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rim was tonched by tho finger. Franklin, in a letter dated I8th July 1762^ to Padre
Beccaria. at Turin, mentions the history of Ids Invention. It had already been
kuowu that Iieautiful sounds could be produced by friction of the finger on
the rim of an ordinarv drinkiug-glass. An Irishman, named Pucketidge, was tlie
first who hit on the idea of playing airs on a row of glasses, which he tuned by
patting water into each. He performed publicly In London ; but he and his gkiases
were bamed In the great fire in London in 1760. When Franklin fiuishi^ his Inven-
tion, he found an excellent performer in a Miss Davis, to whom he made a present
of his harmonica. Miss Davis, in 1765, performed on the harmonica in Paris,
Vienna, and alt the large cities of Germany with great effect TlUs fascinating In-
strument found many admirers, but none of them ever succeeded in improving it. ^
Tlie compass of its notes was from C to F, including all the chromatic semitones.
The producing of the sound by the points of the fingers produced such an effect on
the nerves of the performer as In some Instances to canse rnintmg fits. All attempts
to make the harmonica, through means of keys, easier for amateurs, ended in fall-
are, as' no snbstatic« was found to act as a snostitute for the human finger, which
doubtless imparted an expression to the sotmd which no dead substance could pos-
sess. The harmuulca gave rise to a host of similar instmments by Chladlnl, Kanf-



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Hartmattan
Harmonics

naiio, Bleffelaeo, and others, which were not eminently sncceeefnl. Other instm-
neots of no merit or importaooe took the rame name, bnt hid not the most remote
retemblance to tbo original. The harmouica was somewhat similar to the luatm-
meot now known as mnaicai-glasses.

HARMONICA, ChemicaL This teiln is applied to the mnsicnl note which Is
evolved when a long dry tabe, open at both euda, is held over a }et of burning hydro-
con. A rapid current is prodoced through the to be, which occasions a flickering, and
w attended by a series of small explosious that succeed each other so rapidlv, and at
each regular Intervals, as to give rise to a musical note, whose pitch and qnnlity vary
with the length, thickness, aud diameter of the tube. The explanatton of this phe-
nomenon, which was discovered by Lampndius, bnt long remained unaccounted for,
is due to Faraday. A curious modiflcatioii of the experiroeut is given by BOttger, in
the 94th vol. of PoggendorlTs *' Aunaleu," 1859.

HARMO'NICS. the accessory, or concomitant sounds which nre produced by a
fundamental musical sound, either naturally, or by a division into aliquot parts.
Every musical sound, aItlion«;h to the ordinary etir it appears to be only one sound,
win, on close observation, be perceived to consist of a priuci{>al or fundamental
sound, accompanied by otlier feeble acute sounds in perfect harmony (see Harmony).
Ttie rxli*tence of such accompanying sounds, which are called Harmonica, can be
bert demonstrated by the vibrations of a string stretched between two points, or
bridges. Eight feet is a good length for such a string, although 16 feet, or even 81,
wonid be^better, from bridce to bridge. A scale or measure, accurately dividing the
length of the siring into aliquot parts, from 1-2 up to 1-16, is plsced aloncsido of it.
When a violin-bow is drawn across the string, it vibrates from end to end. and gives
out its fundamental sound. Divide the string into lialves bv slightly touching it with
the iloger at the mark ^ ou the scale, or better, with a stretched thread lightly pressed
upon it at that point ; when 8onnde<i it will be found to vibrate lu tw o halves, each part
vibrating as fast again as the entire string, and producing a sound an octave above the
fundamental one, or as 8 to 1. Divide in the same manner iit K« and the sound produced
is the fifth above the lost octave, being in the proportion of 8 lo 8. It is not necessary
to touch the string on more than one of the points of the division, for the long side of
the string always divides of Itself naturally, which can be seen by the eye. The parts
where the string seems at rest, are called the nodal points. Divide as t)efore at >^,
and the second octave above the lowest sound is heard, being to the first octave as 4
to 8. At 1-5 the major third alx)ve the last octave Is found,T)eing as 6 to 4. At 1-4
the octave of the former fifth, 8 to 2. At 1-7 we find the true fiat seventh, or 7 to 4 ;
at 1-8. again the octave of tiie lowest ; at 1-9 the major second, or 9 to 6 ; and above
this, at I-IO. 1-12, 1-14, we find the octaves of the ronjor third, the fifth, and the fiat
seventh ; while at 1-15 wc obtnin the sharp seventh, or 16 to 8 ; and at 1-16 another
octave of the fundamental sound.

