Near the beginning of the course, we familiarized ourselves with the common scales necessary for learning diatonic function: major, natural minor, melodic minor, harmonic minor, major pentatonic, minor pentatonic, and chromatic scales. If you need to refresh your memory of those scales, please review Unit 2.
Most music–whether folk, pop, jazz, classical, etc.–can organize the pitches into what you would identify as a scale, but in most of these styles, rarely do these scales conform to a simple major or minor scale. Some of these scales, like the various diatonic modes and the pentatonic collection, are relatively familiar to most listeners. Others–such as octatonic and whole tone collections/scales–are more novel, and most often associated with compositions of the last 100 years.
When characterizing scales, the word “collection” is often more appropriate than “scale.” A collection is any group of notes–usually five or more–that can be ordered in an ascending and repeating fashion. Imagine a collection as a source from which a composer can draw musical material–a kind of “soup” within which pitch-classes float freely. Collections by themselves do not imply a tonal center. But in a composition, a composer may establish a tonal center by privileging one note of the collection, which we then call a scale.
Use the following arrangements of Happy Birthday to determine the intervallic pattern of each of these scales/collections. After discussing this with your group and writing the scale/collection out in standard ascending form, practice transposing the scale into various keys to ensure that you understand its structure. Finally, please read through the descriptions on the following page for background and the common usage for each of these scales/collections.
We covered the standard major and minor pentatonic scales in Unit 2b, and you hopefully can see how the Hirajoshi pentatonic scale combines aspects of both standard Western pentatonic scales–the hirajoshi uses the scale degrees of the major pentatonic but the accidentals from the natural minor scale.
| Pentatonic scales | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Major | ^1 | ^2 | ^3 | ^5 | ^6 |
| Minor | ^1 | ^b3 | ^4 | ^5 | ^b7 |
| Hirajoshi | ^1 | ^2 | ^b3 | ^5 | ^b6 |
The name clearly states this, but this scale is constructed entirely of major seconds, and because it has six pitches, we call this a hexatonic scale. Interestingly, the whole tone scale is one of the few collections of pitches that is both symmetrical and constructed entirely of one interval. It shares this trait with a fully diminished seventh chord (all minor thirds) and an augmented triad (all major thirds). Any whole tone scale also contains two augmented triads, separated by a M2.
Because there are only six pitches, you will have to choose to insert a skip of a diminished third when writing a whole tone scale on a staff, assuming that you want to keep your tonic the same in every octave. If you stack only use major seconds, your octave will be an enharmonic equivalent. There is no preferred place to put the interval of a third; most people just place it where it eliminates as many accidentals as possible.
The symmetry of the whole tone scale means that there are actually only two unique whole tone collections, because you can use any pitch of a given whole tone scale as a tonic. In this chart, you can see that for each of these two collections, you can start on any pitch within the collection and create a whole tone scale.
| The two whole tone collections | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | C | D | E | F# | G# | A# |
| 2 | Db | Eb | F | G | A | B |
Its symmetry also contributes to the whole tone scale’s general malleability–when all pitches are equal, it is both easy to manipulate but hard to solidify. It is often used in compositions to denote confusion or the supernatural.
The other two hexatonic scales require a combination of two intervals, the minor second and minor third. By alternating these intervals, you can create a six-note scale which we will label as either a 1+3 hexatonic scale or a 3+1 hexatonic scale. Like the whole-tone scale, 1+3/3+1 hexatonic scales contain two augmented triads, but in this case, the two triads are separated by a minor second.
We always label these hexatonic scales by looking at the first two intervals when the scale is written in ascending form. This often confuses students, because when you write this scale in descending form, the first interval will be the opposite of the name. For example, look at the 1+3 hexatonic scale starting on C:
C-C#-E-F-G#-A-C
You can clearly see that this scale begins with a minor second and then alternates with minor thirds. If you write it in descending form, however, the first interval is a m3. To avoid this confusion, we will always label these based on their ascending form.
3+1 and 1+3 hexatonic scales do not have symmetry as obvious as the whole tone scale, but they do have strong symmetrical traits. There are only four unique 1+3/3+1 collections, because like the whole tone scale, each note of a given collection can be used to form another hexatonic scale. For example, if we examine the C 1+3 hexatonic scale above, you can see that this are also the same pitches for the E 1+3, and G# 1+3 scales. If you arrange this scale to start on C#, F, or A, you would create the 3+1 hexatonic scales for those three pitches. This means that every collection contains three 1+3 and three 3+1 hexatonic scales.
| The four 1+3/3+1 hexatonic collections | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | C | Db | E | F | G# | A |
| 2 | C# | D | F | Gb | A | Bb |
| 3 | D | Eb | F# | G | A# | B |
| 4 | Eb | Fb | G | Ab | B | C |
The two variants of the octatonic scale, the half-whole and whole-half, are similar to the 1+3/3+1 hexatonic scales in nearly every way. Both:
The differentiator between the two scales is the intervallic pattern. The octatonic scale alternates between minor seconds and major seconds, as opposed to the 1+3/3+1 hexatonic scales’ minor seconds and minor thirds. The slightly smaller interval pattern of the octatonic creates a collection of eight pitches with many symmetrical properties. And like hexatonic scales, we will always label an octatonic scale starting from its first interval in its ascending form, because in its descending form the pattern will be reversed. If the first interval of your ocatonic scale is a minor second, you will label this as a half-whole (HW) octatonic scale; if the first interval is a major second, you will label this a whole-half (WH) octatonic scale.
You can divide any octatonic collection into two fully diminished seventh chords, as demonstrated in the C Half-whole (HW) scale written out here.
C-C#-Eb-E-F#-G-A-Bb-C
You can see that this collection can be separated into a Co7 and a C#o7 (If you do not see this, make sure to consider all of the enharmonic equivalents). And because a fully diminished seventh chord is symmetrical–as we discussed when studying them for enharmonic modulations in Unit 20b–we can then infer that this scale would have an identical interval pattern if we started on any of the pitches of that diminished seventh chord. For example, if you rearrange the collection to ascend from Eb, F#, or A–the other members of the Co7–you will find that the resulting scale is still alternating between minor seconds and major seconds, just with a different tonic.
Also like the 1+3/3+1 hexatonic scales, if we start the scale from the other pitches–for the C HW listed above, these would be the pitches of the other diminished seventh chord, C#, E, G, and Bb of the C#o7–you create a scale based on the other octatonic scale pattern, the WH. Therefore, every octatonic collection contains four HW octatonic scales and four WH octatonic scales, which means that there are only three unique octatonic collections.
| The three octatonic collections | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| 1 | C | Db | Eb | E | F# | G | A | Bb |
| 2 | C# | D | E | F | G | Ab | Bb | B |
| 3 | D | Eb | F | Gb | Ab | A | B | C |
The octatonic scale has long been a favorite of modern composers, because it not only has the tonal fluidity and symmetry of a hexatonic scales, but it also contains many of standard tonal structures such as triads and seventh chords. In a HW octatonic scale, you can create a major triad, minor triad, diminished triad, minor seventh chord, dominant seventh chord, and fully diminished seventh triad off of four of different pitches within the collection. This gives composers an amazing flexibility to use tonally familiar structures in a non-standard manner.