A regular vibration at 440 Hz (440 CPS) produces the pitch A.

Doubling the frequency (880 Hz) produces A an octave higher.

The great staff is a theoretical construction consisting of eleven lines and spaces with middle C as the middle or sixth line.

If tempo is fast, a time signature with an upper numeral of 3 may call for a count of one beat per measure, which may require compound interpretation.

This metrical stress is referred to as compound single.

If tempo is slow, a time signature with an upper numeral of 6, 9, or 12 may call for a count of 6, 9, or 12 beats per measure, and may require simple interpretation.

If tempo is slow, a time signature with an upper numeral of 2, 3, or 4 may call for a count of 4, 6, or 8 beats per measure.

A time signature with an upper numeral of 7, 10, 14, 15, 21, etc. may require simple or compound interpretation.

Rhythm is the occurrence of varying lengths of sound and silence. Meter is the pattern of beat groupings and the nature of the divided beat. Rhythm does not always coincide with meter. The two must not be confused.

The sum of note and rest values in each measure equals the number of beats indicated by the time signature, Relationships between rhythm and meter can be shown in two categories: regular rhythm and irregular rhythm.

REGULAR RHYTHM

Regular rhythm occurs: when long notes coincide with strong beats and shorter notes (when present) occur as non-syncopated divisions of weak beats; or when repeating non-syncopated divisions occur on all beats.

Uniform rhythm is regular rhythm that occurs: when the measure is filled by one note; or when the measure is filled by two equal notes in quadruple meter; or 4-2.when the measure is divided equally into units of beats; or when the measure is divided into equal divisions of the unit of beat.

Irregular rhythm occurs: when long notes coincide with weak beats or weak parts of beats; or when the rhythm has been syncopated.

Syncopated rhythm occurs when notes alter the normal or expected pattern of rhythm, accent, or meter by appearing on weak beats or weak parts of beats.

Syncopation may be created: when a weak beat or weak part of a beat is accented; or when a weak beat or weak part of a beat is tied to the strong beat which follows it; or when a rest occurs on a beat after a note on a weak beat or when a rest occurs on any beat after a weak part of a beat.

The first beat in a measure is called the thesis. A phrase (a short musical thought, normally two to four measures long) that begins on the first beat has a thetic beginning; the phrase is said to begin thetically. The thesis is also called the down-beat. Down-beat derives its name from the downward stroke of a conductor indicating the principally accented note of the measure.

An unaccented beat in a measure is called an arsis. An anacrusis, also called upbeat or pick-up, consists of one or more notes that precede the first down-beat of a musical phrase. Normally, when a composition begins with an anacrusis, the last measure contains only the rhythmic values that will complete the first measure. However, some composers and arrangers end their compositions with a complete measure regardless of the material contained in the first (incomplete) measure.

When the last attack of a phrase coincides with the thesis, the ending is called a masculine ending. If the last attack does not coincide with the thesis, the ending is called a feminine ending.

Related meters have the same metrical stress but a different unit of beat. In related meters, the upper time signature numeral is the same but the lower time signature numeral is different. Therefore, it is possible to notate the same rhythm in more than one time signature; the notation, which differs, reflects a choice of the unit of beat.

A scale (from the Latin scala - ladder or staircase) is a graduated series of musical tones ascending or descending in order of pitch according to a specified interval scheme. An interval is the difference in pitch between tones. Music depends on the succession of pitches and certain measurable patterns of intervals used with regularity. These patterns may be extracted from musical examples, arranged in order, and expressed as scales.

The basic intervals used for scale analysis are the half step (semitone) and whole step (whole tone). Any two adjacent keys on the keyboard sound a half step. The interval of two half steps sounds a whole step. A whole step (two half steps) occurs between C and D, D and E, F and G, G and A, and A and B. Observe that there are no keys between E and F, and B and C; these intervals are half steps.

The note a whole step above E is F # , not F. The note a whole step above B is are both whole steps below F and C respectively.

To construct a scale other than C major, chromatic signs must be used to maintain the scale formula. The addition of chromatic signs in major scales follows specific, recognizable patterns, When a major scale is constructed on the fifth scale degree ascending in the C major scale, the scale formed is a G major scale and has one sharp:

Scale Formula: MLM

When a major scale is constructed on the fifth scale degree in the G major scale, the scale formed is a D major scale and has two sharps:

When a major scale is constructed on the fifth scale degree in the D major scale, the scale formed is an A major scale and has three sharps: G#.

The pattern continues through the C# major scale with all seven pitch names sharped: F#, C#, G#, D#, A#, E#, and B#.

Figure 6.4: A Major Scale.

When a major scale is constructed on the fifth scale degree descending (the fourth degree ascending is the same note) of the C major scale, the scale formed is an F major scale and has one flat: Bb.

