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I'm preparing for a music institute audition. Say, the task is to name notes in B Maj 7. For doing this, I have to learn by heart:

  • The circle of fifths (to know how many sharps/flats are in B major)

  • The order of sharps and flats (to know which sharps/flats are there)

  • The steps in a major 7 chord

Also, I have to practice counting steps from any letter. In the case of B, to find the necessary steps, I have to calculate B+2 (third step), B+4 (fifth step), and B+6 (sevenths step), which is a bit confusing cause it actually involves adding base-10 numbers (steps) to base-7 numbers (notes). Trying to simplify the matter, I came up with the following:

1 or 8: A

2 or 9: B

3 or 10: C

4 or 11: D

5 or 12: E

6 or 13: F

7 or 14: G

If I want to count the fifth step of B, I just do 2 + 4 = 6, where 2 is B, 4 is the step we need minus 1, and 6 is the resulting note F (to which we then apply a sharp). It's easier to calculate than just B+4, but the caveat is that I have to memorize another thing – the pair of numbers for each note.

So in order to name the notes in any given chord, I have to memorize 4 things.

Could you please suggest whether it is the most efficient way to do the task?

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  • 3
    To name the notes in a chord, you just have to understand that it's a sequence, you have to be able to imagine the notes on an instrument of your choice, and you have to understand the definition of the chord. The circle of fifths and the numbers of sharps and flats aren't needed for this task (but it's a good thing to be familiar with). / Please just answer as well as you can, and trust them to place you in the appropriate course. Admission decisions are generally based on performance in your instrument, not on knowledge of music theory. Dec 14, 2021 at 6:28
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    @aparente001 - Aren't several instruments better to imagine notes on than others for this purpose? For example, piano and guitar are good and trombone is decent due to keeping notes in chromatic scale order, while woodwinds are not very good ideas due to the register key and overblowing, and trumpets are often terrible unless your purpose is to practice overtones instead.
    – Dekkadeci
    Dec 14, 2021 at 12:53
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    You've got several rather mathematical, algorithmic answers. I'll give you the answer that worked for me, as a more intuitive, perhaps visual learner: Build a snowman! This assumes that you're fluently familiar with staff notation, and, yes, that you know the notes in a key. But then, if you want an F chord, picture a big fat whole note on the first space of the treble clef, then "stack" on another note on top—not overlapping (G), but sitting right "on top" of the F—an A. Then add the head—C. Voila! Dec 14, 2021 at 12:54
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    Knowing the notes in BMaj7 is a bit like memorizing your multiplication tables. If you're going into a mathematics degree at university and are sweating about your times tables you're in for a world of eye-opening hurt. This suggests a deep disconnect between your playing practice and your theory. Don't focus so much on pen and paper - play BMaj7 on your instrument and come to learn how it behaves there. You need to connect the dots between the theory and the music; and your instrument. This is how you will remember and internalize it.
    – J...
    Dec 15, 2021 at 14:11
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    @J... If you're anything like me, there is a disconnect between how playing practice and theory are remembered, to the point where playing practice fails to reinforce theory or even reinforces theory wrong. As I've elaborated in another comment, playing arpeggios should hammer the interval sizes between their notes home, ironically including the perfect 4th interval between the 5th and root of an inverted major triad (not normally emphasized when memorizing chords), but my high mistake rate at the piano often prevents me from internalizing this by practicing arpeggios on it.
    – Dekkadeci
    Dec 15, 2021 at 15:36

6 Answers 6

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I'd like to offer a broader answer, and intentionally challenge what you've asked for. You say you have two months to prep, and ask what you "have to know by heart." There's a lot here already about formulas and memorization. I'd like to suggest that some of these "quick ways" are also hard ways, and that the real focus should be: "What do I need to understand?" After all, the intent of the test ought to be not just to find out whether you can construct a chord but whether you understand what it represents.

This is basically just the earliest steps of theory 101. To understand chords, you have to understand intervals and keys (as well as more basic things), and then triads build on the concept of intervals. Start by working your way through some of these foundational concepts, fully and progressively. You can cover this groundwork pretty solidly in two months, with enough time per day.

Yes, you can work on memorizing the circle of fifths, but I also recommend spending enough time in the more "common keys" (the top half of the circle) that you don't have to do mental calculation to figure out the pitches that make up E major. As suggested elsewhere on this page, live with these keys: whether on your primary instrument or on a keyboard (or both), play major and minor scales. Play arpeggios (which, spoiler alert, are the chords!). Be meta-conscious of the quality of the thirds you're playing (maj, min, dim, aug). You'll quickly be able to construct chords without calculation, and can use any formulae simply to check yourself.

