
gunakaaram (sangeetam)

gunakaaram yokka ganita karyakalapalu sangeethaaniki aneka anuvartanaalanu kaligi untaayi. viraamaala yokka pounahpunya nishpattulaku daani anuvartanam kakunda (udaaharanaku, kevalam swaram, mariyu samaana swabhaavamlo rendinti pannendava muulam), idhi pannendu-swara saanketikata mariyu sangeeta samiti siddhaantam kosam itara margallo upayoginchabadindi. adanamgaa ring modulation anedi sangeeta prabhavam kosam upayoginchina gunanamtho kuudina vidyut audeo prakriya.
gunakaara charya anedi vaadana guninchabadina mapping. gunakaaram anedi virama vistaranalo sahajamgaa udbhavinchindi, udaaharanaku belaa bartok mariyu alban burg sangeetamlo, swara varusa kramam sankhya bhramanamtho sahaa. pitch number rotation, "funferehe" ledhaa "aidu-syries" mariyu "seabenrehe" ledhaa "edu-syries", modata ernst creneck "yuber nyuu music" loe varninchaaru. james keey thoo sahaa prinsetton aadhaarita siddhaantakartalu. randall, godfrey winham, mariyu hubert ess. pannendu-tone shrenulaku sambandhinchi matrame kakunda, vaatini charchinchi, sweekarinchina modati vaaru hou.
pitch-class gunakaaram maadyulo 12.
pitch-class setlatho vyavaharinchetappudu, gunakaaram maadyulo 12 anedi oka saadhaarana operation. mottam pannendu tonelu ledhaa oka tone varusatho vyavaharinchetappudu, konni sankhyalu matrame untaayi, veetini oka varusatho guninchi, inca pannendu vibhina tonela samititoe mugustaayi. pradhana ledhaa maarpuleni roopaanni p0 gaa teesukunte, gunakaaram "mx" dwara suuchimchabadutumdi, x gunakamh
krindi pattika varnasambandha pannendu-swara varusa yokka saadhyamayye anni gunakaaraalanu jabita chestundih
m1, m5, m7, mariyu m11 matrame okadaanikokati mapping (12 pratyaekamaina tonela puurti samiti) istayani gamaninchandi. endukante eee sankhyalalo prati okkati saapekshamgaa 12 kii pradhaanamainadi. idhi kooda aasaktikaramgaa undhi, chromatic scale m5 thoo naalugava vruttaaniki mapp cheyabadutundi, ledhaa m7 thoo aidavadi, mariyu saadhaaranamgaa m7 kinda anni sarri sankhyalu oke vidhamgaa untaayi, ayithe besi sankhyalu tritone dwara badilee cheyabadataayi. eee rakamaina gunakaaram tarachugaa transposition operation thoo kalipi untundi. dheenini modata herbert imert mudranalo "quartworwandlung" (nalgava parivartana) mariyu "quintwandlung" (aidava parivartana) anae padaala krinda vivarinchaadu mariyu swarakartalu milton babit, robbert morris mariyu charless vurinen upayoginchaaru. eee operation jaz loe konni harmonic parivartanalaku kooda kaaranamavutundi.
anduvalla rendu ardhavantamaina kaaryakalaapaalato guninchadam (5 & 7) nuu m5 ("a") mariyu m7 ("a") ledhaa m mariyu im thoo suuchimchavachchu.
pitch gunakaaram.
pier boulez pitch gunakaaram anie piliche oka operation gurinchi vivarinchaadu, idhi pitch-class setla cartician utpattiki kontavaraku samanamga untundi. rendu setlanu ichinatlayithe, pitch gunakaaram yokka phalitam asalu rendu setla madhya saadhyamayye anni jatha muulakaala mottaala samiti (maadyulo 12) avutundi. daani nirvachanam
udaaharanaku, c-majer card formulanu c, d formula _ 3 kaligina diedtho guniste, phalitam ilaa untundih
eee udaaharanalo, rendu pitch la samititoe guninchina moodu pitch la samiti 3x2 pitch la kotta samitini istundi. maadyulo 12 ankaganitam yokka parimita sthalaanni batti, eee vidhananni upayogistunnappudu chaalaa tarachugaa nakilee tonelu utpatti cheyabadataayi, ivi saadhaaranamgaa tolaginchabadataayi. eee saanketikata boulez yokka 1955 "leey martue sance maitre", alaage athani moodava piano sonata, "structures II", "daan" mariyu "tombe" nundi "ply selone ply", "eclut" (mariyu "ecclet multiples"), "figures-doubles-prisms", "domains", mariyu "cummings ist derr dictor", alaage upasamharinchukunna coral work, "obli signal lapidae" (1952) loe atyanta prasiddhi chendindi. eee operation, ankaganita gunakaaram mariyu sett taragatula sthaanaantara kalayika vale kakunda, naan-commutative.
