Frekvence kytarové struny e – naměřeno v AUDACITY 1.2.3

podladěné cca na c1 (f1 = 258,4 Hz) (přesná přirozená frekvence by byla 264 Hz)

v jednotlivých harmonických se objevují tóny C  E G  tvořící kvintakord - základ diatonické stupnice                                1 : 5/4 : 3/2

 

 

ale jsou i všechny ostatní tóny diatonické stupnice, kromě f(4/3) a a(5/3), ty se tu nemohou objevit, protože násobíme-li 4/3 nebo 5/3 mocninami 2 (tedy 2,4,8,…), tak se ty trojky ve jmenovateli nevykrátí.

 

c    d    e     f     g     a     h     c

 

1  9/8  5/4  4/3  3/2  5/3   15/8  2

 

2  9/4  5/2  8/3   3   10/3  15/4  4

 

4  9/2   5   16/3  6   20/3  15/2  8

 

8   9    10  32/3  12  40/3   15   16

 

16  18   20  64/3  24  80/3   30   32

…

s rostoucím n se čím dál více začínají objevovat harmonické, které do diatonické stupnice nepadnou: 7, 11, 13, 14, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, …

 

 

Frekvence (Hz)     Level (dB)

10,766602   -59,549988

21,533203   -56,202328

32,299805   -61,265881

43,066406   -59,317272

53,833008   -59,173241

64,599609   -52,506653

75,366211   -54,538334

86,132813   -52,638630

96,899414   -34,461124

107,666016  -28,949766

118,432617  -34,470119

129,199219  -52,294022

139,965820  -59,977654

150,732422  -61,637871

161,499023  -56,879303

172,265625  -56,154274

183,032227  -59,975590

193,798828  -50,339149

204,565430  -46,959785

215,332031  -44,316612

226,098633  -46,496433

236,865234  -41,046253

247,631836  -17,563122

258,398438  -9,207596    1. harmonická c1 – základní frekvence f

269,165039  -13,146451

279,931641  -37,485909

290,698242  -50,905613

301,464844  -56,843864

312,231445  -64,191383

322,998047  -66,064232

333,764648  -64,460968

344,531250  -65,319992

355,297852  -68,875839

366,064453  -66,562309

376,831055  -61,706665

387,597656  -61,252789

398,364258  -62,096077

409,130859  -65,022263

419,897461  -62,515064

430,664063  -62,769470

441,430664  -64,564171

452,197266  -63,779716

462,963867  -62,360661

473,730469  -61,337769

484,497070  -57,279037

495,263672  -46,879765

506,030273  -28,587305

516,796875  -18,286915  2.  harmonická c2 OKTÁVA (2f)

527,563477  -20,465048

538,330078  -38,755207

549,096680  -52,439396

559,863281  -57,108517

570,629883  -63,570107

581,396484  -60,880554

592,163086  -61,285019

602,929688  -53,693481

613,696289  -48,670956

624,462891  -55,574169

635,229492  -68,985664

645,996094  -68,753792

656,762695  -68,351616

667,529297  -67,844742

678,295898  -65,740204

689,062500  -63,958179

699,829102  -64,678123

710,595703  -64,413445

721,362305  -65,746979

732,128906  -59,169376

742,895508  -57,555416

753,662109  -46,978466

764,428711  -29,584486

775,195313  -16,931555  3.  harmonická g2 (3 = 3/2*2)

785,961914  -17,635021

796,728516  -32,864994

807,495117  -47,882668

818,261719  -56,118290

829,028320  -59,287910

839,794922  -60,086338

850,561523  -64,698753

861,328125  -68,738724

872,094727  -66,507721

882,861328  -65,152206

893,627930  -66,079842

904,394531  -67,299034

915,161133  -72,979942

925,927734  -71,270332

936,694336  -70,497002

947,460938  -72,406898

958,227539  -71,666733

968,994141  -68,689552

979,760742  -68,923843

990,527344  -64,069275

1001,293945 -59,704643

1012,060547 -49,866467

1022,827148 -34,521088

1033,593750 -18,152323  4. harmonická c3 (2. oktáva – 4=22)

1044,360352 -16,689192

1055,126953 -27,776617

1065,893555 -46,287140

1076,660156 -58,865543

1087,426758 -62,149326

1098,193359 -64,822945

1108,959961 -67,037582

1119,726563 -70,107620

1130,493164 -68,845428

1141,259766 -71,767830

1152,026367 -73,023308

1162,792969 -73,071747

1173,559570 -75,101845

1184,326172 -70,366570

1195,092773 -68,482964

1205,859375 -70,415390

1216,625977 -72,766640

1227,392578 -73,484375

1238,159180 -77,026489

1248,925781 -72,072838

1259,692383 -71,258110

1270,458984 -68,719734

1281,225586 -56,247089

1291,992188 -36,753231  5. harmonická e3 (5=5/4*22)