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  • I find that I think of viscerally played arpeggios and theoretical chords differently - and for the purposes of this question, only the second one matters. While playing arpeggios should hammer the interval sizes between their notes home, ironically including the perfect 4th interval between the 5th and root of an inverted major triad, my high mistake rate while playing arpeggios (higher than when I play scales) on the piano and my strong tendency to think of arpeggios as note names only on the clarinet and bass clarinet do not help.
    – Dekkadeci
    Dec 15, 2021 at 13:04
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    @Dekkadeci And as noted plenty elsewhere on this page, some instruments are poorly suited to conceptualizing distances in pitch-space. I just think the fastest way to get the most solid understanding is to get your actual ears involved. Personally, even with my extremely limited keyboard skills, I'd always prefer to do theory homework at a keyboard. Dec 15, 2021 at 13:37
  • @Dekkadeci (Also, I'd argue, for somebody who was about to start trying to construct 7th chords by counting half steps, even knowing them as note names only is a step in the right direction...) Dec 15, 2021 at 13:39
  • As in my answer - can't see how knowing minor scales will help. With 3 to contend with, they're confusing, and everything can be found from the major scale notes/intervals.
    – Tim
    Dec 15, 2021 at 16:21
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    It's strange, but I rarely think of say, Dm as being a misplaced/displaced FM, BUT I regard modes as just that. D Dorian = C Ionian, et al. However, knowing just the major scale, it's easy to adjust 3s and 7s to their appropriate #/b, M/m, with no reference to minor scales - of any variety - in my humble opinion.
    – Tim
    Dec 15, 2021 at 16:41
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To name the notes in any chord, you need the following:

  1. Associate every note with a number:
C     = 0
C#/Db = 1
D     = 2
D#/Eb = 3
E     = 4
F     = 5
F#/Gb = 6
G     = 7
G#/Ab = 8
A     = 9
A#/Bb = 10
B     = 11
  1. Associate every chord type with a sequence of intervals — the half steps between one chord note and the next:
TRIADS
diminished = 3-3
minor      = 3-4
major      = 4-3
augmented  = 4-4

SEVENTH CHORDS
fully diminished    = 3-3-3
half diminished     = 3-3-4
minor seventh       = 3-4-3
minor major-seventh = 3-4-4
dominant seventh    = 4-3-3
major seventh       = 4-3-4
  1. Given a chord, start with the root note's number and add each successive interval number to the previous number, mod 12.

  2. Translate the sequence of numbers back to note names, remembering that chords are built on every other letter name.

Examples

C major = [0, +4, +3] = [0, 4, 7] = C-E-G
F minor = [5, +3, +4] = [5, 8, 0] = F-Ab-C
  (Ab rather than G#, because of the every-other-letter-name rule)
Bb maj7 = [10, +4, +3, +4] = [10, 2, 5, 9] = Bb-D-F-A
A# maj7 = [10, +4, +3, +4] = [10, 2, 5, 9] = A#-Cx-E#-Gx
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  • This procedure does not tell us whether the third of the chord is D sharp or E flat.
    – phoog
    Dec 14, 2021 at 8:51
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    @phoog "4. ... remembering that chords are built on every other letter name." That uniquely determines the third of the chord, as shown in the examples.
    – Aaron
    Dec 14, 2021 at 10:29
  • Hm, ok, but what about e.g. augmented 6th chords? These are not typically conceived as an inversion of a triad with a diminished third.
    – phoog
    Dec 14, 2021 at 10:48
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    @phoog - This is part of why I tend to think of extended chords as triads with other, larger intervals put with the root (e.g. German augmented 6th = major triad w/augmented 6th). One of the only exceptions is the French augmented 6th, which I actually don't think about as having a triad bottom (it's more Italian augmented 6th w/additional perfect 4th from the root).
    – Dekkadeci
    Dec 14, 2021 at 12:59
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    @phoog You're correct that this approach would not work for augmented 6th chords without some kind of adjustment. I was not looking to address such chords, as my sense is that they are well beyond the scope of what the question is looking to address.
    – Aaron
    Dec 14, 2021 at 16:08
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To name the notes in a chord, you can:

  1. Memorize the intervals in each kind of chord. For example, a major seventh chord comprises a root, the major third above the root, the perfect fifth above the root, and the major seventh above the root. There is a table at the end of this answer.

