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Scale of G
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Scale of D
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Scale of A
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Scale of E
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Scale of B
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Scale of F#
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Scale of C#
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Scale of F
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Scale of Bb
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Scale of Eb
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Scale of Ab
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Scale of Db
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Scale of Gb
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Scale of Cb
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There are two forms of minor scales,harmonicandmelodic, both differing in construction from the major form.
The minor key having no sharps or flats in the signature isa. Starting ataand sounding the seven white keys in order to the right produces a form of scale with whole steps between 1 and 2, 3 and 4, 4 and 5, 6 and 7, 7 and 8, and half steps between 2 and 3 and between 5 and 6. This scale isunsatisfactory to the ear as its subtonic is not aleading tone. The effect of a leading tone should be urgent, restless, and demand its tonic in order to obtain a restful effect. This urgent effect can only be obtained by the subtonic being one half step below the tonic. This may be obtained by simply raising the seventh one semi-tone in the above scale formation and thus is produced the so-calledharmonic minorscale.
The symbols for raising a note are thesharp(#), thedouble sharp(x), and thecancel(⊄) (also callednatural) when placed before a note that has been previously affected by a flat. The symbols for lowering a note are theflat(b), thedouble flat(bb), and thecancelwhen placed before a note that has been previously affected by a sharp. By these statements it can be seen that the cancel (⊄) is both a lowering and a raising symbol. Thecancellowers a tone when it cancels a sharp and raises a tone when it cancels a flat.
The harmonic minor scaleis formed by whole steps between 1 and 2,—3 and 4,—4 and 5,—half steps between 2 and 3,—5 and 6,—7 and 8, and an interval of one and one-half steps (called an augmented step) between 6 and 7. In demonstrating the minor keys, a curved line will be used to connect those figures representing tones one half step apart and a bracket to connect those figures representing tones an augmented step apart.
The key ofa minor(harmonic form) is as follows:—
a b c d e f g#a1 2 3∼4 5∼6∪7∼8
a b c d e f g#a1 2 3∼4 5∼6∪7∼8
The student will notice that this scale has one sharp (g). Nevertheless, thea minoris the minor key which has neither sharps nor flats in its signature. The raised seventh of all minor keys isneverpresent in the signature, but appears asaccidental.
When a sharp, double sharp, flat, double flat or cancel, which is not present in the signature, is placed before a note, it is called an accidental. If the raised seventh were present in the signature, uniform signatures in the minor would be impossible. It may also be remarked here that the seventh is not always raised during the course of a composition and is necessarily raised only when the composer desires the listener's ear to come at rest on the tonic, in which case the tonic must be preceded by the raised seventh, if the subtonic precedes the tonic in the melody or harmony.
The same rules (pages 13 and 15) used in the major for finding the key having the next number of sharps and the key having the next number of flats are applicable in the minor. The order of the letters in both the sharp and flat signatures is the same in the minor as in the major.
Aminor has no sharps, the fifth ofaiseand has one sharp (f):—
e f#g a b c d#e1 2∼3 4 5∼6∪7∼8
e f#g a b c d#e1 2∼3 4 5∼6∪7∼8
The fifth ofeisband has two sharps (fandc):—
b c#d e f#g a#b1 2∼3 4 5∼6∪7∼8
b c#d e f#g a#b1 2∼3 4 5∼6∪7∼8
The fifth ofbisf#and has three sharps (f,candg):—
f#g#a b c#d e#f#1 2∼3 4 5∼6∪7∼8
f#g#a b c#d e#f#1 2∼3 4 5∼6∪7∼8
The fifth off#isc#and has four sharps (f,c,gandd):—
c#d#e f#g#a b#c#1 2∼3 4 5∼6∪7∼8
c#d#e f#g#a b#c#1 2∼3 4 5∼6∪7∼8
The fifth ofc#isg#and has five sharps (f,c,g,danda):—
g#a#b c#d#e fxg#1 2∼3 4 5∼6∪7∼8
g#a#b c#d#e fxg#1 2∼3 4 5∼6∪7∼8
The student will notice that in this key,fis double sharped.Fis sharped in the signature, but because the subtonic requires raising,fdemands a double sharp.