Prom these harmonics, the true ratios of all the Intervals of the diotonlc scale, in
relation to a fundamental kcy-notc, are found, and In the most perfect tuue ; they
are as follows :

Degrees of the scale.. L II. HI. IV. V. VI. VII, VIIL
Notes of the scale.... C D B F O A B C

Ratios to key-note.. 1 9-8 5-4 4-3 8-8 6-8 16-8 8-1

AP»nmlDg»4 as the number of vibrations of C in any given lime, the other notes
of the scale may be expressed In whole nombers thus :

Notes of the scolo.. O D B P <* ^ 5 ^^

In #hoie numbers. 84 87 80 88 86 40 45 48

Id the artificial division of the octave into a chromatic scale of ^^«^7® f^°J,\!t"*!l
tOD«»,allthe intervals must necessarily be made somewhat *°™i?fJ^®?;5?n^S {lxi„
calia temperament (see Tbmpbrambkt). This must l»e f»P»E.**"T>t«^?e mikllS
keyed lustmmcnts. Singers, and performers on stringed !'i»t™J"3"\5I?riSen^
by tlieir ear, being free from the fetters Of fixed notes, to wlricli ^^^S^^^""^^!^
are necessarily subject. Even in the natural diatonic scale as P^JJJjLJJJt i- JL
monies, it will l>e found, ou analysis, that a certain degree of *®?|K^flrtif«" frim F
qiUred to make the fif tbs within the octave equal. For cxampio, Vi\t am, f mmC to
U) C, aud from B to B, will be found to be accurately the same as the Attn irom ^ lo



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Ilarmonlnin AQ9

Bonoon ^•'^

G— vis.. S-3 , which Is e&sfly asoertained by redndng their nsflpectfre omnbera to the
lowest fttiction: thus, F to C is 48-83 = to S-S; from B to B is 45^ =S-S; while
from D to A, which in pnctical mnsic must siso be treated as a flfth, will be foaod
to be too flat; thus D to A is 40-tT, which cauDot be reduced toS-8; but when both
are broaght to the fractious of a common denominator, which is done by ma)tlplT-
ing 40-87 by S = 80^ and 8-S hr 27 - 8r-54» it is shevQ that D to A, In the scale
of natmie, is flatter tliau a perfect fifth, in the proportion of 81 to 80 ; so that withoai
temperament A cannot at the same time be a perfect major sixth to C, as a key note,
and also a perfect fifth to B, the tme major second of C.

HARMIKNIUM, a mosical instmment ot modem Invent ion, for which there are
many claimants. The principle by wtiich the M>unds of the harmoulam are pro-
dnced is called theAM vibrating reed, supposed to hare been a modem discovery,
bnt now ascertained to have been Icnowu in China long before it was ever heard of
in Europe. Its construction is as follovrs : A narrow rectaogolar sUt being made la
a piece of brass-plate of a quarter of an inch in thickness, a thin elastic sprins of
tlie same metal, and of nearly the exact breadth of the silt, is fixed at one end by
two small rivets to the surface of the plate, close to one end of the slit, being so
adjusted as to fill the area of the slit, and that when pressed into it at the free end
it may pass inwards without touching the end or the sloes of the sift, and when
left to itself it shall return back to its position of coveriugthe slit The spring at
the freei * * .... . ^ .

forced t

musical 1 , ^ . - - -

tions. This kind of reed is termed **free,^ In contradistinction to the reed of the
organ-pipe, the spring or tongue of wliich entirely covers an oblong slit, in the side
of a braM tube closed at one end, and vibrates against the cheeks or outside of the
silt, instead of within it After many attempts, In various countries, to constract
a keyed instmment of really a nseful kind witli the free reed, Debaiu of Paris pro*
duced his invention of the harmonium, which became more or less the model of all
the others that have followed. The harmonium occupies comparatively but little
space, being only about 8 feet 8 inches high, and 8 feet 9 inches broad; the depth
being according to the number of the stops. It has a compass of five octaves of
keys from C to C, the kev-board being placed on the top, immediately below the
lid. Under the key-boara is the wind-box, on which are valves for each key ; while
bslow the valves, and inside of the wind* box, the dlflieront rows of reeds are
placed. The sizes of the reeds differ, accordlog to pitoh, from about 8)^ inclies
long to X t°cb t ftod the qtiality of sound is affected and modified by the breadth of
the vibrating part of the reed, and the shape of the aperture in the wind-box cov-
ered by the valve. The pressure of wind is from a bellows with two feeders,
which the plaver moves aiteraatelv with bis feet, filling a magazine, similar to
the bdlows of a small organ. When a key is prcsac<l down, the valve below It
opens, and the wind, which has access from the bellows to the wind-box, rushes
through the slit of the reed, and produces a sound which continues while the
valve is kept open. It is a peculiarity of the free reed that an increafe or a
diminution of the pressure of wind does not alter the pitch of the sound, bnt
merely Increases or diminishes Its volume. Advantage is taken of this peculiarity to
effect, in the harmonium, a beautifully expressive swell, or diminution in the sound,
by gradually increasing or diminishing the preMure of the wind. The vibrations
of tne spring being like those of a pendulum, isochronous, remain fixed in rapiditv
or slowness, sccoraing to the length and elasticity of the vibrating slip of metal,
and thus regnlatc the pitch of the sound without reference to the pressure of wind.
For the deep boss-notes the springs are heavily loaded at the loose end, lo make
them vibrate slowly ; while in the higher notes they are made thinner at that end.
Harmoniums are made of various sizes, and from one row of reeds (or vibrators,
as they are now called) to four or more rows ; each row is divided near the middle,
between an E and F ; and each lialf has its separate draw-stop. Lately, a ** knee '*
movement, erroneously called a pedal, for producing a small degree of crescendo on
either bass or treble, has been attached. Home harmoniums are made with two
rows of keys, thus af^ordins a greater variety in playing solo with an accompani-
ment; and for more skilfm perfomiers, pedal-keys for the feet, like those of a
church organ, are added. The mannfactare of the harmonium in Paris has, of late



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433



begot 1



HarmonioiB
Hannonf

, iocressed tlmost IncrediblT. The Tarioas parts o( the barmoninm can now
t got made there, and f arniabed from a single reed to a comnlete set. Mun y at-
tenipta were formerly made in England to accompliah the making of a similar iu'
Btrument called the aenipbiue, but It was « much inferior iiistrameut, although
more expensive. Eren now, the harmonlnms said to bo made in this country, are
all ^t piecemeal from Paris, and put together in London. The best makers in
Pans are Debaiu and Alexandre ; and in Germany, Schiodmayer of Stuttgart and ]
Kaofroann of Dresden. The latter Is the inventor of the Percumon action for the .
bannonlam, which consists of a small hammer like that of a pianoforte, which
strikes a blow on the vibrator the moment the kev la pressed down, and sets it In-
stantly into vibration, thus assisting the action of the wind. Harmoniums may now
be had of varioos sizes and qualities, at prices from £5 to X50. Valuable cliieflv for
accompanying psalmody, tliey suitably take the place of organs in temporary places
of pabiic worship, or among the less opulent clast of congregations. For domestic
use, they are not likely to supersede the planofcrte. but possessing the important
advantage of not going out of tune through humlaliy of atmosphere, they will be
found available where pianos cannot properly be kept.

