Henri Arnaut de Zwolle(ca.1400, in Zwolle-1466 in Paris)
また、ヴェネツィアの音楽家で器楽に関する重要な論文の著者となった Silvestro di Ganassi dal Fontego(1492-1565)が、1542年に Viola da gambaに関する研究書として出版した”Regola Rubertina”と、1543年刊の”Lettione Seconda”にも、振動比に関して興味深い事柄があらわされています。
Silvestro di Ganassi dal Fontego(1492-1565)
Silvestro di Ganassi dal Fontego(1492-1565)Venice, 1543年頃
US 126848 A, US 126848A, US-A-126848, US126848 A, US126848A
発明者
C. F. Theodor Stedtway
IMPROVEMENT IN DUPLEX AGRAFFE SCALES FOR PIANO-FORTES.
UNInn STATES’ PATENT OFFICE.
G. F. THEODOR STEINWAY, 0F NEW YORK, N. Y., ASSIGNOR TO HIMSELF, .elli-BART STEINVAY, AND WILLIAM STEINWAY.
Speciiication forming part of Letters Patent No. 126,943, dated May 14, 187
To all whom it may concern:
Be it known that I, (l. I?. Trinonon S’rnnt WAY, of the city, county, and State of New York, have invented anew and Improved Duplex Agrai’e Scale for Piano-Fortes; and I do hereby declare the following to be a full, clear, and exact description thereof, which will enable those skilled in the art to make and use the saine, reference being had to the aecompanying drawing forming part ot this specification, which drawing represents a plan of a grand piano-forte with my improved scale.
My invention consists in brin ging the vibrations of that portion or’ the string which is situated between the agrade and the tuningpin, in proportion to those ot’ the main portion of the string, in such a manner that the tone produced by said a gratie section is brought in harmony with that of the main section, and thereby the purity and fullness of the tone of the instrument is materially increased, also,4
in bringing the longitudinal vibrations of that portion ot’ the string which is situated between the sounding-board bridge and the hitch-pin in proportion to the vibrations of the main section of the string, so that the sounds due to these longitudinal vibrations are brought in harmony with the tone ot the main section of the string, and the purity and fullness of the tone of the instrument is improved.
In order to enable others to understand my invention, I will here remark that the term scale77 of a piano-torte comprises the position of the strings side by side or above each other, their length and thickness and their tension; and my improvement is applicable to all stringed instruments in which the sounds are produced by the action ol hammers.
If the bass tones of a stringed hammer instrument are sounded -irom octave to octave toward the trcblea great diiierence appears in the effect of the various strings, according to their length, as far as the partial tones of the strings are concerned, which are duc to the spontaneous subdivisions of said strings in halves, quarters, eighths, sikteenths, 85o. rl’he longest duration ofthe vibrations and the highest quality’ to subdivide in partial tones is found in the strings between the contra C and the small c. Within these limits each string subdivides itseli` by the blows of the hammer and by the transverse vibrations due to the same in a large number of nodes whereby the so-called harmonic overtones are produced, and whereby the fundamental tone is rendered rich and brilliant. At the same time this portion of the strings, particularly, produces, by the longitudinal vibrations, a number of unharmonic side tones, making a whistling sound, which disturbs the purity of the tone. Both these qualities disappear as the height of the tone increases, so that the limit of producing a pure fundamental tone is found at a4, while it is in most cases desirable to obtain a clear tone from c5,- but the inherent firmness of the thick strings generally employed, and the great tension required on account of thickness prevents the string ot’ the above-named o5 to make the proper transverse vibrations due to the fundamental tone, and a division into partial tones is out of thc question. In order to eft’ect or promote the subdivision of the string and to produce the desired partial tones, I combine with that portion of the string which is situated between the tuning-pin a (see drawing) and the main agrafte b a secondary agratt’e, c, which supports the string and is placed at a distance from the main agrae corresponding to one of the above-named subdivisions of the main section d oi’ the stringthat is to say, at a distance equal to l, l, 15, or of the length of the main section, or to any combination ot’ these fractions. The main agrafte Z), which supports the string only at one point, allows the transverse vibrations to extend to that part of the string between the said agrafte and the tuning-pin, the vibration of this part being in a direction opposite to that of the main section of the string. By inserting the second agrafi’e c at a distance from the main agraffe equal to gf, gg, ,15, 517 or E13 of the length of the main section oi the string, the subdivision of the string into partial vibrations, and the consequent production of harinonic overtones is effected or promoted7 and a clear, strong, and brilliant tone is obtained up to the highest note.
