17.-Tone Thinking Ear-1909

TONE

THINKING

EAR

JESTING

TONE

THINKING

AND

EAR TESTING

A

work

that directs

the

student

in

_{helping himself}

to

_develop

discriminative

_hearing

from

the

simplest

beginning

to difficult

modu-lations

and

chromatic

harmonies

by

CAROLYN ALDEN

ALCHIN

Author_of "APPLIED

HARMONY"

PRICE $2.00

Publishedby

C.

A.

ALCHIN

1227

SOUTH

HOOVER

STREET

LOS

ANGELES

::

CALIFORNIA

Copyright, 1919, byCarolynA. Alchin.

Music

PREFACE.

Music isthe union of toneand _rhythm,soit_naturallyfollows

that the study of music should begin with the _{training of} the

Ear

andFeeling.

Thinkingin terms of sound is_{a pre-requisite for} sight-sing-ing and all truly creative work,

and

as the _study of

_Harmony

and Counterpoint should be the study of tonal _{and rhythmic}

relations, Tone-Thinking and Ear-Training should precede or

accompany

the study of those_subjects.

Every

advance in music education renders

more

clear the

advantage

and

the necessity of understanding the

NATURE

OF

Music, hence the need and

demand

for _{ear training} of a _high

order,

work

which includes something

more

than

mere

pitch

of sounds.

Another advantage of value is the habit ofobservation that iscultivated. In time, one finds his

_power

of attention _always on the alert; not

by

conscious effort, but

by

habit.

The

per-ceptive facultiesare always onduty.

As

_rhythm

is the most elementary factor of _music, and as

there isno music without rhythm, the first

command

should be,

feel

and

hear rhythm, and the second and third are like unto it.

Rhythm

includesthe_grouping of tonesin abeat: beatsin a

measure or bar: the _grouping of measures or bars into sections and phrases, followed

by

the longer phrases that are _equivalent to line or verse in _poetry; and the _grouping of lines or verses into stanzas.

The

increased lengthsareintroduced asthe ability

to think and hearincreases.

Much

ofthe spirit ofa composition

depends

upon

the _rhythm.

The

_expression of ideas is _{impossible except through} form.

Thinking and hearingin _phrasesisas_{necessaryfor appreciation,} interpretation and composition, as form is to a picture, or the grouping of words_togetherfor _{the expression} of ideas.

Since _melody is intoned _rhythm, it merits the next

con-sideration. Absolute _pitch is _{unnecessary, but} relative _pitch is

most _important if one _expects to feel and hear the _quality of

toue resulting from key-relationship.

If the real _beauty of the tone world is not a sealed book,

one _{should hear the nature of}the_{material of}music, not onlythat

arising fromkey-relationship,but theharmonic relations andthe relation of both to _rhythmic accents.

As

every ray of _light includesall color, so every tone includes the harmonic prism.

A

studyof overtonesas illustrated in

modern

musicwill illuminate

this fact.

Much

is_being said and written about_{self-expression.}

How

is one to _{express himself} if he has

no

_feeling for, or

under-standing of the material that he is _using?

We

_{cannot express}

ourselves in a _language that

we

do

_{not understand,} so

_why

expect todo it in music?

Do

thecolor blind _{attempt to paint?}

It is _{really pathetic to see} students of

_harmony

toil over

their

work which

they neither hear _{or think, trying} towrite

acceptablywith noidea of tonal or rhythmic relations, trying to

create with

what

to them, islifelessmaterial.

Those

deficient in the

_power

to think music resort to ar-bitrary rules, and as rules apply to _{specific cases only, they}are valueless as a

means

for _development of the music sense,

ex-cepting asthepupil deduces

them

fromhis

own

experience. In

the examinations of so-called advanced students, only a small

proportion

show any

signsof real musicianship.

Why?

There are teachers of technic

and

teachers of music.

The

latter should so direct the

work

of _{the pupil that hearing}

and

feeling are unavoidable.

To

listen well and profitably in the

way

of appreciation, one's

_knowledge

_of and feelingfor tonal

and

_rhythmic relationsshould be so complete that it is _{a part} of one's self.

One

should unconsciouslyhearas _{the discriminating} artist sees shades

and

effects of color. _Training should be

continued until the _beauty of a _great

work

_{can be appreciated}

without being marred

by any

detail orfactor.

In this

work

the author _{has provided self-help} with every

lesson. First, because effort

means

life.

One

neverassimilates until he

makes

independent effort

and

_application. Second,

because no teacher has the time for all that should be done.

For_{the average}student,the cultivation ofdiscriminative hearing

is a matter of years, requiring persistent, well-directed effort.

The

necessity of dictation

makes

theteacher'shelpindispensable,

but a_pupil should be required to _studyand _preparelessons as in

other branchesof music education.

The

material has been introduced_{progressively,} and in each

case related to all of _{the preceding material}in _{various ways, the}

requirements increasing in difficulty as the.

power

and

under-standing of the student increases.

Harmonies

are introduced

before the melodies

_upon

which they are _based, because it is

easier

and

better _pedagogy to first _perceive synthetically, then

followwith the analytical hearing ofthe _parts.

Much

_emphasis

hasbeen _placed on the various relationships, because

upon

that

depends the

_power

to anticipateand think in _larger units.

Small children

_may

not be able to

do

allof the

home

_work,

but if _{properly presented} and with but one

new

_fact in a lesson,

they will do everything but play

some

of the

more

difficult

examples. Because a _{thing never has} been done, is no reason

why

it could not or should not be tried. Successful teachers

continually set _{higher standards} forthemselves.

CAROLYN

ALDEN

ALCHIN.

CHAPTER

I. 1. Musicis the_{union of}tone

and

_rhythm.

As

it _appealsto theearand_feeling, the first _{step instudying}

it should be _training the ear to discriminate between sounds

and

rhythms.

2. Since there is

no

music without rhythm, begin

by

first

observing the regularity of beat or pulse, then the regularity of

strong and

weak

beats.

Some

students feel the former only.

In that case, they should listen to music with _strongly defined and

marked rhythms

until _{they not only} feel the beat, but the

measure; that is, strong, weak,strong,

weak

(two-pulse measure);

or _strong, weak,

weak

(three-pulse measure).

The

harmonies

accentuate the rhythm, so it is easier for the student to hear

the accents than in a _{single part.}

Use

only

two

or three-pulse

measure in _{the beginning:}

Ex.l.<

Direct attention to _{and exaggerate} the _{feeling of progress}

from the

weak

_pulse tothestrong, lettingthe voiceconnect

"two-one," or "three-one" as _though the

weak

and _{following strong} were inseparable.

