Carl E. Gardner

“ The number of letters comprised in the notation of two tones determines the ordinal name of the interval. Example: c to d is 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. ”

“ 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 called melodic minor and 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 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 of C major is a [C] as they both have neither sharps nor flats. ”

“ Students who do not have a teacher daily, should have a member of the household play the exercises in ear training and correct the mistakes. If no member of the household is musical, the student should co-operate with another student.
Each exercise should be thoroughly learned before proceeding to the following exercise. It may be recognizable and properly intonated at once or it may take several sittings. The pitch A at 435 is the standard for orchestral tuning and is recommended to the student for a fundamental. ”

“ The first measure of exercise 2 contains the major second which is an easily recognized interval. The last measure but two of exercise 2 contains the major seventh. This interval is ordinarily a difficult interval to intonate but coming as it does in exercise 2 it is easy to intonate because of the ascending scale on the second half of the measures. For the present, it is not advisable to practice the major seventh except in some such sequence as exercise 2. All other normal intervals may be practiced separately and in combinations. ”

“ The student must constantly keep in mind the order of whole and half steps in all scales explained. In each scale explained the letters will be numbered and a curved line will connect those figures representing tones one half step apart.
All major keys except C major require one or more black keys. The number of sharps or flats required for a key is placed at the beginning of the staff and this is called the signature.
A sharp (#) placed before a note raises the tone one half step and a flat (b) lowers a tone one half step. ”

“ The theory name system is a movable system, the tonic being always the key-tone or 1. The alphabet system is a fixed system which means that a letter is always the same tone or its octave. The Italian system is treated as both a fixed system and a movable system. This book treats of the movable do, do always being the key-tone, 1 and tonic.
THE MAJOR SCALE.
A major scale is a progression from any tone to its octave in which chromatic steps are omitted between 1 and 2,—2 and 3,—4 and 5,—5 and 6,—6 and 7 ”

“ Wind and temperature are the only circumstances affecting the velocity of sound in the air to any extent. Sound travels about four times faster through water than through air, and about ten times faster through solids such as metals and wood than through air. ”

“ The seventh chord on the mediant in the minor mode is formed with the augmented triad and the major seventh. The seventh chord on the tonic of the minor mode is formed with the minor triad and the major seventh. In four voice writing, all the seventh chords with the exception [Pg 43] of those on the subtonic of both modes are often written without the fifth and with the doubled fundamental. All seventh chords are dependent chords and their natural resolution is to the chord the fundamental of which is situated a fourth above or a fifth below the fundamental of the seventh chord. ”

“ In the writing of the work the student's practical development has been uppermost in the author's mind and to this end he has provided not a mere treatise on musical grammar, along conventional, hackneyed lines, but a new method which will allow and encourage the student to compose as he advances and develops. ”

“ Music Appreciation, as a cultural course of study, is growing in popularity and large enthusiastic classes in this subject are to be found in all our colleges. These students are frequently handicapped by poor preparation in the essential rudiments of music such as are treated in this volume. ”

“ The quality and intensity of sound do not alter the rate of speed. If this were not true, ensemble music would be impossible. Intensity of sound is greater in condensed air; velocity of sound is greater in a warm temperature. ”

“ Singers almost invariably intonate them out of tune. When these intervals exist as constituent parts of an arpeggio chord progression, they are comparatively easy. As altered intervals these skips are given to instruments (instruments being capable of properly intonating all skips) when a dramatic effect is desired.
3. The diminished fifth is analogous to the augmented fourth. Being the inversion of the augmented fourth, it is [Pg 58] found as a scale interval between the seventh and fourth steps (te to fah) . The following exercise contains the diminished fifth built upon the tonic ”

“ Middle C is the tone which all voices can sing. It is in the lower register of the high female voice and in the upper register of the low male voice.
The G clef (treble clef) is for high voices or instruments. Its symbol shows the position of the G next above middle C thus: . Middle C is found on the first ledger line below the G clef, thus: .
The tenor or C clef is for the use of medium voices or instruments. Its symbol shows the position of middle C. This clef is movable and may place middle C on any line or space of the staff. ”

“ In practicing ear training, only a few minutes at a sitting are advised. Too much time at once devoted to this practice tires the ear and does more harm than good. On the other hand, these sittings should be many each day. ”

“ A sudden displacement of the molecules of a medium produces sound which travels in waves at an equal velocity in all directions. An idea of the manner in which sound waves travel may be obtained by throwing a stone in water ”

“ Occasionally a group of two notes occurs. This group differs from other artificial groups inasmuch as it is played more slowly than the tempo notes. A group of two notes is played in the time and summed in the value of [Pg 6] three of its own kind. Artificial groups are designated by a curved line over or under the notes with a figure showing the kind of group, thus:—
triplet
sextuplet
group of two notes
In "counting" music, it is customary to give as many counts to each measure as the numerator of the fraction indicates. Each of these counts is called a pulse. ”

“ Pupils should be impressed with the structure of scales rather than be taught their keys and signatures by rote. Rote methods have little to recommend them in modern pedagogical ideals, and are used principally in teaching the young. ”

“ The majority of piano students have an absolute disregard for note values and tempo marks which are so important [Pg 8] that the pupils fail to gain any good results from their study unless they understand and pay strict attention to these marks. ”

“ The lack of knowledge of the whys and wherefores of scales, intervals, and chords among instrumentalists and singers is appalling, and is due partly to the neglect of text books and partly to incompetent teachers. ”

“ As stated in the first chapter, the pitch of a tone is determined by the note's position on the staff. The staff of five lines with its spaces allows of the designation of but one octave and one step, whereas, in modern music, there is need of the notation of at least six octaves. This necessitates the use of symbols called clefs, and lines added to the staff called ledger [Pg 19] lines. Ledger lines are short lines parallel to the staff lines added above or below the staff lines.
There are three clefs:—
1. ”

“ Many experiments have been made to determine the velocity of sound, the most reliable of which vary not over seven feet per second. The average of six of the best experiments, made in the early part of the nineteenth century, is 1089.7 feet per second at 32° Fahrenheit. ”

“ In this scale all the notes are sharped. The b# as well as the e# is a white key.
The fifth of C# is g# and has eight sharps. This key necessitates one double sharp and f is double sharped. The double sharps are added in the same order that the single sharps are. The double sharp (designated thus: x) raises a tone one whole step. ”

“ The student will notice that this scale has one sharp (g) . Nevertheless, the a minor is the minor key which has neither sharps nor flats in its signature. The raised seventh of all minor keys is never present in the signature, but appears as accidental. ”

“ The teacher should combine these intervals in various ways and in several different rhythms and the student should notate the exercise. The teacher may also choose some melody free from accidentals and play it slowly while the student notates. Such practice accomplishes a two-fold result, ability to notate rhythm as well as intervals. ”

“ 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.
A minor has no sharps, the fifth of a is e and has one sharp (f) ”

“ Dbb has taken us back to our starting key called by a different name as was the case when we had twelve sharps. To continue counting four would take us over the same keys called by different names. As was advised in the sharp keys, this research should be continued by the student. If more than fourteen flats are considered, it will be necessary to add triple flats. ”