8/2/2019 Torno a Pedal II
http://slidepdf.com/reader/full/torno-a-pedal-ii 1/8
D
8/2/2019 Torno a Pedal II
http://slidepdf.com/reader/full/torno-a-pedal-ii 2/8
Dl`}I
} ndd ajgnk whjk I wjk} }l sibf zs oy mnzgh/
}jq Qnbhjdd n} }hj jkm l` hjq `qjrhonk yjnq
n} blddjgj+ Wj hnm ezr} ̀ ikirhjm dlnmikg hjq
ajdlkgikgr whjk I rsl}}jm n sidj l` sikj = x =r
nkm rzbh ik n kjnqay mzosr}jq+
—Whn}’r ndd }hn} wllm<‟ I nrfjm hjq+
—]hjy’qj/ldm/dl`}r/`qlo/sjlsdj’r/mlqo/qllor$/
Mnm$/}hjy’qj/}qnrh/klw/ik/}hj/mzosr}jq/sdjnrj/
dj}’r/gl.‟ rhj rnim$ rikfikg n di}}dj ik hjq rjn}+ Hjq
`qijkmr nkm bdnrron}jr wjqj ndd nqlzkm$ nkm I rzm/
mjkdy qjndiujm }hn} }hir wnr n sjq`jb} lsslq}zki}y
}l mjolkr}qn}j oy blkbjqk `lq }hj jkpiqlkojk}+
Wlzdmk’} rhj aj sqlzm.
—Dj}’r gl }nfj n dllf+ ]hjy jpjk hnpj n azkbh
l` bnqqingj ald}r wi}h }hjo. I blzdm onfj n }qjn/
mdj dn}hj ̀ qlo ndd }hir.‟
—I}’r/}qnrh/ik/n/mzosr}jq$/Mnm$/dj}’r/gl/klw+
Sdjnrj.‟ rhj rnim$ szddikg n rwjn}rhiq} lpjq hjq `nbj
nkm rikfikg jpjk dlwjq+ I gzjrr }hj rzk wnr al}h/
jqikg hjq+
—Bloj lk. Dj}’r rhlw jpjqylkj hlw wj mlk’}
dj} wllm gl }l wnr}j.‟ I rnim nr I bdioajm zs ik}l
}hj mzosr}jq nkm ajgnk szddikg ldm siuun alxjr
l`` }hj }ioajqr+ Whn} n }qjnrzqj. Nkm ajr} l` ndd$
ay Qly Zkmjqhidd
Qly Zkmjqhidd ir }hj hlr} l` }hj }jdjpirilk rjqijr$ !]hj Wllmwqigh}'r Rhls$! klw bjdjaqn}ikg hir }wjk}ij}h yjnq
l` rzapjqripj wllmwlqfikg lk szadib ]P+ Hj ir }hj nz}hlq l` ̀ ipj allfr lk }qnmi}ilknd wllmwlqfikg$nkm ̀ lq }jk yjnqr hj wnr onr}jq hlzrjwqigh} n} Bldlkind Widdinorazqg+
Hj }qnpjdr jx}jkripjdy$ }jnbhikg nkm r}zmyikg }hj }jbhkldlgy l` }hj sqj/ikmzr}qind jqn+
n}hj
]hj hlr} l` SAR’ }hj Wllmwqigh}’r Rhlsazidmr n `ll}/slwjqjm dn}hj nkm eigrnw+Ay zrikg qjbybdjm dzoajq hj hjdsr }hj jkpiqlkojk}$ nmmr rloj
‘kjw’ j~zisojk} }l hir rhls nkm iosqjrrjr hir mnzgh}jq+
`qlo n
S h l } l a y N d S n q q i r h
8/2/2019 Torno a Pedal II
http://slidepdf.com/reader/full/torno-a-pedal-ii 3/8
whjk I hnm ̀ ikirhjm dlnm/
ikg }hj }ioajqr$ I dllfjm
n} Qnbhjdd nkm rnw }hn}
hjq sqimj ik hjq ldm onk hnm olpjm hjq
}l }jnqr. Rloj}iojr jpjk I ml }hikgr qigh}+
]hj @qnoj nkm }hj @dywhjjd
]hj rndpngjm }ioajq wnr sjq`jb} `lq oy
kjw }qjnmdj dn}hj mjrigk+ ]hir kjw dn}hj
wlzdm aj ozbh riosdjq }hnk oy ldm lkj$
zrikg nk —ikalnqm‟ ̀ dywhjjd wi}h }hj blk/
kjb}ikg qlm n}}nbhjm }l i}r ̀ nbj$ qn}hjq }hnk
}l n bqnkfrhn`} }hn} wnr mi``ibzd} }l onfj
nkm hnqm }l qjsniq+ I} wlzdm ndrl hnpj n eig/
rnw n}}nbhojk} nkm$ olr} ioslq}nk}$ wlzdm
aj n wllmwlqfikg }lld }hn} fimr blzdm
onfj ̀ lq }hjorjdpjr+
Nr I wnr }l aj }hj sqionqy fim zrikg }hir
dn}hj$ i} hnm }l bloj nsnq} nkm snbf zs
rondd jklzgh `lq jnry }qnpjd+ ]hj `qnoj
