We have seen that the 7 Standard IDPLMAL modes can be build on any key center and that any key center may contain a combination of these modes in the course of a composition. We Like Major and minor, we saw that these 7 standard modes consisted of specific interval relationships on their 7 respective scale degrees. These interval relationships always consisted of M2,m2nds.

Scale Materials

Synthetic Scale Formations
The synthetic seven-tone, one octave scale,is made of a pair of four note groups. These four note notes are called a tetrachord

1. New 7 note Scale Formations based on M2 m2
a. If we consider all possible successive combinations of M2, m2 we far surpass IDPLMAL
Some of the most common are:

1. Super Locrian = m2, M2, m2, M2, M2, M2, M2
2. Neapolitan Major = m2, M2, M2, M2, M2, M2, m2
3. Major Locrian = M2, M2, m2, m2, M2, M2, M2
4. Lydian Minor = M2, M2, M2, m2, m2, M2, M2
5. Overtone = M2, M2, M2, m2, M2, m2, M2
6. Leading Whole tone = M2, M2, M2, M2, M2, m2, m2

b. Of course, composers striving for new and interesting scale material have invented their own by combining other orders of M2 and m2

1. PAndy1 = M2, m2, M2, m2, M2, M2, M2
2. PAndy2 = M2, m2, m2, M2, M2, M2, M2

2. New 7 note Scale Formations based on M2 m2 & A2
a. The addition of a possible augmented 2nd further expands our synthetic scale formations:

1. Neapolitan Minor = m2, M2, M2, M2, m2, A2 , m2
2. Oriental = m2, A2, m2, m2, A2, m2, M2
3. Double Harmonic= m2, A2, m2, M2, m2, A2, m2
4. Enigmatic = m2, A2, M2, M2, M2, m2, m2
5. Hungarian Minor = M2, m2, A2, m2, m2, A2, m2
6. Hungarian Major = A2, m2, M2, m2, M2, m2, M2

b. Similarly, composers strving for new and interesting scale material have invented their own synthetic scales by combining other orders of M2 and m2 & A2

1. PAndy3 = A2, M2, m2, M2, M2, m2, m2
2. PAndy4 = M2, m2, m2, M2, M2, A2, M2

In class assignment 1. pick a "common" synthetic scale and write 2 transpositions 2 Create your own synthetic scale based on M2,m2, and A2s 3. Determine the synthetic key signature for your scale 4. Note the placement of all tritones 5. Note the placement or necessity of a L.T. and P5

3. Polymodal Construction of Synthetic Scales

a. Following the same procedure that yielded the 7 standard ID PLMAL modes from Ionian, we can repeat the sequence of M2,m2,A2 relationships in our synthetic scale on each scale degree to produce an additional 6 modes from our original synthetic scale.

4. Derivitive Construction of Synthetic Scales with fixed tonal center

a. By keeping a fixed tonal center but maintaining the intervalic relationships we can establish a tonal center and move, at will, to the given modes derivitives.

5. Charactrization of Synthetic Scales and their modal derivitives
We saw with the 7 standard ID PLMAL modes, we could determine their characteristic tones by identifying those tones that deviate from the modes most closely related Major or Natural Minor key. The identification of a characteristic tone(s) can become more challenging at time. In fact, TCH presents a rather complicated analysis of the characteristic tone(s) of synthetic scale formations. This analysis is based upon tetrachords that do not fall on ^1 nor ^5 and, in my opinion is weak as a result.

As such we will identify the characteristic tones in a manner similar to our analysis with the 7 standard modes.:

a. When identifying the characteristic tone of a synthetic scale or its derivitives, look for those tones that deviate from the key centers relative Major AND natural minor.
b. The tonic is always characteristic
c. If a tone is an enharmonic spelling of a tone in that keys relative Major or natural minor AND that tone is followed by a tone that contradicts its relative Major or natural minor representation, than the tone is a characteristic tone.
d. If a tone deviates from either the Keys relative Major OR Natural minor (but not both) it is a secondary characteristic tone

6. Triadic formations within the modes

a. Since each synthetic scale contains 7 scale degrees we may assign our familiar roman and arabic designations to each triadic formation.

b. Primary Chord = the I chord and any chord that contains the "characteristic scale degree(s) but NOT the tritone"
(The tritone would create a gravitational force to resolve into some other mode or key)
c. Secondary Chord = any chord that does not contain the "characterisitc tone" and does not contain the tritone.
d. Tritone Chord = any chord that contains the tritone.

 

Other Scale Formations

1. Pentatonic Scales
a. Not all scales must be confined to the 7 scale degrees of the diantoic scale. Penatatonic Scales utilize only five tones within the one octave range of a scale formation. As such the interval relationships between notes will, at times exceed a 2nd of any kind. There are 4 common pentatonic scales

1. Diatonic = M2, M2, m3, M2, m3
2. Pelog = m2, M2, M3, m2, M3
3. Hirajoshi = M2, m2, M3, m2, M3
4. Kumoi= M2, m2, M3, M2, m3

b. Just as we could create modal derivitives of synthetic scales, so too can we create modal derivitives of pentatonic scales

c. Because the limited tonality in the pentatonic scale often excludes a L.T. and/or P5 it can be difficult to achieve harmonic and melodic direction in a pure pentatonic form. You can combat this by:

1. Changing the modal derivitive via modal interchange
2. Changing the modal key center via modal modulation
3. Use lavish ornamental tones and pedal points
4. Counter pentatonic melodies with non pentatonic harmony
5. Counter pentatonic harmony with non pentatonic melody
6. Change the type of pentatonic scale on the same or different key center.

Please see Ex. 2-34 in TCH for an excellent example of a composition that changes modal derivitives at every bar.

In class assignment 1. pick a "common" Pentatonic scale and write 2 transpositions 2 Create your own synthetic Pentatonic scale based on M2,m2, and A2s, m3, and M3s 3. Determine the synthetic key signature for your scale 4. Note the placement of all tritones 5. Note the placement or necessity of a L.T. and P5 6. Write a short melody that retains the color of your pentatonic scale

2. Hexatonic Scales
a. Hexatonic scales are formed via the employment of 6 tones within the scale. The additional interval in the hexatonic scale helps to add harmonic interest. Most common of the hexatonic scale is the "whole tone" scale which was very popular during the impressionistic period. Other common hexatonic scales are:

1. Six-tone symmetrical = m2, A2, m2, m2, A2, m3
2. Prometheus = M2, M2, M2, m3, m2, M2
3. Prometheus Neapolitan = m2, A2, M2, m3, m2, M2
4. Whole Tone= M2, M2, M2, M2, M2, M2

b. Like the synthetic and Pentatonic scales, derivitives and transpositions may be employed with modal modulation and modal interchange.

c. Modal Modulation, Interchange and Derivitives of the Whole Tone Scale:
a. One excepetion to b. above is the Whole Tone Hexatonic scale. The absolute symmetry of the scale yields exactly the same intervalic relationship in every derivitive. This renders modal interchange to a new derivitive or key area somewhat ambiguous as the tonality of the modified mode, will be identical to that of the original

b. A half step modulation of the hexatonic whole tone scale will yield a completely new set of 6 tones with no common tones to its original whole tone formation. This lack of common tonality will prove equally problematic when trying to move between the two in a smooth and graceful manner. (One may think of the two derivations of the whole tone scale as completely lacking any accessible pivot)

 

c. It should be noted that TCH considers the whole tone hexatonic scale to be limited in its harmonic scope. To be sure the chordal formations of the scale are limited.

1. Every triadic formation yields an Augemented triad
2. 4 of these 6 triads are inversions of themselves.
3. Only one type of 7th chord is formed (Augmented triad, minor 7th)
4. Only one type of 9th chord is formed (Augmented triad, m7, M9)

d. Whereas the scope of the harmonic formations of the whole tone scale may be limited, it does not yield the scale formation any less significant. Persichetti's words "The true value of the whole tone scale lies in the contrast it provides when it is used incombination with other scales and techniques. When amalgamated with other materials it can be creatively stimulating" is certainly worth noting.

1. Judicious use of the whole tone scale can prove to be an excellent means of modulating between two very remote key areas within other modes.
2. Contrary motion within the scale can help to define other tonalities
3. Shifts between the two possible scale formations (a half step apart) exposes the entire 12 tone series
4. Registral consideration can help to define tonal areas.

