Intervals and Transposing via Tuning and Capo Use

Intervals are the foundation of many aspects of music. This lesson will give the reader some tools to deal with translating songs to different keys and instrument tunings.

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Ultimate Guitar
Intervals and Transposing via Tuning and Capo Use
11

Intervals are the foundation of many aspects of music. This lesson will give the reader some tools to deal with translating songs to different keys and instrument tunings. This also gives a primer on related UG functions and how to use them.

Preliminary discussion on notes

In the current Western system, there are 12 different sounds that repeat. These sounds are called notes. These notes are the same distance apart. The distance between each adjacent note is called either a half-step or a semitone. The distance between a note X and another note 2 notes away is called either a (whole) step or a (whole) tone.

Notes are named based on letters A-G and sharp (♯) or flat (♭) symbols. There are no sharp/flat notes between E and F, as well as B and C.

In certain parts of Europe (primarily Germanic and Slavic), H is used to mean the note exactly below the note called C, and B is used to mean the note directly above the note called A. This is a historical consideration from the early 2nd millennium (1000-1999).

For the remainder of the article, steps will be used, as well as the conventional B and B♭. Any chord shape discussed will follow EADGBe string order, i.e. 022000 is an E minor chord.

Chord charts can be too difficult to play as-is

Take this chord submission as an example (will be referred to as (1) [1]):

Some of the chords are more accessible from a beginner's point of view: D can be played as xx0232 (lowest string written first and muted, open D string, and so forth). However, the others require a barre chord to be played normally. This can be a large problem. Fortunately, there are ways to bypass this, even if they require a larger understanding of intervals, to be discussed in the following section.

About intervals

An interval is the distance between any two given notes. Steps/tones are intervals. This section will show how to describe intervals with relation to both note names and steps and starts with generic intervals. Later on, specific intervals will be discussed.

Generic Intervals

Take any two notes and compare their letters and direction.

F♯ and F♭ share the same letter.

If F♯ is fret 4 on the D string and F♭ is fret 2 on the D string, they are a generic unison. (They are on the same note level and make similar sounds.)

If F♯ is fret 2 on the E string and F♭ is fret 2 on the D string, they are a generic octave. (The F♭ is on a higher note level, but they still make similar sounds.)

There are other intervals. Each will have an example following it. These are all smaller than an octave:

Seconds: one letter apart (D up to E, F down to E)
Thirds: two letters apart (B up to D, A down to F)
Fourths: three letters apart (F up to B, G down to D)
Fifths: four letters apart (B up to F, F down to B)
Sixths: five letters apart (D up to B, C down to E)
Sevenths: six letters apart (E up to D, B down to C)

There are some intervals that are greater than an octave. They build on the intervals above:

Ninths: Octave plus a second
Tenths: Octave plus a third
Elevenths: Octave plus a fourth
Twelfths: Octave plus a fifth
Thirteenths: Octave plus a sixth
Fourteenths: Octave plus a seventh
Fifteenths: Octave plus another octave

Some of these intervals are not useful for anything but academic purposes, but the 9th, 11th, and 13th are often used for chord extensions and added tones. The 15th can be used in standard notation to show that a note or group of notes is 2 octaves higher (15va) or lower (15vb) than written.

Specific Intervals

While general intervals mainly deal with the relation between the note letters, specific intervals combine this with distances expressed in half-steps and steps. There are some principles to understand before naming these intervals:

  • Simple intervals are major, minor, perfect, augmented, or diminished.
  • The only intervals that can be perfect are the unison, fourth, fifth, and octave.
  • An interval that is one half-step larger than a perfect or major interval is an augmented interval.
  • An interval that is one half-step smaller than a perfect or minor interval is a diminished interval.
  • An interval that is one half-step smaller than a major interval is a minor interval.

Specific intervals may be easiest to derive from the major scale. Take C major for example (numbers on top represent scale numbers):

1 2 3 4 5 6 7 8
C D E F G A B C

Starting from C, only major or perfect intervals can be found:

  • C (1) to C (1) is a perfect unison
  • C (1) to D is a major second
  • C to E is a major third
  • C to F is a perfect fourth
  • C to G is a perfect fifth
  • C to A is a major sixth
  • C to B is major 7th
  • C (1) to C (8) is a perfect octave

Based on this, the distance of these intervals (in half-steps) can be deduced:

  • Perfect unison: 0
  • Major second: 2
  • Major third: 4
  • Perfect fourth: 5
  • Perfect fifth: 7
  • Major sixth: 9
  • Major seventh: 11
  • Perfect octave: 12

(Note that these can also map to frets and the major scale on one guitar/bass string.)

There are missing intervals in between. These, along with more names, are listed in the table below [2] :

These intervals will come into play later, as musical relations (the distance between chords) need to be preserved.

Capos, Tunings, and Intervals

One way to deal with the chords in (1) is to transpose them - move the chords and notes up or down from how they are - by some offset and then use a capo. Transposing them down 3 half-steps (1 ½ steps) will yield these chords (will be referred to as (2)) [3] :

These are much more basic chords (with the possible exception of the barre chord B). However, these can't be played with the recording without sounding something polytonal. Similar to Newton's Third Law, an equal and opposite correcting factor must be given. For transposing instruments such as trumpets and saxophones, this is done within notation. For guitar (also a transposing instrument but written with octave correction, i.e. the notes are the pitch class - same letter and accidental - unlike the aforementioned trumpets and saxophones), this can be done by changing the tuning or using a capo.