When a major scale is constructed on the fifth degree descending (fourth degree ascending) of the F major scale, the scale formed is a B major scale and has two flats: B and E.

The pattern continues through the:

Keys that have different names but sound the same are enharmonic keys.

The formula for the harmonic minor scale is mLH. The scale’s half step/whole step interval relationship does not correspond to any white key scale.

Scale Formula: mLH

Harmonic minor scales derive from natural minor scales. When constructed on the same tonic, the natural minor scale has a subtonic while the harmonic minor scale has a leading tone.

Harmonic minor scales share the key signatures of natural minor scales.

They are formed by a chromatic alteration of the subtonic upward to a leading tone. Chromatic signs used outside the key signature are called accidentals.

The harmonic minor scale evolved because of the relative lack of tendency tones in the natural minor. Using the harmonic form of the scale develops a better balance of tendency tones in minor keys.

The melodic minor scale has two formulas, one ascending and one descending. The formula for the ascending melodic minor scale is mLM. The formula for the descending melodic minor scale is NLm, which is the same as the natural minor scale.

Melodic minor scales derive from natural minor scales. The ascending melodic minor scale has a raised submediant and leading tone (which eliminates the objectionable melodic interval) that return to a subtonic and lowered submediant when descending to achieve a more minor sound.

Melodic minor scales share the key signatures of natural minor scales. They are formed by chromatic alterations of the submediant upwards a half step and the subtonic upward to a leading tone.

STABLE ACTIVE Tonic Supersonic Mediant Subdominant Dominant Raised Submediant (passes to Leading Tone) Subtonic (passes downward to lowered Submediant) TENDENCY Lowered Submediant (pulls to Dominant) Leading Tone (pulls to Tonic)

Keys having the same key signature are called relative. Relative keys will not have the same tonic. The keys of a minor and C major have no sharps or flats. Therefore, the relative major of a minor is C major, and the relative minor of C major is a minor.

To find the relative minor of any major key, descend three half stepson three successive staff degrees, or determine the sixth degree (submediant) of the major scale.

To find the relative major from any minor key, ascend three half steps on three successive staff degrees, or determine the third degree (mediant) of the minor scale.

Keys having the same tonic are parallel. Parallel keys do not have the same key signature. The keys of C major and c minor have the same tonic: C. Therefore, the parallel major of c minor is C major, and the parallel minor (or tonic minor) of C major is c minor. Note that their key signatures differ (no s or s and 3 s).

Scales of eight tones containing half steps and whole steps in specified positions are called modes or modal scales. Historically, the modes have been used in many periods and styles of music. They are also called church modes, ecclesiastical modes, and medieval modes. Although the techniques for their use have changed, they retain their interval patterns and their traditional Greek names.

The formula for the lydian mode (scale) is LMM. The scale’s half step/whole step interval relationship corresponds, on a keyboard, to a white key scale from F to F. The link (L) occurs at the beginning of this scale.

The remaining lydian scales are constructed on fifth scale degrees ascending and lowered fifth scale degrees descending from F lydian through seven sharps and flats. This creates fifteen lydian keys that can be represented in a circle of lydian keys (circle of fifths). Although lydian tonics differ from major and minor, the order of sharps and flats remains the same.

C major and F lydian are relative keys. Likewise, C lydian and G major; B lydian and F major; A lydian and E major; and D lydian and A major are examples of relative keys. The relative lydian tonic is the fourth scale degree (subdominant) of the major scale.

The lydian scale has a raised subdominant (4) when compared to its parallel (same tonic) major scale.

The formula for the dorian mode is mLm. The scale’s half step/whole step interval relationship corresponds, on a keyboard, to a white key scale from D to D.

The remaining dorian scales are constructed on fifth scale degrees ascending and descending from d dorian through seven sharps and flats. This creates fifteen dorian keys that can be represented in a circle of dorian keys (circle of fifths). The order of sharps and flats remains the same as in previous key signatures.

C major and d dorian are relative keys. The relative dorian tonic is the second scale degree (supersonic) of the major scale.

The dorian scale has a lowered mediant (3) and a subtonic (7) when compared to its parallel major scale. When compared to its parallel natural minor scale, the dorian scale has a raised submediant (6).

Figure 8.9: d Dorian Scale.

Chromatic, whole tone, and pentatonic scales cannot be analyzed using tetrachords. These scales do not form regular keys; therefore, none have regular key signatures. Chromatic and whole tone scales require accidentals when they are used with key signatures.

The chromatic scale consists entirely of half steps. There are twelve half steps (thirteen pitches) in an octave. If all thirteen pitches (twelve half steps) within an octave are represented in an ascending or descending order, the result is a chromatic scale. The name of the chromatic scale is the first note of the scale regardless When written as of the key signature.

notating chromatic scales, any pitch requiring an accidental is a chromatic alteration of the previous pitch.

Double sharps and double flats should be avoided when notating chromatic scales. Therefore, natural signs on adjacent staff degrees are used to avoid double sharps and double flats.

The same chromatic scale can be notated several ways. The key signature determines the notation of the chromatic scale.

Figure 9.2: and A Chromatic Scales.

The whole tone scale, as its name implies, is a scale arranged to sound in whole steps. The whole tone scale is notated using accidentals to create whole steps.

The same whole tone scale can be notated several ways. The key signature often determines the notation of the whole tone scale.

Since the whole tone scale consists of seven pitches instead of eight (including the octave), one of the staff degrees within the scale will not contain a note. The whole step that is indicated by non-adjacent staff degrees may occur anywhere in the scale.

A pentatonic scale consists of five tones (six pitches including the octave).

Two common pentatonic scales are the pentatonic major and the pentatonic minor. No half steps occur in either of these scales.

When constructed on the first degree of a major scale, apentatonic major scale contains the tonic, supersonic, mediant, dominant, and submediant of that scale. The pentatonic major scale corresponds, on a keyboard, to a black key scale from G to G.

The tones omitted are the tendency tones in major: the subdominant and leading tone.

When constructed on the first degree of a natural minor scale, a pentatonic minor scale contains the tonic, mediant, subdominant, dominant, and subtonic of that minor scale. This corresponds to the first, lowered third, fourth, fifth, and lowered seventh scale degrees (1, 3, 4, 5, 7) of the parallel major scale. The pentatonic minor scale corresponds, on a keyboard, to a black key scale from E to E.

An interval is the difference in pitch between two tones. Intervals are named according to the number of letter names, or the number of successive staff degrees, encompassed by the interval.

When interval tones sound simultaneously, the interval is a harmonic interval. When interval tones sound in succession, the interval is a melodic interval.

To identify a specific interval both its name and quality must be stated. The quality of an interval may be described by one of five terms: perfect, major, minor, augmented, or diminished.

A perfect prime (PI) consists of two notes of the same pitch on the same staff degree. A perfect fourth (P4), a perfect fifth (P5), and a perfect octave (P8) consist of the intervals formed between the tonic and the subdominant, dominant, and octave of a major or minor scale.

The perfect prime contains no half steps; the perfect fourth contains five half steps; the perfect fifth contains seven half steps; and the perfect octave contains twelve half steps.

A major second (Maj 2), major third (Maj 3), major sixth (Maj 6), and major seventh (Maj 7) consist of the intervals formed between the tonic and supersonic, mediant, submediant, and leading tone of a major scale.

The major second contains two half steps; the major third contains four half steps; the major sixth contains nine half steps; and the major seventh contains eleven half steps.

A major interval made smaller by a half step becomes minor. A minor 2nd (min 2), minor 3rd (min 3), minor 6th (min 6), and minor 7th (min 7) consist of the intervals formed between the tonic and lowered supersonic (2), mediant (3), and submediant (6) of a major scale, and between the tonic and subtonic (7).

The minor second contains one half step; the minor third contains three half steps; the minor sixth contains eight half steps; and the minor seventh contains ten half steps.

A perfect interval made greater by a half step becomes augmented. The augmented prime (Aug 1) contains one half step; the augmented fourth (Aug 4) contains six half steps; the augmented fifth (Aug 5) contains eight half steps; and the augmented octave (Aug 8) contains thirteen half steps.

A perfect interval made smaller by a half step becomes diminished. The diminished fourth (dim 4) contains four half steps; the diminished fifth (dim 5) contains six half steps; and the diminished octave (dim 8) contains eleven half steps. There is no diminished prime because it is impossible to make a prime smaller.

A minor interval made smaller by a half step becomes diminished. The diminished second (dim 2) contains no half steps because the two pitches sound the same; the diminished third (dim 3) contains two half steps; the diminished sixth (dim 6) contains seven half steps; and the diminished seventh (dim 7) contains nine half steps.

Major intervals made smaller by a half step become minor; minor intervals made smaller by a half step become diminished; therefore, a major interval made smaller by a whole step becomes diminished.

The following diagram illustrates the relationships of various intervals when moved by half steps.

Intervals that have different names but sound the same are enharmonic intervals. Enharmonic intervals will always have the same number of half steps but different notation. For example, the Aug 5 and min 6 shown in Fig. 10.12 are enharmonic intervals. Both intervals contain eight half steps.

Inversion is a change in the relative position of the notes in a simple interval. When the upper note in a simple interval becomes the lower note, or the lower note becomes the upper note, the interval has been inverted. Inversion is accomplished by moving the lower note up an octave or the upper note down an octave.

Three simple intervals do not invert: the perfect prime, perfect octave, and augmented octave.

The perfect prime will not invert because there is no upper or lower note.

The perfect octave will not invert because this would create a perfect prime, which has no upper or lower note.

The augmented octave will not invert because the upper note would remain the upper note and the lower note would remain the lower note.

The names of inverted simple intervals are predictable. The sum of a simple interval and it’s inversion is always NINE:

The qualities of inverted simple intervals are also predictable:

Compounding and reducing intervals are other methods of changing the relative position of the notes in an interval. Compounding a simple interval is accomplished by moving the upper note up an octave or the lower note down an octave. Moving the upper note down an octave or the lower note up an octave reduces a compound interval. Compounding intervals may continue indefinite-ly, but reduction can continue only until the interval becomes simple, then inversion rules control further movement. When compounding or reducing intervals, the name of the interval changes while the quality remains the same.

When compounding a simple or compound interval, the number SEVEN is added to the name of the interval for each octave displacement. The quality of the interval remains the same.

The perfect prime, which is not inverted, maybe compounded. The perfect prime compounds to a perfect octave (P1+7 equals P8).

Reducing Intervals

When reducing a compound interval, the number SEVEN is subtracted from the name of the interval for each octave displacement. The quality of the interval remains the same.

The basic sound of intervals may be generally described as consonant or dissonant. Consonant intervals tend to remain stable. Dissonant intervals tend to be unstable, requiring movement to a consonance. Perfect primes, thirds, perfect fifths, sixths, and perfect octaves are generally consonant intervals. Seconds, perfect fourths, sevenths, augmented, and diminished intervals are generally dissonant intervals.

Although the minor third (3 half steps) and the augmented second (3 half steps) are enharmonic, one is classified as a consonance, the other as a dissonance. This is true of several enharmonic intervals (Maj 3 and dim 4, dim 2 and P1, dim 6 and P5, Aug 5 and min 6, etc.). The musical context determines consonance and dissonance when the intervals are enharmonic.

Pitches that belong to a scale or key are called diatonic. Pitches foreign to a scale or key are called chromatic. The pitch C is diatonic to the keys of C major (tonic), e  melodic minor ascending (raised submediant), and b  minor (supersonic). However, the pitch C is chromatic (not diatonic) to the keys of D major (subtonic), G lydian (lowered subdominant), and minor (raised mediant).

Intervals are diatonic when both the upper and lower notes of the interval are found in the key. Intervals are chromatic when one or both notes of the interval are foreign to the key. The simple interval formed by the pitches G up to B is a diatonic interval in B Major, E   mixolydian, and c natural minor, but it is a chromatic interval in G major, e minor, and D lydian.

The augmented triad has three tones on alternate staff degrees with two major thirds (4 half steps) for the upper and lower intervals. The interval between the root and fifth is an augmented fifth (8 half steps). When constructed on the first degree of a whole tone scale whose fifth is raised, the augmented triad contains the tonic, mediant, and dominant of that whole tone scale. This corresponds to the first, third, and raised fifth (1, 3, and 5) scale degrees of the parallel major scale.

The diminished triad has three tones on alternate staff degrees with two minor thirds (3 half steps) for the upper and lower interval. The interval between the root and fifth is a diminished fifth (6 half steps). When constructed on the first degree of a locrian scale, the diminished triad contains the tonic mediant, and dominant of that locrian scale. This corresponds to the first, lowered third, and lowered fifth (1, 3, and 5) scale degrees of the parallel major scale.

The basic sound of triads may be generally described as consonant or dissonant. Consonant triads tend to remain stable. Dissonant triads tend to be unstable requiring movement to a consonant triad. Major and minor triads are generally consonant triads. Augmented and diminished triads are generally dissonant triads.

When the root of a triad is its lowest note, the chord is in root position. Inversion is a change in the relative position of the notes from root position.

When the third of a triad is the lowest note, the triad is in first inversion regardless of the placement of the root and fifth above it. When the fifth of a triad is the lowest note, the triad is in second inversion regardless of the placement of the root and third above it. The root of the triad remains the root regardless of its position. The same is true of the third and fifth.

Writing the diatonic third and fifth above each scale degree of a given scale will construct the triads diatonic to a particular scale or key.

Constructing diatonic triads on major scale degrees produces:

Constructing diatonic triads on natural minor scale degrees produces:

Constructing diatonic triads on harmonic minor scale degrees produces:

The harmonic use of the major quality dominant chord gives the harmonic minor scale its name. Altering the third of the dominant chord creates this scale. The third of the dominant chord is the leading tone of the minor key.