4. Clap the hands or

make

any movement

that will _help

to _acquire a _physical sense of _rhythmic accents.

The

writer

uses _{the following}movements, suggested

by

the Dalcroze system:

For _{the strong pulse, drop} the hands at the sides, letting the

weight fall from the shoulder. This is valuable for _{any one}

who

needs _{practice in relaxation,} and _{especially so for pianists.}

a.

For

the

weak

_pulse, raise the hands above the head.

As

one should feel that the

weak

_{pulse progresses} to the strong,

this

movement

is_{very significant.}

b. For _{a three-pulse} measure, the arms

_may

IDC raised toa horizontal position on the second _pulse, then to _the perpendicu-lar _position, a position always used for the weakest _pulse of a

measure, or bar, as

some

prefer to call it.

5.

When

one can hear and feel the measure and

make

the

arm movements

with _precision, the following

may

be used for

eartests, the student

naming

the measure, two or three-pulse:

Ex.4.

-0-0-U4J

JIJJ4

-0-0-a. These _{should be expressed}

by

physical movements, also

written on the blackboard

_by

the students.

As

_they should

be written in perfect time, there should be no _attempt to

make

round note-heads.

A

small stroke is _sufficient, and forthe half

notes a second stroke above the first which will _{be complete}

when

thestemsare added, this _{too being}done _{in perfect time.} Hearingthesewithout_{a changeofpitch} directs theattention to

the_{one purpose of}thelesson, therhythm.

6.

When

the student writes

what

has been heard, he

may

be told that the bars are _placed to locate the accented notes.

Be

sure that the _grouping within the bars is felt, also their

relation to_{the following}accent. Isolated measures should never

be considered.

7.

The

sense of

rhythm

is

more

rapidly developed

by

the

use of the divided beat.

For

the very young, or those lacking

in _{rhythmic feeling,}the divided beat

_may

be illustrated

by

words of

two

or

more

syllables, also

by

playing or singing

two

orme/re

notes while the student_{sings one. For example:}

Ex.6. J J r

cr

j j r

cr

j j

rccrr

j j j

J

r

j j r r r j j j r r r

r

8.

_Employing

_syllabic accentuation _{corresponding} to the

rhythmical, care should be taken that one does not _depend

_upon

that _{indefinitely,} and so fail to _{develop a} keen sense of

_rhythm

from the music itself.

a.

The

writer has a _{strong objection} to the use of the

word "and"

in _{counting, as} it takes too

much

time and stress. Tu'onotes inone_pulse shouldbe heard

and

_{felt as} a unit, or a two syllable word, nottwodistinctwords.

TRY

THIS:

To

the count, add a _light, unaccented syllable

such as _{"ly"; counting,}

one-ly, two-ly, etc.; and for the triplets, one-a-ly, two-a-ly, etc.

Whatever

is used should be _something

CHAPTER

II.

OVERTONES,

TONE

RELATIONS,

KEY,

BIRD

NOTES

AND OTHER

DICTATION

EXERCISES.

9. In

rhythm

we

have time relation. Nature gives us

space relationin theovertones,

some

of

which

arehere given:

Ex.6.

3rd- 7th- 9th.

Root.

.

As

seen in the foregoing, after the octave occurs the_fifth,

which

isfollowed

by

theharmonicroot_{or generator}above. After

years of _teaching

and

observation, the writer isconvinced that

the order of _{presenting material according} to Nature's Plan is

not only the most scientific and _logical, but it is

_by

far the

easiest

_way

and _brings infinitely betterresults.

10. _{Sight-singing}

and

_{tone-thinking are factors of} ear

train-ing. Sight-singing associatesthesound withthe symbol,

and

if

one can think the sound of a tone or _interval, he is_{quite likely}

to_recognize it

when

_given in dictation.

11.

THE

FIRST

STEP

IN

TONE-THINKING

is

TO ESTABLISH

THE

MEASURE,

PREFERABLY

THREE-

PULSE, AS

THAT

is

EASIER

THAN

TwO-PULSE.

12. _{Next, play} and count

two

measures as at Ex. 7,

exaggerating the accents, then sing

some

tone higher

on

the

next accented _pulse.

No

_{pitch should} be taken

on

the piano,

but the student should sing just

what

seemsto

"go

itself."

Ex.7.

Sing.

a.

One who

feels the

_rhythm

will _sing either the fifth or

the octave above. Should it be the octave, singanoctave both

above and below

any

pitch that is _possible for the _voice,

and

after singing, test the accuracy

by

playing it.

For

_example,

6

15. Seconds are said to be large, when, as theyappear on

the keyboard, there is a tone between them.

For

_example,

F|

lies between

F

and G, so the interval from

F

to

G

is a _large

second, and from either to

_F$

isasmall second.

16.

The

octave that includes

two

small seconds as in the

foregoing examples is said to be

PURE.

The

term

PERFECT

is _{also applied.} Fifths and _{fourths including} one small second

are said to be

PURE

or

PERFECT.

For eye training, write the

pattern at

Ex.

n

in several keys, singing and

naming

while

writing:

2o. _{Beginning with any} pitch that is _easy, take a tone as

Tonic,

nd

sing the

Dominant

below, returning to the Tonic on

the accentas in Ex. 14:

b

One

can use scale

numbers

or _{syllables, according} to preference.

21. _Beginning with the

weak

_pulse, take a _given tone as Sol thescale-fifth and_{sing the} Tonic above, asat Ex. 14, b.

EMPLOY AT LEAST

Two

ACCENTS,

NEVER

LESS.

MORE

ARE

BETTER.

An

inexperienced student should be

shown

how

to find the

intervals on the _keyboard so that _{they can be played correctly}

from the first.

22.

The

syllable

name

of the tone located a third above the

root is _{Mi, and} as both of the steps from Tonic are _large, it is

said to be a_largethird.

Sing and write Ex. 15 in several keys, doing it in _perfect time:

Ex.15.

P

m

23. Sing Ex. 16

and

_supply

two

tones for the vacant

8

Forindividual

work

or_{self-help,sing the tonesconsecutively,}

takingwiththe piano afterwards and holding until one hears the

voice part as a

component

of the whole.

25.

A

THREE-TONED CHORD

is

CALLED A

TRIAD.