In the drawing I have marked opposite to each tuning-pin the proportion existing between the distance of the two agra’es and the length of the main section of the string.
By allowing the vibration of the strin g to extend beyond the main agraie the durability of the string is materially increased, since by cutting oft` the vibration of the string at this bration of the strings, I avoid by supporting that portion of the string between the sounding-board bridge and the hitch-pin at distances from the outer bridge-pins equal to l, or 51T of the length of the main portion of each string, or kto any combination 0f these fractions. By the sounding-board bridge the continuation of the transverse vibrations must necessarily be interrupted, owing to the width of the bridge supporting the string, whereby these vibrations are ei’ectually stopped; but particularly With strings of’great thickness, as generally used in piano-fortes of recent construction, the longitudinal vibrations ofthe strings .extend to those portions which are situated between the kbridge and the hitchpins; and in order to avoid unharmonic tones due to these longitudinal vibrations I apply between the bridge and the hitch-pin g, under each string, a support, e, at a distance from the outer bridge-pinf, corresponding to T15, 3 1? or of the length of the main section d of the’ string, or to any combination of these fractions.
In the drawing I have marked opposite to each hitch-pin the proportion existing between the distance from the support c to the bridgepin and the length of the main section of the string. By these means the unharmonic tones due to the longitudinal vibrations ofthe strings are converted into harmonious tones, whichl being transmitted through. the bridge to the sounding-board reach the ear and strengthenl and enrich the fundamental vtone of the string, instead of disturbing the purity thereof, as heretofore. The supports c and e may be made of metal, ivory, or any other material capable of resisting the pressure of the string.
What I claim as new, and desire to secure by Letters Patent, is
l. rIhe arrangement, in a piano-forte, of a g series of successive strings, in each of which the vibrations of that portion situated between the agraie and tuning-pin are brought in har- Witnesses W. HAUFF, E. F. KASTENHUBER.
古い思い出話しで恐縮です。
ヴァイオリンの表板や裏板に見られる『巾接ぎ(はばはぎ)』より、概して チェロのそれは 大胆です。
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Wolfgang Boettcher(1935-2021)
Henri Arnaut de Zwolle(ca.1400, in Zwolle-1466 in Paris)
Henri Arnaut de Zwolle(ca.1400, in Zwolle-1466 in Paris)
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●9 Antonio Casini(1630-1690) Violin, Modena 1690年頃 
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Carlo Bergonzi(1683-1747) Violin, “Appleby” 1742年頃
Andreas Ferdinand Mayr(1693-1764) Violin, Salzburg 1750年頃
Tommaso Carcassi( worked 1747-1789) Violin, “EX STEINBERG” Firenze 1757年頃
Giovanni Battista Ceruti(1755-1817) Violin, “Ex Havemann” 1791年
「螺鈿紫檀五弦琵琶」700年～750年頃（全長108.1cm、最大幅30.9cm )
“Vihuela de arco” ( around the mid-16th century ) The collection of the Encarnación Monastery in Ávila.