Constructing diatonic triads on ascending melodic minor scale degrees produces

Constructing diatonic triads on descending melodic minor scale degrees produces triads identical to those of the natural minor scale. Eliminating the augmented second in the ascending form of the scales creates a major subdominant triad. Using the descending form of the scale creates a minor subdominant triad, resulting in a more minor sound.

A sound source vibrates as a whole unit, in halves, thirds, fourths, fifths, sixths, etc., continuing on indefinitely by fractions. The sounds these fractional vibrations produce are called overtones and are generally present in varying strengths.

Although the overtone series continues with complex vibration indefinitely, it is necessary to put an upper limit on the series for practical purposes. The first sixteen partials are the ones most commonly used in music.

Figure 12.2: C Overtone Series.

The first, second, fourth, eighth, and sixteenth partials are the tonic degrees in successive octaves. The tonic degrees are derived by doubling partial numbers starting with the first partial.

The third, sixth, and twelfth partials are the dominant degrees found in the second octave (3rd partial), third octave (6th partial), and fourth octave (12th partial) of a given series. The dominant degrees are derived by doubling the partial numbers starting with the third partial.

The fifth and tenth partials are the mediant (major) degrees found in the third octave (5th partial) and fourth octave (10th partial) of a given series. The upper partial is derived by doubling the lower partial.

The seventh and fourteenth partials are the out-of-tune subtonic degrees found in the third octave (7th partial) and fourth octave (14th partial) of a given series. The upper partial is derived by doubling the lower. It may help to think of the seventh partial as a simple interval to remember its scale degree although it is actually a minor 21st from the fundamental.

If the ninth through fourteenth partials are thought of as intervals and then reduced to simple intervals, the scale degree numbers are produced. That is, the ninth partial (9 -7 equals 2) is the supersonic; the tenth partial (10 -7 equals 3) is the mediant; the eleventh partial (11 - 7 equals 4) is the out-of-tune raised subdominant (the only time the subdominant occurs it is raised and out of tune); the twelfth partial (12 -7 equals 5) is the dominant; the thirteenth partial (13 -7 equals 6) is the submediant (major); and the fourteenth partial (14 -7 equals 7) is the out-of-tune subtonic. The fifteenth partial is not carried through the interval reduction process; it is considered the leading tone to the sixteenth partial (tonic). (See Figure 2.4).

Overtones do not include the fundamental as a numbered part of the series.  Therefore, to convert from partials to overtones, subtract one to get the overtone number; from overtones to partials, add one to get the partial number. When comparing overtones and partials in an overtone series, the overtone number will always be one less than the partial number.

Because the physical nature of a musical instrument affects timbre, the relative prominence of overtones varies with different instruments and is a major factor in producing the timbre of a particular instrument. Usually, overtones are not heard as individual pitches but as variations in the tone quality of the most prominent pitch, the fundamental.

For example, the most prominent overtones on the saxophone are the first (2nd partial), third (4th partial), fifth (6th partial), etc. The most prominent overtones on the clarinet are the second (3rd partial), fourth (5th partial), sixth (7th partial), etc. These overtones decrease in intensity as they are further removed from the fundamental and alternate indefinitely.

Transposition is the process of moving a note or group of notes to a specific higher or lower pitch level. To transpose is to write or perform in a different key or at a different pitch level. Pitch relationships must remain intact during transposition.

The most direct means of organizing pitch relationships for transposition is to identify the pattern of scale degrees in the original key, then to perform or write the pattern in a different key. Using numbers will help identify the scale degrees. (see Figure 13.1).

Transposition in minor keys that have accidentals may require chromatic signs that differ from the accidentals in the original music. The purpose is to keep the pitch relationships intact (see Figure 13.2)..

Figure 13.2: Scale Degree Transposition (harmonic minor).

Transposing by individual intervals may increase accuracy in music that has many accidentals, creates a complex key relationship, or has complex scale degree relationships. Interval transposition may also make a half step or whole step transposition easier. A transposition written or played the same exact interval above or below the original will keep the pitch relationships intact.

Melodic intervals in the transposed music will correspond to the same melodic intervals in the original key.

When a transposition desired is a half step higher or lower and the notes remain on the same staff degrees, transposition by key signature maybe used.

This is accomplished by imagining the different key signature, reading the same staff degrees, and correcting accidentals to keep the pitch relationships intact.

Copying instrumental parts requires that a copyist know the following: clefs keys and transpositions of instruments written ranges sounding ranges While most instruments use a single clef, there are instruments that use more than one clef. For some instruments, music is written with pitches differing from actual sound; therefore, their parts must be transposed. Wind instrument ranges are determined as much by the instrumentalist’s ability as by the instrument itself. Extreme ranges (particularly in upper registers) cannot be stated definitely; only minimum ranges for the qualified instrumentalist are presented. The sounding ranges for transposing instruments should be clearly visualized when copying from concert pitches.