The fifth ofg#isd#and has six sharps (f,c,g,d,aande):—
d#e#f#g#a#b cxd#1 2∼3 4 5∼6∪7∼8
d#e#f#g#a#b cxd#1 2∼3 4 5∼6∪7∼8
The fifth ofd#isa#and has seven sharps (f,c,g,d,a,eandb):—
a#b#c#d#e#f#gxa#1 2∼3 4 5∼6∪7∼8
a#b#c#d#e#f#gxa#1 2∼3 4 5∼6∪7∼8
The minor keys having more than seven sharps should be found by the student and submitted to the teacher for correction. For the sake of brevity, they are not given here, but the student should be thoroughly capable, by this time, of finding them all.
Aminor has no flats, the fourth ofaisdand has one flat (b):—
d e f g a bbc#d1 2∼3 4 5∼6∪7∼8
d e f g a bbc#d1 2∼3 4 5∼6∪7∼8
The fourth ofdisgand has two flats (bande):—
g a bbc d ebf#g1 2∼3 4 5∼6∪7∼8
g a bbc d ebf#g1 2∼3 4 5∼6∪7∼8
The fourth ofgiscand has three flats (b,eanda):—
c d ebf g abb⊄ c1 2∼3 4 5∼6∪7∼8
c d ebf g abb⊄ c1 2∼3 4 5∼6∪7∼8
The student will notice a contradiction in the above scale; it is stated thatchas three flats and in the example,bis cancelled. This cancel, however, appears asaccidental(the raised seventh) and must be a flat in the signature.
The fourth ofcisfand has four flats (b,e,aandd):—
f g abbbc dbe⊄ f1 2∼3 4 5∼6∪7∼8
f g abbbc dbe⊄ f1 2∼3 4 5∼6∪7∼8
The fourth offisbband has five flats (b,e,a,dandg):—
bbc dbebf gba⊄ bb1 2∼3 4 5∼6∪7∼8
bbc dbebf gba⊄ bb1 2∼3 4 5∼6∪7∼8
The fourth ofbbiseband has six flats (b,e,a,d,gandc):—
ebf gbabbbcbd⊄ eb1 2∼3 4 5∼6∪7∼8
ebf gbabbbcbd⊄ eb1 2∼3 4 5∼6∪7∼8
The fourth ofebisaband has seven flats (b,e,a,d,g,candf):—
abbbcbdbebfbg⊄ ab1 2∼3 4 5∼6∪7∼8
abbbcbdbebfbg⊄ ab1 2∼3 4 5∼6∪7∼8
The student should find the minor keys having more than seven flats.
The harmonic minor scale is awkward in formation on account of the augmented second step between steps six and seven. All augmented intervals sound harsh and are difficult to sing tunefully. For this reason, another form of minor scale is sometimes used which eliminates the augmented second step. This form is calledmelodic minorand is used, as its name implies, only for melodic purposes. It defies harmonization for the obvious reason that its ascending form differs from its descending form.
The melodic minor scalehas the sixth as well as the seventh raised byaccidentalin ascending, but in descending, both the sixth and seventh are restored. The ascending form has whole steps between 1 and 2,—3 and 4,—4 and 5,—5 and 6,—6 and 7, and half steps between 2 and 3 and between 7 and 8. The descending form has its half steps between 6 and 5 and between 3 and 2. Notice that the descending form is as its signature dictates.
raisedraisedAscending: —1 2∼3 4 5 6 7∼8Descending:—8 7 6∼5 4 3∼2 1
The ascending form of the melodic minor is nearly the same as the major scale, and for this reason it is best not to retain the raised sixth and seventh in descending. The subtonic in a descending scale does not lead (progress) to the tonic and therefore need not necessarily be situated one half step below the tonic.
Any minor key is called the relative of the major key having the same signature; therefore, the relative minor ofCmajor isa[C]as they both have neither sharps nor flats.
Rule 5. The Relative Minor is found on the Sixth of the Major Scale.
Rule 6. The Relative Major is found on the Third of the Minor Scale.
Some writers have called therelativeminorparallelminor, usingrelativeandparallelsynonymously. This is a usage to be regretted as it causes considerable confusion. By most writers, the parallel minor is treated as the scale commencing on the same key-note as the major and will thus be treated in this book, therefore:—
the relative minor of C isa;the parallel minor of C isc.
the relative minor of C isa;the parallel minor of C isc.
The parallel minor scale has three more flats or three less sharps in its signature than the major scale. In other words, by lowering steps 3, 6 and 7 of the major scale one semi-tone, the signature of the parallel minor is obtained.
