Graded Parameters

Musical parameters (rhythm, pitch, dynamics, and timbre) can be graded like earthquakes or temperature, by different degrees of force or heat. Force, from weak to strong, like the Richter scale for earthquakes, is a clear characteristic of dynamics , graded traditionally in Italian: pianissimo, piano, mezzo piano, mezzo forte, forte, fortissimo, with possible extensions to fortississimo on the strong side, and pianississimo on the weak.

Heat is measured by degrees that are in direct relation with the speed at which molecules vibrate. This is analogous to pitch , which is also a result of vibration. Before talking about actual notes, we can say whether pitches' register is high, medium or low, like temperature or air pressure on a spring day.

Tempo or speed is fast, medium, or slow, and register and tempo can further be graded by the word "very", and like mezzo forte and mezzo piano , we can talk about medium high, medium low, medium fast, and medium slow. Italian terms are traditional here too, with its indications Largo, Adagio, Andante, Moderato, Allegro, and Presto.

Timbre is more difficult to grade, since it is the result of the combination of overtones, from low to high. Sine waves have no overtones, and square waves have only even numbered ones. Sawtooth waves have all the overtones, and as square waves become pulse waves of ever narrower width, they acquire even numbered overtones. The filters on synthesizers can cut out or emphasize overtones in different registers, and acoustic instruments, use resonance or lack thereof to the same effect. A scale of timbres is indicated by vowels, which range between dark to bright, like the registers of light: U, O, ô, A, E, é, I.

If light is analogous to register and timbre, actual pitches are analogous to color. Many synaesthetic artists have felt an empirical relationship between pitch and color, but since color is also a function of vibration, and we now know the frequencies of different colors in nanohertz, it is possible to calculate exact correspondences, by multiplying pitch frequencies by two to arrive in the nanohertz range, the factor two giving an octave relationship. It takes forty octaves to reach the frequency of color from the upper middle register of the piano (F# 4 to F# 5 ).

These figures are approximate, but since colors cover a continuous range of frequencies, the interesting thing is that pitches can be projected into one color range or another, and our "chromatic" scale is in fact a spectrum of pitch characteristics that reproduces itself an octave higher when the frequency is doubled. The color spectrum also falls within a frequency range between infrared and ultra-violet that is n to 2n, about 3.25 x 10 14 Hz. to 7.5 x 10 14 Hz. The colors are also equally spaced, like the whole tone scale, separated by half-tint colors like orange between yellow and red and turquoise between blue and green (C#). These correspondences could make a fascinating area of research one day. They don't mean we should see red when we hear G#!

What is the use of these graded parameters? We can use them for analysis; either aural or written, becoming more aware of neglected parameters and their relationships, like nuances and register. Some composers like Stockhausen have even serialized nuances, register and tempo.

I also use graded parameters to plan improvisations, to avoid playing mezzo forte and moderato in the middle register all the time. Instead of assigning the number one to the bottom of a scale of registers, tonalities, tempos, dynamics and timbres , 1 represents the center of a set of possibilities. The other numbers fan out towards the extremes. For example:

7: very high, F(#), Prestissimo, fff, I .

5: high, E, Presto, ff, é .

3:medium high, D(#), Allegro, f, E .

1: medium, C(#), Moderato , mf , A .

2: medium low, B(b), Andante, mp, ô .

4: low, A, Adagio, p, O .

6: very low, G(#), Largo, pp, U .

I choose a number between 1 and 7, either by chance or by choice for each or all of the parameters. Modifications can be made between sections of a piece, and also between phrases and measures. They can concern all parameters and can be either sudden or gradual. Written composition can also be constructed more intelligently using these scales of values, if intelligence is useful therein!

Pitch, rhythm, and form can be graded even more precisely, using scales of complexity, but in direct order, starting with the simplest materials.

Rhythm and form:

1: no pulsation (prose rhythms),

one stanza, repeated or not.

2: simple binary measures, couplets,

alternating stanzas (refrains).

3: simple ternary measures,

tercets, arch forms (ABA).

4: double binary measures, quatrains,

refrain with two different stanzas (s1,R,s2,R).

5: quintal measures, quintinas,

arcade forms (rondo, palindrome).

6: double ternary measures, sestinas,

complex forms with six sections.

7: septal measures, septinas,

seven part structures.

Gender, mode and range:

1 and 2: pentatonic gender,

major and natural minor modes,

ranges of less than an octave.

3 to 5: diatonic gender,

church modes,

harmonic and melodic minor scales, ranges of an octave or more.

6 and 7: chromatic gender,

modes mixing major and minor,

whole tone, diminished and other "artificial" modes, including those of limited transposition,

ranges of an octave and a half to 2 octaves or more.

Harmonic textures also proceed from simple to complex:

1: monody, with or without drone.

2: organum.

3: triads.

4: tetrads, with or without polytonality by diatonic thirds.

5: pentads, polytonality by fourths and fifths.

6: hexads, polytonality by chromatic thirds.

7: heptads, polytonality by diminished fifth.

Since the seven levels present a gradual increase in complexity for form, rhythm, scales, and harmony, they can be useful to describe different musical styles :

Primitive (from 120 000 B.C.): form 1, rhythm 2 or 3, scales 1 or 2, harmony 1.

Ancient Greek (500 B.C. to 500 A.D.): forms 1 to 7, rhythms 1 to 7, scales 1 to 7, harmony 1.

Early Middle Ages (500 to 1200): forms 1 or 2, rhythms 1, 2, or 3, scales 1 to 4, harmony 2.

Late Middle Ages and Renaissance (1200 to 1600): forms 1 to 4, rhythms 1 to 3, scales 1 to 5, harmony 3.

Baroque and Classical (1600 to 1800): forms 1 to 7, rhythms 1 to 4, scales 3 to 6, harmony 3.

Romantic and Impressionist (1800 to 1920): forms 1 to 7, rhythms 1 to 5,

scales 3 to 6, harmonies 3 to 5.

Expressionist and Neoclassic (1900 to 1945): forms 4 to 7, rhythms 2 to 7, scales 6 and 7, harmonies 6 and 7.

Total Serialism (from 1945): form 7, rhythms 1 and 7, scales 7,

harmony 7.

Minimalist ( from 1970): form 5, rhythms 2 to 7, scales 1 to 5,

harmonies 2 to 5.

Entertainment Music (from 1870): forms 1 to 3, rhythms 2 to 4, scales 1 to 4, harmonies 2 to 4.

If these styles are treated as modes, in a musical as well as a general sense, it might be possible to create music of a wide modal variety that transcends historical style.