  2. Memorize the procedure for finding the note a given interval above another note. (Mere counting of semitones is insufficient; the procedure must yield the correct enharmonic equivalent, so, for example, a major third above B is D♯, while a minor third above C is E♭). You probably need this procedure more generally, as you are likely to be tested on it independently of chord building.

    • Find the letter name of the upper note from the ordinal designation of the interval by counting inclusively. For example, to find a seventh above B, count B-C-D-E-F-G-A. (As you become familiar with this step, you will probably note that you can instead count down for larger intervals thanks to interval inversion. Interval inversion is also likely to be tested in a theory examination.)

    • Find the accidental, if any, to apply to the note using the following table of semitones:

Interval Diminished Minor Perfect Major Augmented
2nd 0 1 2 3
3rd 2 3 4 5
4th 4 5 6
5th 6 7 8
6th 7 8 9 10
7th 9 10 11 12

Rather than memorizing the whole table, it is probably more fruitful to memorize just the perfect and major columns, keeping in mind that chromatic alteration of a perfect interval such as the fourth or fifth changes it to a diminished or augmented interval, while imperfect intervals have two positions between diminished and augmented, namely minor and major.

Additional chromatic alteration is possible, yielding doubly augmented or doubly diminished intervals, or even more, but these intervals do not appear in standard chords, so they are beyond the scope of the question. Such intervals might be the subject of a theory examination, however, so it is a good idea to be aware of them.

If you treat the question of interval finding separately, therefore, all you need is to memorize the following table:

Chord Third Fifth Seventh
Major Major Perfect
Minor Minor Perfect
Diminished Minor Diminished
Augmented Major Augmented
Dominant 7th Major Perfect Minor
Major 7th Major Perfect Major
Minor 7th Minor Perfect Minor
Diminished 7th Minor Diminished Diminished
Half-diminished 7th Minor Diminished Minor

Again, it's not strictly necessary to memorize the whole table as there are some principles you can use to derive much of it. Major and minor triads are so called in order to identify the third, which is in both cases combined with a perfect fifth. Augmented and diminished triads are so called to identify the fifth. In those cases, the third is "pulled" by the fifth, constrained to be larger (major) when the fifth is augmented and smaller (minor) when the fifth is diminished. Similarly, seventh chords have a perfect fifth unless the name of the chord includes the word "diminished," in which case the fifth is diminished. A fully diminished seventh chord has two diminished intervals, the other one being the seventh, while a half-diminished seventh chord has only one, the seventh being minor. The dominant seventh chord you just have to memorize, but it's such a common chord that this isn't a problem. The other two types of seventh chord, major and minor, are constructed by adding a major seventh to a major triad or a minor seventh to a minor triad, respectively. (There is also a minor-major seventh chord, seen infrequently in the wild but often mentioned as a theoretical generalization of seventh chords as a triad with an added seventh; as the name indicates, it's a minor triad with a major seventh added.)

The notes in a B major seventh chord, for example, are major third, a perfect fifth, and a major seventh above B, which must be some sort of D, F, and A. Since D is three semitones above B, but the major third is four semitones, we need D♯. Analogously, we also need F♯ and A♯.

You mention memorizing the circle of fifths to know how many sharps are in the key signature of B major, and which sharps these are. That approach will yield correct results, but I can tell you that I never memorized the circle of fifths as such. Furthermore, knowing the key signature of B major or B minor does not directly tell you what notes are in every chord built on B. To find the notes of a B diminished 7th chord, for example, you have to know that its prototype is the seventh chord built on the chromatically altered leading tone of C minor. This is more complication than an elementary theory student ought to be asked to deal with.

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    I for one think that intervals are the key
    – eftshift0
    Dec 14, 2021 at 16:17
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Knowing the circle of fifths and number of sharps/flats in key signatures is all basic info that you will need to learn, but I don't think it is the direct way to name the notes in a chord.

Also, skip the math addition stuff your doing. I think it's better to think of this in terms of "spelling" with and reciting the musical letters.

You really need are two principle sets of knowledge:

  • know the intervals of the various chord types
  • know how to "spell" the intervals with the letters of the musical gamut

So, for a Bmaj7 chord, you need to know that any maj7 chord is a root with the follow intervals above the root: major third M3, perfect fifth P5, and major seventh M7. Then, given the root of B natural you need to know what letters (and possibly sharps/flats) are used to form the intervals.

The first part, knowing the intervals of various chords, is the easier part. I won't explain it here. You can find those descriptions easily online or in reference books.