Com-prised ofa large third

and

pure fifth, it is said to be a

MAJOR

TRIAD.

Observing the structure of a_{major triad,}

what

are the _steps

or seconds

from

third to fifth?

With

one _{small second, the}

in-terval issaid tobea small third*

26.

With

the different positions of atriad, as at Ex. 17, one sees that it is either a combination of _thirds, or a third

and

a fourth. Since

two

of the three _positionsinclude a_fourth,

by

all

means

learn tothink and hear_{them, beginning with} the different chord _degreesand not_always theroot.

A

fact to

remember

is, thatin atriad, the interval_{of a fourth}

is_always

_from

_chord-fifth

_up

to root.

27. In taking the intervals from dictation, one

means

of

identifying or distinguishing the fourth from the fifth is the

effort _{to place} achord _{degree within the}

two

notes _forming the

interval. It is easy to_{sing a} chord _{degree within a}fifth,

much

lessso within a_{fourth, especially at this stage} of the work.

28.

What

is the interval from fifth _up to third? Sixths

that include butone smallsecondaresaidto_{be large.}

29.

What

is the interval from third

_up

to root?

A

sixth including two smallseconds issaidtobesmall.

30.

With

either piano or voices, hold

two

tonesof

a

chord

and

_{sing the} third one.

For

_{example, a} third should be added

to the fifth in thefirst measure of

Ex.

18,

and

both above

and

below thefourth inthe secondmeasure:

Ex.18.

31. Beginning with chord-third

and

_{finding the} fifth

and

root above is

much

more

difficult _{than beginning with} other

chord _degrees. It is

made

more

easy

by

establishing rhythmic

progresslike thefollowing:

*The writer uses the term large andsmallin _preferenceto_major and

minor because they convey a better idea of distance or size, just as

diminished isusedtodistinguishsomething smaller,andaugmented some-thing larger. Theorists who use theseterms have a_verygood reason for

Ex.19.

Do

this, beginning ondifferent _{degrees of pitch.}

32.

Although

they are _{incomplete, as}

we

understand

mel-odies, the following bird notes are well worth using. If,

incidentally, one is led to a _{larger interest} in _birds, the little

songswillserve a_{double purpose.}

When

the exercises are _given for dictation, the student should

First, tell the _rhythm.

Second, sing with a neutral syllable to

show

that the melody hasbeen correctly retained.

Third,

name

it

_by

scale

numbers

or_{Sol-fege syllables.}

Fourth, write it in_{perfect time.}

Having made

the note-heads in time, put onthe stemsin the

same

_{way, and lastly,} the_{bars, just as}the accent occurs. Dots, flags, etc.,

may

be added afterwards.

Summarizing

the order of

work:

_FEEL,

SING,

NAME,

WRITE,

and a child should play

them

if he is_doing

work

at _{the keyboard.}

Ex.20. 1

BIRD

SONGS.

2 3

^=S=:^^:

=s=f

:=*=:^j=*=;

F=f=-n

p

irrr^

ri

~HLJ|

^

g--r

^^^

s=t 10 11 12

10

The

next

number

includesa dotted-eighth and sixteenth,the

latter almost _seeming to_{slip in} between the beats. If onecares

to _{apply a syllable} to _it, use the vowel a, saying "two-acne";

and in No. 17, "one-a two-ly", etc.

13 8va. 14 15 J"1

HI*

IIJx

J * J ' I J-' 16 17 8va. 18 ,.,

H'sf

.

,,,,

i

iEa"*

S

^:

19 20 22 23 24

33

CHAPTER

III.

TONAL

RELATIONS CONTINUED:

MINOR

MODE

OF KEY.

CADENCE.

SCALE-SECOND

IN

MELODIC

AND HARMONIC

RELATIONS.

33.

As

a result of relation to the tone-center, every tone in key possesses either thequality of progression or repose.

Sing-ing the patterns at

Ex.

21 and noting the character of eachscale

degree, one hears and feels that

Do

and Mi, scale i and _3, are tones of _repose, and the _remaining ones, tones of action

pro-gressing to the repose tones, such

movement

being called the

resolution.

Ex.21.

IPS!

t-0-Notice that Re, scale-second,

moves

both ways.

Which

is

the stronger tone of repose,

Do

or Mi?

a. Sol, scale-fifth _{has a synthetic quality, combining with}

both progressionand_{repose tones}in harmonic relation.

Melodic-ally, it isa tone of action resolving on the Tonic. Occurringat

theclose ofamelody,or in contrast to _{preceding tones} of action,

Sol has the qualityof repose, Ex. 21, b.

34. Before doing detail

work

with all of the

key

material,

it iswell to useSol, theDominant,asa distinct _{progression tone}

in melody, as in

Ex.

_24.

The

law of contrast _{compels one} to hear a _{change of quality}

in successive measures, especially between the last two, or the

last

two

_{pulses ofa melody.}

35.

A

change of melodic _{quality (progression} or _repose)

means

a _change of_harmony.

EVERY MELODY

SHOULD HAVE AT

LEAST

Two

MEASURE

ACCENTS AND AT

LEAST

Two

DIFFERENT

HARMONIES.

36.

SECTION

isa term _{applied to} the rhythmic group next larger than a bar or measure.*

A

section

may

be

two

bars

or three, not more.

At

Ex. 22 each _pattern consists of

two

*Asthereisnouniversally acceptedterminologyformuchof theoretical

work, the writer has _employed that which seems themost significant and

comprehensive.

12

sections.

Number

i of Ex. ₂₄isa three-bar section. In _groups

of four or

more

bars, rhythmic balanceorproportion is maintained

by having

an

equal

number

ofaccents in eachsection.

a. In learning to hear in sections, the ear

must

have

distinguishing points or places torest, so it is well to_change the

rhythm, or repeat a _{distinct pattern, as at}Ex. 22:

Ex.22.

b. In the _beginning, the harmonic contrast should be

associated with rhythmic accents, then one learns to anticipate

the _changes of

_harmony

on the accented beats of the measure andsection.

c. Ina three-measure _phrase, the contrast

must

_necessarily

fall on the second measure. In a four-measure _melody, the

contrasting quality

may

fallon thesecond or third measure, but

the _beginning of the third measure

which

is also the section accent, should be progression quality, in contrast to the close,

which

would naturally be the tonic _quality. See

Ex.

₂₄

and

others.

37.

PHRASE

is a term _applied to a _group of

two

or

more

bars or measures

marked

_by

a _pause that is _equivalent to a

punctuation

mark

in literature.

