1024 samples long one cycle waveform at 44.1 kHz

A chart of what hertz the frequencies should be to get a cycle that is 1024 samples long.

43,06640625 Hz

To get a 1024 samples long one cycle waveform at 44.1 kHz set an oscillator or tone generator to 43,06640625 Hz or 43,07 Hz depending on how accurate your gear can be set. The truncated 43,07 Hz will work fine and when working with some analog gear there’s no way to really set the frequency by numbers and you will have to go by trial and error using a chromatic tuner. When you have it tuned you can run it through filters or effect pedals. Some processors will change the tuning, for example choruses, while for example filters will leave the tuning intact.

Harmonics / overtones / more oscillators!

To add in some more oscillators into one sample is one of the strengths of sampling single cycles, you can use one single cycle waveform to contain a number of oscillators at different tuning as long as the cycles zero crossings add up to the root oscillators cycle. Octaves is the easiest as it doubles for each octave, and probably the most useful as it sounds clean. So the root is 43,07 Hz and runs one cycle in 1024 samples, the first octave of the root is 86,13 Hz and runs two cycles at 1024 samples. The same is true for the third harmonic it will run three times within 1024 samples. I think you get the idea that they run a number of times within 1024 and therefor can be perfectly looped.

Cycles Relationship Hz Hz trunc(2) Smpls/cycle
1 ROOT 43,06640625 43,07 1024
2 OCT 86,1328125 86,13 512
3 129,1992188 129,20 341,3333333
4 OCT 172,265625 172,27 256
5 215,3320313 215,33 204,8
6 258,3984375 258,40 170,6666667
7 301,4648438 301,46 146,2857143
8 OCT 344,53125 344,53 128
9 387,5976563 387,60 113,7777778
10 430,6640625 430,66 102,4
11 473,7304688 473,73 93,09090909
12 516,796875 516,80 85,33333333
13 559,8632813 559,86 78,76923077
14 602,9296875 602,93 73,14285714
15 645,9960938 646,00 68,26666667
16 OCT 689,0625 689,06 64
17 732,1289063 732,13 60,23529412
18 775,1953125 775,20 56,88888889
19 818,2617188 818,26 53,89473684
20 861,328125 861,33 51,2
21 904,3945313 904,39 48,76190476
22 947,4609375 947,46 46,54545455
23 990,5273438 990,53 44,52173913
24 1033,59375 1033,59 42,66666667
25 1076,660156 1076,66 40,96
26 1119,726563 1119,73 39,38461538
27 1162,792969 1162,79 37,92592593
28 1205,859375 1205,86 36,57142857
29 1248,925781 1248,93 35,31034483
30 1291,992188 1291,99 34,13333333
31 1335,058594 1335,06 33,03225806
32 OCT 1378,125 1378,13 32
33 1421,191406 1421,19 31,03030303
34 1464,257813 1464,26 30,11764706
35 1507,324219 1507,32 29,25714286
36 1550,390625 1550,39 28,44444444
37 1593,457031 1593,46 27,67567568
38 1636,523438 1636,52 26,94736842
39 1679,589844 1679,59 26,25641026
40 1722,65625 1722,66 25,6
41 1765,722656 1765,72 24,97560976
42 1808,789063 1808,79 24,38095238
43 1851,855469 1851,86 23,81395349
44 1894,921875 1894,92 23,27272727
45 1937,988281 1937,99 22,75555556
46 1981,054688 1981,05 22,26086957
47 2024,121094 2024,12 21,78723404
48 2067,1875 2067,19 21,33333333
49 2110,253906 2110,25 20,89795918
50 2153,320313 2153,32 20,48
51 2196,386719 2196,39 20,07843137
52 2239,453125 2239,45 19,69230769
53 2282,519531 2282,52 19,32075472
54 2325,585938 2325,59 18,96296296
55 2368,652344 2368,65 18,61818182
56 2411,71875 2411,72 18,28571429
57 2454,785156 2454,79 17,96491228
58 2497,851563 2497,85 17,65517241
59 2540,917969 2540,92 17,3559322
60 2583,984375 2583,98 17,06666667
61 2627,050781 2627,05 16,78688525
62 2670,117188 2670,12 16,51612903
63 2713,183594 2713,18 16,25396825
64 OCT 2756,25 2756,25 16
65 2799,316406 2799,32 15,75384615
66 2842,382813 2842,38 15,51515152
67 2885,449219 2885,45 15,28358209
68 2928,515625 2928,52 15,05882353
69 2971,582031 2971,58 14,84057971
70 3014,648438 3014,65 14,62857143
71 3057,714844 3057,71 14,42253521
72 3100,78125 3100,78 14,22222222
73 3143,847656 3143,85 14,02739726
74 3186,914063 3186,91 13,83783784
75 3229,980469 3229,98 13,65333333
76 3273,046875 3273,05 13,47368421
77 3316,113281 3316,11 13,2987013
78 3359,179688 3359,18 13,12820513
79 3402,246094 3402,25 12,96202532
80 3445,3125 3445,31 12,8
81 3488,378906 3488,38 12,64197531
82 3531,445313 3531,45 12,48780488
83 3574,511719 3574,51 12,3373494
84 3617,578125 3617,58 12,19047619
85 3660,644531 3660,64 12,04705882
86 3703,710938 3703,71 11,90697674
87 3746,777344 3746,78 11,77011494
88 3789,84375 3789,84 11,63636364
89 3832,910156 3832,91 11,50561798
90 3875,976563 3875,98 11,37777778
91 3919,042969 3919,04 11,25274725
92 3962,109375 3962,11 11,13043478
93 4005,175781 4005,18 11,01075269
94 4048,242188 4048,24 10,89361702
95 4091,308594 4091,31 10,77894737
96 4134,375 4134,38 10,66666667
97 4177,441406 4177,44 10,55670103
98 4220,507813 4220,51 10,44897959
99 4263,574219 4263,57 10,34343434
100 4306,640625 4306,64 10,24
101 4349,707031 4349,71 10,13861386
102 4392,773438 4392,77 10,03921569
103 4435,839844 4435,84 9,941747573
104 4478,90625 4478,91 9,846153846
105 4521,972656 4521,97 9,752380952
106 4565,039063 4565,04 9,660377358
107 4608,105469 4608,11 9,570093458
108 4651,171875 4651,17 9,481481481
109 4694,238281 4694,24 9,394495413
110 4737,304688 4737,30 9,309090909
111 4780,371094 4780,37 9,225225225
112 4823,4375 4823,44 9,142857143
113 4866,503906 4866,50 9,061946903
114 4909,570313 4909,57 8,98245614
115 4952,636719 4952,64 8,904347826
116 4995,703125 4995,70 8,827586207
117 5038,769531 5038,77 8,752136752
118 5081,835938 5081,84 8,677966102
119 5124,902344 5124,90 8,605042017
120 5167,96875 5167,97 8,533333333
121 5211,035156 5211,04 8,462809917
122 5254,101563 5254,10 8,393442623
123 5297,167969 5297,17 8,325203252
124 5340,234375 5340,23 8,258064516
125 5383,300781 5383,30 8,192
126 5426,367188 5426,37 8,126984127
127 5469,433594 5469,43 8,062992126
128 OCT 5512,5 5512,50 8
129 5555,566406 5555,57 7,937984496
130 5598,632813 5598,63 7,876923077
131 5641,699219 5641,70 7,816793893
132 5684,765625 5684,77 7,757575758
133 5727,832031 5727,83 7,69924812
134 5770,898438 5770,90 7,641791045
135 5813,964844 5813,96 7,585185185
136 5857,03125 5857,03 7,529411765
137 5900,097656 5900,10 7,474452555
138 5943,164063 5943,16 7,420289855
139 5986,230469 5986,23 7,366906475
140 6029,296875 6029,30 7,314285714
141 6072,363281 6072,36 7,262411348
142 6115,429688 6115,43 7,211267606
143 6158,496094 6158,50 7,160839161
144 6201,5625 6201,56 7,111111111
145 6244,628906 6244,63 7,062068966
146 6287,695313 6287,70 7,01369863
147 6330,761719 6330,76 6,965986395
148 6373,828125 6373,83 6,918918919
149 6416,894531 6416,89 6,872483221
150 6459,960938 6459,96 6,826666667
151 6503,027344 6503,03 6,781456954
152 6546,09375 6546,09 6,736842105
153 6589,160156 6589,16 6,692810458
154 6632,226563 6632,23 6,649350649
155 6675,292969 6675,29 6,606451613
156 6718,359375 6718,36 6,564102564
157 6761,425781 6761,43 6,522292994
158 6804,492188 6804,49 6,481012658
159 6847,558594 6847,56 6,440251572
160 6890,625 6890,63 6,4
161 6933,691406 6933,69 6,360248447
162 6976,757813 6976,76 6,320987654
163 7019,824219 7019,82 6,282208589
164 7062,890625 7062,89 6,243902439
165 7105,957031 7105,96 6,206060606
166 7149,023438 7149,02 6,168674699
167 7192,089844 7192,09 6,131736527
168 7235,15625 7235,16 6,095238095
169 7278,222656 7278,22 6,059171598
170 7321,289063 7321,29 6,023529412
171 7364,355469 7364,36 5,988304094
172 7407,421875 7407,42 5,953488372
173 7450,488281 7450,49 5,919075145
174 7493,554688 7493,55 5,885057471
175 7536,621094 7536,62 5,851428571
176 7579,6875 7579,69 5,818181818
177 7622,753906 7622,75 5,785310734
178 7665,820313 7665,82 5,752808989
179 7708,886719 7708,89 5,720670391
180 7751,953125 7751,95 5,688888889
181 7795,019531 7795,02 5,657458564
182 7838,085938 7838,09 5,626373626
183 7881,152344 7881,15 5,595628415
184 7924,21875 7924,22 5,565217391
185 7967,285156 7967,29 5,535135135
186 8010,351563 8010,35 5,505376344
187 8053,417969 8053,42 5,475935829
188 8096,484375 8096,48 5,446808511
189 8139,550781 8139,55 5,417989418
190 8182,617188 8182,62 5,389473684
191 8225,683594 8225,68 5,361256545
192 8268,75 8268,75 5,333333333
193 8311,816406 8311,82 5,305699482
194 8354,882813 8354,88 5,278350515
195 8397,949219 8397,95 5,251282051
196 8441,015625 8441,02 5,224489796
197 8484,082031 8484,08 5,197969543
198 8527,148438 8527,15 5,171717172
199 8570,214844 8570,21 5,145728643
200 8613,28125 8613,28 5,12
201 8656,347656 8656,35 5,094527363
202 8699,414063 8699,41 5,069306931
203 8742,480469 8742,48 5,044334975
204 8785,546875 8785,55 5,019607843
205 8828,613281 8828,61 4,995121951
206 8871,679688 8871,68 4,970873786
207 8914,746094 8914,75 4,946859903
208 8957,8125 8957,81 4,923076923
209 9000,878906 9000,88 4,899521531
210 9043,945313 9043,95 4,876190476
211 9087,011719 9087,01 4,853080569
212 9130,078125 9130,08 4,830188679
213 9173,144531 9173,14 4,807511737
214 9216,210938 9216,21 4,785046729
215 9259,277344 9259,28 4,762790698
216 9302,34375 9302,34 4,740740741
217 9345,410156 9345,41 4,718894009
218 9388,476563 9388,48 4,697247706
219 9431,542969 9431,54 4,675799087
220 9474,609375 9474,61 4,654545455
221 9517,675781 9517,68 4,633484163
222 9560,742188 9560,74 4,612612613
223 9603,808594 9603,81 4,591928251
224 9646,875 9646,88 4,571428571
225 9689,941406 9689,94 4,551111111
226 9733,007813 9733,01 4,530973451
227 9776,074219 9776,07 4,511013216
228 9819,140625 9819,14 4,49122807
229 9862,207031 9862,21 4,471615721
230 9905,273438 9905,27 4,452173913
231 9948,339844 9948,34 4,432900433
232 9991,40625 9991,41 4,413793103
233 10034,47266 10034,47 4,394849785
234 10077,53906 10077,54 4,376068376
235 10120,60547 10120,61 4,357446809
236 10163,67188 10163,67 4,338983051
237 10206,73828 10206,74 4,320675105
238 10249,80469 10249,80 4,302521008
239 10292,87109 10292,87 4,284518828
240 10335,9375 10335,94 4,266666667
241 10379,00391 10379,00 4,248962656
242 10422,07031 10422,07 4,231404959
243 10465,13672 10465,14 4,21399177
244 10508,20313 10508,20 4,196721311
245 10551,26953 10551,27 4,179591837
246 10594,33594 10594,34 4,162601626
247 10637,40234 10637,40 4,145748988
248 10680,46875 10680,47 4,129032258
249 10723,53516 10723,54 4,112449799
250 10766,60156 10766,60 4,096
251 10809,66797 10809,67 4,079681275
252 10852,73438 10852,73 4,063492063
253 10895,80078 10895,80 4,04743083
254 10938,86719 10938,87 4,031496063
255 10981,93359 10981,93 4,015686275
256 OCT 11025 11025,00 4
257 11068,06641 11068,07 3,984435798
258 11111,13281 11111,13 3,968992248
259 11154,19922 11154,20 3,953667954
260 11197,26563 11197,27 3,938461538
261 11240,33203 11240,33 3,923371648
262 11283,39844 11283,40 3,908396947
263 11326,46484 11326,46 3,893536122
264 11369,53125 11369,53 3,878787879
265 11412,59766 11412,60 3,864150943
266 11455,66406 11455,66 3,84962406
267 11498,73047 11498,73 3,835205993
268 11541,79688 11541,80 3,820895522
269 11584,86328 11584,86 3,80669145
270 11627,92969 11627,93 3,792592593
271 11670,99609 11671,00 3,778597786
272 11714,0625 11714,06 3,764705882
273 11757,12891 11757,13 3,750915751
274 11800,19531 11800,20 3,737226277
275 11843,26172 11843,26 3,723636364
276 11886,32813 11886,33 3,710144928
277 11929,39453 11929,39 3,696750903
278 11972,46094 11972,46 3,683453237
279 12015,52734 12015,53 3,670250896
280 12058,59375 12058,59 3,657142857
281 12101,66016 12101,66 3,644128114
282 12144,72656 12144,73 3,631205674
283 12187,79297 12187,79 3,618374558
284 12230,85938 12230,86 3,605633803
285 12273,92578 12273,93 3,592982456
286 12316,99219 12316,99 3,58041958
287 12360,05859 12360,06 3,567944251
288 12403,125 12403,13 3,555555556
289 12446,19141 12446,19 3,543252595
290 12489,25781 12489,26 3,531034483
291 12532,32422 12532,32 3,518900344
292 12575,39063 12575,39 3,506849315
293 12618,45703 12618,46 3,494880546
294 12661,52344 12661,52 3,482993197
295 12704,58984 12704,59 3,471186441
296 12747,65625 12747,66 3,459459459
297 12790,72266 12790,72 3,447811448
298 12833,78906 12833,79 3,436241611
299 12876,85547 12876,86 3,424749164
300 12919,92188 12919,92 3,413333333
301 12962,98828 12962,99 3,401993355
302 13006,05469 13006,05 3,390728477
303 13049,12109 13049,12 3,379537954
304 13092,1875 13092,19 3,368421053
305 13135,25391 13135,25 3,357377049
306 13178,32031 13178,32 3,346405229
307 13221,38672 13221,39 3,335504886
308 13264,45313 13264,45 3,324675325
309 13307,51953 13307,52 3,313915858
310 13350,58594 13350,59 3,303225806
311 13393,65234 13393,65 3,292604502
312 13436,71875 13436,72 3,282051282
313 13479,78516 13479,79 3,271565495
314 13522,85156 13522,85 3,261146497
315 13565,91797 13565,92 3,250793651
316 13608,98438 13608,98 3,240506329
317 13652,05078 13652,05 3,230283912
318 13695,11719 13695,12 3,220125786
319 13738,18359 13738,18 3,210031348
320 13781,25 13781,25 3,2
321 13824,31641 13824,32 3,190031153
322 13867,38281 13867,38 3,180124224
323 13910,44922 13910,45 3,170278638
324 13953,51563 13953,52 3,160493827
325 13996,58203 13996,58 3,150769231
326 14039,64844 14039,65 3,141104294
327 14082,71484 14082,71 3,131498471
328 14125,78125 14125,78 3,12195122
329 14168,84766 14168,85 3,112462006
330 14211,91406 14211,91 3,103030303
331 14254,98047 14254,98 3,093655589
332 14298,04688 14298,05 3,084337349
333 14341,11328 14341,11 3,075075075
334 14384,17969 14384,18 3,065868263
335 14427,24609 14427,25 3,056716418
336 14470,3125 14470,31 3,047619048
337 14513,37891 14513,38 3,038575668
338 14556,44531 14556,45 3,029585799
339 14599,51172 14599,51 3,020648968
340 14642,57813 14642,58 3,011764706
341 14685,64453 14685,64 3,002932551
342 14728,71094 14728,71 2,994152047
343 14771,77734 14771,78 2,985422741
344 14814,84375 14814,84 2,976744186
345 14857,91016 14857,91 2,968115942
346 14900,97656 14900,98 2,959537572
347 14944,04297 14944,04 2,951008646
348 14987,10938 14987,11 2,942528736
349 15030,17578 15030,18 2,934097421
350 15073,24219 15073,24 2,925714286
351 15116,30859 15116,31 2,917378917
352 15159,375 15159,38 2,909090909
353 15202,44141 15202,44 2,900849858
354 15245,50781 15245,51 2,892655367
355 15288,57422 15288,57 2,884507042
356 15331,64063 15331,64 2,876404494
357 15374,70703 15374,71 2,868347339
358 15417,77344 15417,77 2,860335196
359 15460,83984 15460,84 2,852367688
360 15503,90625 15503,91 2,844444444
361 15546,97266 15546,97 2,836565097
362 15590,03906 15590,04 2,828729282
363 15633,10547 15633,11 2,820936639
364 15676,17188 15676,17 2,813186813
365 15719,23828 15719,24 2,805479452
366 15762,30469 15762,30 2,797814208
367 15805,37109 15805,37 2,790190736
368 15848,4375 15848,44 2,782608696
369 15891,50391 15891,50 2,775067751
370 15934,57031 15934,57 2,767567568
371 15977,63672 15977,64 2,760107817
372 16020,70313 16020,70 2,752688172
373 16063,76953 16063,77 2,745308311
374 16106,83594 16106,84 2,737967914
375 16149,90234 16149,90 2,730666667
376 16192,96875 16192,97 2,723404255
377 16236,03516 16236,04 2,716180371
378 16279,10156 16279,10 2,708994709
379 16322,16797 16322,17 2,701846966
380 16365,23438 16365,23 2,694736842
381 16408,30078 16408,30 2,687664042
382 16451,36719 16451,37 2,680628272
383 16494,43359 16494,43 2,673629243
384 16537,5 16537,50 2,666666667
385 16580,56641 16580,57 2,65974026
386 16623,63281 16623,63 2,652849741
387 16666,69922 16666,70 2,645994832
