Tag: perfect 4th

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.

18. Listen & Sing: Learn Major And Perfect 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.

Learning To Sing Intervals

Interval names are based on scale notes. 

If we can sing, hum or imagine the sound of a scale, we can teach ourselves the character and name of various intervals by ear. We can count how many scale notes there are from the lower note of the interval to the higher note.

The easiest scale to sing, at least in Western culture, is the major scale. If you can’t sing a major scale straight away, please have a look at 17. Listen And Sing: How To Sing The Major Scale before reading on.

Major scale intervals

In 16. Intervals 1: Major, Minor And Perfect Intervals we saw that intervals are always counted from the lower note to the higher note, regardless of the order in which they’re played. The lower note of the interval becomes the root note of a major scale. We count scale notes to find the higher note and name the interval.

Counting up from the root note, the major scale contains the major 2nd, major 3rd, perfect 4th, perfect 5th, major 6th, major 7th, and, of course, the octave.

  • Treat the root note of the scale as the lower note of an interval.
  • Now sing from the root note to the 2nd note. This is a major 2nd.
  • To sing a major 3rd, sing the first 3 scale notes in a row but sing the 2nd note quieter or shorter than the first and third notes (see below). After a few times, leave the second note out altogether.
  • Repeat this exercise from the root note to each of the other notes in the scale.

Tip: the most useful intervals to become really good at are the major 3rd, perfect 5th and the octave. They are the notes of a major triad, a sound which will feel familiar to the ear and provide a shortcut for larger intervals (more on triads in Part 2 of my course).

Try These…

Below are the intervals of C major. Most voices can find a comfortable way to sing a C in the lower part of their range. The note number/scale degree is indicated below the notes.

  • In the first line, sing along to the first bar, then sing the same notes again in the second bar while you hear the interval played together. Feel your voice hit the lower and higher notes of the interval at the start and end of the bar.
  • In the second line the in-between scale notes are left out. Again, keep singing the first bar while you hear the interval played together in the second bar.
  • Practice each interval long enough until you don’t need to listen to the example while you sing.

Major 2nd

Major 3rd

Perfect 4th

Perfect 5th

Major 6th

Major 7th

Octave (perfect 8th)

Once you build a little confidence, choose a slightly lower or higher note for your intervals.

The more you do exercises like these, the easier it will be to recognise the interval between two notes, whether you hear them as a melodic interval (consecutive notes) or as a harmonic interval (both notes sounding together).

How To Sing An Interval Above A Note

This is just like how we learnt the intervals starting on C

  • Choose a major or perfect interval by name, such as a perfect 4th.
  • Play a note towards the bottom of your range.
  • Sing that note, then sing a note that’s the chosen interval above it 
  • If you need to, you can quietly sing the in-between scale notes like in the first exercise.

How To Name An Interval You’re Hearing

You can use the same method to name an interval that you hear.

  • First, identify both notes of the interval by singing them. They are a little harder to pick when played together.
  • Sing the lower note, then sing the notes of the major scale until you hear your note match the higher note, counting notes as you sing (the starting note counts as the first note). 
  • 2 notes is a 2nd, 3 notes is a 3rd, etc. The 2nd, 3rd, 6th and 7th are major intervals, the 4th and 5th are perfect. (Technically the octave is also perfect, we just don’t need to say so. An octave is just called an octave.)

Try These…

Below are audio files of a few harmonic intervals. Remember to sing both notes of each interval before singing (or thinking) scale notes. To make it a little easier, the two notes are quickly played as a melodic interval before hearing the two notes together.

Name each interval using the steps outlined above:

Answers at the bottom of this post.

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.

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.

NEXT LESSON: 19. Listen & Sing: Learn Minor Intervals By Singing

PART 1 CONTENTS: Basic Music Theory Course Contents

___

___

___

___

___

___

___

___

Answers to Try These…

  • major 2nd
  • major 3rd
  • major 6th
  • perfect 4th
  • major 7th
  • perfect 5th
  • octave