As

a phrase refers to the

con-tent, it

_may

beindicated

by

a

_comma,

_{interrogation point, period,}

etc. Likesentences in _{language, aphrase}

_may

be_{long or}short,

the length depending

upon

the harmony, while the section is

only a

rhymthmic

grouping of twos or _{threes, like pulses in} a

measure.

Ex.

23 contains

two

sections, but one phrase.

38. The close of

a

phrase is called

a CADENCE.

When

the

Tonic falls

on

the last of a _{rhythmic group, the} close is in

the nature ofa _{period or completion} ofasentence.

a.

When

_{a progression tone} falls

on

the lastofa _rhythmic

group, as it _{frequently does} in melodiesof

more

than fourbars,

theclose isin the nature of an _{interrogation,} soit

_may

_properly

be called a _{"Rising Cadence."}

39. In

Ex.

23, the repose tones falling on the

weak

pulses

and the

weak

measure of _{the phrase give}

no

senseof _{pause, so}

there is no cadence until the last _measure,

when

theTonicand

the strong rhythmicaccent occur_together:

13

Rhythmically, the

weak

pulses

demand

the strong: Harmonically,

the_progression tones_{seek equilibrium.}

When

the twooccur simul-taneously, there isa cadence,

and

the_phraseis

complete.

a.

FORM

is outlined or _{given shape}

_by

the _cadences, so

hear everything as_leading to

some

kind ofcadence.

The

teacher will observe that in the first _{tone-thinking}

required, andthefirst dictation _{work, the stronger tones}fall on

theaccented _pulses.

The

_patterns of

Ex.

₂₄ are so written that _{the progression}

tone, Sol, fallson both _progressionbeats and measures.

40. Using the material of

Ex.

24,first _{tap the} measure and

time values, one

hand marking

the former, and the other

hand

the latter.

For

_{example, No.} 2 should be _tapped as indicated in the following: Right hand: j Lefthand: f J r r

J

J r r r

j

r r

Reverse the _{operation, letting} the _right

hand

tap the pulses and the left the time values.

a. _Sing the _melodies, and if the Tonic and

Dominant

harmoniescan be played with them, so

much

the better, as that

accentuates the harmonic _{quality of} each measure. The _melody

should not beplayed, but only the harmonies on

which

they are based. Sight-singing means tone-thinking,

and

tone-thinking

precedesorgreatly assists_{discriminative hearing.}

b.

The

better one feels the harmonic _regulation of a

melody, the

more

sure one is_{of pitch.}

With

_{the simple melodies}

taken at a lively tempo,

many

have but one

harmony

to a

measure.

_Many

of

them

have been so written, because that

enables a student to think the measure as a unit, and not note

by

note which is fatal to sight-singing, ear-training, or the

harmonization of melodies_{at sight.}

41.

Taking

the melodies from dictation, the student should

first

name

the _{measure (two} or three-pulse): second, state the

harmonic _{quality of}each measure,progression or reposeorTonic,

Dominant, etc., if one _happens tobe familiar with the technical

names

of the _{harmonies employed:} third, sing the melody with a neutral syllable to prove that the tune has been retained; then

name

_{by syllable} or scale

number

and write in _perfect time as directed in _paragraph 32.

14 Ex.24. 1

f=T

&^

_^^i

f

ru

f^-c

i fe J _ii j ig

42. Introducing the dotted-quarternote,compare the length

with _{quarter notes}

by

tapping the beatof the measure with one

hand

and the time values with the other, as in _{the preceding}

lessons. If one is

weak

in _rhythm, this should be done with each

_example

beforeit is _sung.

Ex.25. 1 2

m

v^r

^j.^iJ-J-jir;iJ.ii^''jir-^jijpa

i

^*

la 10

11 12

h 1

16

45-

ANACRUSIS

is the technical

name

applied to the frac-tional _part of bar or measure at the _beginning of a _phrase.

The

anacrusis throws

more

_{weight on} the first accent than it

would

otherwise have,soa tone

_may

be_{emphasized by beginning}

a _phrase with an anacrusis:

IJ

As

shown

in Ex. 21,

when

moving

directly to resolution,

Re, scale-2nd

_may

resolveon theTonic or thescale-_3rd.

46.

Taking

the following exercises from dictation, observe

the_closingtone

and

how

it is _approached from above or'below. If one isvery slow in retaining the melodies, follow thedirection

of the melodic

movement

with chalk or _pencil, then,

remem-bering

what

is above or below thecadence tones,one

must

surely

recognizedefinitely.

Observe especially the harmonic character of the second

measures, which, in a four-bar

_melody

_may

be either Tonic or

Dominant.

By

listening for the measure and section quality,

one _{acquires the habit} of _thinking

and

_{hearing in larger} units,

an absolute _{necessity for} correct _{phrasing, breathing,} and

in-telligent

work

in harmony.

Ex.28.

123

4

m

a tt

FT^?

10 L "5 .

17 13 14

m

JIJ.

II J

JUU

15 16

ru

17 18 19 rfc 20 P |~ f2

P

m <3

_^

21 22 -

_r^

^r=Ff

23 24

Jir

25 26

e

27 28 29 30

'V

*

-18 31 32 .

-0-V^

4-33 34

E!

ESS

=*=L

47. Returning to the triplet again, tap the rhythm,

and

proceed as before:

g?J|J

JT>|J

J^T^~r^

=

H?^

ri lrr!^~l^

fl"

10

19

48. Drilling on the dotted-eighth and sixteenth, observe the imitationor _{repetition of either}melodic or _{rhythmic figures.}

Mark

the _groups as _A, B, etc.

For

_{example, Nos.} 2 and _{3 are}

A

+

A, rhythmically, and No. 4 is

A

+

B.

Do

this before

tryingto write the melodiesfrom dictation:

-*

K^

^ J ! i * 0~

\

-I h-^

p-<* i j 3

0-)T.

[

.il; I'-*

^

b^fr^r^Tr-^i?^^

m

&"

;or*"A

_TT s:

20

49- In the minor

mode

of a scale or chord, the third is

small.

The

scale syllable is _{Me, pronounced}

_"May".

_Sing Do,

Re, Me, npt La, Ti, Do, or 1-2-3, n t_6-7-8.

Ex.

