Intervals – Theory

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It all starts with the major scale

The major scale is the starting point for the intervals we define in Western music.

The major scale is built from the following formula which describes the distance between the 7 notes in the major scale:

  • T T S T T T S

where:

  • T = a tone = 2 frets on the guitar
  • S = a semitone = 1 fret on the guitar

Using this formula, we can start on any root note and build a major scale.

Example 1

Let’s start on C as our root note, and apply the above formula:

  • we first go up 1 tone, and get to D,
  • going up another tone we get to E,
  • going up a semitone we have an F,
  • another 3 tones takes us to G, A and B
  • the final semi-tone brings us back round to C again.

Therefore, we now know that the C major scale is built of the notes:

  • C, D, E, F, G, A, B

Example 2

If we use Eb as the root note and apply the same formula:

  • we go up 1 tone to F,
  • going up another tone we get to G,
  • going up a semitone we have an Ab,
  • another 3 tones takes us to Bb, C and D
  • the final semi-tone brings us back round to Eb again.

Telling us that the Eb major scale is built of the notes:

  • Eb, F, G, Ab, Bb, C, D

Reference Names

When we have a root note, we can describe a scale in terms of the actual note names as we have done above.

However, as the scale can begin on any root note, we use reference names for the notes in a scale.

The reference names of the notes in the major scale are:

  • 1, 2, 3, 4, 5, 6, 7

We can use these relative names to talk about and get information about the major scale

Let’s look at some examples:

Example 1

If we are asked for the 4th of C major:

  • In the example above we established that notes in the C major scale are: C, D, E, F, G, A, B
  • We want the 4th so we get the 4th name of the scale
  • The 4th of C is F

Example 2

If we’re asked for the 4th of Eb major, we use the same logic:

  • The notes in the Eb major scale are: Eb, F, G, Ab, Bb, C, D
  • The 4th is Ab

More Examples

  • The 7th of C is B
  • The 2nd of Eb is F
  • The 6th of C is A.

What about the rest of the notes

In western music, there are 12 notes in an octave. So far, we have named 7 of them.

As the major scale is the starting point in western music, the reference names for the remaining intervals are based on the major scale names:

No. Symbol Name
1 Root Root
2 b2 Flat Second
3 b3 Flat Third
4 3 Third
5 4 Fourth
6 #4 / b5 Sharp Fourth / Flat Fifth
7 5 Fifth
8 #5 / b6 Sharp Fifth / Flat Sixth
9 6 Sixth
10 b7 Flat Seventh
11 7 Seventh
12 Octave Octave

Note that a couple of the notes have two names – one name based on the note above and one based on the name below.

The reason for this is beyond the scope of this article, but if you’d like to know more, please take a look at my book here.

Why do we need to know intervals

Scales, modes, chords and arpeggios are all defined by the intervals they contain.

If we know the intervals that each contain then we have the ability to built any scales, arpeggio, etc, starting from any note, anywhere on the fretboard.

This kind of knowledge is power over the fretboard and the music you make.

Of course, before you can build the desired scale, arpeggio, etc, you will need to know where the intervals lie in relation to your root note.

This is what this app is aimed at teaching you.

The App

This app is aimed at getting you to instantly find the relative intervals on the fretboard when starting on any root note on any string.

A random note is highlighted on the fretboard and you are asked to find an interval in relation to that note.

Intervals on the fretboard:

Now that you know the theory, let’s look at some diagrams which show the intervals.

The diagrams show the intervals when starting on 2 different root notes

So that it doesn’t look too complex, both examples are split into two diagrams:

  1. The major scale intervals
  2. The remaining intervals

Major scale intervals with roots on the bottom E string:

  • Root note and it’s octave are red
  • Intervals in the octave above the first root note are blue

Intervals_Major

The remaining intervals with roots on the bottom E string:

  • Root note and it’s octave are red
  • Intervals in the octave above the first root note are blue

Intervals_Others

Major scale intervals with the root on the G string:

  • Root note and it’s octave are red
  • Intervals in the octave above the root note are blue
  • Intervals in the octave below the root note are yellow

Intervals_Major2

The remaining intervals with the root on the G string:

  • Root note and it’s octave are red
  • Intervals in the octave above the root note are blue
  • Intervals in the octave below the root note are yellow

Intervals_Others2

You can see from the diagrammatic examples that the relative positioning of the intervals is different when starting on different root notes.