1302,758789 -33,919811

1313,525391 -43,317997

1324,291992 -62,133991

1335,058594 -64,823051

1345,825195 -68,645676

1356,591797 -75,505707

1367,358398 -71,901443

1378,125000 -68,375229

1388,891602 -67,564171

1399,658203 -69,468391

1410,424805 -71,591248

1421,191406 -73,128716

1431,958008 -72,085526

1442,724609 -75,716904

1453,491211 -73,174492

1464,257813 -74,395416

1475,024414 -73,818626

1485,791016 -73,613167

1496,557617 -73,682571

1507,324219 -70,713425

1518,090820 -73,589417

1528,857422 -67,828606

1539,624023 -55,724091

1550,390625 -31,624561  6. harmonická g3 (3/2*22 = 6)

1561,157227 -27,492670

1571,923828 -35,339401

1582,690430 -59,326927

1593,457031 -63,073853

1604,223633 -65,980957

1614,990234 -65,840408

1625,756836 -69,334236

1636,523438 -69,623215

1647,290039 -72,342873

1658,056641 -74,450066

1668,823242 -76,974045

1679,589844 -77,785522

1690,356445 -79,964874

1701,123047 -79,016609

1711,889648 -75,615768

1722,656250 -73,565567

1733,422852 -75,383293

1744,189453 -78,394569

1754,956055 -77,209923

1765,722656 -75,666718

1776,489258 -76,523140

1787,255859 -74,332603

1798,022461 -68,612610

 

1808,789063 -41,561371  7. harmonická (7/4*22) ta do diatonické nepadne

1819,555664 -36,310345

1830,322266 -42,426003

1841,088867 -58,602139

1851,855469 -68,656654

1862,622070 -72,165070

1873,388672 -75,912910

1884,155273 -70,019424

1894,921875 -69,601479

1905,688477 -72,691360

1916,455078 -77,111107

1927,221680 -75,337929

1937,988281 -73,781845

1948,754883 -71,259254

1959,521484 -75,021118

1970,288086 -75,670181

1981,054688 -74,556511

1991,821289 -74,549492

2002,587891 -72,523178

2013,354492 -74,203018

2024,121094 -74,695183

2034,887695 -76,710594

2045,654297 -74,553024

2056,420898 -71,791168

2067,187500 -49,140015  8 harmonická c4 (3.oktáva – 8=23)