HARMONY (Or., a joining or flttiuf of pieces into one another), in Music, is no-
derstood to be the onion of sounds which Individnaily appear different, but when
beard together, form a collective sound called a chord (see Chobd) ; or it may be ex-
plained as the melting or flowing together of several sounds into, as it were, one
soood ; in consenoence of, or arising from, the couconant nature of their relative
proportions to a fundamental soimd. All musical compositions can be reduced to
a fundamental harmony of snccosslve chords, which, in their progression, are rec-
ulated by the rules of the tlieory of muoic. Dissonant, ns well as consonant, chords
are included as forming harmony, as they are a nuiou of several sonnds ihat have
bat one fundamental sound, or bass note, in common. The harmony of chords can
either be close or spread, which the position or dis-tance of the sounds or intervals
from one another, forming the chords, determines. Close harmony is when the
sounds composing each chord are pUiced so near to each other, that no sound be-
longing to the chord could ngnm be interposed between any of those already present.
Spread harmony Is when the sonnds of a chord are placed at a greater distance f ron»
each other, so that some of theui might be again intcrposea l>ctwecn the parts of
those sounds already present. Close harmony generally takes place in music lu
which there exists a near relationship among the different parts, as in compositions
for f oar male voices, in which case it becomes nuavoidable, and spread harmony
impoesible. In choruses for mixed voices, and in instrumental compositions,
■pmd harmony is more used, and the intervals of the chords are frequently inverted,
which produces what is called double Counterpoint (q. v.). In the inversion of in-
terralB, great care most be taken to avoid a consecutive progression of such inter-
vals as become fifths by inversion; also that an alto part should never approac a
nearer a bass part than the distance of an octave. Close and spread harmony are
often mixed, hi order that Individual parts may become more melodious and ca?ler lo
sing, as u ell as to prevent unpleasant or abrupt skips in the melotly ; or to avoiu an
equally faulty monotonous formality of movement. .

Although it has been said that every chord, whether consoimiit or "'"Ol-";*
forms harmony, it must not be understood that any combination of houiuVs ^'*!^"
one may chooee to sound together Is harmony. A dissonan t chord t rent ed as ^ *J™y " J^
IS always judged of according to the nature of its different intervalH, of w'''J^n ,\V*\'5
are often some that are treated as dissonances, although they are /»'"°""'*'!l^IX
conf»onances, only more or less imperfect All harmony in masic *" °**[v ^ tiJi^ic that



of the whole system of harmony In music is built. From the "™«tiJ»t»Cl or nrWlnal
tions and the relaUons of the accompimying sounds to tlie fn"^*";®'Crmoiiv in ita
sound from which they all arise (see Habmonios), it follows «*;»Vil,fid^ wH^" or
first and natural state, can only be in four parte, and it is ^»»«"h cLnnSTbTcom
complete ; lu oppoaitiou to harmony of two or throe ports wUtcn w»umv



