Tag: basic music theory

Perfect 5ths & Perfect 4ths: An Octave Of Two Halves

An octave is 12 semitones. However, half an octave is 7 semitones – and the other half is 5 semitones!

How is this so? Surely half of 12 equals 6?

Frequencies

Each note pitch produces a repeating sound wave. Lower notes produce longer waves which repeat more slowly, whereas higher notes produce shorter waves which repeat more quickly. The speed at which a sound wave repeats is it’s frequency, measured in Hz (Hertz). 1 Hz = 1 wave cycle per second.

Composite Wave

When two (or more) notes are played together, their sound waves combine to form a composite wave. This wave also has a frequency. Playing two notes produces three!!!

The frequency of this combination wave is also a note. For example, below is an interval of a major 3rd.

Consonant intervals (intervals that sound musical) have frequencies which are closely related. The composite wave’s frequency is an octave of one of the two notes that make up the interval.

Dissonant (musically unpleasant) intervals such as a semitone or a tritone (augmented 4th/diminished 5th) have frequencies that are not closely related. As a result it takes many cycles of each note before they meet up to produce one cycle of the composite. The composite wave has a low frequency unrelated to either note which, if below our ability to detect pressure waves as continuous sound, can be felt as a disturbance known as beats or beating. 

For more on beats see The Secret To Tuning: How To Tune An Instrument To A Reference Note.

Octaves

When two notes are an octave apart, their sounds match so well together that we think of them more as being in different registers rather than as completely different notes. Notes which are whole octaves apart are considered to be different versions of the same note, to the extent that they share the same name.

When two notes are an octave apart, the upper note is 2x the frequency of the lower note. For example, if A = 440 Hz then the next A an octave higher is 880 Hz.

The composite wave is 440 Hz, the same as the lower note. 

Half An Octave

Half an octave is half-way between the frequencies of the two notes. In the above example, half an octave is half-way between 440 Hz and 880 Hz, which is 660 Hz.

660 Hz is E, 7 semitones above A 440 Hz.

Two Halves

  • A to E, the lower half of the octave, is 7 semitones
  • E to A, the upper half of the octave, is 5 semitones
  • A to E, the lower half, is a perfect 5th
  • E to A, the upper half, is a perfect 4th

If you’re wondering why a 5th plus a 4th is an 8th, please visit B5. Inversions Of Intervals.

Let’s look at the composite wave’s frequency of each half.

The interval between A 440 Hz and E 660 Hz has a frequency ratio of 3:2. That is, it tales 3 cycles of E and 2 cycles of A to form the composite wave. The composite’s frequency is 220 Hz, the A an octave below the played note A 440. This reinforces the lower note of the interval, making it stronger.

The interval between E 660 Hz and A 880 Hz has a frequency ratio of 4:3. The composite’s frequency is also 220 Hz, which is 2 octaves below the played note A 880. This reinforces the upper note of the interval, making it stronger.

In other words, the upper half of an octave, a perfect 4th, behaves upside down compared to the lower half, a perfect 5th.

  • In a perfect 5th, the lower note is stronger
  • In a perfect 4th, the upper note is stronger

Perfect 5ths and perfect 4ths are literally inversions of each other!

Half An Octave In Scales And Melodies

In a scale, the 5th note, the note half an octave above the root note, is called the dominant. The dominant has a double function:

  • The half-octave point is as far away from the root note as you can get
  • It is also a strong supporter of the root note, as seen by the composite wave examples

The dominant provides a polar opposite point allowing melodies to venture away from the root note and to return from.

This is easily demonstrated in the most simple melody of all, the scale. By splitting it in two, we can see that the first half of the scale leads away from the root note and towards the dominant and the second half of the scale leads from the dominant up to (the octave of) the root note.

In the example below I’ll use the major scale but it works equally well for the melodic minor.

Perfect 5ths And Perfect 4ths In Chords

The presence of a a perfect 5th or perfect 4th in a chord helps us to identify the root note. The root note will be the lower note of a perfect 5th/the upper note of a perfect 4th.

If a chord contains more than one perfect 5th (or perfect 4th), the chord has more than one possible root note and its interpretation is determined by the musical context.

For example, the notes A C E G could be seen as either

  • Am7
    an A minor chord; A C E, plus a minor 7th; G, or
  • C6
    a C major chord; C E G, plus a major 6th; A

If you found this post helpful, please feel welcome to like, share or leave a comment. If you have any questions, leave them as a comment and I’ll respond as soon as I can. To stay up to date with new posts, please subscribe.

See It, Hear It: Dynamics

The contrast of loud and soft (quiet) is important in shaping a performance.

 Dynamics is the musical term for how a musician varies loudness. When printed, dynamics are written below the stave with symbols and words in bold italics.

In a score, each part can have its own dynamics, whereas tempo/character markings apply to the whole score. As with character and tempo markings, symbols are based on Italian words.

The following list shows the most commonly used dynamics. The default dynamic, when nothing is written, is mf (mezzo forte), or moderately loud.

Dynamics Flyover

If you found this post helpful, please feel welcome to like, share or leave a comment. If you have any questions, leave them as a comment and I’ll respond as soon as I can. To stay up to date wth new posts, please subscribe.

19. Listen & Sing: Learn Minor Intervals By Singing

This post is one of a 2-part series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here. Please feel welcome to make a comment or ask a question.

The minor intervals are minor 2nd, minor 3rd, minor 6th and minor 7th. There are a few ways we can learn to sing these intervals.

Phrygian mode

The minor intervals are based on the phrygian mode. The phrygian mode is not easy to sing!

Most people aren’t used to starting a scale with a minor 2nd (1 semitone). However, if you listen to early music or traditional folk genres, you may be able to sing it.

Give it a try if you like. Don’t worry if you find it hard because there are easier options below.

If you can sing this scale, you can teach yourself the minor intervals by counting scale notes in the phrygian mode, just as we did for major intervals in the previous lesson. If not, read on…

Natural Minor

The next option is to sing the natural minor scale. That works for all except the minor 2nd, 1 semitone. See below for how to learn to sing a minor 2nd.

Most people find this much easier to sing than the phrygian mode. Again, the best way to find out is to try it.

Try It…

If you can comfortably sing the natural minor scale without following the video, you can use it to find the minor 3rd, minor 6th and minor 7th. Learn to sing the minor 2nd separately (see later in this post).

Example: minor 7th by singing the minor scale

Major Scale

The final method, outlined below, is to start to sing a major scale. To sing a minor 2nd, 3rd, 6th or 7th, drop down by 1 semitone from the major to find the equivalent minor interval, much like the interval ruler in 16. Interval names 1: major, minor and perfect intervals.

This method is great when you want to name an interval that you hear, because at first you won’t know whether it’s major or minor.

Rather than having to try both major and minor scales, just sing the major scale. If the major scale overshoots the upper note of the interval it’s probably a minor interval. (There is one exception to this but we’ll leave that until Part 2 of this course).

This requires one trick; the ability to sing 1 semitone below a note. This may seem hard, but I’m sure you can already do it without even realising it…

How To Sing 1 Semitone Up Or Down

Try This…

  • Sing the first 4 (or the last 4) notes of a major scale.
  • Now go back and forth between the last two notes you sang – that’s 1 semitone.
  • Feel how close together these last two notes are, almost squeezed together… Remember that feeling when you want to sing two notes 1 semitone apart.
  • Does it remind you of something? Start slowly and speed it up… The theme of the all-time classic movie, Jaws…
  • Now you’ve sung 1 semitone up and down a few times, reverse it. Sing down before going up (start on the higher note if you like). Below we have 1 semitone as a minor 2nd on C, first upwards, then downwards. Focus on keeping the two notes squeezed tightly together.
  • After a little while, you‘ll be able to sing a semitone up or down down by itself.

How To Sing Minor Intervals By Singing The Major Scale

  • For a minor 2nd, learn to sing 1 semitone up as outlined above.
  • For other intervals, sing the major scale indicated by the degree of the interval name (3rd, 6th or 7th).
  • Sing down 1 semitone.
  • Repeat this a few times.
  • Now just sing the first and last note as an interval.
  • Repeat a few times. Build up to being able to sing it by yourself, without the video.
  • Once you’ve sung a few intervals, try to sing the in-between scale notes more quickly and quietly, until they’re just a thought.

Try These…

Minor 2nd by singing the major scale

Sing the first bar again while you listen to the 2nd bar.

This is just a semitone up rather than down, as we learnt earlier.

Minor 3rd by singing the major scale

NOTE: For this and the following intervals, repeat the 3rd bar while listening to the 4th bar.

Minor 6th by singing the major scale

Minor 7th by singing the major scale

How To Name An Interval That You Hear

  • Identify the lower and higher note of the interval and sing them.
  • While listening to the interval, start to sing the major scale of the lower note, counting degrees (note numbers).
  • If it’s a major or perfect interval, you’ll find the upper note and have the answer.
  • If it’s a minor interval, at some point you’ll be too high. As soon as you notice this, sing 1 semitone below your last note. If you’re still too high, you went too far up the major scale and you should start again.
  • You may need to repeat this a few times until you feel sure that your upper note matches the upper note of the interval.

Try These…

Name the following intervals:

Answers at the end of this post.

NOTE: There is one interval we haven’t covered in the last two lessons, an interval of 6 semitones, often called a tritone (we’ll learn its proper interval name in Part 2 of this course). It’s a bit harder to sing than the other intervals and isn’t all that common so we’ll leave that one out for now.

Coming Soon! The Interval-Singing Project

The interval-singing project is survey of well-known songs in many genres, each of which starts with a specific interval. For each genre I hope to collect song titles to cover each interval.

Instead of having to learn intervals from scratch, students will be able to draw on their own knowledge, needing only to remember which song represents which interval.

Anyone who subscribes to my blog will have access to the database at no cost.

If you found this post helpful, please feel welcome to like, share or leave a comment. If you have any questions, leave them as a comment and I’ll respond as soon as I can. To stay up to date wth new posts, please subscribe.

NEXT LESSON: 20. How To Read Rhythms 1

PART 1 CONTENTS: Basic Music Theory Course Contents

———

———

———

Answers To Try These…

  • minor 3rd
  • minor 6th
  • minor 2nd
  • minor 7th

Middle C

Each note can occur at various octaves. The exact octave of a note can be indicated using octave numbers. Octaves are numbered starting on C.
The lowest C is C1.
The range of a piano keyboard is from A0 to C8.

Middle C is the name given to C4. Middle C is a pitch that most instruments, high to low, can play and is considered to be in the middle of the range of instrument pitches.


Middle C is the link between the treble and bass clefs. It sits on an imaginary line just above the bass clef and just below the treble clef.
This line, called a ledger line, is drawn through the notehead when needed.
Middle C is the C below A440.

Remember BCEF

Remember BCEF

There are 12 semitones in an octave.

All the naturals (letters) are 2 semitones apart except B to C and E to F, which are 1 semitone apart.

Not only that, but B-F is 6 semitones, whereas every other interval of 5 naturals is 7 semitones apart, such as A-E or C-G. This is important in understanding keys and key signatures.

BCEF is easy to remember because it’s so odd, like a hip-hop band name gone wrong: the BCEF.

So remember BCEF

If you found this post helpful, please feel welcome to like, share or leave a comment. If you have any questions, leave them as a comment and I’ll respond as soon as I can. To stay up to date with new posts, please subscribe.