Mandolin, Antonio Stradivari(ca.1644-1737) 1700年～1710年
Andrea Guarneri(1626-1698) Viola, “Josefowitz” 1690年頃
Andrea Guarneri(1626-1698) Viola, “Primrose” 1697年
Matthias Albani(1621-1673) Viola( 436mm )
Giovanni Francesco Leonpori( The work of a little-known 18th-century maker ) Viola, Rome 1762年頃
Matteo Goffriller(1659–1742) Cello, Venice 1710年頃 ( Paris, “COLLECTIONS DU MUSÉE” )
Rainer Leonhardt Cello, Mittenwald 2014年
Rainer Leonhardt Cello, Mittenwald 2014年 
Rainer Leonhardt Cello, Mittenwald 2014年
Gustav Franz Wurmer ( Stuttgart ) Cello, 1994年
そこには下の写真のように 両方のエンドブロック端の位置に35∼40 mmほどの フレッシュな割れが入っていました。
Rainer Leonhardt Cello, Mittenwald 2014年
因みに、このヴァイオリンは痕跡をつきあわせると 最初のエンドピン穴は割れた A- B ライン上の中心と表示した位置で、二重に書いた円の 小円の直径6ｍｍから 6.5mmで開けられていたと推測できます。
このように 表板の変形により生じた「逆反り ( warp )」は、最後に 裏板の割れを引き起こします。 
その参考として 撮影時点で割れは修復済みの状態ですが、ストラディバリと ヨーゼフ･ガルネリが製作したヴァイオリンに入った割れ痕を
Aegidius Klotz ( 1733-1805 ) Violin, Mittenwald 1790年頃
また、変形が緩慢に進行している場合は Ｆ字孔に段差が発生しやすいので、私は その確認をおすすめしています。
Cello 1930年頃
Cello 1930年頃
(左) Wilfried Leonhardt Cello, Mittenwald 1995年 ( F
Joseph Naomi Yokota ( 1960 – ) Cello, 2022年
Antonio Stradivari (ca.1644-1737 ) Violoncello “Stauffer – ex Cristiani” 1700年
Antonio Stradivari (ca.1644-1737 ) Violoncello “Stauffer – ex Cristiani” 1700年
Hendrik Jacobs (1639-1704) Violin, Amsterdam 1690年頃
Tommaso Carcassi ( Worked 1747-1789 ), Firenze 1786年
Ksh Holm, Cello / DENMARK, Copenhagen 1791年
Ksh Holm, Cello / DENMARK, Copenhagen 1791年
Ksh Holm, Cello / DENMARK, Copenhagen 1791年
Andrea Guarneri ( 1626-1698 ) Violin, Cremona 1658年
Andrea Guarneri ( 1626-1698 ) Violin, Cremona 1658年
Hendrik Jacobs (1639-1704) Violin, Amsterdam 1690年頃
Andrea Guarneri ( 1626-1698 ) Violin, Cremona 1686年
Carlo Antonio Testore ( 1693-1765 ) Violin, Milan 1740年頃
現代では‥ 少数派となった膜鳴型の弦楽器は、長い歴史の末に 今でも 民族楽器としてチベット地方、バルカン半島地域、北欧、エチオピアなどの北東アフリカ地域、そしてアジア地域などで 製作され 演奏に用いられています。
“Sgra-Snyan ( ダムニェン )” Tibetan lute, 全長 752mm
その “大転換”は、 敦煌郊外にある 4世紀半ばから穿ち始められた 莫高窟 ( ばっこうくつ ) 壁画に琵琶などがいくつも描かれていることなどから考えると、少なくとも 3世紀以前であったと推測できます。
例えば A部とB部 の差も そうですし、 ナットにあたる「乗絃」から上の揺れかたを左右する C部とD部 の角度の選び方も確信に満ちていると思われます。
その上、あたかも念を入れるように‥ 紫檀材で製作された 転手 ( 絃巻き = ペグ ) の配置も 海老尾の方から 左( P3 )・左( P4 )・右( P2 )・左( P5 )・右( P1 )の順で 強い非対称設定とされています。
私は TORO社のテールガットを本結び（ リーフノットまたはヘラクレスの結び ）で 長さの調整をして使用しています。弦楽器に取り付ける場合の技術的な熟練には数年を要しましたが、私はこの製品を使用していて今までほとんど不都合を感じたことがありません。
TORO 直径 No.230（ Contrabass G string ）
TORO 直径 No.220（ Viola tail gut ）
TORO 直径 No.200（ Violin tail gut ）
ここで反対側のガット端の工程に移ります。長さは おなじく 7.0mm位とします。
こちらも、こんな感じに加工します。