The notation in the treble clef of all the minor scales (harmonic and melodic) follows:—
Scale of a HarmonicScale of aMelodic[Midi] [[audio/mpeg][XML]Scale of eHarmonicScale of eMelodic[Midi] [[audio/mpeg][XML]Scale of bHarmonicScale of bMelodic[Midi] [[audio/mpeg][XML]Scale of f#HarmonicScale of f#Melodic[Midi] [[audio/mpeg][XML]
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Scale of c#HarmonicScale of c#Melodic[Midi] [[audio/mpeg][XML]Scale of g#HarmonicScale of g#Melodic[Midi] [[audio/mpeg][XML]Scale of d#HarmonicScale of d#Melodic[Midi] [[audio/mpeg][XML]Scale of a#HarmonicScale of a#Melodic[Midi] [[audio/mpeg][XML]Scale of dHarmonicScale of dMelodic[Midi] [[audio/mpeg][XML]Scale of gHarmonicScale of gMelodic[Midi] [[audio/mpeg][XML]Scale of cHarmonicScale of cMelodic[Midi] [[audio/mpeg][XML]Scale of fHarmonicScale of fMelodic[Midi] [[audio/mpeg][XML]Scale of bbHarmonicScale of bbMelodic[Midi] [[audio/mpeg][XML]Scale of ebHarmonicScale of ebMelodic[Midi] [[audio/mpeg][XML]Scale of abHarmonicScale of abMelodic[Midi] [[audio/mpeg][XML]
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ORALANDWRITTEN
1. Into how many parts does modern custom divide an octave?
2. What is each part called?
3. What is the difference between a chromatic scale and a diatonic scale?
4. How many forms of diatonic scales are there and what are their names?
5. Name and define the four ways in which the tones of the diatonic scales are named.
6. What is the key-tone?
7. Describe the movable and fixed systems.
8. Describe the major scale.
9. Describe the effect of a sharp; of a double sharp; of a flat; of a double flat; of a cancel.
10. State the rule for finding the key having the next number of sharps and the rule for finding the key having the next number of flats.
11. Write on the staff, using the treble clef, all the major keys to eleven sharps and eleven flats. Write several scales (the teacher deciding the number) using the bass and tenor clefs. (Show by curved line those notes situated one semi-tone apart.)
12. What is the order of the letters in the sharp signature? In the flat signature?
13. What is meant byenharmonic?
14. What are theenharmonicscales used in practice?
15. Giveenharmonicletter names for each of the twelve keys.
16. What is the sum of sharp and flat signatures of enharmonic keys?
17. By the use of this enharmonic sum, find all the theoretical keys.
18. What is the construction of the harmonic minor scale? Of the melodic minor?
19. Write on the staff all the minor scales (both harmonic and melodic) to eleven sharps and eleven flats, letting the teacher determine which clef or clefs to use.
20. What is the reason for raising the seventh in harmonic minor?
21. What is the reason for raising the sixth in melodic minor?
22. Why does the descending form of melodic minor differ from the ascending form?
23. Why does not the raised sixth or seventh appear in the signature?
24. What is an accidental?
25. What is therelativeminor and how is it found?
26. What is theparallelminor and how does its signature differ from its parallel major?
N. B. Before proceeding to the next chapter all these exercises should be properly answered and corrected by the teacher.
N. B. Before proceeding to the next chapter all these exercises should be properly answered and corrected by the teacher.
INTERVALS AND INTRODUCTION TO CHORD BUILDING.
An interval is the distance between two tones; intervals are named by the ordinals. The number of letters comprised in the notation of two tones determines the ordinal name of the interval. Example:ctodis an interval of a second because two letters are comprised. It makes no difference whether or not either or both of the above tones is affected by an accidental, the interval still comprises two letters and is a second.
Reckoning from the tonic of the major scale to each degree of the scale produces the following intervals:—
8th or prime. 2nd 3rd 4th 5th 6th 7th octave 9th
The interval of the ninth is often called a second, the octave not being considered.
These intervals are the normal intervals of the major scale. These normal intervals are qualified in two ways. The prime, fourth, fifth and octave are called perfect. The second, third, sixth and seventh are calledmajor;thus:—
All intervals should be reckoned from the lower note, which is considered a major key-note. If the upper note is in the major scale of the lower note, the interval is normal; that is, either perfect or major. If the upper note is not in the major scale of the lower note, the interval is a derivative interval. The derivative intervals are calledminor,diminishedandaugmented.