In class assignment 1. pick a "common" Hexatonic scale and write 2 transpositions 2 Create your own synthetic Hexatonic scale based on M2,m2, and A2s, m3, and M3s 3. Determine the synthetic key signature for your scale 4. Note the placement of all tritones 5. Note the placement or necessity of a L.T. and P5 6. Write a short melody that retains the color of your Hexatonic scale

3. Charactrization of Pentatonic and Hexatonic Scales and their modal derivitives
It should now be clear that the characteristic tones of any given scale formation are those tones that deviate from some tonal norm. In the original ID PLMAL the characteristic tones were those that deviated from Major or Natural Minor. In the Synthetic Scales, we added the stipulation that a characteristic tone included any enharmonic spelling of a tone in Major or Nat. Minor but immediately followed by a tone that contradicted that tones relative Major or minor representation. This "contradiction" is an essential ingredient of identifying a characteristic tone within the less traditional scale formations. Consider the following:

A composition proceeds in C Lydian. Its tonal center and scale material, as well as all harmonic material may be derived from the C Lydian Scale formation.

A skilled composer will identify the tonic C and the raised ^4 as the characteristic tones. The composer will exploit those tones to expose the unique colors and textures of C Lydian.

Within close proximity of a section in C Lydian, the piece proceeds through Modal Interchange to the 1st derivitive of the Pelog formation of a Pentatonic scale on the same key center. Its tonal center and scale material, as well as all harmonic material may be derived from the 1st derivitive of the Pelog formation of a Pentatonic scale in C:

But now, the composer is faced with quite a problem. What is the characteristic tone of C Pelog 1st Derivitive?

In the context of Major and Minor we could identify that tone as the 3rd scale degree F# (note that F# is the 3rd tone within the scale hence it is the 3rd scale degree of this pentatonic formation) By simply avoiding the 3rd, the 1st derivitive lends itself nicely to a characteristic deviation from both Major and Natural Minor. However, in this case, C Lydian shares all characteristic tones with C Pelog 1st Derivitive. The fact that the C Pelog 1st Derivitive immediately follows the C Lydian will render any concept of modal interchange ineffective.

In order for a mode or scale formation to yield a characteristic tone, a tone must be present that deviates from the harmonic context within its immediate proximity.

In class assignment 1. Using your own Pentatonic and Hexatonic Scales from above, 2 Identify the characteristic tones when in close proximity to the following modes in the same key center: a. Major b. minor c. Lydian d. Phrygian e. Hungarian Major f. Double Harmonic g. One another.

Other Derivitives of Scale Formations

Any of the compositional devices that can be employed to manipulate melodic or scale material can be utilized with synthetic and modal scale formations.

1. Mirrored Derivities
a. Mirror = a mirrored scale formation is one in which the intervalic relationship between the original scale degree and the central (mirrored) tone is inverted.

2. Inverted Derivitives = Like a mirror, an inverted scale formation is produced when the order of intervals are maintained but led in the opposite direction of the original.

3. Retrograde Derivities = a retrograde derivitive is simply that scale formation backwards

3. Compound Derivitives. = a compound derivitive is the combination of various modal or scalar formations.

In class assignment 1. Using your own Pentatonic and Hexatonic Scales from above, 2 create derivitives that employ the following techniques: a. Standard b. Inversion c. Mirror

Conclusions:

1. The use of scale material beyond Major and minor can be a very rich and exciting method of expanding your tonal vocabulary. The 7 Standard ID PLMAL modes have all reappeared in the 20th century in a manner comfortable to the ear. To be sure, these modes as well as the more common synthetic scale formations have been utilized to varying degrees in many contexts of modern music and one should not hesitate to call upon them as necessary.

2. Through manipulation of interval ordination, one may create their own unique scale formations

3. Through modal modulation, modal interchange and Derivities implementing mirror, retrograde and inversionsion techniques, the scale formations that lead to ones melodic and harmonic context are limitless.

4. When implementing a modal or synthetic scale formation it is critical to identify and focus on the Characteristic Tones. In general, these tones are the ones that deviate from the harmonic context within that tones immediate proximity.

5. One should pay great attention to the inclusion or exclusion of the tritone, leading tone, and Perfect 5th within the mode or synthetic scale as these intervals will carry the strongest gravitational force to any given key center.

Homework: Assignment 2: Due next class 1. Write a short passage ( double period) for Pizz Strings, and woodwinds of your choice. 2. Begin the piece in a hexatonic scale formation of your choice. 3. Between the two periods, transition into any synthetic scale formation (either presented here or original) in any other key center by judicially utilizing chromatic alterations to create a gravitational force into the key of the new scale formation. 4. If you use chromatic alterations of the scale material within each period to provide stability to your key center make sure you retain the color of that scale or mode you are utilizing. Your piece should demonstrate a clear understanding of the characteristic tones and primary, secondary and TT chord formations. 5. Realize your composition with Garritan and submit your score and mp3 to: hmu415@gmail.com