For the second part, the spelling of intervals, you want to know how to recite the gamut of letters ABCDEFG in thirds ACEGBDFAC... and fifths AEBFCGDAE.... Literally, recite it out loud, forward and backward, or at least recite mentally, when dealing with chord spelling and things related to keys like the circle of fifths/order of sharps and flats. Then the "trick" for chords is knowing the specific spellings with naturals, sharps, or flats for the qualities of the thirds and fifths: major third, minor third, perfect fifth, and diminished fifth.

The traditional way to learn this is at a keyboard, first learning intervals and chords with only the white keys (or C major), and then learning to transpose those intervals and chords to all other key signatures. But you can also use charts.

First, interval abbreviations to make things easy to read, these are standard abbreviations...

INTERVAL ABBREVIATIONS

M3 major third
m3 minor third
P5 perfect fifth
d5 diminished fifth

Next, the diatonic intervals with no sharps/flats (intervals in C major...)

THIRDS, diatonic, no sharps/flats

AC m3 -----------------
BD m3 -----------------
CE M3 -----------------
DF m3 -----------------
EG m3 -----------------
FA M3 -----------------
GB M3 -----------------
FIFTHS, diatonic, no sharps/flats

AE P5 -----------------
BF d5 -----------------
CG P5 -----------------
DA P5 -----------------
EB P5 -----------------
FC P5 -----------------
GD P5 -----------------

...notice that most thirds are minor and all but one fifth are perfect.

Next, change the quality of intervals with sharps and flats. You can speak generally in terms of making an interval bigger or smaller. Sharpen the lower letter or flatten the upper letter to make the interval smaller. Flatten the lower letter or sharpen the upper letter to make the interval bigger.

Make the minor thirds bigger for major thirds...

THIRDS, major thirds

AC m3 - A♭C M3 - AC♯ M3 
BD m3 - B♭D M3 - BD♯ M3 
CE M3 -----------------
DF m3 - D♭F M3 - DF♯ M3 
EG m3 - E♭G M3 - EG♯ M3 
FA M3 -----------------
GB M3 -----------------

Make the major thirds smaller for minor thirds...

THIRDS, minor thirds

AC m3 -----------------
BD m3 -----------------
CE M3 - C♯E m3 - CE♭ m3
DF m3 -----------------
EG m3 -----------------
FA M3 - F♯A m3 - FA♭ m3
GB M3 - G♯B m3 - GB♭ m3

Make the diminished fifth bigger for perfect fifths...

FIFTHS, perfect fifths

AE P5 -----------------
BF d5 - B♭F P5 - BF♯ P5
CG P5 -----------------
DA P5 -----------------
EB P5 -----------------
FC P5 -----------------
GD P5 -----------------

Make the perfect fifths smaller for diminished fifths...

FIFTHS, diminished fifths

AE P5 - A♯E d5 - AE♭ d5
BF d5 -----------------
CG P5 - C♯G d5 - CG♭ d5
DA P5 - D♯A d5 - DA♭ d5
EB P5 - E♯B d5 - EB♭ d5
FC P5 - F♯C d5 - FC♭ d5
GD P5 - G♯D d5 - GD♭ d5

At this point I am skipping augmented fifths to keep things basic.

Any of the intervals above can be transposed up or down a half step by putting either sharps or flats on both letters. In the case that a sharp or flat is doubled, that is OK, those become double sharps or double flats. For example, major third CE can be transposed up to C♯E♯, perfect fifth AE can be transposed down to A♭E♭, minor third GB♭ can be transposed down to G♭B♭♭, etc. etc.

That is a bit of chart overload! But the idea is not to memorize all those charts. I gave the various charts to illustrate the process of spelling intervals. The idea is to memorize the diatonic gamut in thirds and fifths, memorize the specific qualities of those intervals, and then learn how to modify and transpose those interval qualities with sharps and flats.

For spelling seventh chords you really want to know the various seventh intervals, but you can also think of those chords in terms of all stacked thirds or a triad (a third and a fifth) with one more third above the fifth.

With these charts and the method you can now spell chords.

Remember that tonal harmony spells chords in thirds (that's called tertian harmony) so that, for example, an A major triad is spelled AC♯E not AD♭E.

Start with the root, recite up in thirds for the other letters, adjust the intervals above to get the specific interval qualities and final spelling. For your example of `Bmaj7...

  • start with root B natural,
  • then recite up the letters in thirds B D F A, those letters are a sort of "place holder" to be adjusted with sharps and flats,
  • the specific intervals of a maj7 chord are R M3 m3 M3
  • BD is a m3 so modify, raise the upper letter to make M3 of BD♯
  • DF is a m3 but the D was raised so transpose up to m3 of D♯F♯
  • FA is a M3 but the F was raised so transpose up to M3 of F#A♯
  • the final spelling is B D♯ F♯ A♯.

