John Almon.

The American journal of science and arts online

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" buiU for the Exhibition of 1861, and an Appendix tracing the
identity of design with the Enharmonic of the Ancients, London,
1850. 8vo. I also obtained, after much search, and by the kind
efibrts of the author, what appears to be the initiative work of
Gen. Thompson in musical doctrines. Although a work requir-
ing thorough classical and mathematical knowledge, as well as
information in several departments of literature and taste, it
bears the modest title, ^^Instructions to my Daughter for Playing
on the Enharmonic Ouitar, being an attempt to effect the execution
of correct harmony^ on principles analogous to those of the ancient
Enharmonic, By a Member of the University of Cambridge. Lon*
don, 182d." In folio, with illustrations. This work seems to
have been stimulated by a fine perception of the delicate har-
monies of which the guitar strings are capable, and by falling
upon the collection of the " Seven Ancient Greek authors on
Music," collected and published by Meibomius, and printed on
the Elzevir press in 1652, a copy of which is in the library of
Harvard College. The Euclid of geometry is one of these
seven, and there is an eighth author who is not reckoned an an-
cient, as he lived as late as A.D. 470. It is clear that there was
something which these called " enharmonic" which is declared
to be the " most accurate^ (Aristides Quintilianus, lib. i, p. 19,
ed. Meib.) That "the name of enharmonic [or harmony] is
given to the genus abounding in the smallest intervals ; from
the harmonizing." (Idem, i, 18.) " The enharmonic, so called
from being taken in the perfect intervalling of whatever is sub-
jected to harmony." (Id., ii. 111.) With much more to justify
Gen. Thompson in adopting the title of Enharmonic: which name
I also take as appropnate to a system of perfect harmony, and
to the instruments which are constructed on its principles.

16. The enharmonic organ of Gen. Thompson had key-boards
in which, without any change in the interior of the organ, all
sounds contained therein could be given. Every sound of the
organ was represented in three key-boards, except some very
rarely called tor, which had exchangeable pipes. The organ of
Mr. Alley and myself had a key-board like that of the common
organs, and the fingering was the same : all changes were made



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8 H.W. Poole on Perfect Harmony ^ etc.

by pedals, one for each key, wbich put the organ in tune for its
own scales. It could be played without the player knowing what
sounds he used — he only needed to keep the organ in the right
key. Gen. Thompson justly remarks that his system would
have merits over ours, in compelling a musician to know what
he is doing. Bat in the dark days of enharmonic scienoe it
may be excusable not to demand too much of the organists.

16. There are great difficulties which present themselves in
admitting to a key-board the multitude of sounds required if
several transpositions or signatures are to be played in. K the
five series of sounds already described, § 1-2, are carried into the
keys from nine flats to nine sharps — nineteen signatures— just
one hundred notes to the octave are required I But an octave
is limited in width by the span of the nngera Six and a half
inches is about the convenient average measure, and this is
adopted by organ and piano-forte makers. If the notes we
want are divided equally into this space each will get the hund-
redth part of it, or sixty-five thousandths of an inch. The pins
■of a barrel organ might play upon them, but with human fin-
^rs it is hardly possible.

17. But there is a fortunate circumstance in the relation of
the sounds which comes to our aid. All are not wan&d at the
same time ; when we are near the key of nine sharps there is
no possibility of our requiring the notes of nine flats. These
we may arrange therefore at a distance front or back, and place
near by the related notes which may be required in connection
with those already in use.

18. At least seven finger-keys should be in convenient rela-
tion to each other, and of sufficient size and position to allow
of their being touched, and for the changes of fingers necessary
in running scales and taking chords in dififerent positiona Such
a key-board I have endeavored to devise, the result of which
may be seen from the following description and figures.^

19. The first point I took in the resolution of the problem
was, the convenience of the broad white ivory keys of tne com-
mon key-board, and the elevated black keys — the white espe-
cially affording room for shifting the fingers, and the raised
keys making it easy to touch a narrow key, which it would be
hard to do if all were in one level. The second : that the key-
notes and the thirds, being of different classes, might be assigned
to these two classes of finger-keys, naturally giving to the first
class the more extended keys, or the white. So the octave
ought to have its seven notes. Pieces of bristol board were cut
to the width of the common white keys, or nearly an inch, and
in length double that of the part in front of the black keya

* At the time of writing (April, 186*7) I have made application for a patent for
this key-board.



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H. W. Pook on Perfect Harmony, etc. 9



With the same material I made elevated black keys of the width
and height of those of the common key -board, and of the length
• of 2*7 inches, which were arranged in hopes of getting at least
the diatonic scales, triple and double, wnich could be easily
managed, and in a manner uniform for all keys.