This may lead you to think that there is much to learn.

However, do not worry – as you work out the intervals starting on different roots, you will find that there are many patterns which do repeat.

For example, when starting on the bottom E and A strings, the shapes are the same.

I will not give diagrams for all the shapes here as I believe it would be more beneficial for you to work them out yourself.

Outro

You now have enough information to start using the second app in my series – Intervals.

FriendlySanj – Find Out More

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Android app on Google Play
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Intervals – Instructions

FriendlySanj – Find Out More

Download the App


Android app on Google Play

Instructions

The Purpose

The purpose of this app is to teach you intervals on the guitar fretboard in relation to a root note.

This is the second in my series of guitar apps which aim to teach you how to apply music theory to the guitar fretboard.

Learn about more apps in this series on my website at:

I don’t know any intervals – where do I start?

If you:

  • don’t yet know any intervals on the fretboard
  • want to know how to go about learning the intervals on the fretboard

then please read this blog post.

My Experience

After completing the Notes app, I was so pleased with how much I learnt from it that I went straight into writing Intervals more for the purpose of my own learning than any commercial reason.

My knowledge of intervals in an upwards direction from a root note has been good for a number of years, but knowledge in a downwards direction less good.

After playing the app for a bit, I realised that I was most shaky on the G and B strings.

Using the string range settings in the app, I focused first on the G string and then on the B string.

After a few days, I was answering almost 100% accurately within 5 seconds.

At the time of writing these instructions, I am focusing on improving my speed and am looking forward to moving onto the next app in the series.

Playing the Game

The Basics

When starting the game, you will be presented with the image of a fretboard upon which a single fret will be highlighted with a red circle.

Beneath this, a line of text will indicate which interval is required and whether to find the interval above the root note (higher in pitch) or below the root note (lower in pitch).

The text will be of the form:

  • “Find the 3rd in the octave ABOVE Eb”

The text can be broken down as follows:

  • “3rd” – the interval which is being requested.
  • “ABOVE” – whether the interval is required above or below (in pitch) the root note
  • “Eb” – the root note name

Selecting an Answer

The requested interval will always be:

  • within a 3 fret range
  • within 1 octave

of the root note.

On the fretboard, touch the fret you believe is being asked for. Your selected fret will be highlighted with a blue circle.

Hit the GO button to submit your answer.

For some intervals, there will be more than one possible answer. If this is the case, the app will see either answer as correct.

Fretboard Scrolling

If playing the app on a small device where less than 6 frets are visible, the app will scroll the fretboard accordingly so that the requested interval is visible on your screen.

If more than one answer is available, the app will choose one of the possible answers and scroll so that the apps’ preferred answer is visible on your screen.

You may scroll the fretboard to find your preferred answer.

If playing on a small device, I believe that landscape mode provides a better gaming experience.

Correct Answer

If you are correct, the:

  • “Answer is correct” message
  • note name of the requested interval

will be displayed on screen and the next question will be posed.

Incorrect Answer

If you are incorrect:

  • the “Answer Incorrect” message will be displayed
  • the note name of the requested interval will be displayed
  • the correct answer(s) will be shown on the fretboard highlighted with a yellow circle
  • the GO button will be replaced with a NEXT button

Hit the NEXT button to move on to the next question.

Possible Intervals

the full list of intervals which can be requested is:

  • b2nd – flat second
  • 2nd – second
  • b3rd – flat (minor) third
  • 3rd – (major) third
  • 4th – (perfect) fourth
  • #4th – sharp fourth
  • b5th – flat fifth (tritone)
  • 5th – (perfect) fifth
  • #5th – sharp (augmented) fifth
  • b6th – flat (minor) sixth
  • 6th – flat (major) sixth
  • b7th – flat (minor) seventh
  • 7th – (major) seventh
  • Octave

Note Names and Enharmonic Equivalents

Some notes may have more than one name. At the time of randomly choosing a root note, the app also randomly chooses one of the possible note names for the selected root note.

For example, for the 6th fret on the A string of a standard tuned guitar, the name “D#” or “Eb” may be chosen.

When presenting the interval note name, the app will select the correct name based on the chosen root note name.

