MORE SCALES

This page is a supplement to The Complete Musician: Chapter 30 - Pitch Classes and Collections

PITCH CLASS

The concept of pitch class may be elusive but you’ve already been studying pitch class for years at this point! PITCH CLASS refers to the undefined octave or placement of a pitch in terms of its note name. For instance, when we refer to the abstract note “C”, that conjures a sounded pitch or placement on keyboard in our mind, but just describing the note “C” doesn’t give enough information to imply what octave. The pitch class “C” is a productive way to handle notes abstractly when thinking about scales, chords, and intervals because we can easily relate to the concept of the note regardless of what voice part we sing or instrument we play.

As a side note, when wanting to get more specific, you can translate this pitch class into a specific octave placement with the use of octave numbers. In this diagram, we can see 10 octaves of the note C spread out across bass and treble clef. An easy way to remember these octave placements is that “middle C” is C4. The B directly below it is B3 and the D directly above it is D4 (the octaves begin on C).

While octave placements don’t have much to do with pitch class or the scales we will be discussing below, this may help round out your understanding of notational reference.

When using only pitch class to reference something like a C major scale, spelling the scale C D E F G A B C is completely appropriate as this pattern will be constant no matter what octave it’s performed in.

SCALES vs. COLLECTIONS

What is a scale and what is a collection? All scales are collections but not all collections are scales. COLLECTION is a broader term used to reference a grouping of musical pitches that are utilized to create a given piece (or section) of music. A SCALE is a more specific term because scales have a comprehendible pattern and they are arranged sequentially (usually from lowest to highest pitch). Broader, more “amorphous” collections may not have a “tonic” but almost all scales have a tonic which, in this context, can be called a PITCH CENTER (the note the scale starts on and is named after).

In Western European Classical music, there are twelve constant notes that make up the CHROMATIC SCALE (in order) or CHROMATIC COLLECTION (not necessarily in order) which might also be referred to as the total chromatic, aggregate (which just means “everything”), or universal set. Western European Classical music theory does not have terms to define pitches that occur outside this established chromatic collection other than vague terms like “microtones” or “quarter tones”. In music traditions like Indian Classical, the term RAAG replaces “scale” or “collection” and syllables similar to Western solfege are used to define microtonal distances between pitch degrees in a given raag. These syllables are : Sa - Re - Ga - Ma - Pa - Dha - Ni - Sa. For more information on Indian Classical music theory, check out the website DEMYSTIFYING INDIAN CLASSICAL MUSIC.

PENTATONIC (FIVE NOTE) COLLECTIONS

The most globally prevalent scale type is the five-note PENTATONIC. This scale type contains no half-steps because the two half-step distances in a “standard” major scale (scale degree 3-4 and 7-1) are removed by the extraction of the 4th and 7th scale degree. A default major pentatonic scale is, therefore, scale degrees 1 - 2 - 3 - 5 - 6 (as in C - D - E - G - A). This scale is used heavily in the folk music traditions of East Asia, Europe, America, and parts of Africa and Polynesia. If we start on the 6 (like we do in relative septatonic minor), we get the pentatonic minor which is 6 - 1 - 2 - 3 - 5 or 1 - b3 - 4 - 5 - b7 (C - Eb - F - G - Bb).

HEPTATONIC (SIX NOTE) COLLECTIONS

The six-note HEPTATONIC scale has the interesting property of being the most balanced of Western Classical scales because of the mathematical relationship between 6:12 (2). By spreading out scale degrees evenly along a chromatic scale, each degree is a whole step above the last until the octave is reached. This collection of whole steps is called the WHOLE TONE SCALE. The whole tone scale delivers a sense of wandering aimlessness because the lack of intervallic diversity allows for equal weight to be given to each scale degree. The C whole tone scale (C - D - E - F# - G# - A#) has all the same notes as the D, E, F#, G#, and A# whole tone scales (A# - C - D - E - F# - G#). In fact, there are only TWO possible whole tone scales. The one that starts on any of the notes above, and the one that starts on Db/C# (Db - Eb - F - G - A - B). Every other note of a whole tone scale outlines an augmented triad (C - E - G# etc.).