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Harmony A^A

Harold rtO-*

plcte, as Borac of the fntervala of the chorda, ementlal to characterise the key or
scalt*, may be awantiug. A fonr-part banuouy may be so arranged that live, or
eveu more parts may appear, by incuiia of doubting otie or more of the intervals iu
the octave. From this iucrensiug of the parta arises what i» called the sub-
ordinate hnrmouy, accompanying the principal or fundamental. In order to
avoid faulty progreswous in the subordinate harmony, care mupt be taken to
strictly observe tlic rults which apply to the intervals iu their fundamental state.
The purpose of the subordinate harmony is only that of oioiameuring the originnl,
widen the Germans cull JLjuriruw}^ commonly called figured harmony, but they
should be more properly cailed florid counterpoint. If it be admitted that the in-
terval.-^ and chords that are most consonant are also most harmonious, it uatnniltj
follows that the union of similar sounds nmst be the most perfect, therefore the
ordv-rof perfection in which they rank mnst arise from thoir mathematical propor-
tion!! in relation to the f imdamentnl sound or unison. The common chord of a
third, fifth, and octave to u ba>«s note is the most pure and perfect harmony ; after
wliich follow the chord of the seventh, and the chord of the ninth. The inversions
of any of these chords are all in various degrees less perfect than their orgiual
fundamental harmony. The position of the intervals In respect to the fundamental
note is also an element in the purity of chords ; as, for example, a chord of tlie
seven I h in close harmony, is far less satisfactory and pleasing than it is In spread
harmony, where the different intervals are at, or near, their natural distances from
the fuuJamental note. Such considerations are of great importance to the umsiciaa
who has to accompany from a figured bass ; and also to organ-builders In arrangifig
the compositiou ot mixturj-stops. HurmoLy, iu moderu music, is therefore a sac-
cession of chords according to certain laws. In the early ages of the science, the
laws of harmony were most arbitrary. Nature presents us with solitary chords, but
she does not cstjiblish their succession. A collection of chords Is not mnsic, any
more than a collection of words is a speech. Music, like a dlscourso, must also
have its phrases, periods, punctuation, &c., and all in harmony. The most uscfal
works on harmony are those of Dr Marx, Professor Dehn, and Dr Fred. Sclmeidcr.
HARMONY OF THK GOSPELS. Thenarralivesof the EvangeMata, and especi-
ally those of the first three, are iu many things close repetitions of each other, and
not nnfrequently relate the same incident in words which are all but Identical. On
the other liand, they occasionally exhibit seemingly grave discrepancies, whether of
facts or of circumstances ; one relating an occurrence not noticed by another, or
placing an occurrence at a time or iu circumstances which it la hard to reconcilo
with the narratives of his brother-evangelists. At a very early period of ChrLotiaa
literature this difficulty was felt, and with a view to its more complete and easy eluci-
dation, the passages of the several gospels which bore upon each subject or incident
were collected for the purpose of comparison and of mutual illustration. The title
under whicli the earliest compilation of this nature, which dates from the second
half of the 2d c, wjw known, was '* DSatessaron," because it consisted of extracts
from the /oitr Evangelists. The author of this compHatlon w:i8 the heretic Italian,
and it is remarkable that, iu order to give a color to his own peculiar opinions ae to
the mirealitv of the flesh of our Lord, he omitted from his collection the entire his-
tory of the birth and childhood of Jesus as related by Matthew and Mark (BasebiuR,
•* EccL Huju" Iv. 29). St Jerome slates that a similar harmony wa? compiled abont
the same time by Theophllns of Antiocb, although no trace of such a work is now
discoverable ; but in the middle of the following century the celebrated Neo-platonirt
convert. Ammouius Saccas, undertook a new ** Diatessaron," which formtMi the
basis of the well known "Ten Indexes," or canons, of the Harmony of theG08pels«,
in the Greek text, by Euseblus, which were afterwards adapted to the Latin text by
St Jerome, and continued to be used as a key to the concordauce of the gospels by
readers both of the Greek and of the Ljitin text, do\vn to the* 16th centuij. The
canons of Euseblus consist of ten tables. Of these the first, which contains four
columns, exhibits all the passages which are common to the four gospels ; the sec-
ond, third, and fourth contain three columns, and shew the passages which are
found iu any three of the gos|)e!s ; the fifth, sixth,'8eventh, eighth, and ninth ar«
in two columns, and shew the passages which occur In any two of the gospels ; and
the tenth contains the passages whlcn are found only in one of the gospel narratives.
The convenience and utility of such a scheme arc at once apparent, and It has led In



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435 g^SS""

later times to the nnmeroas and nsefnl compflationa, Roman Catholic as well as
Protestant, known ondcr the name ot Syuopeca of the Gospels, the beat and most
popular of which are euameruted bv Tischendorf in tbtf iutroduciiou to his own
'* Synopses Evangelidc," p. 9, and folL

HARMONY OF TUB SPHBRBS. If anr of the ancients supposed the motions
of the stors and planets to produce a kind of music, wliich they called the hnr-
mouy of the spheres. Tlfey attributed this music to the various proportionate Im-
pressions of the heavenly bodies on one another acting at proper jutervals. Krplef
wrote a work on the harmonies of the world, and particnlarly of tlie celestial
bodies.