21

Si

10 r c/ 11 12

g

Tl ' b \j

^

13 14 15 fcrft f: 16

fUJjU-uJfir

J

22 17 I

y

1= J ^ J f: 18 19

i

=:r=M:

2

t3-a: 20 u

23

52. Sing the _degrees of a minor triad, holding each with

the piano, orif in class, with other voices until theentire chord

is heard. The tones should not be _{played for} the student,

who

shouldbeableto think them withoutaid. Ifone is_{studyingalone,}

the _pitch

_may

be tested

_by

the instrument.

It iswell to alternate the _{major and minor mode, changing}

Me

to

Mi

if thesyllables are used.

Ex.34.

CHAPTER

IV.

SCALE-SEVENTH

IN

MELODIC AND

HARMONIC

RELATION.

AUTHENTIC

CADENCE.

CHORD

INVERSIONS.

53.

Every

tone generates a pure fifth

and

_{large third,} so

the next tone to be considered after the Dominant-fifth is its

third, the scale-seventh. This tone should not be _given to the

student, but let

him

find it if

possible, by singing the following

pattern or something similar, supplying a tone for the _pulse

between

D

and

A:

Ex.36.

-0-r

Solution.

Ifone should not sing Ti, scale-yth, play it as _given in the

solution.

When

it is _{found, observe} its scale relation to the

Tonic, alsoitschord relation to the Dominant.

54.

They

who

use the syllable

names

are less likely to be

confused with the scale and chord

numbers which

are not the

same, excepting in the_{Tonic harmony.}

Whatever

the

names

or

means

employed to _keep thescaleand chord

numbers

distinct, it

mustbedone.

The

lack of this_knowledge isa great _handicap in

the study of _harmony. If _necessary to drill

on

it, sing both

relations.

For

_example, Ti, chord-three to

Do

will go; Re,

chord-five to

Do

and Mi. Using the scale _{numbers, scale-yth} chord-third: scale-2nd chord-fifth. _Playing the harmonies,

Tonic and Dominant, with the various _{degrees, helps vastly in}

acquiring thefeeling forharmonic quality.

55.

What

is the interval

from

Do

down

to Ti?

_Moving

directly to resolution,

what

does Ti

demand?

What

other tones

demand

Do?

56.

Employing

the three tones in chord relation,

we

have

the

Dominant harmony which

the teacher

and

more

experienced

studenthas used in _{the preceding} lessons.

57. In class work, all _sing a _given Tonic,

and

different

ones the three tones of the

Dominant

triad, closing with the

Tonicas at Ex. 36, a; thenwith the variousresolutions as given

in this_example:

58. This relation of the

Dominant harmony

followed by

the Tonic iscalled the

AUTHENTIC

CADENCE.

Play the different positions of the cadence in both modes,

both open andclose position.

In_doing individualwork>playtwo tones_ofthechord

and

_sing

the other.

59.

The

chords of a

key

are designated

by

Roman

nu-merals that _correspond to the scale _degree of the root. Inthe

minor

mode

theyare smaller and with dots above:

Ex.37. r\

For

home

_work, these _patterns taken from dictation should

be _expressed in music notation and the full triad written as in

Ex.

_37.

The

work

should_{be brought} toclass forcorrection.

61. _{Sing the following}exercises in_{both modes,} after

which

they should be written fromdictation:

Ex.38.

*t

3.

fe

3

"

U

'f J i* J IJ J J

|J

==g=_*=1- * |J

'-^

F^

~

^|.

j ,

[p^z

10 ii ft f tt J _J J -1 r I-

^

i' J

-^

12

*fi

^

-!--14 -frr 15 ' I J r J 16 17 18 19

27 20 21 M- . 22 23 24 25 26 27 a: 28 29 30 31 32 33

dt

34 35

^s

36 37 38

28 40

^

47 3 3 45 46 , u,

Ex.39. 1

For_{self-help, play the chords}and

mark

_{the degrees} of both

the outside parts.

By

all _{means, transpose every pattern} into several_keys. This is one of the very best

means

of ear_training aswell as

hand

training, and should bedone persistently. This

should beoneof _{the important} tests _required

_by

the teacher.

64. In taking from dictation, the student

may

only beable

to_{recognize the} harmoniesand write the

Roman

numeralsatthe

first _hearing; and it

_may

be _necessary to have _{the pattern}

re-peated

when

taking the outside parts. Eventually, all should be

recognized atone _hearing.

Reversing the _process of the _preceding lesson, write the

Roman

numerals that indicate the harmonies _played, then the

two

outside _parts in staff notation. Nos. i and 2 of Ex. 39

would

_appear like this:

30

For

home

_work, the chords should be completed, the

in-versions indicated, also the chorddegreeofthe _{upper parts.}

66.

When

_{the chord-5th occurs} in the bass, the chord is

said to bein the second_inversion,

which

isindicated

by

the figure 5 belowthe

Roman

numeral.

In this inversion of a triad,the bass noteis_{usually doubled.}

I

and

V

are of similar quality, the former _possessing

more

5

ofthe

Dominant

quality than ofthe Tonic. If onehas difficulty

in _{distinguishing} them,

remember

that I is followed

by

a

Domi-5

nant, almost invariably, while

V

demands

the Tonic only.

67.

When

the Authentic Cadence closes with the root

posi-tion of both

V

and I, it is said to be _"Perfect." Otherwise, it

is _"Imperfect" and less final in effect. Because of the

pro-gression quality, the second inversion of the Tonic (I) is not

usedfor thelastchordofa cadence.

68. _Play the following in both

modes

and

mark

the

in-versions beforetheyare writtenfromdictation:

Ex.41. 1 J

Jij

|| j ji'j II j

JJ

4 4-

d

=_i

=

_*- <c) -_-9 4-_-*

^

J^

^tfif-^tHffr

V

5

V

5

i

31

fcfc

m

i

32 13

j^d^Ud

f

T

T

J

,. j

^^-6

r

r 14

J.

,J

r;;Jr^

1.^=1^

r,ii [

v

'I

. j

j.

^

~^ ' i r

70. Sing the following and

mark

the sections or phrases,

A, B, C, etc., after

which

they

may

bewritten from dictation: Ex.42. 1

i

m

m

i

.j i. R: 5

^

33

&

e: 8 10 ftdt 11 ?fe

HJIJ

J

P*

12 -a_{j-ffjt f}. _{f?f-4- J ^}

_y

I

^

, I I

^-^-h^~

|p

T^H

f>-

-?-ii44j

x x

IJ bj I _=fg=*M

=^=H

J I ^ h J -tr- ~^

_I

^.m

&

13

^

14

S

f-X-X- >>

?