Learning this process takes time, but it can be treated as just a mechanical method. Some of it is memorization, and some of it is just familiarity. You kind of learn it, then forget it, and do it automatically. A practical way to learn it is playing cadences or the circle of fifth harmonic sequence in all keys while paying attention to the spelling of the various chords.

Practicing all keys can be hard a first, and overwhelming yourself is not helpful. You can build up to working in all keys by first doing C major and then just two keys to contrast, like two sharps for D major and two flats for B flat. Pay attention to how the intervals can in transposing between keys. For example, in C major DF is a m3, but in D major it becomes DF♯ which is a M3.

Two months of prep time with daily practice will allow you to make real progress on this topic.

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Learn the scales! This answer is from a piano perspective - but it does apply, with some players, to many instruments - question involves chords, so keys or guitar spring to mind - although arpeggios work the same way as chords, note-wise.

Knowing the 12 major scales, all major triads, major 7ths and 9ths will be clear.

Knowing the minor scales will help, but not that much.

EDIT: having read the answers which advocate all sorts of formulae, I feel by the time you've committed them to memory, you might just as well learn each chord make-up individually!

Knowing which notes constitute which chords is good - 1,3,5,7 - maj7, 1,3,5,♭7 - dom 7, 1,♭3,5, ♭7 - m7, etc.

Knowing the simple (white key root note scales on piano) will make the other 5 easier to compute. E.g. F = F A C E (F▵7); F♯ A♯ C♯ E♯ = F♯▵7.

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  • Does it perhaps depend in the terms in which you know the scales, though? I can easily play you all the scales, triads etc. you mention, but when i am playing them on guitar i am thinking chiefly in terms of number offsets - i don't actively think about note names at all. Dec 14, 2021 at 9:02
  • @topomorto - that's right. I saw this from a piano perspective - but on guitar and bass, , you're the same as me - never consider the note names (root apart), but relative positions. Maybe OP should specify the instrument.
    – Tim
    Dec 14, 2021 at 9:48
  • @topomorto - since the question considers theory, then reference to an instrument seems pointless. Or is it? Being able to vissualise a keyboard layout while answering questions should make the job easier. Guitar, not so. But notes making up scales play an important part - and maybe won't confuse sharps and flats.
    – Tim
    Dec 14, 2021 at 10:25
  • Now that you mention learning without reference to an instrument, it strikes me that I don't recall being asked by a teacher to "learn scales" (i.e. note names in each scale) in a 'pure' way (i.e. without learning on an instrument) - but maybe it's actually a very useful exercise? Having bought a cheap keyboard recently I am groggily becoming a little more note-name-aware again... Dec 14, 2021 at 11:38
  • @topomorto - learning theory without an instrument. Might as well learn to swim on the living room carpet ! Or diving off the table. Never seen the point - in either.
    – Tim
    Dec 14, 2021 at 12:24
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This answer may seem more rudimentary than the others, but maybe it will be a good starting-place now that you've dipped your toes into more advanced chords. It's easy to get overwhelmed. Start simple. Begin by making yourself what I call a chord wheel. Draw a circle, and write the letters C-D-E-F-G-A-B around it, clockwise.

enter image description here

To make a triad, pick your starting note and then move clockwise. Skip the second note and keep the third, skip the fourth note and keep the fifth. So to make a C chord, start on C, skip D, keep E, skip F, and keep G. That gives you C,E,G for a chord built on C. Starting on F, you'd get F-A-C.

For a seventh chord, skip one more note and keep one more, like G-B-D-F. The advantage of this is that there is little to memorize. You could easily scribble down this little wheel on the corner of an exam and refer to it when you need to.

To make it work in different keys, just add the sharps or flats to your chord wheel. Here is a wheel for the chords in B major. You can use it to see that the chord built on B will be a B major-seventh, B-D#-F#-A#, but the chord built on F# will be a dominant-seventh, F#-A#-C#-E.

enter image description here

The part that will take a good bit of study are the intervals, scales, and key signatures. Any introductory theory book will have these in great detail. This is where you will pick up which chords will be major, minor, etc. If you're diligent you can get there in a couple of months. It will be easier if you find a decent teacher! Many composers are willing to take on students in theory for reasonable rates.

Your question didn't say whether you play an instrument. Many theory students find the piano a great aid to visualizing chords and intervals.

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