Johnson Foundations of Diatonic Theory

Textbooks - Music Theory, Notation & Writing

  • Johnson

    Foundations of Diatonic Theory

    Foundations of Diatonic Theory is the first introductory, undergraduate level book published on diatonic set theory, an important but often overlooked sub-field of music theory. It provides an easy entry point into this challenging field and is appropriate for introductory music majors, motivated non-majors, music theorists, and mathematicians with musical interests.

    This book supplements any Music Theory or Fundamentals of Music course which includes music theory, and is suitable for self-study of basic music theory in a mathematical context. It requires only general mathematical knowledge, and provides the solutionfor nearly all exercises.

    This book is part of the NSF-funded Mathematics Across the Curriculum (MATC) project at Dartmouth College developed to achieve the goal of allowing students to focus on their disciplines while improving their mathematical skills.

    • Category: Textbooks - Music Theory, Notation & Writing
    • Item: 047784
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Woodwind Instrumentation Codes

Following many of the titles in our Wind Ensemble catalog, you will see a set of numbers enclosed in square brackets, as in this example:

Description Price
Rimsky-Korsakov
Quintet in Bb [1011-1 w/piano]
Item: 26746		 $28.75

The bracketed numbers tell you the precise instrumentation of the ensemble. The first number stands for Flute, the second for Oboe, the third for Clarinet, the fourth for Bassoon, and the fifth (separated from the woodwinds by a dash) is for Horn. Any additional instruments (Piano in this example) are indicated by "w/" (meaning "with") or by using a plus sign.

Flute   Oboe   Clarinet   Bassoon   —   Horn

This woodwind quartet is for 1 Flute, no Oboe, 1 Clarinet, 1 Bassoon, 1 Horn and Piano.

Sometimes there are instruments in the ensemble other than those shown above. These are linked to their respective principal instruments with either a "d" if the same player doubles the instrument, or a "+" if an extra player is required. Whenever this occurs, we will separate the first four digits with commas for clarity. Thus a double reed quartet of 2 oboes, english horn and bassoon will look like this:

0,2+1,0,1-0

Note the "2+1" portion means "2 oboes plus english horn"

Titles with no bracketed numbers are assumed to use "Standard Instrumentation." The following is considered to be Standard Instrumentation:

Brass Instrumentation Codes

Following many of the titles in our Brass Ensemble catalog, you will see a set of five numbers enclosed in square brackets, as in this example:

Description Price
Copland
Fanfare for the Common Man [343.01 w/tympani]
Item: 02158		 $14.95

The bracketed numbers tell you how many of each instrument are in the ensemble. The first number stands for Trumpet, the second for Horn, the third for Trombone, the fourth (separated from the first three by a dot) for Euphonium and the fifth for Tuba. Any additional instruments (Tympani in this example) are indicated by a "w/" (meaning "with") or by using a plus sign.

Trumpet     Horn     Trombone   .   Euphonium     Tuba

Thus, the Copland Fanfare shown above is for 3 Trumpets, 4 Horns, 3 Trombones, no Euphonium, 1 Tuba and Tympani. There is no separate number for Bass Trombone, but it can generally be assumed that if there are multiple Trombone parts, the lowest part can/should be performed on Bass Trombone.

Titles listed in our catalog without bracketed numbers are assumed to use "Standard Instrumentation." The following is considered to be Standard Instrumentation:

People often ask us about "PJBE" or "Philip Jones" instrumentation. This is a special instrumentation adopted and perfected by the Philip Jones Brass Ensemble. It consists of the forces 414.01, and often includes Percussion and/or Tympani. In addition, there are often doublings in the Trumpet section - Piccolo and Flugelhorn being the most common. While this instrumentation has come to be common, it is still not "Standard" as many Brass Dectets use very different forces, most often with more Horns than PJBE.