haward hanson eee commutative ganita convolution operation nuu "superposition" ledhaa "@-projection" anie pilicharu mariyu "/" sangnaamaanaanni parasparam maarchukogaligaaru. anduvalla "p@m" ledhaa "p/m" antey "majer moodava sthaanamlo khachitamaina aidavadi", e.zii.: {c e g b}. rendu trayam roopaalanu guninchavacchu ledhaa oka trayam guninchavacchu, tadwara phalita sthaayini utpatti cheyavachani ayana pratyaekamgaa paerkonnaaru. trayam yokka taruvaati "chaturasram" muulam trayam yokka sandarbhaalalo atyanta santruptamaina nirdishta sthaayini utpatti chestundi. anduvalla "pmn", pradhana trayam kosam hanson paeru, square chesinappudu, "pmn", ii.zii.: {c d e g b}.
nicolus slonimsky eee operation nuu, saadhaaraneekarinchani, 1300 pramaanaalanu samaroopa tritonelu, augmented teegalu, taggina edava teegalu mariyu hooletone pramaanaalanu 3 kaarakaala mottamto guninchadam dwara roopondinchadaaniki upayoginchaadu, veetini athanu interpolation, infrapolation mariyu ultrapolation anie pilichadu. interpolation, infrapolation mariyu ultrapolation kalayika, valuga infra-interpolation, infra-ultrapolation mariyu infra-inter-ultrapolation yerparustundi, idhi samarthavantamgaa rendava sonoriteeki adanamgaa untundi. eee rendava sonarity, modati daanitoe guniste, pramaanaalanu mariyu vaati samarasyalanu utpatti cheyadaaniki athani suutraanni istundi.
joseph shillinger 19va sataabdam mariyu 20va sataabdam praarambhamlo saadhaarana harmonic sailulanu kshitija samaantara harmonic ruut-motion mariyu niluvu harmonic nirmaanam yokka utpattigaa vargeekarinchadaaniki abhivruddhi chendani aalochananu upayoginchaaru. ayana udaharinchina swarakartala sailulu konni eee krindi gunakaara pattikalo kanipistaayi.
modulus-12 ganitam dwara paaschaatya sangeetam yokka 12 swara shrenula anchanaa, ardha dasala vruttaanni yerparustundi, antey sangeeta viramalanu dhruva samanvaya vyavasthalo konaalugaa kooda bhaavinchavachchu, harmonic kadalika yokka vidhulugaa oke vidhamaina viramalanu amarchavacchu mariyu oka aksham chuttoo bhramanam vale badilee cheyavachu. anduvalla, hanson nundi paina perkonna gunakaara udaaharanalo, "p@m" ledhaa "p/m" ("majer 3 va sthaanamlo khachitamaina 5 va", e.zii.: {c e g b}) antey "paripuurna aidavadi, ardha dasala vruttam yokka chuttukolatalo 1/3 vanthu tirigina paripuurna aidavadaanipai adhirohinchabadindi". viraamaala yokka marpidi pattikanu koneeya kolatagaa (savyadisalo bhramanaaniki pratikuula sankhyalugaa teesukobadindi) krindi vidhamgaa untundih
viraamaala yokka eee koneeya vivarana sangeetamlo gunakaaram yokka chaalaa aacharanaatmaka udaaharananu drushyamaanam cheyadaaniki sahaayapadutundih keyboard vaayidyaala yokka kevalam swara tuningnu vivarinchadamlo upayoginche euler-facker genra. prati jaathi "3 paripuurna aidavadi" ledhaa {c g d f} vanti itara sonarity vanti oka harmonic functionnu suuchistumdi, idhi coppy yokka saraina konam (la) thoo guninchinappudu, aidava vruttam yokka 12-tett chuttukolata sthalaanni sumaruga nimputundi. sangeetaparamgaa andamgaa laenappatikee, rendu paripuurnamaina naan-beating majer moodava bhagala yokka augmented tridenu tune cheyadam saadhyamavutundi, taruvaata (guninchadam) augmented card yokka prati note paina aidava mariyu krinda 1 rendu tempered tune cheyandi; idhi euler-facker genus [555]. 3 paripuurna aidava" thoo praarambhinchadam dwara mariyu eee naan-beating notla nundi paina mariyu krinda moodava bhaagamlo oka tempered majer tuning cheyadam dwara vaerae phalitam pondabadutundi; idhi euler-facker genus [333].
