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ELEMENTS

OF

THOROUGH BASS AND HARMONY,

DESIGNED JOR THRE USE OF

Schools, Glasses, und Conservutories,

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ART OF PLAYING CHURCH MUSIC,, =a a eke ok eee EXTEMPORIZING: > °° BY é

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The following work has been prepared for the purpose of supplying the want, very generally felt and expressed, of a short and lucid statement of the elementary laws of Harmony, suited to the needs of singers, and of those who wish to acquire a moderate facility in playing church music, and extemporizing.

It is proper to state that the Rules and Examples are mostly condensed from Ricuter’s ‘*‘ Lenrpucw DER Harmontis,’’ now the text book of the Leipzig Conservatorium, the National Academy of Music, London ; and other schools of note.

It is earnestly recommended to those who may use this book with a view to playing Church Music, that they finish the course by re-writing all the exercises 7 score (that is, on a set of four staffs, with only one voice-part on each staff,) and practising till they can play them with precision.

The rules and examples contained in Chapters I to X. are sufficient to enable the learner to write correct and graceful plain harmony in four parts ; although much instruction is given by implication, in the Exercises, which is not expressed in the text. The teacher should explain these points from time to time, especially the necessity of giving a clear and decided progression to the bass part, of a judicious and tasteful mixture of fundamental and inverted chords, and of close and dispersed harmony, of avoiding perfect closes in the middle of a phrase, and such other points as may occur.

i* ete Le eek

WP OK Weed ay YAY DGD Ae

ELEMENTS OF

THOROUGH BASS AND HARMONY.

INTRODUCTION.

As a perfect comprehension of what is called the Transposition of the Scale is necessary to enable the learner fully to appreciate the tone-rela- tions of the different keys, the following explanation is prefixed to the main portion of this work.

The difficulties in the way of understanding the different place of the notes of the scale in different keys, lie chiefly in an imperfect compre- hension of musical notation.

q A. The learner must bear in mind that the scale-intervals are not equal; those between the third and fourth, and the seventh and eighth sounds of the scale, being only half the distance of the others. By universal usage we represent the scale first in the key of C; not that the scale in that key is more primary or fundamental than any other, but simply because according to our system of representing musical sounds by arbitrary characters, it presents fewer difficulties to the learner.

The scale in the key of C, will appear as follows :

CD & ("iad *. pombe. pcm: < “Meme, The smaller intervals are indicated by the ties.

6 ELEMENTS OF THOROUGH BASS AND HARMONY.

The learner will find by experiment that between C and D, D and E F and G, G and A, and A and B, a sound can be given with vieeaaions which is neither so low as the lower of the two, or so high as the hiehion’ but practically midway between them. But the intervals E, F, and B, C, do not admit of this intermediate tone, for we cannot sing a note with precision, a little higher than B, without actually sounding the note C ; nor a little lower than C without sounding the note B.

{ B. These intermediate definite sounds are represented in two ways; 1, by writing a note on the lowest of the two notes, with a # before it ; or, 2, by writing a note on the highest of the two notes, with a b before it; thus: the F4# and Gb being identical iu pitch.

—— a Bo. tee 3G G Gb F

The scale with all these intermediate sounds represented as above, is technically called the Chromatic scale, not that it forms a distinct and separate scale, but merely for convenience.

A shght acquaintance with the key-board of a Piano-Forte will render the following example plain, and the statement of { A perfectly obvious. |

7 La IE CRT EER BEEN Te II —— ee c= Zo- = ta C c# D p# EF FH G GHA AB C

a ae Le ee ee ee es

-=—S—be—>— ps -S— 7 Seeactanepnamnnar er errr 77 72E >

LEE OCS S-—/O~ eS e- aae CB Bb‘A AbG Gb F E Eb D Db C

+ ee Se —===f

It will appear, then, that C# is practically the same sound as Dh, D+ the same as Eb, G+ the same as Ab, aad As the same as B, ; although they are represented on different degrees of the staff. :

Nore.—To this is applied the term Enharmonic, which technically means a differ- ence of place on the staff, but identity of pitch.

ELEMENTS OF THOROUGH BASS AND HARMONY. 7

q C. Now let us suppose that owing to the construction of a melody renilering it impracticable to be sung, if we take C as the foundatioa- note of the scale, (for by common consent and ancient custom retained to this day,the note C has an individual and fixed pitch ; and by consequence, all the other notes and intermediate sounds of the scale), we find it neces- sary to take some other pitch as the foundation or key-note. Naturally, for reasons which will appear throughout the work, we shall select the fifth from C, which is G, as our new key-note.

§ D. But upon investigation we discover that the scale is not thus properly represented, for according to A, the small intervals should occur between the third and fourth, and the seventh and eighth sounds of the scale; whereas the small intervals above, when we commence with G, are between the third and fourth, and the sixth and seventh sounds. How shall we remedy this? Obviously by substituting one of the intermediate sounds, namely the one sharper than F, but lower than G. We will represent it on the same degree as F, because if we repre- sent it on the same degree as G, we shall fall into confusion. It becomes necessary, then, to use the +.

a, a.

i sc Le ee a CC i é : > SS SS ==}

Peer oa Boas Cac Dr ens Fe,

And, to avoid the necessity of writing a + before every F, as it may occur, we agree to put it at the commencement of the piece, once for all, immediately after the Clef.

By repeating this process, taking always the fifth of the key for the

8 ELEMENTS OF THOROUGH BASS AND HARMONY.

foundation-note of the new one, and sharping the fourth of the scale, which becomes the seventh (or leading-note. See § 14), we shall pass through the keys of C, G, D, A, E, B, Fe and C#, having respectively after the clef (the signature, or indication of the letter which is the foun- dation-note) no sharp, one sharp, two sharps, three sharps, four, five, six, and seven sharps.

{ KE. But suppose G is too high for our purpose; we shall then naturally (for the same reasons as were alluded to in ¥ C,) take the fourth of scale in the key of C, as our new foundation-note.

nr en es Geen SEE ee See

As in J D, we find that the succession of intervals is not correctly given, as our small intervals will come between the fourth and fifth, and the seventh and eighth tones of the scale. We must then, as before, substitute one of the former intermediate sounds, namely the one lower than B, but higher than A, and it should be written on the same degree as B; we therefore take the sound Bb, as the fourth of the scale in our new key of F, and find the order of intervals to be correctly represented. For the reason before given, we write the b immediately after the clef.

soleil SS SE ES A

Po SG CAC Bb + 6 “Dp a eee

Repeating this process, taking always the fourth of the key for the foundation-note of the new one, and flatting the seventh of the scale which becomes the fourth of the new key, we shall have successively the keys of Bb, Eb, Ab, Dp, Gb, and Ch, with two flats after the clef, three flats, four flats, five, six, and seven flats.

ELEMENTS OF

THOROUGH BASS AND HARMONY.

rer ee er

CHAPTER Tf.

INTERVALS.

§ 1. All music is founded on THE scALE, a succession of sounds differing from each other in pitch according to certain fixed relations, established by nature.

§ 2. These differences of pitch are called InteRvazs, and receive special names derived from the manner they are repre- sented on the staff

Example 1. a b Cc d é f V5 Seo OSS RA EE BRETT) Gea TE Ss = f= == F- =f == == f= -=f a ae al ame gees aoe [Tee g h t k l m

ad

10 ELEMENTS OF THOROUGH BASS AND HARMONY.

Ataand fthe different notes comprise two degrees of the staff, ¢d the interval is called a Second: at b the notes comprise three degrees of the staff, and the interval is called a Third ; the same at g: at c and h the interval is a Fourth; atd and i are Fifths; ate and kare Sizths; atl is a Seventh, and at m, the Lighth, or, as it more usually named,

Octave. ‘These names apply equally, whether the sounds are successive or simultaneous.

Example 2.

a b Cai, e fh eye DE | t k l

SS Oe ST BE Pl Pe eos RS EE Gog aoe be iG =-l = =[2[lelelslelz=!

—7

The intervals at a, b, c, d, e, f, and /, are respectively the same as at f, g, h, i, k,l, and m of Ex. 1; at g andi are Fourths, at ha Sixth, at ka Third, and at 1 an Octave.

§ 3. Intervals are always reckoned upward from the lowest note, unless expressly stated otherwise ; thus, the Fifth from C is G; the Seventh from D is C; but the Fifth below C is I, and the Seventh below D-is EH.

$4. The intervals between the third and fourth, and seventh and eighth sounds of the scale are smaller than those between the other adjoining sounds ; being practically only halt the distance. These are called Minor seconds, the others Major seconds. (See Introduction. )

Example 3. The Diatonic and Chromatic scales. Major Major Major Major Major REA AEE EINE RATS EERE SL hh, SEMEN, TS AOE EL RELEASE See ie “7 -s-}e ¢ | eek 1 2 3 4 5 6 7 8

Minor Minoa

ELEMENTS OF THOROUGH BASS AND HARMONY. Il

$5. It follows from this, that the other Intervals are unequal, except the Octave. To make this clear, let us name the interval between every adjacent key of the Piano Forte a Semitone, and counting by semitones, we shall find that some sixths contain eight semitones, and other sixths nine ; some thirds four semi- tones, and others three. EK. G.

Example 4. A Nine Semitones B Fight S Semitones ii.” a oe a Sa 1 a Ee Re SS SSS Ss. 8) Sse cael elon = ee zor aa face E aa sea feet! ot gene ae sts rnd kl he por Sixth C Four Semitones D ee. __ Three Semitones ; Ef ——-—-— ——— |e = —_—— be FEE eS roe = Cento Third Third HH Five Semitones ay Six si

Se ees (oes ere

-S- ge-¢

Fourth Fourth G Eleven Semitones H Ten Semitones a?) manera ae a ere re = a 2 4% i 2s 2 BSS hid el Se aS a a fee ape iee --—— - )-S She! 4 Egedass ceo Seventh * Seventh L Seven Semitones K Six Semitones ee Ye Ie gg Oc ari =3=|—} oes we =s- ect ee eg 2a raat 17 hal RA! Daa en ANY tama naa Ela als cleaner aera Lifth Lfth

Obs. It will be observed that some intervals, different in name, con- sist in reality of an equal number of semi-tones, as at F and K above. This need cause no confusion if it be carefully borne in mind that intervals veceive their distinguishing name from the degrees of the staff cc mprised, without reference to the number of semitones.

12 ELEMENTS OF THOROUGH BASS AND HARMONY,

§6. Thirds, Sixths, Sevenths, and Seconds, (as above in § 4,) are classed as Major or Minor ; Fourths, are classed as Pe-fect or Sharp; Fifths are classed as Perfect or Flat.

Example 5. A B EE VEER PROT LEE EEE ET + “Tad chant a, Pa ed Mp St a eee eee ——_—_ SS —_ as | PUAN P SR, TES SEAS —— BE ES) de EMT ES RISEN ti =—|= Bi —— aN STW NE WSL -=—2o-} ——— a —_=— S——_t_s— Major Minor Minor D E EF _=- FES is SR ARDEA CNET, —— I isi ial pp ag en ot fap tet SR noes ———_—_- SS ——_ -S -—_ —— i a RECS i MEARE MERE YES Brann dvd ATs FTE, =~ Li SSMS: ERE Nas STR Pa mn 5 eS. A ee RS PARROT it p= TI ———— AEE NG TNT Major Major Minor Been Tl a ge 2 ep AOE ipiviess 3 Te ESE TS EE A TT 2 ad BE EGY BF MEE A—— A Geet SESSA, TERE 2B A 5759) REE Sagi 0d) Bee 2 —_Ss-S—s— -s[Sfs-= iB = Sans =f te —sS ———_ ea teas ——. eee Ss Fe Perfect Sharp Perfect Flat

Obs. 1. These intervals all occurring between the sounds of the Diatonic scale, are called Dratonrc Intervals.

Obs. 2. Most of the modern writers on Harmony call the Sharp Fourth the augmented Fourth, and the Flat Fifth, the Diminished Fifth ; but as the terms Augmented and Diminished apply more properly to Chromatic Intervals, it is here preferred to name them as above.

Obs. 3. The Sharp Fourth is also called the TRITONE.

§ 7. A perfect, or major interval increased by either sharping the upper note, or flatting the lower note, is said to be Augmented ; and a perfect, or minor interval lessened by either flatting the upper note or sharping the lower, is said to be Diminished.

ee 6.

: crag ake Bae an fae fo ee else == = te sa iam

ELEMENTS OF THOROUGH BASS AND HARMONY. 13

I Pes N

Fae re ee eee

a

At A, B; C, D and E, are Augmented intervals; at F, G, H, and I are Diminished intervals; while K, L, M and N, are merely instances of minor intervals made major, sharp and flat intervals made perfect, and major made minor by the use of the # or p.

Obs. 4. Augmented and Diminished intervals, properly so called, are classed as CHROMATIC INTERVALS, not so much because they are writ- ten with the aid of chromatic signs, as because they belong to chords whose component parts are notes not found in the Diatonic scale.

Let the learner now name the intervals of the following exercise, stat- ing also the species, whether Minor or Major; Perfect, Flat or Sharp, augmented or Diminished. Similar additional exercises may profitably be given by the Teacher.

ExercisE i. = =o oes F =S pea eee Pa et ee ee $=4 2--S tS hs-o $= Sao pS Ste

Ses iS ss as

=-1$S— ete tS = ts -S pS ==

eo pas SURELY CRE Nar oA ol | pom Selle Ee ee eaea

=r ge fete . Se Ee: seg pt —S-35- SS St ee == =s J]

—— er ee

The last measure of the foregoing contains an example of the Unison, or coincidence of two parts or notes on the same sound; which although not s‘rictly an interval, is yet classified as. such, for the sake of-conve-

nience. [2]

\4 ELEMENTS OF THOROUGH BASS AND HARMONY.

§ 8. The Unison, Second, Third, Fourth, Fifth, Sixth, Seventh and Octave are further classified as Srmpxe intervals. Increased by an octave, or even two or more octaves, they retain their original names, (except under certain circumstances to be explained hereafter, when they receive different names,) and are also called Compounp intervals.

Example 7. Simple Intervals.

-S>--

-=S ~~ —=_—-- ——— -_— nee ee eee —— ——a ae 5-0) =

S eneemaanetiaediieaeemneseel ee a oe

Nin inth T. onth Eleventh Twelfth Thirteenth Fourteenth Fifteenth]

The ninth is evidently a compound second ; the eleventh a compound fourth ; the thirteenth a compound sixth.

§ 9. Whenever the upper note of a simple interval is trans- posed an octave lower, and consequently below the original lower note, the interval is said to be InvERTED, and a new interval is formed, not the same as the first, but closely related - to it.

Example 8. Original Intervals.

a

—Se- o-oo. rsions. Inversi Dh ae

| o- -S SCTCEIeG WMC Asad nal ed ss a = == |==E zoe === a AA tt = oe -Se FS

ELEMENTS OF THOROUGH BASS AND HARMONY 15

It will be discovered on examination that the relations of intervals to sach other are reciprocal ; thus sixths inverted, form thirds ; while thirds inverted form sixths, and so of all intervals.

Obs. 1. To find the inversion of any interval, subtract its number of degrees from nine, the remainder will indicate the inversion. ‘Thus, a fifth is required to be inverted ; subtract five from nine; the remainder, four shows the inversion to be a fourth.

Obs. 2. The following table also gives the inversions of all the simple intervals.

1 2 3 4 5 6 7 8 8 7 6 D 4 3 2 1

§ 10. Intervals change their species by inversion, except Perfect intervals. (See §§ 6 and 7.)

The following table gives the result of the inversion of all the simple Diatonic and chromatic intervals.

Example 9.

ORIGINAL INTERVALS. Octave Seconds Thirds

= eeie = Asse

as =

INVERSIONS. aes ae, Berk TA =- = Sea fe p= ehaey asics Unison Sevenths 2 Sixths Fourths

——*

ORIGINAL INTERVALS.

16 ELEMENTS OF THOROUGH BASS AND HARMONY.

It appears from the above that major intervals inverted, form minor, aigmented form diminished intervals, and conversely; while perfect intervals continue perfect ; hence their name ; the perfect intervals being Unison, Octave, Fourth, and Fifth.

The learner should now invert the intervals of Exercise 1, and name them. Other exercises in inversion may here be given by the teacher.

§ 11. Intervals are also classified as Consonant or Disso- nant. All the perfect intervals, with the major and minor thirds and sixths are Consonant; the major and minor seconds and sevenths, together with all Augmented and Diminished intervals are theoretically Dissonant.

Obs. 1. It is not intended to imply that all consonant intervals are agreeable to the musical sense, or that all dissonant intervals are disa-

greeable. This will appear more fully hereafter. Obs. 2. The perfect intervals are further known as Perfect Conso-

nances, and the thirds and sixths as Imperfect Consonances.

RECAPITULATORY AND ADDITIONAL.

§ 12, 4A. The difference of pitch between any two succes- sive sounds is a Melodic interval ; the simultaneous occurrence of two sounds is a Harmonic interval; and both are named from the number of degvrees of the staff atinrte ecg real by the notes representing the sounds.

{ B. Intervals differ in species, being Minor, Major, Augmented, Diminished, and Perfect; and inverted, change ‘heir species, except perfect intervals. :

q C. Intervals are Simple or Compound.

{ D. Intervals are Consonant or Dissonant.

{ E. It is convenient sometimes to express an interval by a figure, instead of writing the note which forms it ; thus:

ELEMENTS OF THOROUGH BASS AND HARMONY. 17

Example 10. eee ee a ee I ame —— Seep oe sar 8 Get 4:8 6 6 Site D 6 aa SSS

oe oe GO gS BS SG 3

Above is given a portion of Exercise 1. The learner is recommended to complete it; observing that whenever the note forming the interval is affected by a chromatic sign, that same sign must be prefixed to the figure indicating the interval, as in the fifth measure of the above.

The figures do not tell the species (whether Major or Minor, or other, ) only the name of the interval, 1 meaning a unison, 2 a second, 3 a third, and soon. Observe, also, § 8.

§ 18. Observe. This system of representing intervals by fioures, is called Zhorough Bass, which also includes the knowledge of chords, their names and formation. A knowledge of the laws which regulate a succession of chords is called Harmony, ee may be further defined as the Syntax of music.

[2°]

18 ELEMENTS OF THOROUGH BASS AND HARMONY.

CHAPTER II.

THE TRIAD.

INTRODUCTION.

§ 14. The sounds of the scale are harmonically named as follows :

The key-note is called the Zonze.

The second note of the scale is called the Supertonie.

The third note is called the Medvant.

The fourth note is called the Swb-Dominant.

The fifth note is called the Dominant.

The sixth note is called the Sub-Medvant.

The seventh note is called the’ Leading-note.

Example ll.

1 2 3 4 9)

Above is the scale in the key of C. C is the Tonic, G is the Domi- nant, F is the Sub-Dominant, E the Mediant, A the Sub-Mediant, D the Supertonic, and B the Leading-note.

Example 12. a) HEGRE fa == ee : iea3 [ent Sai na ee 2 3 4 5 7 a

Above, A is the Tonic, E the Dominant, D the Sub-Dominant ; C# the Mediant, F4# the Sub-Mediant, B the Supertonic, and Gi the Leading-note.

ELEMENTS OF THOROUGH BASS AND HARMONY. 19

Obs. 1. These Technical terms are relative, and change their applica- tion in any piece of music, with every decided change of key.

Obs. 2. The most important sounds of the scale, Harmonically considered, are the Tonic, Dominant, and Sub-Dominant. The learner _ should now find the Dominants and Sub-Dominants in every Key, in

the following order, C, G, D, A, E, B, F#, Gb, Dp, Ab, Eb, Bb, F.

Tue Trrap, orn Common Cuorp.

§ 15. <A note, with its Third and Fifth, form the Trrap, (otherwise named Common Chord) ; and the note on which the combination is founded, is called the Roor of the Chord.

Example 13.

ae Sa —~@- 2 —_ OO a ——-—--- = Sa ie mee c ener tees. : tae a Scan ae SF decor Peat creme AL i i eee ee ———EEE eye To —_—S--- a b e d ra

Above are Triads founded on every