HARMS, Clans, a distinguished German divine, was bom 26th May 1778, at



Fahrstedr, In Soutli Dituiarsch. In 1797 iiu went to the gymnasium at McTdorf, :nid
iu 1799 to the university of Kiel. The rationalism of the 'time, in wliich lie had
been to some extent eaucuted, failed to give lilm satisfaction ; and Schieierntach-
er's " Reden Ciber die Ri'litrion ^ at lost settled his faith. After supporting himself as
family tutor from 1802 till 1606, he was appointed Dean of Luuden, iu Northern
Dltmarsch, whence he wns called, in 1816, to Kiel, as archdeacon and aftenioon
preacher iu the NIcolai-Kii-clie. NfXt year, shortly iHifore the tricentenary of tho
Reformation iu Germany, tie issued, in defence of Protestant orthodoxy. 95 theses
under tlie title, ** Das stud die 95 Theses oder Streitsiltzo Dr Luther^s." These
produced a deep Impression tlironghout Germany, and brought him n call to be
bishop of the consistory about to be instituted for the Protestant Church of Russia,
lliia, as well as a call in 1834 to succeed Schleiermaclier in Trinity Church, Berlin,
H. refused. In 1886, he was made ciiief pastor ond provost In Kiel, but was com-
pelled to resign, in consequence of an attack of almost total bliudnesv. The rest of
tits life was spent iu retirement, devoted to literary activity. He died 1st Pebnniry
1666. H.'s published works ore chiefly sermons, wiilch may be reckoned among the
best specimens of modem puipit eloquence in Germany. Of tiiese, the mof t fa-
mous are his ** Winterpostille *' (1808, 6te AulL 1846) and ''Sommcrpostille " (1815.
6te Aufl. 1816), to which a new series was added—** Nene Winterpostdfe'* (1826) and
" Neue Sommerpostillo " (1827). On H.'s life maybe consulted **Doracr's Bliltcr
der Erinuemi)g an das Jnbilfium von H.'* (1842), and **H.'s Lcbensbeschreibnng,
verfAsst von ihm sclbst" (1851;.

HA'RO, a small town of Spain, In the province of Logrofio, and 26 miles west-
north-west of the town of that name, i^ prettilv situated in a fertile plain on the
right bank of tiie Bbro. It has manufactures of hats, leather, brandy, and iiquenrs.
Much wine is grown iu the neighborhood. Pop. 6i:00.

HAROERIS, the elder Horus, son of Seh^ the Egyptian Saturn, and iVti, or Rhen.
eaid to have been bom on the second day of the epuct. He was the brother, and
not the son of Osiris, from whom he is to be distinguished. In the inscriptions, ho
is said to be the son of Atum, of Ptah or Vulcan, and Athor or Venus, according to
different legends. He was also lord of the South and Nubia, ond particnlarly ruler
over the heaven, illuminating the world with the brightness of his eyes. As such,
he was identified with the sun and Apollo, and represented as hawk-headed, weor-
Ing the crown of the upper and lower world. His name is nlso found In the Grwk
dedlcatious to him of the temples of Onibos and Apollinopolis Pnrvn. His connec-
tion with the sun is, however, undoubted, as he is made on one inscription a child



of the styi, and typo of Mentn Ra or Mara. The festival of his eyes, which mythi-
cally represented the sun and moon, took place on the 30th Epiphi.— -Birch,
"Gallery of Antiquities,'* 1. p. 86; Wilkinson, ^' Manners and Customs," iv. p. 395.



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