l` oy dn}hj ir lkdy =3! dlkg ̀ lq }wl qjn/
rlkr+ @iqr}$ }hjrj djkg}hr nqj jnrijq }l snbf
whjk }qnpjdikg$ rjblkm$ }hj rbnpjkgjm 1
x =r wjqj 83! dlkg+ Ylz bnk bjq}nikdy onfj
i} nr }ndd nkm nr dlkg nr ylz wnk}$ }hj lkdy
jrrjk}ind ir n bdjnq sn}h ̀ lq }hj mqipj ajd}
aj}wjjk }hj ̀ dywhjjd nkm }hj mqipjk szd/
djy+ I ndrl zrjm olq}irj/nkm/}jklk elik}r
}l blkkjb} }hj }hqjj D/rhnsjm ̀ qnojr nkm}hjiq aqnbjr rl I blzdm ~zibfdy fklbf }hjo
nsnq}+ ]hjy blzdm ezr} nr jnridy aj blk/
Rbhjmzdj l` On}jqindr ‡ @ll} Slwjqjm Dn}hj
Kl+ D}q+ I}jo Miojkrilkr ] W D On}jqind1 N Djgr 2> ⁍ 1! x 2> ⁍ 1! x 23> ⁍ 1!% Sikj> A @ll} >> ⁍ 1! x 2> ⁍ 1! x 19> ⁍ 1! Sikj1 B @jj} 2> ⁍ 1! x 2> ⁍ 1! x 19> ⁍ 1! Sikj1 M R}qj}bhjqr >> ⁍ 1! x 2> ⁍ 1! x =3! Sikj1 J Dn}hj ajm qnidr >> ⁍ 1! x 2> ⁍ 1! x =3! Sikj1 @ Aqnbjr >> ⁍ 1! x 2> ⁍ 1! x 2=> ⁍ 8!% Sikj> G Hjnmr}lbf qjnq >> ⁍ 1! x 2> ⁍ 1! x 20!% Sikj> H Hjnmr}lbf ̀qlk} >> ⁍ 1! x 2> ⁍ 1! x >>> ⁍ 1! Sikj
> I Hjnmr}lbf szddjy 12 ⁍ 8! min+ x 2! Sikj> E ]nidr}lbf 2> ⁍ 1! x 2> ⁍ 1! x >1! Sikj> F ]nidr}lbf wjmgj 7 ⁍ 8! x >> ⁍ 8! x 0! Sikj> D ]lld qjr} 2 ⁍ =! x 22 ⁍ 8! x 0! Sikj> O ]lld qjr} anrj 2 ⁍ =! x =! x 8! Sikj> K Gzimj adlbf 1> ⁍ 1! x 1> ⁍ 1! x 2> ⁍ =! Sikj> L Dlbfikg snkjd 2 ⁍ =! x 1> ⁍ 1! x :> ⁍ 1! Sikj0 S @dywhjjd 2 ⁍ =! x 7> ⁍ 1! x 11> ⁍ 1! Sikj2 ^ @dywhjjd >> ⁍ 1! x 7> ⁍ 1! x 11> ⁍ 1! Sikj> Q ]ij qlm 2 ⁍ =! x >> ⁍ 1! x >2! Sikj> R ]qjnmdj 2 ⁍ =! x 2> ⁍ 1! x 19! Sikj> ] Blkkjb}ikg rsnbjq 2 ⁍ =! x >> ⁍ 1! x >> ⁍ 1! Sikj%Djkg}h ikbdzmjr }jklkr+
Eigrnw> Z ]nadj 2 ⁍ =! x 9! x 12! Sikj
> P @qlk} aqnbj >> ⁍ 1! x 1! x >>> ⁍ 1! Sikj> W Anbf aqnbj >> ⁍ 1! x 1> ⁍ =! x >8! Sikj> X Al}}lo qnid >> ⁍ 1! x 2! x 11! Sikj1 Y Nqor > ⁍ 1! x 1! x 11! Lnf > U Nqon}zqj dikf 2 ⁍ =! x >> ⁍ =! x => ⁍ =! Sikj> NN Ikmjx adlbf 2 ⁍ =! x 1> ⁍ 1! x 1> ⁍ 1! Sikj> AA Dlbfikg snkjd 2 ⁍ =! x 1> ⁍ 1! x :> ⁍ 1! Sikj
HnqmwnqjDn}hj=/ > ⁍ 1! r}ls blddnqr=/ > ⁍ 1! }hqzr} ajnqikgr>/ > ⁍ 1! ̀ jkmjq wnrhjq>/ > ⁍ 1! x 20! r}jjd qlm (nxdj$mqipj & mjnm bjk}jq$ bqnkf)0/ ">1 x =! wllm rbqjwr ̀ lq n}}nbhikg r}qj}bhjqr }l ̀ jj}
=/ 0! x2
⁍ 8! bnqqingj ald}r$kz}r nkm wnrhjqr1/ 2! x 2 ⁍ 8! bnqqingj ald}r blkkjb} }ij qlm$whjjd nkm }qjnmdj>/ 2! !]! hikgj ̀ lq }qjnmdj
Eigrnw1/ 2> ⁍ 1! x 2 ⁍ =! jyj min+x 2 ⁍ >0! }hqjnm$jyj ald}r>/ 2 ⁍ >0! }hqjnm x 1> ⁍ 8! }zqkazbfdj1/ > ⁍ 1! aqlkuj rdjjpj ajnqikg (rnwk ik}l }wl > ⁍ 1! djkg}hr)1/ >> ⁍ 1! djkg}hr l` > ⁍ 1! rhn`}1/ Blsikg rnw jkmr>/ 0! x > ⁍ =! ald}$wikg kz} nkm wnrhjqr `lq olzk}ikg rnw+>/ 2> ⁍ 1! ojkmikg sdn}j> > ⁍ 1! }hqzr} ajnqikg
N
A
B
M
H
G
@
J
IE
F
D
S
LK
O
^Q
R
]
NJ
S
S
^
Mjnmbjk}jq
Mqipjbjk}jq
!]!,r}qnshikgj
Ajnqikgr ikhjnmr}lbf
Rhn`} dlbfrik szddjy
Rhn`} dlbfrlk rhn`}
Rhn`}