Taking the present example, if a 3rd was requested: the root note name:

  • “D#” would yield an answer of “F##”
  • “Eb” would yield an answer of “G”

The Timer

If the timer is enabled, then you have a limited time in which to answer the question.

The timer decrements in one second intervals and when only five seconds remain, is displayed in red.

The timer can be enabled/disabled and the interval altered using the game play options.

If you fail to provide an answer in the alotted time then:

  • the “Time Up” message wil be displayed
  • the note name of the requested interval will be displayed
  • the correct answer(s) will be shown on the fretboard highlighted with a yellow circle
  • the GO button will be replaced with a NEXT button

Hit the NEXT button to move on to the next question.

If the timer is enabled, then the average time in which questions have been correctly answered is displayed on screen and is updated following each correct answer.

The Skip Button

A skip button is provided in case you wish to skip a question.

If a question is skipped then:

  • the “Skipped” message wil be displayed
  • the note name of the requested interval will be displayed
  • the correct answer(s) will be shown on the fretboard highlighted with a yellow circle
  • the GO button will be replaced with a NEXT button

Hit the NEXT button to move on to the next question.

If scoring is enabled then the skipped question is treated as an incorrect answer.

No.Correct / Incorrect

The number of correct answers and the total number of questions so far posed is displayed in the format:

  • No Correct/Total No. Questions So Far

Set Size

The number of questions which constitutes a game is referred to as the:

  • “Set size”

and is displayed on screen.

This value can be altered in game play options.

Scoring

Scoring and Rating have been added to the game to give you a way to track your progress.

Scoring Algorithm

The scoring algorithm is as follows:

Timer Disabled

  • Incorrect answer : 0 points
  • Correct answer : 10 points

Timer Enabled

  • Incorrect answer : 0 points
  • Correct answer :The score depends on the time taken to answer the question
    • >=10 secs : 10 points
    • 9 secs : 20 points
    • 8 secs : 30 points
    • 7 secs : 40 points
    • 6 secs : 50 points
    • 5 secs : 60 points
    • 4 secs : 70 points
    • 3 secs : 80 points
    • 2 secs : 90 points
    • 1 secs : 100 points

As each game can consist of a different number of questions, the final score is divided by the total number of questions answered.

This results in a final score with a possible maximum of 100.

Ratings

A rating system is employed consisting of the following 5 ratings:

Score:

  • 80-100 : Dominant
  • 60-80 : Augmented
  • 40-60 : Major
  • 20-40 : Minor
  • 0-20 : Diminished

Your score and rating is displayed at the end of each game and all ratings/scores can be viewed on the high score screen.

Hi Score Screen

The hi-score screen displays the following information about each game:

  • Score
  • No. correct answers
  • No. questions asked
  • Average answer time
  • Rating
  • Fret range
  • String range
  • Date and time of game

Settings

Game Play Options

  • Question set size: Alters the number of questions which constitute a game
    • Range: 5 – 50
    • Default: 25
  • Enable Timer: Select whether a timer is to be used
  • Timer Interval : Timer interval in seconds
    • Range: 1 – 60
    • Default: 30
  • Enable Scoring: Select whether scoring is to be used
  • Enable Sound Effects: Select whether sound effects should play. Sounds are played for the following:
    • Correct Answer
    • Incorrect Answer
    • Question Skipped
    • Time Up
    • Game Over

Fretboard Range Options

  • Lowest (Pitch) String: Set the lowest pitch string which the app can choose as the root note
    • Range: 1 (Top E String) – 6 (Bottom E String)
    • Default: 6 (Bottom E)
  • Highest (Pitch) String: Set the highest pitch string which the app can choose as the root note
    • Range: 1 (Top E String) – 6 (Bottom E String)
    • Default: 1 (Top E)
  • Lowest Fret: Set the lowest fret which the app can choose as the root note
    • Range: 0 – 24
    • Default: 0
  • Highest Fret: Set the highest fret which the app can choose as the root note
    • Range: 0 – 24
    • Default: 24

Fretboard Settings Options

  • Fretboard Type: Select whether a right handed or left handed guitar fretboard should be displayed
    • Values: Right Handed Guitar | Left Handed Guitar
    • Default: Right Handed Guitar

FriendlySanj – Find Out More

Download the App


Android app on Google Play