Although a complete list of instrumental classification would be far longer, the most likely instruments to be encountered are:

Woodwinds may be divided into transverse, double reed, and single reed woodwinds. Single reed woodwinds may be further divided into clarinets and saxophones. When a woodwind player plays written C on the instrument, the name of the instrument sounds: for example, B instruments sound B  , and E  instruments sound E . The interval between the written and sounded pitches determines its transposition. Transposed woodwind parts allow the instrumentalist to use the same fingerings for more than one instrument. The following list gives:

Clarinets

Bb Bass Clarinet

Saxophones

Most brasswinds use three or more valves in combination to produce more than one overtone series, allowing chromatic pitches. Trombones use slides for the same purpose.

Brasswinds maybe grouped into treble clef brass and bass clef brass. When a treble clef brasswind player plays written C on the instrument, the pitch name of the instrument sounds. The interval between the written and sounded pitches of an instrument determines its transposition. Bass clef brasswinds sound as written. The pitch name of a bass clef brasswind is its open or first position sounding overtone series.

Brasswinds are constructed with various ratios of cylindrical and conical bores. Cylindrical bore brasswinds are more cylindrical than conical; conical bore brasswinds are more conical than cylindrical. The ratio of cylindrical to conical tubing affects the timbre of the instrument. The following list gives: Name of the instrument (open/first position sounding series) Transposition relationships (Remarks about individual instrument) Written and sounding range TREBLE CLEF BRASS Bb Trumpet, Cornet, and Flugelhorn.

Sounds a Maj 2nd lower than written.

Written a Maj 2nd higher than it sounds.

Trumpet - Cylindrical Bore (3 valves).

Cornet - Conical Bore (3 valves).

Flugelhorn - Conical Bore (3 valves).

14-7.Horn l?/Bb (called Double Horn).

Sounds a P5th lower than written.

Written Conical a P5th higher than it sounds.

Bore (3 valves).

Baritone Horn. d * lower than written.

higher than it sounds.

Sounds a Maj 9th Written a Maj 9th Conical Bore (3 valves).

BASS CLEF BRASS Bb Baritone Horn. 9: Sounds as written (non-transposing).

Conical Bore (3 valves).

B~ Euphonium.

Sounds as written (non-transposing).

Conical Bore (4 valves).

14-8.13b Tenor Trombone.

Sound as written (non-transposing).

(Makes use of tenor and alto clefs).

Cylindrical Bore (Slide).

Sounds as written (non-transposing).

(Makes use of tenor and alto clefs).

Cylindrical Bore (Slide).

Bb /F/D Bass Trombone.

Sounds as written (non-transposing).

(Makes use of tenor and alto clefs).

(high extreme of instrument infrequently used).

Cylindrical Bore (slide).

C Tuba.

Sounds as written (non-transposing).

Conical Bore (4 valves).

Sounds as written (non-transposing).

Conical Bore (3 valves).

Sounds as written (non-transposing).

Conical Bore (4 valves).

The percussion instruments may be divided into indefinite pitch and definite pitch percussion. Due to the large number of instruments in the indefinite pitch grouping, placement in notation is very irregular and will vary greatly. Definite pitch drums (timpani) are notated in bass clef. Mallet percussion (keyboard percussion) instruments are normally notated in treble clef.

3rd space bass clef, Rhythm Line.

1st space bass clef, Rhythm Line.

Below, 1st space, above bass clef Rhythm Line.

Hands (in pairs), sticks, brushes, mallets, etc.

3rd space, 4th space, or above bass clef, Rhythm Line.

3rd space, 4th space, or above bass clef Rhythm Line.

Below or 1st space bass clef, Rhythm Line.

Timpani - Bass Clef.

Sounds as written.

Mallets (felt, wool, wood).

Sounds a P15th higher than written.

Sounds a P15th higher than written.

Tubular Bells (Chimes)

Sounds as written.

Chime hammer of wood or rawhide.

Sounds a P8ve higher than written.

Sounds as written.

Rubber, wood, plastic, yam, or cord mallets.

Sounds as written.

With the exception of the standard piano, keyboard ranges vary widely depending on the manufacturer. Keyboard instruments make use of notation in treble and bass clefs. The following list of keyboard instruments gives:

Piano (Pianoforte).

Sounds as written.

Electric Piano.

Sounds as written.

Range Varies Widely

Sounds a P8ve higher than written.

Struck metal bars.

Sounds as written Compressed air through pipes or electronically generated.

Synthesizer.

Unlimited transposition.

