Is there a way to quickly calculate relative/enharmonic chords or scales that are based off the same notes as another, like you can with the notes themselves, i.e. C being equivalent to A minor? For instance, if you have a C7 chord, which has one flat, making it the equivalent of an F Major chord, correct? Is comparing the key signatures the only way to quickly find a relative chord?
...Is comparing the key signatures the only way to quickly find a relative chord?
Not necessarily for relative chords.
Relative chords are always a minor triad below a major triad with the root separated by a minor third.
The example above shows relative chord pairs -
Em - we don't really need to know the keys that are indicated before the Roman numerals. In fact, you will notice that pair
C major flip their order to
A minor when we take note of the tonic and mediant chord identities in the key. It's nice to know that about the relationship to the keys, but it isn't absolutely necessary.
You can apply the same rule for chords to scales but swap out the term root (for chords) with tonic for scales. The relative scale pairs are a (natural) minor scale below a major scale with the tonics separated by a minor third.
However, I think it may best best to know relative scales by their shared key signatures for the sake of know the specific tones in each scale. So it's fairly easy to say that
B minor and
D major are relative scales without knowing the key signatures (we know this because the tonics are a minor third apart) but it's very helpful to know that both scales have
Of course all of this relies on knowing the intervals of the musical alphabet. If you don't know
C is minor third (and not a major third) you won't be able to find relative pairs.
As mentioned in comments, you should refer to these relationships as relative rather than equivalent. The term equivalent is usually used for enharmonic equivalent which is a very different meaning. I have seen some people suggest that relative chords can be used for substitutions. For example, an
Am chord could substitute for a
C major chord. Even in that case you should say substitution rather than equivalent.
...if you have a C7 chord, which has one flat, making it the equivalent of an F Major chord
I think you may be fixing up relative major/minor and equivalent with some way to know a particular chord belongs to a particular key.
C7 does indeed have one flat, and so does the key signature for
F major, and the tonic chord of
F major is the
F major chord. But, that doesn't make
F equivalent chords.
C7 is the dominant chord of
If that is sort of what you were thinking, the formula won't work for all chords/keys. Example, the
Bb7 chord uses two flats and is the dominant of
Eb major, but
Eb major uses three flats. The number of flats doesn't match in that case. The chords
Eb major both used two flats, but again that isn't a rule for all tonic and dominant pairs, example:
Ab7 dominant to
Db major, none of the flat counts for chords or key match.
If you meant some other association of chords and keys, please update your question with some more detail.
I’ll try to answer this once more, but because many words used in the question are borrowed from different concepts than what is actually meant, we have to get some things straight first:
- Equivalent: (mathematical term) having the same outcome in some function https://en.wikipedia.org/wiki/Equivalence_relation If A and B are equivalent, it doesn’t matter which one you choose, the outcome will be the same. If A and B are equivalent, and B and C are equivalent, then A and C must be equivalent as well. In this sense, C7 and F cannot be said to be equivalent in any meaningful way.
- Relative: “The relative minor of a particular major key, or the relative major of a minor key, is the key which has the same key signature but a different tonic;“ https://en.wikipedia.org/wiki/Relative_key For chords, you can say that C major and A minor are relative, and Eb major and C minor are relative. F major and C7 are not relative.
- Enharmonic: “if two notes have the same pitch but are represented by different letter names and accidentals, they are enharmonic” https://en.wikipedia.org/wiki/Enharmonic For example, C# and Db are different enharmonic spellings for the pitch that’s played with the same key on the piano. C#m and Dbm are two different names for the same minor triad chord. Enharmonic = same sound, different notation. F and C7 are not enharmonic.
- Chords do not have key signatures. You can’t say what key signature the Am triad has. You cannot compare the key signatures of chords, because chords do not have key signatures. F major and C7 do not have the same key signature, because neither of them has a key signature to begin with. They can be used in songs with different key signatures.
The real question is something like this: if I’m presented with just one chord alone without any context, how can I quickly know possible contexts where that chord might occur, and the sets of other chords and scales that would be used in each of the contexts. And “context” here means a key, centered around a tonic note, and with a basic scale and basic chords and all possible harmonic changes that might happen inside the key while not losing track of the tonic.
If taken literally, this is an impossible task to do with any sort of theoretic logical deduction, because it produces too many possibilities. For example a popular song has F#7 - B7 - E7 - Am. If you see just the F#7 chord, would you consider the possibility that the key might be Am? How about if the same motion is done with dim chords, so A#dim7 - D#dim7 - G#dim7 - Am. Deduction rules for any dim chord would list basically all contexts as possibilities.
Or, an A major chord is often used to get to a Dm chord like: A - Dm - E - Am. If you see an A major chord, remember to add to the logic rules that the key can be A minor. Or the Cm maj7 example… let’s make it simpler: Cm. The key might be G major. It’s a common trick to use a minor IV chord. The list of rules and tricks to consider is endless. Any chord or note can be used in any key. But once you have some context: bits of preceding chords and melody, then the list of plausible possibilities is narrowed greatly. You feel what the tonic might be.
The only practical way to obtain the ability to do what you want is: practice, experience and training. You play songs in different keys and you develop a sensitivity to feel where the tonic, i.e. home base note is. You instantly remember sets of chords that are normally used in each key. You just think of a key, and it instantly brings a set of notes and chords to mind. You develop a sensitivity to feel when the harmony is leaning on the subdominant or dominant or tonic side. When you know your basic tonic - subdominant - dominant thing well, and then you encounter a secondary dominant, you’ll understand how it works. When you’ve played a few songs in G major that has the C minor trick, you’ll remember it. Once you’ve played tritone substitutions, you’ll remember that a dominant V can be replaced with a 7th/9th/13th rooted one semitone above the tonic.
Check out the circle of fifths... study it, it will change your life. The inner ring are the relative minors of the outer ring.
The major and minor chords within a key can be looked at and grouped “SHAPED” two different ways.
C major for example Method 1: the major chords will be on each side. The relative minor is below either the remaining two minor chords on each side.
Method two: same concept just using the outer ring,... the minor chords follow the 5th on the outer ring.
The diminished chord also follows just after the the last minor chord on the wheel.
This a great visual tool to reference. It will help open up your understanding of choosing which key you want your music to be in. For example if you play a C major chord followed by its relative A minor.. you still have the ability to decide if it’s going to stay in that key (C major /Ionian) or F Major (C mixolydian) or G Major (C Lydian). It all depends on the remaining chords you chose to fill that “SHAPE”.
Please note this is only for the Natural Scale, although it covers the majority of the westernized music we hear today.