20. This provisional key-board is not figured here, but may
be understood by reference to figs. 1, 2 and 8, which contain
also the additional series of sounds, lY and Y, §12. In fig. 1
let the black key, d, be moved to the left until its left edge coin-
cides with the right edge of C, its back end as now being in
contact with the front end of the white key D; let e, fl^, and
the two keys (F^ and another not marked but really Eb*) marked
with vertical lines indicating their color, red, be moved in the
same direction and distance as d, till they are in contact, respect-
ively, with D and E. There is no room now for di^ and d^ and
their two companions by f#, but we have all the key-notes,
thirds and perfect sevenths, and the advantage of greater width
in the white keys, which are nearly an inch and a quarter wide
(1*21 in., the black keys being 046). This key-board^ although
deficient in the minor mode, from the absence of the series iV
and Y, is still recommendable where economy is necessarv, as all
the music of the major key, including the beautifiil chord of
the seventh, can be played ; except in cases where certain acci-
dentals are introduced from the minor mode, as illustrated in the
example from Bossini in § 8.

21. A portion of the complete enharmonic kev-board is shown
in perspective in fig. 1, in the natural size — tne length of the
keys being reduced to one-half by the perspective. The keys
are of five different colors — representea here, the white and
black by their natural colors, and the rest according to heraldic
rules, viz., the red by vertical lines, the blice by horizontal, and
the yellow by white stippled with black — and of as many differ-
ent elevationa The following table represents this.



Series.


Color.


Eleyation.


Example.


L Key-notes,

n. Thirds,
m. Sevenths,
IV. Dora. Sds, minor,

V. Dom. Yths, minor,


white

black

red

blue

yellow


0-0

0-4 in.
0-06 "
0-10 "
0-15 "


CD

b,e

F'



22. These keys all have vertical rectilinear motion so that a
touch on any part of their surfece produces always the same
effect. This is attained — in one method — ^by attaching each to
a pair of guiding rods, passing down through a couple of hori-
zontal tables where they are secured to a piece which communi-

Am. Joub. Sol— Becond Sebibs, Vol. XLIV, No. 180.— Jui.t, 1867.
3



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10 H.W. Poole on Perf$ct Harmony, etc.

m

cates in the usual manner with the valves or hammers. It will
be understood that the mechanical construction of the instru-
ment beyond the key-board may be the same as usual, except-
that its number of pipes or strings must be multiplied.

23. As the assemblage of all the notes may confuse the eye
at first sight^ I have drawn on half scale the plan of the finger-
keys which in every signature — or commencing on any white key
whatever — ^give the triple and double diatonic scales. The white
keys are of the width of 0*993 in., the black keys having the
width of 0*45.* The white keys on the common key-board are
but 0-93, or the seventh of 6J inches. The plan in fig. 2 will en-
able a player to judge whether the scale can be executed. It is
immediately intelligible even to a child, who, having learned
the order m one key, knows it in every other. The keys are
considered by their relations to each other, that is, as Do, Be,
etc., and (to repeat it again). Do may be taken on any white key.
The fingering in the triple diatonic scale is the same as in that
of the natural key, and of others, on the common key-board,
and the fingers easily reach the keys and change on Fa and Do
as in the latter case. In the following scales the usual signs
represent the thumb and four fingers ; see fig. 2.

Triple Diatonic Scale— Its fingering.

Do Re mi Fa Sol la &i Do
+ 1 2 + 1 2 8 4(or+)

Double Diatonic Scaled— Its fingering.

Fk Sol la 8e Do Rs mi Fa

+ 12 8 + 128

The player is recommended to complete the octave, Fa to Fa,
bv copying the four lower keys, Do, Ee, mi, Fa, figs. 2, 3, and
placing the lower Do upon the upper one, or by conceiving that
this has been done. Tnis will show the double scale in its reg-
ular order.

24. I regret that the limits of these pa^es did not allow a
larger portion of the key-board, and permit reference to it in
the manner of taking the several chords in their various posi-
tions. But I think that those interested can extend the dia-
grams by the data given, and I shall, therefore, give the finger-
ing for several chords, which being understooa in one key will
be the same in all transpositions.

* The widths are established thus: first determine the width of the octare, aad
that of the black keys. Represeotiog these respectivelj bj 0, aod b, the width of

the white kej (W), is obtained thos: -!|L=W. For the key-board for major
keys, only, § 20, the formaU is ^^=:W.





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11




Q

eft



H

s

o



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12



H. W. Poole on Perfect Harmony, etc.



Fig. 2.^A POETIOlf OF THS EnHABMOMIO SIeT-BOAED, SHOWIXCG the EBLATIYX POfll-
TION OF THE FiNQXE-XBTS WHIOH OIVB THE TeIPLB AMD DoUBLE DlATONlO S0ALE8
IN EYEET XET OE 8IGEATUEX, OE TAEnfO Do ON ANT WHTTX KXT. — ScoU of Otiekalf,

The white and black keyi are repreeented ia their nataral colon ; the red keyi-^rarfect leTenthi
^bj yertical linee ; the bioe keyi— domiDant third* io the miner mode— by horisontal linaa ; the
yelW keje— dominaBt aerenthi in the minor mode— by white itippled with black.













A






Si














Do










Fig. f . — SaonoN iseouoh A B, oe tbeouoh the tded qqaetbe of ant kxt-notb,

BXFOBDCO ALL THE N0R8 OF THAT XET BOTH IN THE MaJOE AND MlNOE HODK8.

flm r7 _ A-,





/ / ,


/ i


r


/


/j|__^f




L - /


M/;;::^




r


^H







:




Do 1 Be
48 64


D«n.7 mi Fa
^,0 ^


Sol
72


Dom.3
R.Min.

16


la
80


ae

84


n
90


r

Do
96




TEIPLB DIA.TOEIO SCALE.

I II m IV V VI V


II VEI




8:9 9:10 16:16 8:9 9:10 8:9

DOUBLE DIATOKIO 8CALS.

V VI VII I 11 in r


16:16
V V


1#

IT

lb


8:9 9 :

Sounds gitsn bt i

G A

C D

F 1 G


10

rHE AB

a'


16:1

OFE

b
e
a


IS 8:<

Fmom-i

C

F

Bb


> 9
cets inth

D

G

C


:10

ESION


20 : 21
^tueesooi

a B^
d Eb^


T:

LEESX

ft
b
e


8

*ONDING.

G
C
F


i


L Fore.


itaodMJ


(Tab


leeeenej


,t page— Eal


tiannoii


icTa


ble.




B



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H. W. Poole an Perfect Harmony, etc.



13



ENHAKMONIC TABLE,

COMFBISIKO THB NOTES OIYEN BT THB SECTION AB, FiGa 2, 8, IN THE BION^-
TUBBS FBOM 9 FLATS TO 9 SHABP8, AND CONTAINING THEIB DiATONIO SCAIJBS,
INCLUDING THB MINOB MODE. 100 N0TB8 TO THE OCTATE.*





TRIPLB DIATONIO BOALB.




1


Do


Re




mi


Fa


Sol




la




A


Do




1


Eet-

NOTE.


Second.




8d.


ForaxB

G#

F#
B
E
A


Fifth.




6th




nth.


OotATI.






E




el'

«•'
di'

gtt'
of
f»'



gt


A#


dx


bi
ei



Of
Ft'

B'


cx
fx




D#

G#

c#




4#




c#


cx

«l
at


di
gt

b

e


E'

A'
O'
C
C
F'


et
at

di


F#

B

E






A
D
G


B
E

A


b'

.0'
a'


ct
b


D
G
G
F


E
A
D




Of


A
I)
G




i


C


D


d'

g'
o'
f

bb'
ob'
ab'
db'
gb'

Ob'


e


G


^1
6


a


Bb'


b







lb

2b

8b


P

Bb

Eb


G
C

F


a
d

g_
c
f
bb

8b
db


Bb
Eb

Ab


C
F

Bb


d

g
c


Eb'
AD'
Db'

cb'
ob'

Fb'

Bob'
Ebb'
Abb'


e
a
d_

e

c
f


F

Bb

Eb




4b
«b
«b


Ab
Db

Gb


Bb
Eb

Ab


Db

Gb
Cb

Fb

Bbb

Ebb


Eb
Ab

Db


«
a
d


f

bb

eb


Ab
Db
Gb ,




'b
8b
»b


Cb

Fb

Bbb


Db
Gb

Cb


Gb

Cb

Fb


9
e

/


ab
db

gb


bb
eb
ab


Cb
Fb
Bbb






FnrTH.


SOCTB.




7th.


HOTB.


Sboohd.




8rd


4th




Fifth.






Do


Si




mi


Fa


Sol




la


Se ' Do






DOUBLE DIATONIO SCALE.





* In coosideriog the relation of the notes in the enharmonic Bystem, there is con-
stant reference to the series of fifths, and the following obeervatioo of their order
maj be of use. A descending series of fifths is a snocession of the following let-
ters, the first four of which form an English word, viz., bead ffcf. When the series
is extended down, a flat is ^dded, always on the beginniDg of this series or on b,
which sign continues without change to /, where another fiat comes in, remaining
also for the seven letters. If the series commences with one or more sharps, the
same rule holds good, remembering that a sharped note is flatted by maldng it
natural. If then we commence with Bf we shall have

Bt. Et, At, D«, G«, 0«, F#— B, E, A, D, G, C, F— B»>. Eb, Ab, Db, Gb, Cb, Fb,
or the key-notes of the keys from twelve sharps to eight flats. Continuing, we
should have a succession of the same letters, with double flats, ending with the
key-note of fifteen flats; next the same with triple flats, leaving us in the unex-
plored regions of twenty-two flats, where for the present we wUl stop. The series
of thirds, sevenths, etc, follow the same succession.

To the perfect sevenths is added the index ^, not as being essential, for the type
alone is sufficient to distinguisfa them, bat in ozder to make them more oonipieaous
at the present time.



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14 H. W. Pook on Perfect Harmony, etc.

JExamples in Fingering Chords on the Enharmonie Key-hoard,




Nom. — 0, subdominuit chord, f and a; b, dommant with Barenth, F'; c, auoe
with ninth, A ; c( dominant aaventh ; e, dominant of relatlTa minor ; the seTenUi, d'
ma.y be added ; /, subdominant with serenth ; g, grave second d, or aizth of solh
dominant The flattened note should be made natural in the next chord.

The devble figures indicate that the key is touched with one finger, which is im-
mediately changed for another, as is customaty in passing smoothly from one cboid
to another. The base will be easily supplied by the musician, who will also ob-
eerre the similarity between this fingering, and that of the common key-board.

25. The chords given belong in part to the triple, and in part
to the double diatonic scales, or more properly speaking, those
scales belong to these chords. For meiodies originate from har-
monies, if either can be said to generate the other, when both
fipring into existence almost at once. When Haydn, who from
poverty could not obtain instruction in the theory of music, was
forced to search for himself, he discovered certain rules which
he was desired to impart. " Try to find them out," is under-
fitood to have been his sensible reply. It was supposed that
they referred to the dependence of melody on harmony. How-
ever this may be, it is certain by the evidence contained in his
compositions, that he had a very complete and delicate knowl-
edge of the laws of harmony and their relation to melody, and
that his inspiration came from a higher source than the tempered
octave of twelve keya The student who would follow Hajdn's
advice will find more aid in an enharmonic key-board with its
pipes, strings, or even seraphine reeds, than in the most thorough
pnmer of tihorough-base that has yet been published A pupil
in harmony taught by an instrument tempered with twelve
sounds is worse off than a student of mineralogy shut up with
twelve specimens, or of chemistry with so many elementary sub-
stances. The latter might learn much that is true and importr
ant, and so might the musical student would he tune his twelve
notes accurately to something. And I would not be understood
as thinking that those thus taught harmony are totally ignorant
of its true principles * I have met with notable instances where
the truth was deniea in words and declared in actions. Musi-



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-ff. W. Poole on Perfect Harmony, etc. 16

dans sometimes learn by intuition, and contrary to what they are
taught. So people are found just and amiable in spite of bad
political or theological creeds and education.

26. Fig. 8 giyes a section through the center of the third
quarter of the key-note of fig. 2, and through all the notes^
major and minor, of the signature to which it corresponds. The
circumstance that a section in this place will cut all these notes
and no others, might be considerea remarkable and eyeli won-
derful, were it not for the fact that this is the first principle on
which the system is based. In constructing the board a certain
number of parallel spaces are laid down from left to right, and
one space is assigned to each signature intended to be proyided
for. In the natural signature, C, the key-note, has its place of
necessity. But C is the fourth of 1# and accordingly is pro-
longed backward, — ^toward what would be the top of a page or
the north point of a map — over the space of 1#. As it is the
fifth of lt>, and the second of 2b, it is brought forward ,M*^ooyer
the spaces of these two signatures also, and the whole key now
18 four times as long as the space originally assigned to each sig-
nature — which I haye taken at nine-tenths of an inch, but whicn
mi^ht have been more or less. So eyery other note wanted in
a signature is placed here, and if wanted, in adjoining ones it is
protracted into them. Thus the e of the natural key is in all
the spaces occupied by its root 0, except in that of 2b, where it
is not used. The perfect seyenths and dominant thirds and
sevenths of the minors being used each in one signature only,
are not extended beyond it Many simple rules for the relative
position of the finger-keys could be given, which quickly fix
their location in the mind, like the following:

27. Eules. — 1. From the back half of a white key to the ad-
joining white key, on the right, is a major tone, 8 : 9, e. g.. Do
to Rk, fig. 2, C to D, fig. 1, and vice versd, 2. From the firont
half of a white key to the nearest black key, on the right, is a
minor tone^ 9 : 10 ; e. g.. Be to mi, fig. 2, D to e, fig. 1, and vice
versd. 8. From the forward part of any black key to the ad-
joining white key into which it is half inserted, on the right, is
a diatonic semitone, 16 : 16 ; e. g., mi to Fa, fig. 2, e to F, fig. 1,
and vice versd. 4. From the back end of any black key to the
next black key on the right, is a major tone; e. g., la to si, fiff. 2,
eto fl^, fig. 1, and vice versd. The distance to the ficht, or leftj
for whole tones is always the same, viz., the width of the white
key or 0-998 in. Other rules will suggest themselves to the stu-
dent^ and these specimens will suffice.

28. The finger-keys supposed to be cut by the section A B,
have their remaining portion in the rear, shown in perspective,
and are marked with their names and the relative vibrations of
their sounds. Below is indicated their order in the triple and



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16 H. W. Poole on Perfect Harmony, etc.

doable diatonic scales. Still below is a part of a table of the
fixed notes which would be cut were this section made through
the key-note of the several signatures indicated in the margin.
The complete table should follow below this section, but as the
space of the page does not allow, it is given entire on the oppo-
site page, ana should be referred to this section ; even the wiath
of the paper on which the sounds are marked corresponds with
that of the finger-key in the place it is supposed to have been
cut. This enharmonic table contains in its eleven columns all
the notes of the major and minor modes, within the limits of
nine fiats to nine sharps, both inclusive, and comprises one
hundred notes to the octave. Owing, however, to the close co-
incidence of two of the series with two others, twenty-two of
these can be dispensed with without an error exceeding the
hundredth of a comma in the fifths alone, and nothing else-
where ; which difference may be neglected, and is, practically,
through the "sympathy " of accordant sounds, in perfect tune.

29. The last named circumstance is of much importance when
the cost of organ-pipes is in question. Although there is no
such thing in music as a "circle" of keys returning into itself
theoretically and mathematically, yet there are certain close ap-
proximations which can be taken advantage of for economical
reasons. If we aacend eight perfect fifths and a major third,
and descend five octaves, we have a note higher than our start-
ing pitch by something less than the eleventh of a comma, or in
the relation of its vibrations to the starting pitch as 100,111 to
100,000. This supposes absolutely exact tuning, which is very
difficult, as the pipes or strings, when near the sound they would
give when sounded singly, draw into tune, and are perfectly ac-
cordant. So that if the tuner should make his fifths one-fiftieth
of a comma flat — which he might do and have them all sound-
ing in perfect tune — he would end as much below the starting
pitch as perfect tuning should, theoretically, bring him above it.
Prom which it is seen that he can, if he choose, flat each fifth
one hundredth of comma and the two series will then coincide.
Indeed, this distant note is useful as a landmark, and as a detec-
tive of small errors accumulating among so many fifths. It
may be compared to the correction of measured distances by as-
tronomical observations, without, like the latter, being subject
to any errors of observation however small.

80. On reference to the table, page 13, two notes thus approxi-
mate are C in the natural key and bf^, the third of eight sharps.
And the key-notes Bbb, 9 flats, to G, 1 sharp, are thus available
for the thirds, from a, in 1 flat to fx, in 9 sharps; in all eleven
pipes saved. Also the thirds, dt>, in 9 flats, to b, in one sharp,
are equally serviceable for the dominant thirds in the minor
mode, c# in 1 flat to a^ in 9 sharps, which include eleven more
pipes, reducing the hundred of the table to seventy-eight only.



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H. W. Pook on Perfect Harmony^ etc. 17

81. With the key-board that has been described, all the play-
ing is doDe with the hands, without aid from the feet, and there
is nothing to prevent the use of the feet for pedal bases. But
the same Key -board is not best for fingers and for feet, especially
with the large number of its sounds, many of which are not
called for in pedal bases, while others are constantly required. I
have therefore devised an enharmonic pedal key-hoard which is
sufficient and convenient for the pedal parts. The notes most
needed are the key-notes. These are ar- ^g. 4.-EKHAEMoiac p«,.l
ranged m front in a straight line and in Ket-boaed.

the order of the fifths ascending from left £b 7 gb t pT

to right. Behind these and in a higher
row and between the key-notes are the
major thirds of the keys in front and to
the left of each. Still above the thirds,
and directly behind the key-notes, are



Online LibraryJohn AlmonThe American journal of science and arts → online text (page 52 of 102)