samaya gunakaaram.
joseph shillinger "bahupadi samaya gunakaaram" ("bahupadi" anedi okati kante ekkuva vyavadhitho kuudina edainaa layanu suuchistumdi) yokka operation nuu paina perkonna pitch gunakaaraaniki anugunamgaa vivarinchaadu. theem yokka prati gamanika yokka quarter, 8va-ledhaa 16va-note vyavadhini soochinche sthiramaina puurnaamkaala shreniki tagginchabadina theemnu, pondikaina mariyu sambandhita vaividhyaanni utpatti cheyadaaniki maroka theem yokka shrenitho guninchavacchu. mukhyamgaa, oka theem yokka shrenini chaturasraakaaramlo ledhaa ghanakaramlo ledhaa sambandhita padaartham yokka santruptatanu utpatti cheyadaaniki adhika saktulaku teesukellavacchu.
parivartanaku kattubadi undandi.
herbert imert pannendu-tone shrenula yokka "enimidi reetulu" anie piliche vaatini vivarinchaadu, anni okadaanikokati addam roopaalu. vilomam kshitija samaantara addam dwara pondabadutundi, niluvu addam dwara tirogamanam, kshitija samaantara mariyu niluvu addam dwara tirogamanam-vilomam, mariyu "naalugava-chakram-parivartana" ledhaa "quartworwandlung" mariyu "chakram-aidava-parivartana" ledhaa "quintwandlung" oka vaalu addam dwara pondabadutundi. eee parivartanalu mariyu pradhana yokka tirogamanaalato, enimidi kramaparivartanalu unnaayi.
joseph shillinger euclidean vector space loe matricks gunakaaram yokka karyakalapalu-contrapantal inverse, retrograde mariyu retrograde-inverse-matrame kakunda vaati layabaddhamaina pratyardhulanu kooda sweekarinchaaru. anduvalla athanu adhe kramamlo adhe pitch lanu upayoginchi theem yokka vaividhyaanni vivarinchagaladu, conny daani asalu samaya viluvalanu tirogamana kramamlo upayoginchagaladu. athanu eee gunakaara viswam yokka paridhini saralamaina pratibimbamku minchinadigaa chushadu, indulo badilee mariyu bhramanam (bahusha muulaaniki tirigi projectiontho), alaage gatamlo upayogamlo unna samaya parimaanaaniki (perugudala mariyu taggimpu dwara) parimitam cheyabadina vistarananu chaerchaaru. anduvalla athanu prati varusa jatha notla madhya sagam dasala gananalanu konni kaarakaalato guninchadam dwara, maadyulo-12 operation dwara ashtakaniki saadhaaraneekarinchadam dwara, theem yokka maroka vaividhyaanni ledhaa praathamika sthaayini kooda vivarinchagaladu, (
z-sambandham.
konni z-sambandhita teegalu "m" ledhaa "im" (5 thoo guninchadam ledhaa 7 thoo guninchadam) dwara anusandhaaninchabadi untaayi, endukante apic vektarpai 1 mariyu 5 kosam okelanti entreelu untaayi.
suuchanalu.
muulaalu