A minor interval is derived from a major interval and is one semi-tone smaller. By lowering the upper tone of any major interval one half step or by raising the lower tone of any major interval one half step (not altering the letter name in either case) a minor interval is formed, thus:—
A diminished interval is one half step smaller than a minor or a perfect interval. By lowering the upper tone of any minor or any perfect interval one half step, or by raising the lower tone of any minor or any perfect interval one half step (not altering the letter name in either case) a diminished interval is formed, thus:—
The tones of the diminished second are the same pitch, but must be called a second because two letters are comprised.The diminished prime is possible melodically, but harmonically, only in theory. It is.
An augmented interval is one half step larger than a major or a perfect interval. By raising the upper tone of any major or perfect interval one half step, or by lowering the lower tone of any major or perfect interval one half step (not altering the letter name in either case) an augmented interval is formed, thus:—
Notice that the tones of the augmented seventh are the same pitch, but must be called a seventh as seven letters are comprised.
The following intervals are the same in sound, but not in name:—
perfect primesoundsthesameasdiminished 2ndaugmented prime""""minor 2nddiminished prime""""minor 2ndmajor 2nd""""diminished 3rdminor 3rd""""augmented 2ndmajor 3rd""""diminished 4thperfect 4th""""augmented 3rdaugmented 4th""""diminished 5thperfect 5th""""diminished 6thminor 6th""""augmented 5thmajor 6th""""diminished 7thminor 7th""""augmented 6thmajor 7th""""diminished 8thperfect octave""""augmented 7th
From the preceding list the following rule is apparent:—
Rule 7. By Changing Enharmonically Either or Both of the Tones of an Interval, a Different Interval is Obtained Which Sounds the Same as the Original Interval.
The distance in semi-tones of all the intervals to an octave is as follows:—
prime=unisoncomprises1letteraugmented prime= 1semi-tone"1"diminished 2nd=unison"2lettersminor 2nd= 1semi-tone"2"major 2nd= 2semi-tones"2"augmented 2nd= 3""2"diminished 3rd= 2""3"minor 3rd= 3""3"major 3rd= 4""3"augmented 3rd= 5""3"diminished 4th= 4""4"perfect 4th= 5""4"augmented 4th= 6""4"diminished 5th= 6""5"perfect 5th= 7""5"augmented 5th= 8""5"diminished 6th= 7""6"minor 6th= 8""6"major 6th= 9""6"augmented 6th= 10""6"diminished 7th= 9""7"minor 7th= 10""7"major 7th= 11""7"augmented 7th= 12""7"diminished 8th= 11""8"perfect 8th= 12""8"
A quicker and better method of determining an interval than by committing to memory the above table is to consider the lower note the tonic of the major scale. If the upper note is in the major scale of the lower note, the interval is normal (major or perfect). After a little practice the number of letters in an interval can be determined at a glance. If the upper note is not in the major scale of the lower note the interval is derivative and is determined by the information heretofore given.
Intervals are said to be inverted when the lower note of the original interval is placed an octave higher, thereby becoming the upper note of the interval thus formed. Example: the inversion ofis. The same letters are in both intervals, but the first interval is a third and the inverted interval is a sixth.
Rule 8. The Sum of an Interval and Its Inversion is Nine.
The above rule, therefore, gives the following inversions:—
a primeinvertstoan octave(1 + 8 = 9)a second""a seventh(2 + 7 = 9)a third""a sixth(3 + 6 = 9)a fourth""a fifth(4 + 5 = 9)a fifth""a fourth(5 + 4 = 9)a sixth""a third(6 + 3 = 9)a seventh""a second(7 + 2 =9)an octave""a prime(8 + 1 = 9)
To find to what intervals ninths, tenths, elevenths, twelfths, etc., invert, consider them respectively as seconds, thirds,fourths, fifths, etc., and consider the lower note placed two octaves higher instead of one octave.
Qualifications invert in the following manner:—
majorintervalsinverttominorintervalsminor"""major"perfect"""perfect"diminished"""augmented"augmented"""diminished"
By the use of the above table and rule 8, all inversions may be determined. Examples:—