0! x 2,8! bnqqingjald}
0! x >, =!ald}
]hj ̀ qnoj ir }hj jnrijr} snq} l` }hj onbhikj+Jrrjk}inddy }hj ̀ qnoj ir }hqjj D/rhnsjm ̀ qnojr$}wl 1x= anrj sdn}jr nkm }wl 1x= aqnbjr+]hj}wl lz}rimj `qnojr nqj onmj `qlo }wl =x=slr}r$ nkm lkj 1x= wi}h }jklkr n} al}h jkmr+]hj}ls l` }hj zsqigh} =x= ir qnaaj}jm lk al}h rimjr}l ̀ lqo nk lsjk aqimdj elik} wi}h }hj }ls aqnbjr+]hj ̀ dywhjjd ̀ qnoj ir onmj l` 1x=r+
I d d z r } q n } i l k r a y E i o
R } z n q m
8/2/2019 Torno a Pedal II
http://slidepdf.com/reader/full/torno-a-pedal-ii 4/8
kjb}jm wi}h rbqjwr lq ald}r nkm n}}nbhjm
sjqonkjk}dy+
Ik }hj snr}$ I hnpj onmj dn}hj ̀ dywhjjdr
difj wnglk whjjdr$ wi}h hzar$ rslfjr$ ̀ jd/
dlwr nkm rzbh+ Nd}hlzgh }hjy dllf kibj$
}hjy wlqf kl aj}}jq }hnk }hir rnkmwibhjm
mirb onmj ̀ qlo > x 8 nkm 1 x 8 sikj+ Rikbj
n ̀ ikirhjm —jigh}/ikbh‟ alnqm ir 7> ⁍ 1! wimj$
}hqjj l` }hjo dnim rimj ay rimj widd gipj ylz
n 11> ⁍ 1!/wimj }l}nd+ Ajbnzrj }hir ir nr wimj
nr ylz bnk gj}$ }hn} gipjr ylz }hj minoj/
}jq l` }hj whjjd$ nkm }hj djkg}hr ylz’dd
kjjm ̀ lq }hj kikj alnqmr l` }hj rnkmwibh+]hj ̀ dywhjjd hnr }l aj hjnpy rl i} widd
r}lqj jkjqgy$ nkm andnkbjm rl i} wlk’} rhnfj
}hj dn}hj nalz} nr i} rsikr+ N 2!/}hibf rldim
mirb l` jpjk }hj digh}jr} sikj widd aj hjnpy
jklzgh$ rl sz} ylzq jkjqgy ik}l gj}}ikg
}hj whjjd andnkbjm+ I` ylz hnpj nky alnqmr
}hn} nqj hjnpijq }hnk }hj l}hjqr$ }qy }l mir/
}qiaz}j }hjo ik }hj rnkmwibh }l bqjn}j nk
jpjk andnkbj nqlzkm }hj bjk}jq+ Sny n}/
}jk}ilk n} }hir slik} nkm ylz wlk’} hnpj
}l n}}nbh nky wjigh}r dn}jq lk+
R}nq} wi}h }hj }hqjj 1 x 8r }hn} widd
aj }hj ̀ iddikg l` ylzq alnqm rnkmwibh$ rnw/
ikg }hjo }l djkg}h nkm }hjk nrrjoadikg
}hjo rimj ay rimj ik}l n 11> ⁍ 1! r~znqj+ @ikm
}hj bjk}jq l` }hj r~znqj ay blkkjb}ikg ls/
slri}j blqkjqr wi}h ik}jqrjb}ikg minglknd
dikjr nkm }hjk mqnw }hj dnqgjr} biqbdj
ylz bnk `i} ik }hj r~znqj zrikg }qnoojd
slik}r lq n r}ibf wi}h hldjr ik i}+ I zrjm n
1> >,1! min+ dnoikn}jm `qlo 2, =! x 7 >,1!nkm > >,1!x 7 >,1!
alnqmr
Ajnqikgr ikrj}ik}l al}h rimjrl` hjnmr}lbf
Ajnqikgrikrj}
ik}l whjjdR}lsblddnq
R}lsblddnq
!]! hikgj
rjbzqjr sjmnd
2, =! 2 >,1! =! > >,1! 2 >,1! 2
, =!
> >,1!
10!
=3!
2 >,1!
12 >,1!
2 >,1!
27 >,1!
> >,1!2 >,1!
12 >,1!
2 >,1!
27 >,1!
: >,1! : >,1!
2 >,1! 2 >,1!11 >,1!
19 >,1!
> >,1!
1 >,1!
> >,1!
=!
0!
2 2,8!
2, =!
2!
> >,8! x 7 ,8!hldj ik
}nidr}lbf$>,8! nalpj
al}}lo jmgjl` qnidr+ ]nsjq
}l >! lkl}hjq rimj
7 ,8!
>,1!x 1 2, =!mjnm bjk}jq
R}ls blddnqrikrj} ik}l szddjy
> >,1!>, =!2!
=!
BD
=!
BDBD: >,1!
2 >, =!
2, =!
2, =!2 2,8!
7 >, =!2, =!8!
1 >,1!
2,8! x :! rdl} ik }lld qjr} anrj
`lq rjbzqikg wi}hald} nkm wikgkz} 0 >,1!
: >,1!
>,1! >,1!1 >,1!
0!2, =!
> >,8!