Guitar - Treble Clef.

Base Guitar - Bass Clef.

String Bass - Bass Clef.

Sounds a P8ve lower than written.

Tuned in P4ths.

Vertical combinations of tones that create the harmonic framework of a piece may be indicated by chord symbols. Chord symbols are a shorthand expression for those combinations. Although a chord symbol indicates which tones are included in the combination, it does not indicate how the tones in the combination are used.

The letter name of a chord symbol is the root of the chord.

The Third

The chord includes the pitch a major third above the root of the chord unless the third is qualified by the chord symbol. Qualifiers that affect the third always lower it a half step (minor third). Minor, diminished and half diminished are the qualifiers that lower the third. The preferred abbreviations are min and dim but may be expressed in other ways.

The Fifth

The chord includes the pitch a perfect fifth above the root of the chord unless. the fifth is qualified by the chord symbol. Qualifiers that affect the fifth raise the fifth a half step (augmented fifth) or lower the fifth a half step (diminished fifth).

Augmented is the qualifier that raises the fifth. Diminished, half diminished and flat five are qualifiers that lower the fifth. The preferred abbreviations are (Aug, dim and 5) but maybe expressed in other ways.

The chord includes the pitch a major sixth above the root of the chord when the numeral Figure 6 is part of the chord symbol.

The chord includes the pitch a minor seventh above the root of the chord (subtonic) unless the seventh is qualified by the chord symbol. Qualifiers that affect the seventh raise the seventh a half step (major seventh) or lower the seventh a half step (diminished seventh or major sixth). Major seven is the qualifier that raises the seventh. Diminished seven is the qualifier that lowers the seventh and the tone may be spelled enharmonically as the sixth. Pitches of a diminished seventh chord may be spelled enharmonically. The preferred abbreviations are Maj7 and dim7 but may be expressed in other ways.

In addition to major, minor, augmented and nine commonly used chord structures:

Major Sixth. Chord

The chord formula for the major sixth chord is 1,3,5,6 of a major scale. It is indicated by a root name and 6.

Major Seventh Chords

The chord formula for the major seventh chord is 1,3,5,7 of a major scale. It is indicated by a root name and Maj 7.

The chord formula for the minor sixth chord is 1, b3, 5, 6 of a major scale. It is indicated by a root name, rein, and 6.

The chord formula for the minor/major seventh chord is major scale. It is indicated by a root name, min, and Maj 7.

Dominant Seventh Chord

The chord formula for the dominant seventh chord is of a major scale. It is indicated by a root name and 7.

Minor Seventh Chord

The chord formula for the minor seventh chord is of a major scale. It is indicated by a root name, min, and 7.

Minor Seventh (Flat Five) Chord

Augmented Seventh Chord

The chord formula for the augmented seventh chord is 1, 3, 5,7 of a major scale. It is indicated by a root name, Aug, and 7.

Diminished Seventh Chord

The chord formula for the diminished seventh chord is 1, 3, 5, 6(7) of a major scale. It is indicated by a root name, dim, and 7. Notes of diminished seventh chords are often spelled enharmonically for ease of identification.

Chord symbols indicate the vertical or harmonic framework of a piece; however, their use may be expanded by using chord scales for horizontal or melodic application. A given chord symbol normally implies use of a particular scale.

The major or ionian scale (MLM) is used for tonic major sixth or major seventh chords. The lydian scale (LMM) is used for all other major sixth or major seventh chords.

The ascending melodic minor scale (mLM) is used both ascending and descending on minor sixth and minor/major seventh chords.

The mixolydian scale (MML or MLm) is used for dominant seventh chords which move from dominant to tonic. The lydian seventh scale (LMm) is used for all other dominant seventh chords.

The dorian scale (mLm) is used for minor seventh chords. Although some minor seventh chords should take other scales, the dorian scale will fit all minor seventh chords.

The locrian scale (NNL) is used for minor seventh (flat five) chords.

The whole tone scale (222222) is used for augmented seventh chords.

The diminished scale (21212121) is used for diminished seventh chords. A diminished scale may be thought of as two superimposed diminished seventh chords a whole step apart.

The blues scale is a scale used primarily as a device while playing blues. It cannot be analyzed with tetrachords. The scale contains the tonic (1), subdominant (4), and dominant (5) plus the "blue notes" which are the lowered third ( 3), lowered fifth ( 5), and lowered seventh ( 7). Enharmonic spellings are frequently used.

The pentatonic major scale may be used with major sixth, major seventh, and dominant seventh chords. The pentatonic minor scale may be used with minor seventh chords or as a substitute for the blues scale.

Anticipation occurs when a note normally on the beat is attacked a half beat early. The result is melodic, harmonic, and rhythmic syncopation (usually sometimes ).