15 i*

Jif

rnrr

r

u

34 16 17 g-18 19 g: 20 21 V.0 f -g i

P

f

^

IP I I

M-l-^Rr

c: 22 23 9 *

35

26

36

74-

What

is the interval from Sol, scale-_5th

_up

to

scale-7th?

What

other large third has been sung?

What

is the

interval from Sol

down

to Ti?

What

other small sixth has been sung?

Add

to these as in _{the preceding example, thinking the}

tonesas indicated:

13 14

76.

What

is the distance from the scale-seventh

up

to the

small third?

How

_many

small seconds are included?

An

interval

thatissmallerthan_pureor smallis said to be DIMINISHED, so this

isa diminished_fourth. It occurs in theminor_{scale only,}

and

in this

one_place, unless

made

so_by chromaticalteration.

FOR

SELF-

HELP,

SING

THE

INTERVAL

IN

DIFFERENT

KEYS,

testing the pitch with an instrument.

77.

What

is the distance from the small _{scale-3rd, Me,}

_up

to large scale-7th?

How

many

large seconds are included?

An

interval larger than _pure or _large is saidto be

_AUGMENTED,

so thisis

an

_{augmentedfifth.}

Diatonically, it occurs

nowhere

else in scale.

The

tendency of an

_augmented

interval isto _diverge, so there are

two

reasons

why

this particular seventh should resolve on the Tonic and

move

contrary tothe principal givenin _{paragraph 72.} Both the

nature of Ti, scale-7th and the

_augmented

interval

demand

this

resolution.

Singingconsecutive large thirdsis difficult for most people,

but it is

much

easier if one thinks it in _{key where} it actually occurs.

Ex.47.

fe^iMf^^^a^teSEH

Sp=g

78.

The

triad built on the small scale-3rd is

known

as an

augmented

triad because of the

augmented

fifth which it

con-tains; a, Ex. 48.

Name

the different types of triads from dictation, or indicate in _{writing by} the signs,

+,

, /, for

38 Ex.48. a

&

-g - *SL_.j*^_n

^=

3^

79.

From

dictation,

name

the _types of sixths of Ex. 49,

then sing a tone

which

will _complete the triad,

making

three

distinct _types asat a:

Ex.49.

A>

One

can do this without the aid of a teacher

by

testing at

the _piano.

Write the root letter under each, using capitals for the majorchords, small letters for _{the minor,} and _{the acute sign} for

the_augmented.

80. In the _{following examples,}

G

is used as _root, third

and fifth of _{both major and minor} triads. For

home

_work,

do

this in

_many

_{keys, keeping the given tone} in each of the

three_{parts as}

shown

in _{the copy.} For _training in tone

-thinking,

sing the tones that are to be added _{before playing them.} For

an ear _test, this _{should be played} in class.

x.60.

i

39

8i.

_Taking

_two-part

work

from dictation is

more

difficult

than three or _four-part.

_Knowing

that the low _part

must

close

with the root or third, listen for the direction of the approach.

Knowing

what

resolves on the Tonic from either_{side, listen} for

what must

be; alsothe

same

_way

forthe _approach to the third.

For _{self-help,sing one part while playing the other, testing} as usual:

Ex.61. 1

30 31 32 33 34

{-

-35 I

r

J

36 37 38 39 I 40

^

f 41 3 42

i

43 3

^p

_0^ 44 45

JT1

46

1

47

IT

i:

T

CHAPTER

V.

SCALE-FOURTH:

DOMINANT

SEVENTH.

82. Play the harmonic series of Ex. ₅₂ and _sing a tone

higher:

Ex.62.

&

Few

there are

who

will _{not sing} F, a small seventh above

root, and

when

placed in scale relation, the fourth of the scale.

83.

From

Ex. 21, one hears that Fa, scale-4th,

demands

or

resolves on the _scale-3rd.

What

kind of a second is it?

What

othersmall seconds have

_you

heard?

The

small seconds are the intervals that determine ascale,

and they

may

be recognized

by

the melodic direction in

which

they

move

to cadence.

84.

What

typeof fourth isthe interval from Tonic to

scale-4th? Sing and resolve the fourthsthat have been considered in

the preceding lessons.

85. Place thescale-4th inmelodicrelationwiththe preceding

scale _{degrees something} like the following, and transpose tc

different _{keys and modes:}

Some

successful teachers think it an excellent _practice to

sing from the scale

numbers

instead of the notes on the staff, at

least_{a part of}the time.

It is _{good practice in tone-thinking,} because one has no aid from the staff _positions. It is sometimes convenient, especially at a concert,

when

_{a passage might} not beremembered.

42

86. _Writing the scale _{numbers, place} adash over or under

the _{figure to indicate} the melodic direction, if the interval

ex-ceeds athird.

For

_example, in the fifth _{group, the}

mark

below

5 indicates the fifth _higher than the _preceding tone. In the

eighth group, the

mark

above 7 indicates that Ti, scale-yth isto

be taken below _{the preceding} tone. _{In other words, sing} above

or below the dash. Ex.64.

14

| 3. r|

24

| 3.

13

|

42

|

17

| 1.

13

|

24

| 3.

13

|_5 4 | 3.

13

|

53

|

42

| 1.

13

|

42

_|j>-5~| 1.

13

|

24

|~7 2 | 1.

13

|

42

|_5 7~| 1.

531

| 2 4 _~7~| i. 5 1 _3~| 4-^7 2 | 1. 5 1 F| 4 2 5_| 1.

531

1427

|

532

| 1.

531

| 7 2 ~5 |J "2 3 | 1.

Melodies takenthis

_way

from dictationshould be writtenon

the staffat

home

and

_{sung by}

letter

names

attheclassrecitation.

It is _unnecessaryto include

more

examples of this _work, as

all ofthe melodiescanbe so writtenifone chooses.

87.

As

seen in

Ex.

52,Fa,scale-4th isa small seventh above

Sol, the root and generator of the

Dominant

harmony. This

four-tonechord is called theDominant-seventhchord.

88. _{Playthe following} exercisesand

mark

thechord_degrees

of the outside _{parts as in the preceding} lessons.

As

it is very

important that one should think and hear the material in both

scale

and

chord relation, singeach part,

naming

both relations.

This

work

should be done at home, as the teacher's time is

needed for

what

a studentcannot do for himself. Ex.55.

1 2

fr-b 1 1 ' '

44

gi.

What

is theinterval fromFa, scale-4th

up

to scale-2nd?

What

other large sixths have

you

heard? Resolve these inthe

keysindicated:

Ex.68. J

13

=td:

.7,

J

=f*P=F

4U

^

45

ip

14 15 < _{o b} ! 1 1 1

J

1

J

I 1

46

Ifthereare_{leaps in} the_upperpart, the bassislikelyto move_by

steporremainstationary.

This is _{especially true}

when

the

_harmony

_changes.

With

different positions of the

same

harmony, all of the parts

may

move

by

leap.

With

only

two

harmonies, it is difficult to retain

two

or

more

_phrases. Listen_forrepetitonor generaldirection to _rhythmic

accents.

There are _advantages in _{taking the} dictation

_by

_writing as one plays. It

means

quick recognition and quick

movements

of

the hand. _{In doing} this, anticipate as

much

as possible.

Ex.60. rtn

i=l

a! J

U:

'g-^

f-T

F

P22

47

^

i

It

-&-r-

_^r

1,1,1

j

_,j

j

.

.i

j

4ikJ

M

d

i:

*Hf

i-J

*

n

^p

it

^

48

17

rtfc

49 18 19 -P3-20 21 22 23 24 25 .s. 26 27

*-*

28 * J I I-

s

S i * J

>

^^ 30

BEE:

32 33 :-^> 34 35

40

g^

*-^ *-41 OldEnglish. J J i |J J J

E

42 Russian Dance.

j-u

96.

When

scale-4thoccursasfifth ofthe Subtonic harmony, on the large scale-yth it forms a diminishedtriad.

As

a result of

thediminished-fifth, there isan augmented-fourth in both of the

inversions of the chord. Hearing that, one is sometimes

51

a.

The

diminished

mode

ofa chord is indicated

_by

the _sign,

o, asat Ex. 62. In four-part work,thethirdof a diminished triad

isusually doubled.

97.

What

is the

mode

of the Subtonic chord built on the

small scale-yth? In this case it is not heard as _{a part} of the

Dominant.

_Why?

98. Before taking

them

from dictation, play and

mark

the

chordsof Ex. 62, indicating both the root and the mode:

Ex.62.

~

L ,? tt-^,

^^

>? \?y^v<'<rrLU*, v_ u_

99. First sing, then write the note that will complete the

various triads of which these sixths could be a _component, as

at b:

b

Ez.63. _(.0)

7-7^^

_L

-C/ "'' &* C/

^

^

m

TOO.

As

one _{takes the longer} and

more

difficult melodies

fromdictation, listen _{for repetition, imitation, sequence or}

strik-ing rhythmic figures.

One

should always hear and feel the grouping.

Tap

the

rhythms which

include the sixteenth notes before

52

X

J Beethoven: _Symphony.

^Trf?

MT*-+

*-=-etc. *

I

2=ri2

9=+

^

-&-(*5 T . ^__|

12

m

53 13 fc&i -f-r 14 15 H j j H*a p*

t*=^-&

i^f^t

*

*

17 18 a: 19 *

CHAPTER

VI.

DOMINANT-NINTH.

SCALE-SIXTH, LA.

SUBDOMINANT

HARMONY.

TETRACHORDS.

101. _Continuing the harmonic series, after the sixth

over-tone which

was

consideredin _{the previous chapter, the} intervals are in _seconds, the root and octave of _{the harmonic-generator}

following the seventh,and after that,anotherlarge second,which

is a ninth above the _generator. Placed in scale _relation,it isLa,

the scale-6th:

Ex.65.

102. In its harmonic relations, the ninth of the

Dominant

is

more

likely to be heard in the upper parts, especially in the

lower _registers.

The

_{distinguishing} characteristic of the

Domi-nant-ninth is its

demand

for resolution on the root before the

chord as awhole resolves, an effect that isnot true ofthe

Domi-nant-seventh.

The demand

is felt _{very emphatically}

when

the

ninth fallsbelow thethird,asatb. Sometimes the ninth resolves

with the chord, as at c, and sometimes it ascends to the third,

asatd: Ex.66. a

-&-103. Play and

mark

the chords in the _following before

taking

them

fromdictation:

Ex.67.

1 2

i-J

-LMU

1

104.

The

syllable

name

of the small sixth is_{Le, pronounced}

"Lay".

It is used in

two

forms of _{the ascending} minorscales and inall three of thedescending forms.

105. There are also

two

sevenths employed in the minor

scales,large and small; thesyllable

name

for the latterbeing Te.

While

there are

_many

different

modes

of scales, only the _major and the three forms of the minor are considered in this work.

The

_studyof other

modes

is

recommended

when

these are fully

mastered.

106.

With

the sixth, the diatonic scales are

now

complete.

With

the natural tendencies of the scale material as

shown

in

Ex. 21, it _groups itself around a tone-center, the Tonic, falling

into the

two

tetrachords of the scale:

Ex.68.

Observethetendencyof thetetrachordasa whole: one

down

and the other

_up

to the tone-center.

107. Considering thescales _by tetrachord _(i to₄and _{5 to 8),}

one sees and hears that the two tetrachords of a _major scale are

identical.

a.

The

small third of the minor

mode makes

a tetrachord

that is distinctive and _peculiar to that one location in scale _(i to

56

108.

The

small 6th and _yth of the original form of the

minor scale locates the small 2nd between 5 and 6 of the

scale.

As

this _type of tetrachord is found in the _original form only, it

_may

be designated as the originaltetrachord.

109.

The

small 6th and large yth is _peculiar to the

har-monic form of the minor scale, so that tetrachord (5 to 8)

may

be designated as theharmonic tetracJwrd.

57

a:

. Considering the _following as i to 4 or ₅ to 8 of _scale,

name

and write

them

fromdictation:

Ex.72.

in.

_Keeping the Tonic as a tone-center, sing both above

andbelow, alternatingthevarious*forms of the_{upper tetrachord,}

5 to 8: Ex.73. 1 r<s-J IJ i,J

J

ii2.

What

is the interval fronithe Tonic

down

tothe small

sixth,Le?

What

other large thirds have

you

heard?

Name

them

in the _following:

Ex.74.

123

=fc=

58

59

1 h '

60

^

-fir 10 11 r 12 13

117.

What

is the interval from scale-2nd

_up

to the small

6th?

What

other diminished fifth have

you

heard?

Sing and resolve these as indicated: Ex.78.