=!> >,1!BD
BD
Qlsj
]lld qjr} ]nidr}lbf
Jdjpn}ilk Sql`idj
RzssdijrAjnqikg Mir}qiaz}lqr Ikb+:>2/70>/3800: ‡ Hjio rjndjm ajnqikgr$ i}jo "Q@8/>8/>1SS$-8+:3 jnbh+
Gqnikgjq www+Gqnikgjq+blo$lq bhjbfshlkj allf ̀ lq dlbnd aqnkbh=/ Rhn`} blddnqr$ I}jo " 1X:08$>+98,sfg+l` 2+
I }qioojm }hj bjk}jq l` }hj `dywhjjd rnkmwibh }l n bdlrj lb}nglk$ }hjk n}}nbhjm lkj rimj nkm blk}ikzjm }l rhnsj }hj }wlsijbjr+ I }hjk n}}nbhjm }hj l}hjq rimj nkm wlqfjm }hj whldj `dywhjjd }l i}r zd}ion}jqlzkm rhnsj+
Ajikg n ̀ iqo ajdijpjq ik hnkmy rbqnsr$ I wnr nadj }l zrj}wl `ndd/l`` sijbj }l hjds oj r~znqj zs }hj rhn`} }l }hjwhjjd$ }hjk onqf }hj ajnqikg dlbn}ilk lk }hj whjjd+
8/2/2019 Torno a Pedal II
http://slidepdf.com/reader/full/torno-a-pedal-ii 5/8
}hik/adnmjm }zqkikg rnw }l bz} }hj biq/
bdj$ az} ylz bnk ndrl onfj n rjqijr l` bdlrj
bz}r wi}h n qjgzdnq snkjd rnw nkm }hjk bhir/jd nkm rhnpj mlwk }l }hj dikj+
Ajbnzrj jnbh l` }hj }hqjj dnyjqr ik }hj
`dywhjjd widd aj l``rj} 03 mjgqjjr ̀ qlo }hj
l}hjqr$ }hj gqnik lk }hj jmgj l` }hj nr/
rjoadjm whjjd ir glikg }l aj hjnmjm jpjqy
whibh wny nkm blosdibn}j roll}hikg wi}h
sqlsjq jmgj }lldr+ ]hjqj`lqj$ I zqgj ylz }l
aqikg }hj oimmdj dnyjq l` }hj rnkmwibh }qzj
}l n biqbdj aj`lqj n}}nbhikg nk lz}jq dnyjq
wi}h rdn}hjqr l` gdzj nkm `ikirhikg knidr+
Ylz bnk }hjk aqikg }hj lz}jq dnyjqr }qzj
}l }hj ikkjq biqbdj wi}h n oikiozo l` bzqr/
ikg+
Olzk}ikg nkm ]qzikg
Hnpikg }nfjk bnqj }l onfj n andnkbjm
whjjd$ ylz kjjm klw }l hnkg i} }qzj lk
}hj nxdj+ @ikm }hj bjk}jq l` }hj mirb ay qj/
sjn}jmdy rwikgikg nqbr ̀ qlo }hj lz}rimj
jmgj wi}h }hj }qnoojd lq l}hjq r}ibf ylz
zrjm }l mqnw }hj lqigiknd minoj}jq+ ]hj
bjk}jq l` }hjrj nqbr ir }hj bjk}jq l` ylzq
whjjd+ I zrjm }wl bhjns }hqzr} andd ajnq/ikgr ik }hj whjjd$ ndigkjm nr ̀ lddlwr5
‡ Rj} nk jxsnkripj ai} rl }hn} i} widd
alqj n rkzg hldj `lq }hj ajnqikg ylz ik/
}jkm }l zrj$ }jr}ikg i} lk n rbqns sijbj }l
aj rzqj+ Alqj ik}l }hj bjk}jq onqf ezr} mjjsjklzgh }l ikrj} }hj ajnqikg+
‡ Klw gj} n 9 ⁍ >0! nzgjq nkm alqj }hj
qjr} l` }hj wny }hqlzgh }hj whjjd+ (Nr nd/
wnyr$ i}’r n dl} jnrijq }l alqj }hj dnqgjq mi/
noj}jq hldj ̀ iqr} nkm }hjk bjk}jq }hj rondd/
jq hldj wi}hik i} }hnk i} ir }l qjpjqrj }hj
sqlbjrr+)
]hj laejb} klw ir }l ikrj} }hj rjblkm
ajnqikg lk }hj lsslri}j ̀ nbj rl }hn} }hj
whjjd widd kl} wlaadj lk }hj rhn`}+ Jnry5
‡ Ikrjq} }hj `iqr} ajnqikg ik i}r rlbfj}
nkm rdimj n djkg}h l` }hj > ⁍ 1! rhn`}ikg }hqlzgh
i}+
‡ Dny }hj whjjd wi}h }hir ̀ iqr} ajnqikg/
rimj mlwk+ Rdis }hj rjblkm ajnqikg lpjq
}hj rhn`} rl i} rdimjr mlwk lk}l }hj zssjq
`nbj+
‡ Ajbnzrj }hj 9 ⁍ >0! hldj jx}jkmikg
}hqlzgh }hj whjjd ir dnqgjq }hnk }hj rhn`}$
ylz hnpj jklzgh sdny }l szrh }hj rhn`}
ik}l n sqjbirjdy r~znqj qjdn}ilkrhis wi}h
}hj ̀ nbj l` }hj whjjd+ Bhjbf ndd nqlzkm
}hj nxdj rhn`} wi}h rjpjqnd r~znqjr n} lkbj$nkm whjk ylz hnpj i} ezr} qigh}$ bnqj`zddy
}qnbj nqlzkm }hj rjblkm ajnqikg+
‡ Qjolpj }hj ajnqikg nkm }hj rhn`}
nkm bnqpj lz} }hj rlbfj} `lq }hj ajnqikg
wi}h glzgjr nkm bhirjdr+ Jpjk i` ylz ̀ ikmylz nqj n di}}dj lz} l` r~znqj$ ylz bnk blq/
qjb} }hj on}}jq wi}h rhior nkm rbqjwr
nqlzkm }hj rimjr l` }hj ajnqikg+
Wi}h }hj whjjd klw qzkkikg lk i}r
rhn`}$ ylz bnk ̀ zq}hjq andnkbj nkm }qzj i}
ay hldmikg }hj rhn`} ik n pirj nkm rsikkikg
}hj whjjd+ I} mljrk’} kjjm }l rsik difj }hj
whjjd lk n qnbikg aifj$ ezr} rl i} mljrk’}
wlaadj nkm rhnfj olqj }hnk ylz ml+ I zrjm
}hj }wl }jj}h l` n olq}irikg gnzgj }l dny
lz} }hj 2 ⁍ 8! gqllpj ̀ lq }hj mqipj blqm }hn}
gljr ndd }hj wny nqlzkm }hj whjjd+ Ik }hj/
lqy$ ylz blzdm }zqk }hir gqllpj ik}l }hj sj/
qishjqy l` }hj whjjd nr i} rsikr$ az} blk/
rimjqikg }hj gqnik bhnkgjr$ ylz’qj aj}}jq
l`` bnqpikg+
]hj `iknd `ikngdikg wi}h }hj whjjd
ikpldpjr olzk}ikg i} r~znqjdy lk }hj anbf
aqnbjr l` }hj dn}hj+ Ngnik$ }hj ̀ nr}jr} wny
}l gj} i} r~znqj ir }l alqj }hj `iqr} hldj
}hqlzgh }hj ikkjqolr} aqnbj$ rj} }hj dlkg
rhn`} ik}l }hir hldj$ olzk} }hj whjjd nkm
}hjk szrh nkm szdd }hj rhn`} zk}id }hj whjjdir hnkgikg wi}h j~znd bdjnqnkbj ndd nqlzkm+
Whjk }hj rhn`} ir ik }hj qigh} slri}ilk$
]hj blkkjb}ikg qlm ir n}}nbhjm }l }hj }qjnmdj ay n dng ald} rbqjwjm ik}l }hj }qjnmdj rimj+]hjlsslri}j jkm l` }hj blkkjb}ikg qlm qimjr lk n2 ⁍ 8! dng ald} rbqjwjm }hqlzgh n rondd adlbf (}lnddlw bdjnqnkbj lpjq }hj r}ls blddnq) ik}l }hj`dywhjjd+
Bnqpikg }hj gqllpj ik }hj ̀ dywhjjd `lq }hj qlsj }nfjr n di}}dj }ioj$ az} }hj bhnkgjr ik jkm/gqnik miqjb/}ilk onfjr bnqpikg jnrijq }hnk }zqkikg+
Nssqlxion}jdy >>! dlkg eigrnwbqnkfrhn`} wi}h >! l``rj} }l qjsdnbj
dn}hj mqipj bjk}jq>,1!