An off-beat eighth note followed by a rest is a method of notating anticipation.

The divided beat in swing time is often interpreted differently from the way it is notated. The dotted eighth/sixteenth or eighth note pattern in notation:

is usually performed as

Tempo determines the interpretation of the divided beat in swing time.

In extremely slow tempi, the notation:

is often performed as:

In double time, the same notation is often performed as:

In medium tempi, the second portion of the beat sounds earlier and requires compound interpretation. The notation is often performed as:

In extremely fast tempi, the second portion of the beat sounds earlier and requires simple interpretation. The notation is often performed as:

The following graph illustrates how the second portion of the divided beat moves.

An anticipation that is not a short percussive note is normally along percussive note in swing time. A long percussive note is often, but not always, An anticipated long percussive note of two or more beats maybe performed with its full value or it may be shortened by the duration of the second portion of the divided beat. The anticipation occurs on the second portion of the divided beat.

A note that occurs beginning on the beat is often a long percussive note. A long percussive note that begins on the beat, and is of more than a beat’s duration, may be performed with its full value or it may be shortened by the duration of the second portion of the divided beat.

A quarter note (or equivalent) that is marked long is usually a long percussive note. It is performed with the duration of the full beat. An off the beat long percussive quarter note occurs on the second portion of the divided beat.

Used to construct melodies may be chord tones or approach tones.

Many melodies are constructed primarily of chord tones. For example, La Curcaracha is composed of chord tones in all but the third and seventh bars.

Approach tones are tones that lead into chord tones by step. Approach tones J) are usually of half beat duration (usually , sometimes ). Two types of approach tones are scale approach tones and chromatic approach tones.

Scale approach tones are non-chord tones within a given chord scale that approach the chord tones of that chord by step.

Notation of the chord scale for a given chord will make the identification of scale approach tones easier (see Fig. 18.4).

Chromatic approach tones are non-chord tones that approach chord tones or scale approach tones by half steps.

A scale approach tone may move to a chromatic approach tone by half step if the chromatic approach tone goes immediately to a chord tone in the same direction.

Figure 18.5: Chromatic Approach Tones in La Cucaracha.

A chord symbol often indicates pitches other than the first, third, fifth, sixth, and seventh. When additional pitches are required, the basic chord is extended in ascending thirds. These pitches are expressed as compound intervals from the root of the chord. The extensions are the ninth, eleventh, and thirteenth above a root.

Extended chords are created when the ninth, eleventh or thirteenth are present in the chord.

The chord includes the pitch a major ninth (major second) above the root of chord when the numeral 9 is part of the chord symbol.

The chord includes the pitch an augmented ninth (augmented second, usually spelled enharmonically as a minor third) above the root of the chord when (9) is part of the chord symbol. The symbol (9) is the preferred indicator, but (+9) is also used. This alteration occurs on dominant seventh type chords.

The chord includes the pitch a perfect eleventh (perfect fourth) above the root of the chord when the numeral 11 is part of the chord symbol. This extension usually occurs on minor ninth, minor ninth (5), and diminished ninth chords.

The chord includes the pitch a perfect fourth above the root of the chord when sus 4 is part of the chord symbol. The perfect fourth replaces the major third as a chord tone. This extension occurs on dominant seventh and ninth, major sixth and major six/nine, and major seventh and ninth chords.

If the symbol sus is present in a chord symbol, it is usually interpreted as a sus 4.

The chord includes the pitch an augmented eleventh (augmented fourth) above the root of the chord when (11) is part of the chord symbol. The symbol (11) is the preferred indicator, but (+11) is also used. This alteration usually occurs on dominant ninth, augmented ninth, major six/nine, and major ninth chords. The altered ninth and raised eleventh may be used on the dominant seventh type chord. Both the altered ninth and (11) are indicated in the chord symbol.

The chord includes the pitch a major thirteenth (major sixth) above the root of the chord when the numeral 13 is part of the chord symbol. This extension usually occurs on dominant ninth (11) and major ninth (11) chords. The (11) should be indicated in the chord symbol. The lowered ninth may be included on the dominant thirteenth (11) but must be indicated with the (11) in the chord symbol.

The chord includes the pitch a minor thirteenth (minor sixth) above the root is part of the chord when (13) is part of the chord symbol. The symbol (13) is the preferred indicator, but (-13) is also used. This alteration usually occurs on dominant seventh type chords with altered ninth and raised eleventh. It also occurs on minor eleventh (13) and diminished eleventh chords. The altered 9, (11, and (13) on dominant seventh type chords should be indicated in the chord symbol.

A bass note which is not the root of the chord is often required in music. One way to notate this is to indicate the chord structure over the bass note.