Musical and Mathematical Properties of the Melodic Minor (Ascending) Scale
History
I was unable to find much reference to the history of this scale on the internet under its own
name. What I did discover is listed in paragraphs 4 and 5 of this section. However,
searching the Lydian Dominant or 4th mode of the melodic minor uncovered a wealth of
information. This mode of the scale (a dominant 7th scale with a raised 4th, so giving a
feeling of excitement and tension) was used exensively by 19th century composers such as
Liszt, Debussy, Stravinsky and Bartok and is also commonly used in the indigenous music of
Northeastern Brazil (which to me suggests it originally comes from Africa).
From my own knowledge of minor scale development (e.g. Howard Goodall’s History of
Music, BBC recent series) the first scale to be used in Western music was in fact the aeolian
or natural minor. This is why the notes are named A-G and we did not start the major scale
with A (this is actually C, the third mode, if you like, of the aeolian scale!)
However, as music developed chromatically (i.e. using notes off the white note scale), it was
found that not all the notes of the chords in a minor sequence fitted onto the aeolian scale.
In particular, the seventh note had to be raised to accommodate the dominant 7th chord (G7
if you are in C minor). This initially resulted in the “harmonic minor” scale, which fits over all
the chords in a II-V-I or IV-V-I in a minor key.
Composers other than Mozart (information from Wikipedia – apparently he preferred the
harmonic minor!), who relied heavily on memorable and singable melodies, found the
minor third jump between the flattened 6th and major 7th in this scale difficult on the ear.
For this reason, they raised the 6th when writing ascending melodies, so that the melodies
flowed smoothly. They then reverted to the natural minor (i.e. with flattened 6th and 7th)
for descending melodies.
In this way the classical melodic minor scale was born, with every music student’s nightmare
of having to learn a different pattern when descending the scale! However, in modern jazz
theory the custom of reverting to the natural minor on descending has been dropped to
simplify learning scales for improvisation, and make sure that melody notes always fit the
underlying chord. The common use of the scale in jazz probably dates from the mid-1950s,
although Billy Strayhorn used it a lot in his (Debussy-influenced) compositions in the 1940s
(viz. “Chelsea Bridge”) and bebop tunes often ended on a 7#11 (see Lydian Dominant later).
Description
The Melodic Minor scale (Ascending) consists of the major scale with a flattened third. For
example,
C D Eb F G A B = C melodic minor scale.
There are 6 modes in common use in jazz. The most common are the Lydian Dominant (4th
mode) and the altered (7th mode). The 5th mode is hardly ever used. This makes the
melodic minor quite a difficult scale to master but an extremely useful one!
Uses
In classical music this serves as a scale upon which to write melodies over a minor chord
sequence, in particular a II-V-I or a IV-V-I. It was also used as the basis for Bernstein’s “West
Side Story” in the form of the lydian dominant mode (see above) to add an air of excitement
and anticipation (previously the Lydian mode had been used; viz. “Mars” from Holst’s “The
Planets”).
In jazz the scale is very widely used, especially (and almost exclusively) by modern jazz
musicians, as a scale to improvise on not only over minor 6th or minor-major 7th chords, but
also over certain dominant 7th chords as well as the Lydian Dominant described above (e.g.
b9b13 chords, e.g. Cb9b13 which consists of C, E, Bb, Db and Ab). One uses the seventh
(altered) mode, described above under “Description”, for this purpose. It is also used for
“half diminished” or -7b5 chords (6th mode), 11b9 (2nd mode) and maj7#5 (3rd mode) –
found in contemporary jazz only.
It can also be used as a good source of “voicings” or alternative ways of playing a chord, for
the above described chords. See below for further reading on this.
Mathematical properties.
It is well documented that the Lydian Dominant (4th mode of the ascending melodic minor)
is the first complete scale to emerge from the harmonic series (see below). This documents
that the notes are to be found in order in the 4th octave of the harmonic series, i.e.
harmonics 8 to 14.
I have not, however, found reference to the following observation in any other material
available on the internet. Whether it is something I have discovered I am not sure, but it
would seem to me that a lot of mathematicians are musical and vice versa, so I would have
thought someone would have discovered it before me!
If one takes the notes of the Lydian dominant scale in the order they appear in the harmonic
series, i.e. for C Lydian dominant:
C G E Bb D F# A
These correspond to the following harmonics:
1 3 5 7 9 11 13
Which are of course the first 7 odd numbers!
This is quite unexpected, as one would expect the most enharmonic scale to have some
direct relatedness (i.e. through even numbered harmonics). However, multiples of
harmonic 3 also indicate relatedness (the 5th) – as such, the 9th is related to the fifth by this
interval. This is also the interval between the 9th and 13th, which can also be described as
the 26th harmonic an octave higher, almost indistinguishable to the 27th harmonic, the true
5th of the 9th!
If one extends this series upwards, one ends up with the Lydian dominant scale starting on
the note a semitone down from the original (e.g. B if one started with C) although the 6th
note of this scale is a little higher than the true value. This roughly ties in with the notes of
the original Lydian dominant scale (in our example, that of C) appearing in the previous
octave in correlation with consecutive harmonic values.
This tells me that there is something very fundamental about the melodic minor (or actually
the lydian dominant) scale. The scale itself has a wave-like formation, with a group of notes
closely clustered together (on the diminished scale, i.e. in C Lydian dominant, F# G A Bb)
alternating with a group more widely spaced apart (on the augmented scale; Bb C D E F#).
For this reason the scale is sometimes known as the diminished-augmented scale.
This (pardon the pun) has overtones of the fundamental properties of reality, as we know
matter is constructed from waves and we can construct these two sets of waves from a
simple series (the odd numbers). I have not calculated further, as the neat correlation
appears to break down in the following octave. I leave it to the theoretical physicists, a lot
of whom I know are musicians too, to think about this one!
Further reading
More on chords and modes to be derived from the melodic minor scale, voicings and
progressions is to be found in The Jazz Piano Book by Mark Levine (Sher Music Co.) and
many other advanced modern jazz educational and academic publications.
Existing and forthcoming publications by the same author:
Mathematical properties of the octatonic “diminished” scale.
Jazz Piano Voicings – Covering all commonly used scales (Shawnuff Music).
Dorothy Shaw October 2014