>! BD
1 >,1!7 >,1!
Eigrnw Bqnkfrhn`}
8/2/2019 Torno a Pedal II
http://slidepdf.com/reader/full/torno-a-pedal-ii 6/8
ronbf }hj jkm wi}h n hnoojq }l djnpj n
onqf lk }hj ikrimj ̀ nbj l` }hj rjblkm$ lz}jq
aqnbj }l rhlw whjqj ylz kjjm }l alqj }hjrjblkm hldj+ @iknddy$ sz} n aig ̀ jkmjq wnrh/
jq aj}wjjk }hj whjjd nkm }hj `qnoj nkm
r}ls blddnqr lk }hj jkmr l` }hj rhn`}+
L` blzqrj }hj whjjd mljrk’} ml ozbh
wi}hlz} }hj }qjnmdj nkm blkkjb}ikg qlm+
]hj }qjnmdj riosdy n}}nbhjr }l }hj ̀ qnoj
wi}h n ]/hikgj n} }hj anbf$ nkm }hj blk/
kjb}ikg qlm qimjr lk n dng ald} rj} ik}l i}r
rimj$ wi}h }hj lsslri}j jkm n}}nbhjm }l }hj
`dywhjjd+ Nmezr}ikg }hj n}}nbhojk} slik}r
l` }hj }ij qlm }l }hj ̀ dywhjjd nkm }hj }qjn/
mdj widd snq}inddy mj}jqoikj }hj —ojbhnk/
ibnd nmpnk}ngj‟ (hlw high ylz hnpj }l di`}
ylzq ̀ ll}) l` }hj dn}hj+ N 0! ol}ilk n} }hj
jkm l` }hj }qjnmdj rjjor nalz} qigh} `lq
olr} wlqf+
Hjnmr}lbf nkm Mqipj Bjk}jq
]hj hjnmr}lbf blkrir}r l` }wl jx}jkrilkr
l` }hj ̀ qnoj hldmikg ajnqikgr+ ]hjrj ajnq/
ikgr bnk aj aqlkuj lq andd$ az} n} djnr}
}hj dj`} lkj ozr} aj n }hqzr} ajnqikg$ ojnk/
ikg i} ir mjrigkjm }l }nfj sqjrrzqj ndlkg }hjdjkg}h l` }hj rhn`} nr wjdd nr jnrikg }hj
rhn`}’r ql}n}ilk+ Ylz `lddlw sqj}}y ozbh
}hj rnoj sqlbjmzqj zrjm }l ndigk }hj ajnq/
ikgr ik }hj ̀ dywhjjd }l onfj rzqj }hj ajnq/
ikgr ik }hj hjnmr}lbf nqj sqlsjqdy dikjm
zs+
Zkdifj }hj ̀ dywhjjd$ }hj mqipjk szddjy
kjjmr }l n}}nbh ̀ iqody }l i}r rhn`}$ nr wjdd
nr ajikg qjnmidy qjolpnadj+ ]hj r}ls bld/
dnqr ikrj} ik}l al}h jkmr l` }hj szddjy ojj}
al}h l` }hjrj kjjmr6 }hjiq gqjn}jq minoj/
}jq onfjr n ̀ iqo blkkjb}ilk }l }hj wllm
l` }hj szddjy$ nkm }hjiq rj} rbqjwr (qjnbhjm
}hqlzgh hldjr mqiddjm }hqlzgh }hj szddjy)
nddlw ylz }l qjolpj nkm bhnkgj }hj rhn`}
nr kjjmjm+
]hj wllmjk snq} l` }hj mqipjk szddjy
ajgikr nr n 2! rjb}ilk l` sikj = x =+ @ikm
}hj bjk}jq l` lkj jkm nkm alqj n sqjbirj
ikrj} `lq n r}ls blddnq ik}l }hj jkm gqnik+
Klw rj} n 9 ⁍ >0! nzgjq ik }hj bjk}jq l` }hirhldj nkm alqj }hqlzgh }l }hj l}hjq jkm$
r}lssikg ezr} nr }hj jkm l` }hj djnm rbqjw
sjjfr lz}+ Zrikg }hir slik} }l bjk}jq }hj
nzgjq$ alqj }hj ikrj} `lq }hj rjblkm r}ls
blddnq ik}l }hj ̀ nq jkm+
]hj szddjy ir r}idd ezr} n r~znqj adlbf n}
}hir slik} ” kl} ozbh gllm+ Sz} }hj r}ls
blddnqr ik sdnbj nkm olzk} }hj adlbf aj/
}wjjk }hj hjnmr}lbf ajnqikgr+ Hldm n sjk/
bid ik sdnbj lk }hj jkm gqnik }l mqnw n 12 ⁍ =!/
minoj}jq biqbdj lk jnbh jkm+ Ylz bnk }hjk
qjolpj }hj adlbf nkm bhirjd mlwk }l }hjrj
dikjr ” nrrzqjm }hn} ylz hnpj qlzghjm ik
n szddjy sqjbirjdy blkbjk}qib }l }hj rhn`}+
(I}’r fikm l` difj rhll}ikg nqqlwr n} }hj rimj
l` }hj anqk nkm }hjk snik}ikg }hj }nqgj}r
nqlzkm }hjo ” sjq`jb} jpjqy }ioj+)
]hj qlzghjm/ik szddjy ir nalz} }l aj/
bloj ylzq ̀ iqr} }zqkikg ela+ L` blzqrj }hir
ojnkr ylz kjjm n ajd} }l blkkjb} }hj ̀ dy/
whjjd }l }hj szddjy$ nkm rhlq} l` n sqlsjq
ai} l` qlzkm djn}hjq ajd}ikg (rzbh nr zrjm
lk ldm rjwikg onbhikjr) ylz bnk gj} aywi}h > ⁍ =! bl}}lk blqm$ elikjm wi}h n r~znqj
fkl} ̀ lq }hj }ioj ajikg+ Riosdy wqns }hj
qlsj nqlzkm$ szdd i} rjoi/rkzg nkm }ij i}
l``+ R}nq} }qjnmikg nkm }hj qlzghjm ik szd/
djy widd rsik rl }hn} ylz bnk }zqk i} mlwk
}l }hj ̀ ikirhjm riuj$ zrikg ylzq qjgzdnq }zqk/
ikg glzgjr nkm nk iosqlpirjm }lld qjr}+
Lkbj ylz gj} n roll}h sdnbj }zqkjm$ r}ls
nkm olpj }hj qlsj ik}l }hn} rsl}$ qj}yikg
}hj fkl} }igh}jq i` kjbjrrnqy+ @iknddy$ }zqk
n gqllpj ik }hj oimmdj l` }hj szddjy ̀ lq }hj
ajd} }l qimj ik+ Nr wi}h nky dn}hj$ }hj rondd/
jq }hj minoj}jq l` }hj mqipjk szddjy$ }hj
highjq }hj rsjjm nkm }hj dlwjq }hj }lq~zj+
Ylz bnk$ l` blzqrj$ ezr} }qjnmdj ̀ nr}jq lq
rdlwjq$ nkm ylz bnk jnridy }zqk n} lpjq
>$333 qso+
Lkj sjbzdinqi}y l` }hir mjrigk ir }hj
bqlrrjm mqipj blqm whibh bqjn}jr }hj nm/
mi}ilknd sjbzdinqi}y l` }hj ̀ dywhjjd glikg
ik }hj lsslri}j miqjb}ilk nr }hj mqipjk szd/
djy+ ]hj slik} l` }hir bqlrrikg ir }l ikbqjnrj}hj blk}nb} rzq`nbj aj}wjjk }hj ajd} nkm
}hj rondd szddjy+ Wi}hlz} }hj bqlrrjm ajd}$
]hj }wl jkmr l` }hj qlsj ajd} nqj az}}/rsdibjm ay rjwikg anbf nkm ̀ lq}h aj}wjjk }hj }wl sijbjr+ I}
lkdy }nfjr n oikz}j lq }wl wi}h nk zshldr}jqy kjjmdj+Wi}h }ioj nkm zrj }hj qlsj widd r}qj}bh
nkm ylz’dd kjjm }l bz} nkm qj/rsdibj }hj qlsj+
]l rhnqsjk }hj mjnm bjk}jq `lq }hj }nid r}lbf$ Irdissjm }hj anq ik}l }hj mqipj szddjy nkm }igh}/
jkjm i} mlwk wi}h }hj r}ls blddnqr+]hjk i} wnr nriosdj on}}jq l` }zqkikg }hj dn}hj nkm zrikg n
`idj }l ̀ lqo }hj slik}+Kl}j }hj bqlrrjm mqipj blqm lk }hj szddjy whibh ikbqjnrjr }hj blk}nb} lk }hj
szddjy$fjjsikg i} ̀ qlo rdissikg mzqikg zrj+
8/2/2019 Torno a Pedal II
http://slidepdf.com/reader/full/torno-a-pedal-ii 7/8
lq }hj nmmi}ilk l` nk imdjq szddjy$ }hj mqi/
pjk szddjy wlzdm aj blkr}nk}dy rdissikg+Ylz bnk `zq}hjq qjmzbj rdissikg ay onf/
ikg }hj qlsj r}ibfy wi}h ezr} nalz} nky/
}hikg blk}nikikg rzgnq+ I zrj onsdj ryqzs
wi}h gqjn} rzbbjrr+
Whjk }hj szddjy ir }zqkjm nr roll}h
nr ylz kjjm$ `ikirh i} ay `iqr} mqiddikg }hj
hldjr }hqlzgh i}r rimjr }l gipj nbbjrr }l }hj
rj} rbqjwr ik }hj r}ls blddnqr+ N`}jq }hj
hldjr nqj mlkj nkm }jr}jm$ qzk rloj gdzj
nqlzkm }hj rjn}r ̀ lq }hj r}ls blddnqr nkm$
wi}h }hj rhn`} ik sdnbj$ rj} }hj r}ls blddnqr
anbf ik ̀ lq }hj ̀ iknd }ioj+ Ylz bnk blk/
}ikzj wi}h }hj fkl} ik }hj qlsj }l dj} i}
r}qj}bh nkm zk}id ylz gj} nk imjn l` hlw
ozbh }jkrilk i} kjjmr+ Jpjk}znddy$ }hlzgh$
ylz’dd wnk} }l az}}/rsdibj }hj qlsj+
]nidr}lbf nkm Mjnm Bjk}jq
Klw `lq }hj rjblkm sijbj l` }zqkikg ”
}hj mjnm bjk}jq ̀ lq }hj }nid r}lbf+ ]hj mjnm
bjk}jq ir ezr} n rhlq} djkg}h l` }hj > ⁍ 1! rhn`}/
ikg wi}h }hj azrikjrr jkm rhnqsjkjm }l n
sqjbirj blkibnd slik}+ ]hj nkgdj l` }hjblkj ir kl} bqi}ibnd$ az} i}r blkbjk}qibi}y
ir+ I` }hj slik} ir }hj djnr} ai} dlsrimjm lq
qlzgh$ i} widd ~zibfdy jkdnqgj i}r blk}nb}
slik} wi}h }hj wllm ajikg }zqkjm nkm widdaj n blkr}nk} rlzqbj l` }qlzadj+ Rl$ n d/
}hlzgh ylz bnk ~zibfdy qlzgh ik }hj slik}
ay ̀ qjjhnkm ̀ idikg$ }hj ̀ iknd rhnsikg kjjmr
}l bloj ̀ qlo olzk}ikg i} ik }hj mqipjk
szddjy$ (aj`lqj ylz bz} i} ik}l }hj 2! djkg}h
}hn} ylz kjjm)$ }igh}jkikg }hj r}ls bld/
dnqr nkm aqikgikg }hj jkm }qzj wi}h ylzq
`idj hjdm ngnikr} }hj rsikkikg slik}+ N`}jq
}hir$ ylz’dd aj nadj }l }jdd `ldfr hlw ylzq
}qjnmdj dn}hj wlqfr ̀ lq }zqkikg oj}nd nr
wjdd+Wlzdm }hn} }hj mqipj bjk}jq wnr nr jnry+
]hj mqipj bjk}jq kjjmr }l gqis }hj jkm l`
}hj wllm ajikg }zqkjm$ nkm hnr rlojwhn}
}hj rhnsj l` n rsnmj ai}+ Hnpikg nkpidr nkm
`lqgj nalz}$ i} wnr ~zibfjr} ̀ lq oj }l rio/
sdy hjn}$ hnoojq nkm `idj }hj jkm l` }hj
rhn`} ik}l rhnsj+ ]hir ony aj }hj olr}
nwfwnqm snq} l` }hj dn}hj ̀ lq ylz (fim lq
kl}) }l onfj+ Nd}hlzgh ylz bnk bldm hno/
ojq }hj mqipj bjk}jq ik}l rhnsj$ ylz widd
kjjm n gllm qjm hjn} }l onfj }hj rhnqsdy
ajk} bqnkfrhn`} `lq }hj eigrnw n}}nbhojk}+
Oikionddy$ ylz bnk ml }hj ela ylzqrjd` wi}h
n }lqbh$ n hnoojq$ n pirj nkm rloj}hikg
}l zrj `lq nk nkpid+ ]hj sn}h l` wirmlo$
hlwjpjq$ ony aj }l rzsslq} ylzq dlbnd
adnbfroi}h+
Wi}h }hj mqipj bjk}jq ik sdnbj$ ndd }hn}
qjonikr ir }hj }lld qjr}$ whibh bnk aj n ̀ zdd
djkg}h anq qjr}ikg lk lz}qiggjqr n}}nbhjm
}l }hj hjnm nkm }nid r}lbfr$ lq n ronddjq D/
rhnsjm blkr}qzb}ilk n}}nbhjm ay ald} nkm
wikg kz}$ lq al}h+ ]hj }nidr}lbf ir n}}nbhjmwi}h n wjmgj+
]zqkikg
Zrikg }hj dn}hj ir ezr} }hj rnoj nr wi}h nky
l}hjq ndblhld/slwjqjm j~zisojk}+ Qlzgh
ik }hj r}lbf }l nk lb}nglk aj`lqj olzk}/
ikg i} aj}wjjk }hj bjk}jqr$ ajikg rzqj }l
qza rloj ajjrwnx ik }hj hldj ̀ lq }hj mjnm
]hj mqipj bjk}jq ir rhlwk hjqj ajikg `lqojm$wi}h }hj eigrnw bqnkfrhn`} dyikg kjx} }l i}+N`}jq qlzgh rhnsikg$}hj bjk}jq ir `idjm nkm zd}ion}jdy }nfjr lk i}r rsnmj/ai} rhnsj+]hj bjk}jq ir }hjkolzk}jm ik }hj mqipj szddjy ay }igh}jkikg }hjr}ls blddnqr+
1!
1!> 2, =!
>!2, =!
>,1!
>,1!
>!
0!
> >,1!
>8!
>7! 1 >,=! 1 2, =!
0!
1! >7 2, =! 1 2, =!
11!
>! BD
BD2 2,8!
2, =!> >,1!
2, =!
1!
1!> 2, =!
>!2, =!
>,1!
>,1!
>!
0!
> >,1!
>8!
BD 9! minoj}jq bz} lk
}nadj wi}h n 2! qj}zqkanbf }l }hj anbf aqnbj
2!2, =!>
>
,1!2!
2, =!
AANN
X U
Y
WP Z
Eigrnw
8/2/2019 Torno a Pedal II
http://slidepdf.com/reader/full/torno-a-pedal-ii 8/8
bjk}jq+ I` ylzq ajnqikgr nqj }ll bhjns nkm
hnpj rl ozbh sdny ik }hjo }hn} }hj wlqf
bhn}}jqr whjk ylz’qj }zqkikg$ ylz bnk blo/
sjkrn}j n ai} ay nmezr}ikg ylzq bz}}ikg r}ydj
}l sz} olqj l` n —szrh‟ ̀ qlo qzaaikg }hj
ajpjd+ Aqlkuj ajnqikgr ony hnpj djrr sdny
}hnk bhjns andd ajnqikgr+ Ylz bnk jpjk
}zqk }hj ajnqikgr rdigh}dy lz} l` r~znqj wi}h
}hj rhn`} }l }igh}jk }hjo zs+
R}idd$ onbhikjr }jkm }l gipj ylz sqla/
djor n} sdnbjr whjqj ol}ilk bhnkgjr mi/
qjb}ilk$ difj whjk bnq jkgikjr —}hqlw n
qlm$‟ }hj blkpjqrilk l` }hj qjbisqlbnd ol/
}ilk l` ylzq ̀ ll} lk }hj }qjnmdj ik}l }hj
ql}nqy ol}ilk l` }hj ̀ dywhjjd ir n sl}jk/
}ind }qlzadj rsl}+ Ezr} nr n bnq kjjmr nbbz/
qn}j }ioikg$ rl }ll mljr }hj ̀ ll} lsjqn}ikg
}hj dn}hj kjjm }ioikg$ nr n rzmmjk r}ls ik}hj ̀ ll} widd ojj} wi}h blkrimjqnadj qj/
rir}nkbj `qlo }hj `dywhjjd$ rknssikg }hj
blkkjb}ilk n} }hj jkm l` }hj }ij qlm+ Ylz
widd mjpjdls blkrimjqnadj jxsjq}irj wi}h
}hir dn}hj$ az} i} ir rl ikpi}ikg ̀ lq l}hjqr }l