2077,954102 -39,716015

2088,720703 -42,111076

2099,487305 -58,177204

2110,253906 -70,694321

2121,020508 -72,618706

2131,787109 -77,331902

2142,553711 -78,321846

2153,320313 -76,468079

2164,086914 -76,944267

2174,853516 -75,750595

2185,620117 -73,880203

2196,386719 -76,602806

2207,153320 -81,400131

2217,919922 -79,803635

2228,686523 -77,915123

2239,453125 -74,663284

2250,219727 -73,514267

2260,986328 -74,572639

2271,752930 -76,876358

2282,519531 -75,657440

2293,286133 -73,789268

2304,052734 -71,892662

2314,819336 -67,871529

2325,585938 -50,993717  9 harmonická d4

2336,352539 -38,674122

2347,119141 -38,931301

2357,885742 -51,827751

2368,652344 -65,711586

2379,418945 -68,352386

2390,185547 -70,162918

2400,952148 -75,108780

2411,718750 -74,975937

2422,485352 -77,010414

2433,251953 -76,929436

2444,018555 -77,338966

2454,785156 -75,761917

2465,551758 -77,716148

2476,318359 -78,920143

2487,084961 -66,664291

2497,851563 -61,667931

2508,618164 -68,895424

2519,384766 -70,380501

2530,151367 -75,079720

2540,917969 -73,204506

2551,684570 -75,257126

2562,451172 -70,636467

2573,217773 -63,621365

2583,984375 -49,331028  10. harmonická e4

2594,750977 -27,667183

2605,517578 -23,209641

2616,284180 -30,009708

2627,050781 -54,468063

2637,817383 -65,546906

2648,583984 -73,409042

2659,350586 -76,007019

2670,117188 -74,385406

2680,883789 -79,897903

2691,650391 -75,251022

2702,416992 -72,796333

2713,183594 -73,250717

2723,950195 -74,403542

2734,716797 -78,348801

2745,483398 -80,524178

2756,250000 -82,214386

2767,016602 -80,931969

2777,783203 -78,531097

2788,549805 -74,288216

2799,316406 -77,554878

2810,083008 -76,909142

2820,849609 -75,585182

2831,616211 -71,650307

2842,382813 -58,802448  11. harmonická nepadne do diatonické

2853,149414 -33,529617

2863,916016 -27,929350

2874,682617 -33,287605

2885,449219 -53,930206

2896,215820 -67,268112

2906,982422 -73,656555

2917,749023 -68,406822

2928,515625 -71,510307

2939,282227 -74,829781

2950,048828 -75,303749

2960,815430 -75,403763

2971,582031 -74,230690

2982,348633 -77,316895

2993,115234 -77,598335

3003,881836 -78,535805

3014,648438 -77,061668

3025,415039 -78,771103

3036,181641 -80,255264

3046,948242 -80,503967

3057,714844 -75,725281

3068,481445 -76,959564

3079,248047 -76,356728

3090,014648 -69,017731   12. harmonická g4

3100,781250 -60,252735

3111,547852 -36,292881

3122,314453 -27,320932

3133,081055 -29,748215

3143,847656 -45,779396

3154,614258 -63,451214

3165,380859 -69,400833

3176,147461 -74,362625

3186,914063 -76,549171

3197,680664 -77,563812

3208,447266 -76,753525

3219,213867 -73,881851

3229,980469 -73,674957

3240,747070 -78,472984

3251,513672 -79,125732

3262,280273 -78,731514

3273,046875 -78,186493

3283,813477 -79,802689

3294,580078 -80,205353

3305,346680 -79,744873

3316,113281 -79,042221

3326,879883 -81,503716

3337,646484 -81,987793

3348,413086 -80,379028

3359,179688 -78,213341

3369,946289 -59,882111     13. nepadne

3380,712891 -49,124798

3391,479492 -49,355186

3402,246094 -58,680542

3413,012695 -71,508499

3423,779297 -77,855759

3434,545898 -75,858894

3445,312500 -79,813805

3456,079102 -82,893402

3466,845703 -81,444168

3477,612305 -82,738518

3488,378906 -81,855507

3499,145508 -80,871071

3509,912109 -80,780319

3520,678711 -81,213493

3531,445313 -83,326736

3542,211914 -81,166321

3552,978516 -79,493706

3563,745117 -77,915039

3574,511719 -78,522232

3585,278320 -84,122353

3596,044922 -79,352142

3606,811523 -73,584015

3617,578125 -70,659195  14. nepadne

3628,344727 -56,708057

3639,111328 -37,729748

3649,877930 -33,506191

3660,644531 -39,572285

3671,411133 -59,813107

3682,177734 -68,743286

3692,944336 -82,101883

3703,710938 -74,187233

3714,477539 -78,289520

3725,244141 -77,807320

3736,010742 -81,444649

3746,777344 -79,452034

3757,543945 -78,475418

3768,310547 -81,581764

3779,077148 -80,447983

3789,843750 -83,063187

3800,610352 -80,855850

3811,376953 -77,595337

3822,143555 -80,434654

3832,910156 -78,918091

3843,676758 -72,151199

3854,443359 -74,820099

3865,209961 -67,034782

3875,976563 -55,776089  15. harmonická h4

3886,743164 -37,435692

3897,509766 -26,450327

3908,276367 -28,354652

3919,042969 -37,536278

3929,809570 -54,641129

3940,576172 -46,027863

3951,342773 -48,791870

3962,109375 -60,131985

3972,875977 -69,246460

3983,642578 -76,292046

3994,409180 -78,681847

4005,175781 -78,675713

4015,942383 -80,603127

4026,708984 -80,911301

4037,475586 -82,590683

4048,242188 -81,064224

4059,008789 -79,836998

4069,775391 -81,320908

4080,541992 -80,920044

4091,308594 -80,556488

4102,075195 -81,726219

4112,841797 -81,224457

4123,608398 -80,025055

4134,375000 -79,622475   16. harmonická c5

4145,141602 -72,407715

4155,908203 -56,516731

4166,674805 -41,149593

4177,441406 -38,087574

Atd….
 
4188,208008 -45,566528

4198,974609 -66,076157

4209,741211 -77,476997

4220,507813 -81,045052

4231,274414 -79,774467

4242,041016 -79,362350

4252,807617 -82,848022

4263,574219 -83,032982

4274,340820 -79,624306

4285,107422 -81,180183

4295,874023 -80,672424

4306,640625 -79,115059

4317,407227 -82,349037

4328,173828 -84,771599

4338,940430 -83,387535

4349,707031 -82,100266

4360,473633 -83,418152

4371,240234 -83,315033