Enharmonic equivalent scales are not to be confused with equivalent scales. An equivalent scale is a scale or mode that is built upon the same root note in a key and can be substituted for another in order to create more unexpected twists and turns in music. For example:
A Harmonic minor A Harmonic Major
In the key of C Major, A Harmonic minor is reached by raising the root of mode V of the Major scale, G Mixolydian (+1) = G# Alt bb7. When the minor third of the A Harmonic minor scale is raised, it becomes A Harmonic Major. So moving from G Mixolydian looks like the example below:
G Mixolydian (+1) G# Locrian bb7
First, the raising of the root of the Mixolydian mode is shown as (+1) and then follows the symbol for an equivalent scale () which shows that the mode from A Harmonic Major is substituted for the equivalent mode of A Harmonic minor (G# Locrian bb7 for G# Alt bb7).
An Enharmonic Equivalent scale simply has the inverse accidental/s in its structure. For example:
G Major = G A B C D E F#
C Ionian b5 = C D E F Gb A B
Both scales have the same note, F# in G Major and Gb in C Ionian b5. The rest of the notes in the scale are filled in without accidentals. This technique occurs in the music of many composers, from Bach to Walton and is a great way of throwing the listener, creating ambiguity and jumping to a distant scale or key with relative ease.
Below is the opening of the third movement from William Walton’s Bagatelles for solo guitar.
The key signature in D Major is followed by an A#:
A Mixolydian (+1) = A# Alt bb7 = B Harmonic minor = B C# D E F# G A#
The next bar has a Bb after the natural A in it, which is the enharmonic equivalent of A#. So, flatten the A# to A once more and instead flatten B to Bb and we have:
D E F# G A Bb C# = D Harmonic Major
B Harmonic minor is one of the Enharmonic Equivalent scales (En. Eq.) of D Harmonic Major. This is written as:
B Harmonic minor D Harmonic Major
This is the musical equivalent of the fallacy in logic known as equivocation, defined as ‘using a word or phrase with multiple meanings, without clarifying which meaning is intended.’ For example, saying something is audible means it is capable of being heard. Visible means it is capable of being seen. Therefore, desirable means it is capable of being desired which is incorrect as desirable actually means it is the preferred outcome.
Say for example, you wanted to modulate from C Major to D Major. The usual approach would be to go through the circle of fifths twice, right.
C Major – G Major – D Major
Well with the En, Eq. technique you could do it like this. D Major = D E F# G A B C#. Change the C# and F# to Db and Gb making C Db E F Gb A B = C Persian natural 6. (1 b2 3 4 b5 6 7). Then change back:
C Major – CPersian nat 6 – D Major
Now that this concept has been explained, lets have a look how the key signature affects the choice of En. eq. scales. First, we'll look at the Major scale.
Major Scale Enharmonic Equivalents
We begin with Enharmonic Equivalents of the Major scale. Believe it or not, the En. Eq. scales change with each key signature but in a sequence unique to itself. Starting with moving clockwise round the circle of fifths:
C Major: C D E F G A B = No En. Eq. (as no accidentals.)
G Major: G A B C D E F# = C D E F Gb A B = C Ionian b5 (1 2 3 4 b5 6 7)
D Major: D E F# G A B C# = C Db E F Gb A B = C Persian nat 6 (1 b2 3 4 b5 6 7)
A Major: A B C# D E F# G# = C Db E F Gb Ab B = C Persian (1 b2 3 4 b5 b6 7)
E Major: E F# G# A B C# D# = C Db Eb F Gb Ab B = C Locrian nat 7 (1 b2 b3 4 b5 b6 7)
B Major: B C# D# E F# G# A# = C Db Eb F Gb Ab Bb = Db Major (C Locrian)
F# Major: F# G# A# B C# D# E# = Gb Ab Bb C Db Eb F = Db Major
C# Major: C# D# E# F# G# A# B# =Db Eb F Gb Ab Bb C = Db Major
We can see from the table that there is an incremental change between C Major and Db Major, altering one note at a time through the scale sequence of:
C Major – C Ionian b5 – C Persian nat6 - C Persian –
C Locrian nat 7 – Db Major
At any time in the sequence the music can switch back again to any of the original Major scale keys, just by following the En. Eq. rules. Its interesting that B Major has Db Major as its En. Eq. as that is like the completion of the whole sequence and it can start again in the new key of Db Major.
Also, the whole process through the circle of fifths has ultimately revealed a unique way of modulating up a semitone, in this case from C Major to Db Major.
Take note also that the changes go no further than Db Major but instead repeat Db Major twice more. The key signature of G# Major has for its En. Eq. the Ab Major scale and this has no effect at all, probably because it is an auxiliary key that is not a key signature to begin a piece with but instead is only reached when, for example, modulating up a fifth from C# Major:
G# Major: G# A# B# C# D# E# F## = Ab Bb C Db Eb F G = Ab Major
What an amazing sequence. I am working this into my toolbox as we speak.
This is an excerpt from my Modal Method of Music book, available here: https://www.bedwellmusic.co.uk/general-7
My group on theory is found at https://www.facebook.com/groups/modalmethodmusictheory
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