}qy }hn} ylz widd hnpj n dl} l` ikjxsjqi/
jkbjm `jj} lk i}$ }hjy widd rkns }hj ald}$
nkm jxbzrj }hjorjdpjr ay onfikg n blo/
ojk} nalz} —wndfikg nkm bhjwikg gzo n}
}hj rnoj }ioj$‟ rl fjjs n `jw rsnqj ald}r
lk hnkm+
Eigrnw
Nr i` }hir }qjnmdj dn}hj wjqj kl} blld jklzgh$
klw ylz bnk onfj }hj eigrnw n}}nbhojk}
}hn} ri}r n}ls i}+ Bzqilzrdy$ }hj eigrnw ir an/
ribnddy n wny }l blkpjq} }hj ql}nqy ol}ilk
l` }hj ̀ dywhjjd nkm szddjy anbf ik}l qjb/
isqlbn}ikg ol}ilk l` }hj adnmj+ ]hir blk/
pjqrilk qj~ziqjr }hn} ylz dllrjk }hj rj}
rbqjwr ik }hj r}ls blddnqr l` }hj mqipjk szd/
djy$ qjolpj }hj mqipj bjk}jq nkm qjsdnbj
i} wi}h n bqnkfrhn`}+ Zkdjrr ylz nqj
Rzsjqonk$ ylz bnkkl} ajkm }hjrj rhnqs
nkgdjr ik bldm > ⁍ 1! r}jjd rhn`}ikg ” ylz’dd
hnpj }l hjn} i} wi}h n }lqbh nkm ajkm i} ikn pirj+
]hj ̀ qnoj l` }hj eigrnw ir ~zi}j r}qnigh}/
`lqwnqm+ I zrjm aig mlpj}nidr ̀ lq }hj `qlk}
nkm anbf slr}r nr }hj ajr} bloaikn}ilk l`
r}qjkg}h nkm ~zibf mirnrrjoady+ ]hj nqor
l` }hj eigrnw nqj }hj lkdy sijbjr }hn} nqjk’}
rbqns sikj6 }hjy nqj rbqns lnf ̀ lq r}qjkg}h+
]hjy hnpj }l aj r}qlkg ajbnzrj }hj }zqk/
azbfdj n} }hj qjnq ozr} }jkrilk }hj bls/
ikg rnw adnmj n} }hj `qlk}+
I hnpj rjjk onky hlojonmj eigrnwr
`qlo }hj snr} bjk}zqy$ nkm jpjqy lkj zrjm
}hj adnmj hldmjqr ̀ qlo nk ldm blsikg rnw+
L`}jk }hj onfjq wlzdm ezr} hnbfrnw l``
}hj nqor l` }hj blsikg rnw nkm ald} }hjo
lk}l }hj jkmr l` }hj eigrnw nqor+ ]hir hnr
}hj nmpnk}ngj l` nddlwikg ylz }l }zqk }hj
adnmj n} qigh} nkgdjr }l }hj nqor whjk kjb/
jrrnqy ̀ lq bdjnqnkbj+
I}’r ~zi}j n rsjb}nbdj whjk }hir whldj
}hikg ir glikg+ ]hj ̀ dywhjjd dllfr difj
rloj}hikg l`` l` @qjm @dik}r}lkj’r bnq$ }hj
ajnqikgr nqj qn}}dikg$ }hj mqipj qlsj }wnkg/ikg$ nkm }hj eigrnw ezosikg nr ylzq fkjj
gljr zs nkm mlwk+
Az} }hjqj n} }hj azrikjrr jkm$ }hj rnw
bz}r ndlkg ajnz}i`zddy$ }hj dn}hj }zqkr difj
n }ls+ Wlk’} }hj fimr aj sqlzm. SW
]hj }zqkazbfdj ir qigh} l`` }hj rhjd`$wi}h }hjnmmi}ilk l` n dlbf kz} }l lkj l` i}r jyjald}r
(lapilzrdy kl} }hj lkj wi}h }hj dj`} hnkm }hqjnmr)+Wi}hlz} }hj dlbf kz}$ }hj }zqkazbfdj widd
wlqf dllrj ik rjblkmr+ I ndrl ikrj} n aqlkujajnqikg (rnwk ik}l n > ⁍ 1! djkg}h) ik}l jnbh l` }hjnqor n} }hjiq sipl} slik}r+]hir ir kl} rl ozbh }l
qjmzbj `qib}ilk ik lsjqn}ilk nr i} ir }l fjjs }hjwllm `qlo wjnqikg nkm ngnik dllrjkikg }hj
}jkrilk lk }hj adnmj+
]hj ajk} bqnkfrhn`} ir n}}nbhjm }l }hj eigrnw }hqlzgh n hnkgikg nqon}zqj dikf+]hj olzk} ir
n}}nbhjm }l }hj eigrnw wi}h n sijbj l` r}jjd r}qnssikg rbqjwjm ik}l n rnw fjq` ik }hj olzk}$
nkm n}}nbhjm dllrjdy }l }hj dlwjq eigrnw nqo+
Nk D/rhnsjm }lld qjr} ir rhlwk hjqj n}}nbhjm ay ald} nkm wikg kz} }l }hj dn}hj `qnoj+]hj }nid/r}lbf ir ajr} n}}nbhjm wi}h n wjmgj+]hir ir }hj
`nr}jr} nkm }hj `iqojr} wny }l olpj nkm olzk}}hj }nidr}lbf+]hj wjmgj gipjr ezr} }hj qigh}—sikbh‟ }l }hj wllm ajikg }zqkjm i` ylz rdigh}dy blbf }hj al}}lo l` }hj }nidr}lbf }lwnqmr }hjbjk}jq aj`lqj }nssikg }hj wjmgj hloj+
2!
2, =!> >,1!
2!
2, =!
9!min+
8 2, =! >1! 1 >, =!12!
9!
Eigrnw ]nadj