The capo option

The chords in (2) are 3 half-steps too low. All pitches need to be moved 3 half-steps up in order to be played with the recording. A capo will do just that - move pitches up. With a capo on the third fret, the chords in (2) will sound exactly like the chords in (1). That the distance between two adjacent frets is always a half-step can help with transposition:

  • Moved the chords 2 steps down? Put a capo on the 4th fret to compensate.
  • Moved them 1 half-step down? Put a capo on the 1st fret.
  • Moved the chords 8 half-steps down? Moving them up 4 half-steps from the original would have saved you time (notes repeat every 12 half-steps), but a capo on the 8th fret will get you back to the sound of the original chords.

The tuning option

The final example can be a bit unwieldy, as the chords are now much closer to the neck joint. Another way to compensate is to down-tune. Moving the chords up 4 half-steps can be corrected by down-tuning 4 half-steps. If the original tuning was standard E, the new tuning is now standard C, after the most conventional or simplest name for the note 4 half-steps down from E.

Correcting for intervals

A piece of modern music usually has some sort of underlying relation between all its chords. If written correctly (see here for a primer [4]), the relations will be preserved through transposition. The flavor of chord (major, minor, augmented, or diminished) is preserved; however, the note names may require change.

This is relevant since UG's transposition function uses sharps exclusively, whether or not they are valid or not. What is "Em G Am C/G" transposes to "Fm G# A#m C#/G#" with the function, but the minor third between Em and G is not preserved between Fm and G#. Fm is a simpler chord name than E#m (though they are the same semitone distance apart), so Fm will stay. To keep the minor second distance between the original and new versions, the note letters have to move a letter up:

Letters

Old: E G A C/G
New: F A B D/A

Then, the new letters need to be corrected to preserve the specific intervals:

     Old: E G  A  C/G
New (+1): F Ab Bb Db/Ab

Finally, the chord qualities can be added as before:

Old: Em G  Am  C/G
New: Fm Ab Bbm Db/Ab

Hopefully this helps in using the site in the future!

Footnotes

[1] Original chord chart can be located here.

[2] The tritone has multiple names in history, but six half-steps is literally three (tri) tones.

[3] The transposition function is available for everyone on any chord chart. Note the highlighted region in the image below:

This will appear on the left side of all Ultimate Guitar chord charts on the desktop version. The current version does not preserve chord location, however.
(Aside: there is a "simplify chords" function, but augmented and diminished chords and offshoots (m75, dim7, 75, etc.) are not exactly major or minor, respectively, so be forewarned about this when chords don't sound quite right.)

[4] This prescriptive primer discusses diatonic chords, chords with notes within a key's scale(s). There are more chords than just these in living music, and there are some specific reasons to have both sharps and flats within music; however, this covers the great majority of cases.

9 comments sorted by best / new / date

    ErnestoFidel
    What really has to be explained is how to play a song in a LOWER key using a capo. Say you want to play Dm F G instead of Em G A. What I see people do, is put the capo on the 10th fret and play it in that position. But it sounds really bad, because the strings get shorter. You can play Em G A a fourth up by playing it a STRING up as Am C and D, which are still easy open chords. Then you move it up to Dm by using the capo on the fifth fret. You have moved down the key by one whole step. It works the other way around. To play Am C D a whole step lower: instead of moving it to the 10th fret you play it a string lower as Em G A and then move it up to G by using the capo on the third fret. 
    Music2Go
    Like this article! I've been trying to explain transposition to my students, but I don't think they're quite getting it. This article gave me a few pointers on how to explain it to them so they understand!
    flezem
    Kudos for making a great indepth article for people who want to learn more about intervals. But I think it is easier than you are making it sound. Yeah, it's pretty annoying they use sharps most of the time regardless of their correctness. It's almost never an A# for instance.  *guitar* 1. Do you want to keep the same key but you want to make the chords easier a.ka. avoid bar chords? For every -1 on the transpose button you have to put the capo 1 higher. Just pick the first that's kind of alright. Sometimes an F chord or Bm chord are unavoidable, you just have to deal with it. I'd rather just play one bar chord instead of playing a very high capo'ed guitar.   Actually if you avoid using a capo  in general you will develop the skill of transposing on the spot by just moving your finger. That way you could even do anything you want without having to know the actual names of the chords. I used to play in a band with lots of horns and stuff so everything was in Bb, F or Eb. That really taught me alot. *anything with a voice* 2. Do you want to change the key for your voice? Anything goes basicly. I find myself changing the key -5 for most tenor rock singers and then it's in my range most of the time. Sometime you have to change the octave for singing. Okay i've probably made it too complicated as well but here goes nothing! Thanks again NeoMvsEu.
    NeoMvsEu
    Thanks for the detailed comment! Music is relational, and I wanted to emphasize that in order to preserve the intervals if correctly written. There have been a lot of user complaints about the transposition function not working ideally, so I wanted to affirm their thoughts while offering a way to explain the display vs function disparity. 1. ErnestoFidel added a good comment regarding transposition methods (moving to a different set of transposed chords, like A minor without capo as opposed to E minor), which would also help with high capos. This is a good bridge until people get comfortable enough with playing barre chords, and this was my intent. 2. What worked in a wedding band I played with: make the singers sing the melody a cappella and figure out the offset (+/- number) from the melody notes. If the chords are transposed, the melody is too!
    flezem
    If that is your goal I understand the whole thing better. What if ultimate-guitar would just fix the whole sharps/flats thing. It would be so much better. Key C / Am G / Em     | F / Dm D / Bm     | Bb / Gm A / F#m   |  Eb / Cm E / C#m   | Ab / Fm B / G#m   | Db / Bbm F# / D#m | Gb / Ebm C# / A#m | Cb / Abm So most likely name is (depending on keys and stuff) C D E F G A B          most likely F# Bb C# Eb G# Ab D# Db A# Gb E# Cb B# Fb                      most unlikely
    NeoMvsEu
    I wish it were that simple to implement; it seems to be stuck between management and the algorithm the site uses to display chords.