SEPTATONIC (SEVEN NOTE) COLLECTIONS

Septatonic (also called diatonic) scales are what you are most familiar with at this point: major, natural minor, harmonic minor, and melodic minor. But did you know there are many more septatonic scales than these? Consider the major scale pattern: W W H W W W H. If we displace the starting note (aka the pitch center) up the scale by one degree, we can find new scales (called MODES) that convey different moods and imagery. The scale patterns available in the septatonic collection can also be referred to as GREEK MODES (since many first originated during the era of Ancient Greece) or CHURCH MODES (since they were subsequently copied by the Catholic Church for use in plainchant composition). The seven modes - including their modal names - are outlined below:

IONIAN MODE (Major)

W W H W W W H - or - 1 2 3 4 5 6 7

This is the major mode.

Example: “Stand By Me” by Ben E. King

DORIAN MODE

W H W W W H W - or - 2 3 4 5 6 7 1 - or - 1 2 b3 4 5 6 b7

This is a minor mode, though not as minor as natural minor, and often found in jazz and folk music.

Example: “Scarborough Fair” as performed by Simon & Garfunkel

PHRYGIAN MODE

H W W W H W W - or - 3 4 5 6 7 1 2 - or - 1 b2 b3 4 5 b6 b7

This is an “extra” minor mode because of the b2 and is used a bit in Classical music; it sounds very “Ancient Greek”.

Example: “Prologue” from The Fellowship of the Ring by Howard Shore

LYDIAN MODE

W W W H W W H - or - 4 5 6 7 1 2 3 - or - 1 2 3 #4 5 6 7

This scale is a major scale with the addition of the #4 which serves as the leading tone for 5. The result is a quite “manic”, bright mood.

Example: “The Simpsons Theme” by Danny Elfman (and pretty much most of his theme songs …)

MIXOLYDIAN MODE

W W H W W H W - or - 5 6 7 1 2 3 4 - or - 1 2 3 4 5 6 b7

This scale is a major scale with the addition of the b7 which gives it a dominant feeling. The scale is very prevalently used in jazz.

Example: “Clocks” by Coldplay

AEOLIAN MODE (Natural/relative minor)

W H W W H W W - or - 6 7 1 2 3 4 5 - or - 1 2 b3 4 5 b6 b7

This is the standard natural minor scale (“relative” minor because it is the unaltered minor scale that uses the same sequence of half and whole steps as a major scale).

Example: “Ain’t No Sunshine” by Bill Withers

LOCRIAN MODE

H W W H W W W - or - 7 1 2 3 4 5 6 - or - 1 b2 b3 4 b5 b6 b7

This is the least-used of the Greek Modes and includes the half-diminished seven in an outline of its arpeggio.

Example: “Army of Me” by Björk (what a queen)

OCTATONIC (EIGHT NOTE) COLLECTIONS

The OCTATONIC scale is an eight-note scale also referred to as the DIMINISHED SCALE, the half-whole scale, or the whole-half scale (depending on where you start in the sequence). Octatonic scales are built off an alternating pattern of half and whole steps rising off the pitch center. Because it is a symmetrical scale (like the hexatonic whole tone scale), there are only three collections in the aggregate: Oct [0,2], Oct [0,1] and Oct [1,2]. The first is generated with a whole step between C and D: C - D - Eb - F - F# - G# - A - B - C and it is called Oct [0,2] where C is 0 and D is 2. The second is generated starting with a half step between C and Db: C - Db - Eb- E - F# - G - A - Bb - C and it is called Oct [0,1]. The third collection missing is one without “C”: Db - D - E - F - G - Ab - Bb - B - Db which is Oct [1,2] with Db as 1 and D as 2. It is the diminished scale because extracting every other note will outline a diminished seventh chord arpeggio.

The scale is used in a great deal of 20th century music as well as neo-Romantic modern classical music.