26

47

62

1 18.

What

is theinterval from the large yth

up

to the_large

6th? Resolve these as indicated:

61

Thinking or _recognizing the _{foregoing examples} without

first

_knowing

the

key

is excellent practice,

and

_{verypractical} in

connection with the study of

modern

music

where

the _tonality

isso oftenobscure.

The

greatest benefit derived is thatof _hearing and _feeling

the difference in the nature of an interval

which

arises _{from key} relation.

As

an interval only, there is

no

difference aside from pitch, but in its key relation, also harmonic relation, there is a vast difference inthe nature of intervals.

_Going

back to Ex._76,

observe the difference in the feeling or nature of the first third

in No. i as_{compared with}that of No. ₃

and

others_following.

121.

The

tones_falling at the extremesof the tetrachord i,

4, 5 of scale are calledthe "primarytones" ofascale, and the

harmoniesof

which

_they areroot, are the "primary harmonies."

As

the _{trend of} the Subdominant tetrachord is

down

to the

tone-center, so isthe_{trend of}the

_harmony

builtonthe Subdominant.

122.

_Employing

scale-4th as chord-root

and

the scale-6th

as chord-3rd, one hears

a

new

harmony, the

_SUBDOMINANT,

resolving

down

to Tonic.

What

scale degreeis _{the chord-5th?} a.

As

root, the scale-4th is free in its _{resolution, falling} a

fourth to Tonic or

_{moving up}

a _{step to} the_Dominant, as seenin

the following example.

b.

We

now

have three harmonies

which

demand

the Tonic

harmony, V, vii

and

IV: Ex.80.

62

a.

As

the harmonic form of the minor scale is _generally

used in chord relations, both the Tonic and

Subdominant

har-monies are in theminor mode. _{Play the following chord groups}

in both modes, and sing and

name

both the scale and chord

degrees of each _part, as in the first lessons with the

Dominant

harmony.

Writing from dictation, after the

Roman

numerals have been recorded, sometimes write the outside parts

on

the staff,

completing the chords and indicating the harmonic degrees at

home;

sometimes write the harmonic_degrees of the outside_parts

from dictation, and expressit all

_by

staffnotationat home.

r.82.

12

3

h 1

63 10 nJA 11 12

m

m

S

Jl

_-

n^rt*--! -P

0-5^=i

:

r

13 14

J"

'

64 20

^

bt

fe^fef

t=-=

=₊₌==:

_P-?-

:

F

_&=:: 21 A S

65 25

J

.

J

^r^

A

<2.

^A

-p-

--

JL -g. -g- *--%-_*-_-%-_ 26 m _p J- /? p

^

* ^

-S

p g)

g

p

124. Sing thesein both

modes

and write from dictation: Ex.83.

1

Wtftt

66 12 13 14 15

^^

16 17

m

18

67 27

s

28

IE

r

L'\>

r 29 30 31 32 33 34 -j*₃ r r 36

68 39 40

^^=

at

41 Mendelssohn.

iSH^

69 47

-I-*

48 49

m

51 52 Beethoven: Symphony. -*

1-*-*-fu-i

53 8va. Beethoven: Symphony.

S

=*=

j

=fii

70 54 Chopin: Op.42.

-r

r r r

t^

r _r r if

f-"i

J _J J 55 5 ^ , \p A f f*! -F1

^

56 ~~ J -57

yftf

71

60 Mendelssohn.

CHAPTER

VII.

BYTONES.

125. In this work, all non-chordal tones are termed

"By-tones."

A

tone generated

by

the harmonic root is a

_harmon^

tone;

any

other is a _bytone, and alwaysdissonant. Sevenths and

ninths are dissonant, but

when

they are _generated

_by

the

har-monic root, as they are in the

Dominant

harmony, they are not

considered _bytones.

So

it follows that while all

bytones are dissonant, alldissonances are not_bytones.

There

are specific

names

for the different kinds of _bytones,

but theorists _disagree

_upon

the terminology of all _excepting

Suspensions

and

Anticipations, so the author has omitted all

names

excepting these _{two, leaving} it for the teacher to _supply

those _preferred.

A

detailed discussion of the various bytones

and their_specific

names

_appears in the author's text, "Applied

Harmony.

''

126,

A

SUSPENSION

is a _bytone that occurred as a

_harmony

tonein tne_{precedingpulse.}

The

rhythmic necessity of changing

the

_harmony

on the accent results in _{a suspension} of _any tone

that does not

move

with theremainder of the chord. Ex. 84,a:

Ex.84.

73

127.

When

one or

more

of the parts resolves prematurely, the effectis

known

as _{"Anticipation."} In this_excerpt

_F$

of the

anacrusis anticipates the chord-3rd of the next measure; and

G

of that measure anticipates the root of the next chord:

Ex.85. ftfa

128.

As

_wijl be seen in the analysis, bytones

_may

occur in

any

part, and in

two

or

more

parts simultaneously.

They

are

all of a decorative _nature, and it is not _always easy to hear the

harmonicsubstructure.

They

have been freelyemployed in _{the preceding} melodies, and from this time they will be included in the harmonies.

They

should be

marked

before

coming

to class and

_may

be

indicated as one finds convenient.

The

writer places a little

mark

_throughthe note-head:

Ex.86.

129

One

must acquire the ability to hear harmonies in

phrases. In so doing, anticipate the natural relations, the con-trasts that are _likely to occur _{on rhythmic} accents, and

con-trasting cadences. In selections of length, and sometimes with no

more

than four measures, there will be _repetition or imitation.

The

repetition of a phrase is not _{always exact, especially}

when

_leading to a different cadence.

The

_rhythm

_may

be the

same, but the

harmony

must necessarily be different.

Sometimes there is melodic and _rhythmic imitation, but harmoniccontrast.

74

130. Before taking the following from dictation,

mark

the

phrases with the punctuation

marks

of literature, indicate the

harmoniesand _{their inversions, also the bytones:}

Ex.87.

1

75 J* I I . I h i . . h . . ' . ft .P I . 1 .. **_{j 3 j}

_'ftjlmtrft

J 3 j

Sjy

3 I*^.\

t

^

i *

H

fi -IV J I

^g-N

I d-*-\f-

^1

^

-^4

J

--

_*fe

^

inrf-r^^

i

rcrrr

r

^^

_^

->

76

10 11

f

W

77

16

79

80 25

m

j j j j ,j

^

j

llf

_^r

r