String Instrumentation Codes

Following many of the titles in our String Ensemble catalog, you will see a set of four numbers enclosed in square brackets, as in this example:

Description Price
Atwell
Vance's Dance [0220]
Item: 32599		 $8.95

These numbers tell you how many of each instrument are in the ensemble. The first number stands for Violin, the second for Viola, the third for Cello, and the fourth for Double Bass. Thus, this string quartet is for 2 Violas and 2 Cellos, rather than the usual 2110. Titles with no bracketed numbers are assumed to use "Standard Instrumentation." The following is considered to be Standard Instrumentation:

Orchestra & Band Instrumentation Codes

Following some titles in our Orchestra & Band catalogs, you will see a numeric code enclosed in square brackets, as in these examples:

  Order Qty Description Price
Beethoven
Symphony No 1 in C, op 21
[2,2,2,2-2,2,0,0, tymp, 44322] 		$150.00
Jones
Wind Band Overture
[2+1,1,3+ac+bc,2,SATB-2+2,4,3+1,1, tymp, percussion, double bass] 		$85.00
MacKenzie
Hines Pond Fantasy (DePaolo)
[2d1+1,1,2+1,1-2,2(+2),3,0, perc, tymp, 44322, Eb clarinet, SAATB saxes, trombone solo] 		$75.00

The bracketed numbers tell you the precise instrumentation of the ensemble. The system used above is standard in the orchestra music field. The first set of numbers (before the dash) represent the Woodwinds. The set of numbers after the dash represent the Brass. Percussion is abbreviated following the brass. Strings are represented with a series of five digits representing the quantity of each part (first violin, second violin, viola, cello, bass). Other Required and Solo parts follow the strings:

Woodwinds—Brass,   Percussion,   Strings,   Other

Principal auxilary instruments (piccolo, english horn, bass clarinet, contrabassoon, wagner tuba, cornet & euphonium) are linked to their respective instruments with either a "d" if the same player doubles the auxiliary instrument, or a "+" if an extra player is required. Instruments shown in parenthesis are optional and may be omitted.

Example 1 - Beethoven:

[2,2,2,2-2,2,0,0, tymp, 44322]

The Beethoven example is typical of much Classical and early Romantic fare. In this case, the winds are all doubled (2 flutes, 2 oboes, 2 clarinets and 2 bassoons), and there are two each horns and trumpets. There is no low brass. There is tympani. Strings are a standard 44322 configuration (4 first violin, 4 second violin, 3 viola, 2 cello, 2 bass). Sometimes strings are simply listed as "str," which means 44322 strings.

Example 2 - Jones: (concert band/wind ensemble example)

[2+1,1,3+ac+bc,2,SAATB-2+2,4,3+1,1, tymp, percussion, double bass]

The second example is common for a concert band or wind ensemble piece. This ficticious work is for 2 flutes (plus piccolo), 1 oboe, 3 clarinets plus alto and bass clarinets, 2 bassoons, 5 saxes (soprano, 2 altos, tenor & bari), 2 trumpets (plus 2 cornets), 3 trombones, euphonium, tuba, tympani, percussion and double bass. Note the inclusion of the saxes after bassoon for this band work. Note also that the separate euphonium part is attached to trombone with a plus sign. For orchestral music, saxes are at the end (see Saxophones below. It is highly typical of band sets to have multiple copies of parts, especially flute, clarinet, sax, trumpet, trombone & percussion. Multiples, if any, are not shown in this system. The numbers represent only distinct parts, not the number of copies of a part.

Example 3 - MacKenzie: (a fictional work, by the way).

[2d1+1,1,2+1,1-2,2(+2),3,0, perc, tymp, 66432, Eb clarinet, SAATB saxes, trombone solo]

In the third example, we have a rather extreme use of the system. It is an orchestral work for piccolo, 2 flutes (1 of whom doubles on piccolo), 1 oboe, 2 clarinets plus an additional bass clarinet, 1 bassoon, 2 horns, 2 trumpets (plus an optional 2 cornets), 3 trombones, no tuba, percussion, tympani, 6 first violins, 6 second violins, 4 violas, 3 cellos, 2 double basses, Eb clarinet (as an additional chair, not doubled), 5 saxes (soprano, 2 alto, tenor & baritone) & a trombone soloist.

Note: This system lists Horn before Trumpet. This is standard orchestral nomenclature. Unless otherwise noted, we will use this system for both orchestra and band works (in most band scores, Trumpet precedes Horn, and sometimes Oboe & Bassoon follow Clarinet). Also, it should be noted that Euphonium can be doubled by either Trombone or Tuba. Typically, orchestra scores have the tuba linked to euphonium, but it does happen where Trombone is the principal instead.

Saxophones, when included in orchestral music (they rarely are) will be shown in the "other instrument" location after strings and before the soloist, if any. However for band music, they are commonly present and therefore will be indicated after bassoon as something similar to "SAATB" where S=soprano, A=alto, T=tenor and B=baritone. Letters that are duplicated (as in A in this example) indicate multiple parts.

And finally, here is one more way to visualize the above code sequence: