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Publication numberUS904325 A
Publication typeGrant
Publication dateNov 17, 1908
Filing dateJun 28, 1907
Priority dateJun 28, 1907
Publication numberUS 904325 A, US 904325A, US-A-904325, US904325 A, US904325A
InventorsJames Heffernan
Original AssigneeJames Heffernan
Export CitationBiBTeX, EndNote, RefMan
External Links: USPTO, USPTO Assignment, Espacenet
Enharmonic musical instrument.
US 904325 A
Abstract  available in
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Claims  available in
Description  (OCR text may contain errors)

\ J. HBFFBRN'AN.' l mmmomo MUswALmaTBUMENT.

V- f i -u rL1duxox rx'LnD :um an, nofr.v 904,325. patented Nov.17,19os.

. s nanars-amm 1 a f 2J 456'? l., nr/aaunrnfrumnzynuu 11m Jb Jim c1 IIJ 116' Saa JAMES l-Il-Ft-liiiN-ih'. OF LEOMIXSTER, ENGLAN ENHARMONIC MUSICAL INSTRULIENT.

Specification of Lettera Patent.

Patented Nov. 17, 190B.

Application tiled June 28, 1907. Serial No. 381,382.

'I'u all whom it may concern:

lle it known that I, J.\.\ii:s llictfrizaszis", a :.uhjeet of llis Majesty the King of Great iiritiiin and Ireland, residing :it 3 The lleasattnce, Lenininster, count v of llereford, England, ltave invettted certiiin new and useful Improvements in llnharinonie Musical Instruments, of which the following is a specification, reference being had thereiii to the accompanytnj?y drawings.

This invention has reference to an impioveinetit in musical instruments, `tnv said imprint-nichts being applicable principally to iii-triiineiits such as the organ and piano` fortithai are irovided with a keyboard vri-ry ltev of which corresponds.- to a note. of determinate pitch; and inv improvements in their a iplicaton to such an instrument have for o iii-ct to enable. a performer to obtiiin therefrom harmonies of more perfect concord aud melodies of a juster intonation than have heretofore heen obtainable from lievi-d instruments ttined to the usual equally tempered scale, this result beinpr mon-aver obtained without tiiidtie complication of tho keyboard or multiplicity of lwvs. These ohjects nre in accordance with niv invention attained by assuming as the basis of in scale, not the octave, as has heretofore Jecn nstiiil. but tite interval usually known as tite twelfth, corresponding to that between middle (7 and the (i next but one nhove it, commonly called G in alt; and this interval is, in accordance with myA invention, divided into twenty-four equal intervals, which, as ii slightly tempered octave contains fifteen such intervals each neail)- ec ual to liiilf of a iiiinor tone, are hereina ter called qundeeimal senitones, niv improved scale being correspontlingly called a quindceinial scale. keyed imtsical instrument in accordance with niv invention will consequently comprise fifteen keys in cach octave instead of twelve keys as heretofore usual. As the musical notation ustiall v employed is not well suited to an in struinent provided with additional keys aeenrdina1r to tnv invention, i have moreover devised for the same a simplified and iinproved notation as herein set foi'th.

ln the accompanying;v drawings, Figure t Is n diagrammatic representation of my first arrangement. of keyboard corresponding to tho quindcciinal scale; Fi". is a diagraininatic representation o a. keyboard similar te the representation in Fig. t, havingI a compass of three octavos; Fig. 3 is a diagrammatic representation of u modified arrangement of a quindeciinal keyboard; Figs. 4, 5 and are. illustrations of my iinproved quindecinial iiotatieii. Fig. 7 is a diagram illustrative of the tuning of an instrument to the t uindeciinal `scale.

The naines o intervals, as fifths, ete. when herein employed, have their ordinary meanings unless modified h v the context.

The twelfth (mid. C te G in alt) hasthe ratio 1:3, and by taking logarithmically the 24th root of 3, the required qiiindceinial seinitone is found. The building tip of the major and minor thirds, tite fifths, and other intervals is set forth in the following table of tite qnindcciinal scale.

The coiniiioti logarithm of .'t is 0,-t77l12, and its 24th mrt is 0.01088, which is the. logarithm of t te quindecinial seniitone. 1n tite table it will he seen that this logarithm, by constant addition of itself gives rise to a series of lngarithins which, i v means of a table of logaritliins, arc converted into absoltite miinbers. 'lhese niiniheis are then omltiplied by 100 in order to get the. vibration nunihersof each interval with C taken at tot) vibrations per second. The a iproxiinzition of the vibration numbers to tiiose for just intonation is shown in tite last column of the table by -t- (plus) fersharpness and (minus) for fiatness.

It will be noticed in the table that the minor third (C to E), the tenth (mid. C to E in the fourth space of treble clef) and tht` twelfth (inid. C te G in alt) are iracticallv perfect. The major third (C to l) is only 0.56 per cent. too wide as compared with 0.70 per cent. too wide of the present (thiedecinial) mejor third, te which the quindeeitniil interval is therefore mitch superior. The fifth (C to G) is 0.65 per cent. too sharp (wide) and the octave the saine percentage too flat (narrow). 1 have carefully calenlated (and practically verified it on my violin) that this sharpness of the fifth is practitcnily equal to that always given to their fifthsin the tuning of the strinws of the violin by the violinists of a goed orchestra. Front these facts it follows, theoretically, that the mn'oi and minor triads of the quipdeeimal scale are almost perfect and a great improvement on the triads of thc ordinary (daodecinml) scale of 12 semitencs to an octave, with its flat fifths, wider major thirds, and with its minor thirds the harmony of which is prac-tilllfi lltl cally destroyed since in the. ordinary (duo decimal) tempered scale they are 0.90 per cent. too lat (narrow).

In the. quindecimal scale Each nilnor third Is to consist of 4 wniltones Il nl or Il Il H Il 5 ll Ilft i ts to constat ot' .l Il l Il Il Il tt nialor thirds 31 nitnor thirds lwettlh 2-t .seniltones minor lhlrds 41 major llilrds The results are shown in the following Table of the quuidecuaal scale.

t r I I I i Divfa- No. of Absolutel Just on Lopn i I Name ot trom soml- 'uhm number .Note www tnlona- ,um tone. l. l on. 1

` l intona I 1 I I Lion. i 0, ami t. C Lntson aniass i. 2 I 0.0111176 l. 3 (LUMH 4! naiss: l a 0.0mm t t 6' o inizs 7 i 0. litll'i B 0.15904 0 0.1720.' l0 0.10650 ll 0.211% 12 D 'LEM I3 0 2M Il 0.2km l5 0.2.5;'0 l0 OJHNH 17 0.33m 1B 0.35751 19 0.37772 N 0.30711) 2| 0. 41TH 22 (l. CITI 2J n. 45721 u amie :4.00 t remet La the last column of the above table the percentage deviation from just intonation is marked i or according as the tuning of the qnindecimal scale is sharp or flat with res ect tojust intonation.

ho qnnideeinial scale has 15 se iarate and distinct keynotes to the octave. it contains a new consonance, C A, which has approximately the ratio 4:7 and the inclusion of which in the musical scale was suggested by the German physicist l'lehnhohz more than 30 Years ago in his work, the Sensation of Tone."

The scinitone of the quindeeinial scale borders upon, but does not. transgress the ultimate limits of narrowness faid down by musicians, viz., it, or the difference between .a major and a minor third; and by the adoption of this scale all concords are rendered more perfect, and all diseords more definite than in the ordinary tempered scale of 12 soinitones to an octave.

The quindeeinml scalo is applicable to all musical instruments whatever be thel source or medium of vibration-string, wind, reed, plate, disk or fork. It is oven a licable to instruments of the violin type, wit. properly adjusted lengths of strings and appropriate tuning.

Fig. 1 illustrates my first application of the quindecinial scale, in major tones (of three quindeeimal scmitoiies each), and minor tones (of two quindeeinml semitones cach) and uindeeimal semitones, in accordance with tevibrationnumbers of the. table to the keyboards of the organ, harmoninin and pianoforte und such like instruments. The long, thin lines show the. white keys, and the short thick lilies show the black keys and the se|ni tones in a twelfth are numbered from t) to 24. 1n the drawing the order of succession of the seven intervals in tho key of C major is minor tone, major tone, cpiindeeiinal semitone; major tone tintervenmg); minor tone. major tone, quindecimal seiuitone and the quindeeinial semitone occurs between the 3rd and 4th, and between the 7th and Sth keys of the octave as in the ordinary scalo of C niajor. I have found, however. thatt-his arrangement is not suitable for the quindeeimal scale of 15 quindecimal semitones to the. octave, for the following reasons. Referring to the table of vibrations, it will be seen that--the fifth C to being too sharp (wide) by vibr. (.65) per 100 vi-` brations, and the octave, C to C, bein; r too flat (narrow) by vih. (.65) per 10U vibrations-they both combine to give a fourth G to C, or its equivalent C to l", which is 1l, vib. (1.3) per 100 vibrations too thit (narrow); and l" is therefore out of time with the tonic C. For this and other reasons-niusieal and mathematical-the key, I", must be relegated lo the black keys. This leaves room for the qnindecimal semitone to occur in its proper place between Eb and E, the minor am ma'or thirds above the. tonic C. With the km ll, there go out of the scale of the so-ealled major tone, F to G, and iis congener, Dto E, both of them ever too wide, and vet wider with 3 quindeeimal seiuitones, and both oriffinally begotten of the difference between a fifth and a fourth. ('l`h`iis:-

C 0-C F- F 0 In major made, tonte C A 1IA D- D E, minor A) There. only remains, within the com iass of a fifth from the tonic, the t uindecima tone, C to D, whereupon to build. 1t is made. up of 2 quindeciinal seinitoncs, and the next higher like interval is, D to Eb. There is then the quindeciiual selnitone, Eb to E, oecui'ring in its proper place between the minor and major thirds from the tonie, Fig. 2. We thus have the major third built up of tone, tone, quindeeinnil semitonez- From E, like synthesis iroeceds to G b two I l l l v I qinndecnnal tones, each of two qnmdeennal semitones, thus:-

(2) E--1 `#.-G. Combining these two syntlioses, we get (s) o..D..Ei E..F..G (Figi:

il tl lili) lltl tito

whereinthe synthesis of the fifth by minor and ma]or thirds is complete and symmetrical.

Tabla of ha 'internals of thc decode calc (white keys only.) See Figs. 2 and 3.

Number ol l l Notes. l Namo of interval. I qulndeelm nl senilwnes.

l C lo C ..1 Unison (1 t to D Second 2 Minor third.. I 4 Mnjer third.. Fourth (dlssonanl). i 7 Filth i) Minor idxlb 10 C lo AQ Sharp slxth 12 llehnhollx's consonance.

C lo 1l Nnlurnlovnlh 14 Octave v alters) ..1 L w l' lileeade (by whlte keys) .Jim

When hereinafter I use the term decade, as applied to the decade scale, it will be as the equivalent of the term octave (ratio 1 :2) of the )resent scale.

lt will be noticed that tho major sixth C to A, although it is concordent with the tonic does not occur in the white keys ol' the decade scale in Fig. 2. A is a major third above F and thereby follows F into the.

black keys. This form of keyboard is very suitable for the organ, harmonium, pianoforte, and such like instruments. rl`he long, light lines in Fig. 2 show the white keys, and the short, thick lines show the black keys, and the quindccimal semitencs in a decade are numbered from 0 to 15. The decade is equally divided into three major thirds, and each major third is closed by the quindceimal selnitonc.

The advantages of the decade scale are as follows (a) The practical perfection of the major and minor triads, c. g., C E G and C Eb G.

(b) Through having F# in the white keys, midway between E and G, it bridges over the "break" (from F to G) that always occuni between the natural fourth and ifth of the human voice in our present scale.

(c) It combines the major and lninor modes in one scale of 10 notes, whereby all relative minor keys are rendered unnecessar For example, each of the notes, C, E, ani A bears, in white keys only, both major and minor triads.

e s: o s A n, A c en ...uaor man. e a d. r. o u, lo a av....iunr mnd..

(d) The succession of' tone, tone semitone, bein Y repeated three times in the deeade C to i, the composer can think, and the ierformer can play in three tonica-viz., C, if. and Ab-hy using only white keys, t. e. without using accidental or black keys, unless the complexity of the theme requires them. The similarity of the arrangement of white ke s of the scale of C to that of the cognate sca es of E and Ab is indioatedbef low the diagrammatic portion `of .2..

(e) The succession of tones and quindecimal semtones for the -two cognate tonies E and Ab, being therein shown with the same white keys as those for the key of C, it follows that the keys necessary for any tonie are only those required for two other cognate tonics, each a major third above the precc ing one; and that, by learning the lingering of the 5 keys-C, C# D, D# and Eb the performer can pla in the tonic correspon( ing to any one of t 1e 15 quindecilnal sernitoncs of which the decade is madeu i. For instance the notes--white or blae 'wused for the decade scale of Tonic?. nrofdentlesl with those furl; andai D Fs.. M: 02,.. Gg.. n, lcv.. u n

By this means, the 30 different ingerings necessary for the 3() tonics, major and minor, at present in use (l natural, 7 Sharps, and 7 flats 15, in both major and minor) are reduced to 5. Such are the advantages of the decade scale.

Now, by referring to the drawing of the decade scale in Fig. 2, it will be seen that among the white keys of the decade scale. there are four, viz., Eb, F, Ab, and A-to which i have been compelled to gne their )resent accidental signatures, and that. this is not only confusing in the key of C, but would become worse in other keys, 4il our present mode of writing music were applied to the decade scale. It would, in fact, gh c rise to irremediable confusion in any score. I obviate this difficulty by the followingr mode of writing music for the decade scale.

'The five lines of the present treble clef and of the bass clef to be, each, replaced by a singie line called the treble or bass clefine accordin to its key-signature--the key signature o the bass clef Ime being uniformly two decades lower than that of the treble. The middle C of the pianoforte to be written simply C, and its decade keys abo-i e and below to be respecth ely written C', C and (l C and so on throughout the whole keyboard. Nie other letters are used on the lines. These clef-lines are to be written-not the literal notes nor black dots, bulthe number of quindecimal semitones contained in the .required interval as shown. For instance the triad C E G would be written in both notationsas in Fig. 5 and the triad C El' G in both notations as in Fig. G a fifth being always 9, a major third 5, and a minor third 4 qumdecimal semitones alim-e the tonie which is denoted by zero.

Leger lines above or below the treble or bass clef-lines are to be used for decades` above or below the literal key signature.

The numerals upon the clef-lines are to indieet@ the num-ber of quindeeiuisl seinitenss above' the literal tome and the numerals belowthe ,clefdines tomdieato the number IIN Hifi


.C (instead of CI) of semitones above the lower decade note of the literal tonic. In Fig. I give three decades, first in the ordinary notation, and then in the numerals ef the semitones of the deeade scale. From these three examples it will be seen that the numeral for the same interval is always constant. If, in the first exam ile, I had written the tonic as C there woulil be no need of a leger line; and if, in the third example, l had written the tonie as the numerals would be under instead of bein upon the clef line. lt will also be seen t. iat the numerals will always be the saine for the same interval no f matter how the key-signature of the tonic may change. Otherwise stated, this means that b v merely changing the key-signature of the clef-line, music, thus numerically written in quindeeimal semitones, is at once transposed into another key.

Fig. 3 is giicn as an example of a keyboard in one of sc.eral possible forms in which the l5 rpiindeeiinal seinitones of the interval C to mav be arranged. The decade scale as shown in Fig. 2 herein and hereinafter de scribed, is however, the inost practicable and natural, and I therefore now more particulailv describe the arran 'ement of flic white and black linger-kava ofwthe decade scale in Fig. .2 of the new lm vboard for the organ, harmonium and pianoforte, bv comparing it. willi the arrangement of the while and black notes of the keyboard in present use.

lt will be noticed that thel() white fingerkeys of the decade scale in Fig. 2 cover the salue interval, viz., C to C', as the 8 white linger-kevs of the octave of the scale at present usually employed, and that there are l5 t nindeciinal seniitones in the former, and l2 duodeeimal semitones in the latter. Also, that there are in Fig. L', l() white and (l black finger-keys instead of 8 white and 5 black finger-keys as heretofore lisual.

l`he material, size, shape, mode of fitting, and workin' appliances of the keys in the keyboard of`the new decade scale can be the saine as any in use at present in the keyboards of the organ, harmoniuni and pianoforte; but the timing and the arraii ement of white and black finger-keys are to e different. The new timing is hereafter described.

lt will he noticed that the first six notes (white and black) of the decade scale in Fig. (C to E), embrace two qnindecimal tones and one quindeciinal seinitoiie, and that each of these two tones,vir.. C to D and D to Eb, is divided into two t uindeciinal seniitones b v a black key, viz., C and D# respectivelyand that the first six notes (C to E) embrace the interval of a major third divided into 5 quindecimal seinitones. Also that the remainder of the decade scale is made up of other two major thirds, the sub-division of which is exactl similar to that of the first--tlie last nete oi'each major third being thefirst note of the major third next following. In fact the decade scale in Fig. 2 is made up of 3 major thirds each of which is similarly divided into three intervals the first and second of which contain two qiiindecimal seinitoncs and the third a quindeeimal semitone. In the decade scale, as shown in Fig. 2 the notes to which I have iven the literal names of C# and Ab may a so be resniectivel)r named Db and G# if that should be convenient to the maker of the new keyboard.

Fia. 7 illustrates the mode of tuning a twelfth freni middle Cto G in alt. iii .24 equal semitones or (i minor thirds of 4 scinitones each.

The )roccdure is as follows:-

(l) he first step is to tune a perfect twelfthhnid. C to G in alt.) which should be divided inte 6 perfect minor thirds. The minor thirds should be tuned u wards from C and downwards from (i as indicated bv thi` arrows and they should be quite cqiial and of perfect intonation-the one care of the tuner being that they are not in any de rree too narrow like the tempered minor thiri sof the ordinary scale of the pianoforte. 'lht` tuner will have three checks in the timing of row (l)see Fig. 7. First, thc upward tuning from C and the downward timing from G must both nieetin A# firing perfect and equal minor thirds throng tout. Second, the tonic C and E will ive the perfect. concord of the tenth (niiddli` (Y to la in the fourth space of treble clef). yThird, the saine pei'- fect concord of the tenth will be found between llb and (.i. The tunin f of the six ierfeet minor thirds in a twelfti in row (1 of Fig. 7 is the foundation of all that followsl and cannet be too carefully performed.

(2) The next step is to tune G a sharp fifth above the tonic (l as indicated by the arrow in Fig. 7. I have calculated this sharpness` as il vih. per 100 vibr. (0.65 per cent. in tab e of vibrations) and I have also found that it is, mathematically, about equal tothe degree of sharpness which is always given to their fifths in the tuning of the violinista of a good orchestra. ln nactiee it is that degrec of sharpness which gives the fifth briliancy without roughness; and the exact amount of sharpness will, after a few trials, become familiar to the tuner's car. From (l the tuner will tune upwards and downwards by perfect minor thirds-saine as in row (1)-as indicated by the arrows in Fie. 7. All the notes in row (2) can be eheckeiihv soundin each of them with the proper notes of row (ll), and I have marked in row (2) of Fig. 7 with a double cross (x x) those which should ive a rather flat (narrow) octave, and witili a single cross (x) those which should give a sharp (violin) fifth with the corresponding notes of row (l). For instance in row (2? we have Cif E and G which should be a rati er narrow octave below Cit i E and G of row (1). So also, in row (2), the notes Bb, D and F will be a sharp (violin) fifth above Eb, Gb and Ai? of 'row (l). Besides these checks there is also the check of the perfect tenth (i, e. twenty quindecimal semltones) which will always be found between the first and last notes of row (2)-C and F--and also between the first and last notes of the two following rows-z`. e. row (3) and row (4).

(3) The third and fourth steps of the tuning are exactly similar to the second. For instance, in row (3) the tuner tunes B a sharp (violin) fifth above E in row (2), and the other notes in row (3) are got by erfect minor thirds, upwards and downwar s from the B thus found. In row (3) the notes D and F are marked with a double cross (X x) to indicate that they can he cheeked as givin narrow octavos with the D and F of row (2 So also, in row (3), the notes Ab, Dl# and Flr are marked with a sin le cross (x) to show that thev can be checke by their giving sharp (violin) fifths with C, G, and Bb of row (2). Besides these three checks there is also the check of the perfect tenth (20 uindecimal semitones) between the first an last notes of row (3) viz. D and F.

(4) In the fourth (and final) step of the tunin A in row (4) is tuned a sha (violin) fifth a ove D in row (3): and the ot er notes are tuned, as before, by erfect minor thirds, u wards and downwar s from A. In row (f) the notes D, F C, Eb and Gb are each marked with a double cross (x x) for check by iving a narrow octa've with the notes D? anfIF 1n row (3) and with C, El; and Gb of row (l). There is also in row (4) the check of the erfect tenth (20 quindecimal semitones) )etween its first and last notes Dfi and Gb.

'Ihe tuner will remember that the ser uence of successive fifths in the uindecimal scale is C, G, D, Ai?, E# (F) an Bi? (C) as conipared with C, G, D, A, E and B of the scale at resent in use.

iat I claim is:- 1. In a musical instrument, a keyboard comprising keys, and sources of sound adapted to be operated by said keys and tuned in such manner that the musical interval between any two successive keys is one twentyfourth of the interval known as a twelfth.

2. In a musical instrument, a keyboard consisting of successive grou s each comprisin five keys whereof the irst'third and ifth eys are long, while the second and fourth keys are short, and a series of sources of sound adapted to be operated by said keys and so tuned that the musical interval between any two adjacent members of said series is equal to one twenty-fourth of the interval commonly known as a twelfth.

In witness whereof I have hereunto set my hand in presence of two witnesses.




It iu hereby ccrtiilcd that iuLcttcrslntcntNo.90-i,32,gruntodNovember17,1908,

upon the application of Juxnca llcIlL-runn. of Leominster, England, for nn improvemvnt iu "Eulmrmonic Musical Instruments, un error appt-nrs in the printed specilcaltinn requiring corrccliun ns follows: In linea 80-83, pago 3, in tho fourth lino nfthn tabulation G nud Bt# should rcml Gb und Bb; und tlmt. tho said Lottcrn lntcnt should bo rend with this correction therein that; the sumo muy conform z lo thu record of the cnsc in tho Pntvnt Oflicc.

Signed mul scaled this 20th duy of Junuury, A. D., 1909.


Acting Commissioner of Iutcnta.

Referenced by
Citing PatentFiling datePublication dateApplicantTitle
US3501849 *Nov 17, 1966Mar 24, 1970Olsen Mildred EMethod and device for teaching typing and language skills
US5306865 *Dec 18, 1989Apr 26, 1994Meta-C Corp.Electronic keyboard musical instrument or tone generator employing Modified Eastern Music Tru-Scale Octave Transformation to avoid overtone collisions
US5874685 *Aug 15, 1997Feb 23, 1999Ellis; James F.Reduction of longitudinal modes in musical instruments strings
Cooperative ClassificationG10C3/12