perfect or imperfect (a classification coined during the common practice period); perfect musical consonance is found in perfect fourths and fifths, octaves or unisons, and imperfect musical consonance is found in major or minor thirds or sixths.

Musical dissonance, on the other hand, is a chord or interval that seems restless or uncomfortable. It can be achieved by playing a chord that doesn’t resolve the song, or two notes that very audibly clash with each other, such as minor seconds or major sevenths (usually notes that lie only a half-step away from each other). The concept of musical dissonance isn’t necessarily universal, however; what one era considered to be a musical dissonance is sometimes considered to be a musical consonance in modern times (for example, perfect fourths were at one time seen as dissonant). And in some eras, musical dissonance was even forbidden, all songs had to be resolved; this was an era in which perfect fourths and fifths were some of the only acceptable chords. In modern music composition, however, musical dissonance is not only allowed, it’s often encouraged. Rock musicians use dissonant chords like minor seconds and tritones to great effect and even classical composers employ musical dissonance to create a dark, specific mood.

In a sense, all music can be viewed as a contest between dissonance and consonance. If a piece of music was all consonance, it would be boring. If it were all dissonance, it wouldn’t be listenable at all. So every piece of music is crafted in a unique way to move back and forth between those two extremes to create both interest and pleasure.

Sight reading is the act of reading and playing a piece of music before having ever seen it: on sight. This technique is an important one for musicians to learn. Being skilled in sight reading makes reading a piece of music easier; the musician doesn’t have to labor over every note and re-teach themselves the common patterns. Sight reading, after a decent amount of practice, becomes like second nature.

A solid knowledge of music theory is absolutely crucial to a musician who wants to become proficient in sight reading. Besides acting as the basis for understanding the notes, a music theory education provides the ability to see patterns within the piece of music, a large part of the sight reading puzzle. Sight reading, after all, doesn’t require the musician to read every single note. Most musicians rarely see the entire piece of music, but rather the patterns that emerge from it. They understand notes and how they function in relation to each other and are therefore able to deduce most of the chords and changes — all from just glancing at the basic structure of the piece.

For example, musicians who know music theory will first determine the key of the song from the key signature, which in turn gives them strong hints about which chords will probably be used most in the song. This knowledge alone enables the sight reader to be mentally prepared when those chords occur, and to be alert for chords which are unexpected.

They will also be aware of intervals such as 3rd and 6ths and 7ths, and they will look for the form of the song - ABA, AABA, ABACA, or whatever. They will be aware of the probably rhythm patterns based on the time signture, and they will quickly scan the score for repeats, tempo signs, volume changes, and so on.

In fact, most sight reading mistakes typically happen when a piece of music takes an unexpected turn, deviates from the common pattern. These mistakes, however, are few and far between with those proficient in sight reading. An experienced sight reader will have learned to not only see patterns but also to read ahead in a piece of music while they are playing it. Looking several bars ahead to catch anything tricky or unexpected is often done while holding a sustain or resting.

Sight reading plays a large role in music education, and students are frequently tested on their ability to do it well. Some sight reading exams will allow the student a few minutes to look over the piece and prepare; he or she will be able to make notes, mark up tricky time signatures or changes. Tempo is rarely a consideration in these sight reading exams as playing the piece well is far more important than playing the piece up to speed.

Advanced sight reading exams, however, aren’t quite as forgiving. These exams give the student minimal, if any, time to prepare, and tempo is absolutely considered into the final grade. Advanced sight reading exams prepare a student for work as a studio musician, a career where near-perfect sight reading is a must. The majority of studio musicians record a piece of music after only seeing it once — sometimes not at all. A flawed skill in sight reading will only prove to be a hindrance to the working musician; it is for that reason considered one of the most important parts of a music theory education.

This does not mean, of course, that musicians can’t reach the top rungs without good sight-reading skills. After all, many top jazz pianists don’t read music at all, but are gifted with incredible ears and improvisational skills. But for most of us “normal” musicians (like me) it is a helpful skill to develop to the best of our ability. Even if we never get great at it, we can always get better!

Transposition is changing the key of a piece of music, or changing the notes without changing their relationship. This is often done to make the piece of music easier to play or sing. It’s a common practice in bands that don’t perform their own material; the singer may wish to cover a song with vocals that are far out of his or her range. Transposition can correct that problem by shifting the key into a range that is comfortable for him or her. Transposition is also used with instruments. Some instruments (called transposing instruments) are not tuned to the same note; for instance, a Bb clarinet is tuned to a B flat and an alto clarinet to an E flat. Transposition of the sheet music for these instruments ensures that they won’t sound discordant when playing with the rest of the orchestra or band.
Transposition may be a simple concept, but it take lots of practice to achieve. The easiest sort of transposition — and technically it is not transposition at all, since it remains in the same key - is done by octave — simply moving the piece of music up or down eight steps. This sort of transposition may work for a male singer wishing to sing a female’s part, but it does little for transposing instruments or other areas of vocal work. In these cases, it’s best to use transposition by either scale degree or harmonic interval.
Transposition by scale degree uses the scale degrees of a piece of music to determine the relationship between the notes. Each note in a piece is assigned a scale degree (tonic, dominant, subdominant, mediant, submediant, etc.) and the same scale degrees are used for the new key. This type of transposition is potentially simple, as the relationship between the notes will always remain the same, regardless of the key.
Transposition by harmonic interval uses intervals as a guide for the transposition. By finding the interval between the dominant notes in the two keys, one can deduce the interval between the all the notes. If the difference between the notes is a major third, then transposition of all the notes will be done by a major third. This type of transposition is also potentially simple but calls for an added carefulness when dealing with accidentals that aren’t expressed in the key signature.
The very best way to transpose is to learn to think in more than one key. Most beginners start learning in the key of C, so after awhile they can think in that key — they know where the notes in that key are, and their fingers can get to them easily. Since every key a person can play in is mathematically the same as every other key, by learning to play in a 2nd key one can learn to think in that key, just as they did in the key of C.
Keys are like languages: if you don’t know Spanish, you certainly can’t think in Spanish, and when you learn to speak it, you will have to rack your brain for the right word for quite awhile before you begin to think in Spanish. Its the same in music — there are only 12 major keys in which you can play (in contract to languages, where there are hundreds) — so if you can eventually learn to think in all those 12 major keys, there is no key left that you couldn’t transpose in to.
Practically speaking, however, most people don’t need to know all 12 keys — just the keys in which most songs are written: C, F, G, D, A, Bb, and Eb. If you can learn the other six too, that’s fabulous, but you can certainly get by with just those 6 keys, or perhaps even less — and least C, F, and G — the “big 3” when it comes to keys.

To learn more about transposing, go to How To Transpose & Modulate
and How To Think In The Key