388 16709,76563 16709,77 2,639175258
389 16752,83203 16752,83 2,632390746
390 16795,89844 16795,90 2,625641026
391 16838,96484 16838,96 2,618925831
392 16882,03125 16882,03 2,612244898
393 16925,09766 16925,10 2,605597964
394 16968,16406 16968,16 2,598984772
395 17011,23047 17011,23 2,592405063
396 17054,29688 17054,30 2,585858586
397 17097,36328 17097,36 2,579345088
398 17140,42969 17140,43 2,572864322
399 17183,49609 17183,50 2,56641604
400 17226,5625 17226,56 2,56
401 17269,62891 17269,63 2,55361596
402 17312,69531 17312,70 2,547263682
403 17355,76172 17355,76 2,540942928
404 17398,82813 17398,83 2,534653465
405 17441,89453 17441,89 2,528395062
406 17484,96094 17484,96 2,522167488
407 17528,02734 17528,03 2,515970516
408 17571,09375 17571,09 2,509803922
409 17614,16016 17614,16 2,503667482
410 17657,22656 17657,23 2,497560976
411 17700,29297 17700,29 2,491484185
412 17743,35938 17743,36 2,485436893
413 17786,42578 17786,43 2,479418886
414 17829,49219 17829,49 2,473429952
415 17872,55859 17872,56 2,46746988
416 17915,625 17915,63 2,461538462
417 17958,69141 17958,69 2,455635492
418 18001,75781 18001,76 2,449760766
419 18044,82422 18044,82 2,443914081
420 18087,89063 18087,89 2,438095238
421 18130,95703 18130,96 2,432304038
422 18174,02344 18174,02 2,426540284
423 18217,08984 18217,09 2,420803783
424 18260,15625 18260,16 2,41509434
425 18303,22266 18303,22 2,409411765
426 18346,28906 18346,29 2,403755869
427 18389,35547 18389,36 2,398126464
428 18432,42188 18432,42 2,392523364
429 18475,48828 18475,49 2,386946387
430 18518,55469 18518,55 2,381395349
431 18561,62109 18561,62 2,37587007
432 18604,6875 18604,69 2,37037037
433 18647,75391 18647,75 2,364896074
434 18690,82031 18690,82 2,359447005
435 18733,88672 18733,89 2,354022989
436 18776,95313 18776,95 2,348623853
437 18820,01953 18820,02 2,343249428
438 18863,08594 18863,09 2,337899543
439 18906,15234 18906,15 2,332574032
440 18949,21875 18949,22 2,327272727
441 18992,28516 18992,29 2,321995465
442 19035,35156 19035,35 2,316742081
443 19078,41797 19078,42 2,311512415
444 19121,48438 19121,48 2,306306306
445 19164,55078 19164,55 2,301123596
446 19207,61719 19207,62 2,295964126
447 19250,68359 19250,68 2,29082774
448 19293,75 19293,75 2,285714286
449 19336,81641 19336,82 2,280623608
450 19379,88281 19379,88 2,275555556
451 19422,94922 19422,95 2,270509978
452 19466,01563 19466,02 2,265486726
453 19509,08203 19509,08 2,260485651
454 19552,14844 19552,15 2,255506608
455 19595,21484 19595,21 2,250549451
456 19638,28125 19638,28 2,245614035
457 19681,34766 19681,35 2,240700219
458 19724,41406 19724,41 2,23580786
459 19767,48047 19767,48 2,230936819
460 19810,54688 19810,55 2,226086957
461 19853,61328 19853,61 2,221258134
462 19896,67969 19896,68 2,216450216
463 19939,74609 19939,75 2,211663067
464 19982,8125 19982,81 2,206896552
465 20025,87891 20025,88 2,202150538
466 20068,94531 20068,95 2,197424893
467 20112,01172 20112,01 2,192719486
468 20155,07813 20155,08 2,188034188
469 20198,14453 20198,14 2,18336887
470 20241,21094 20241,21 2,178723404
471 20284,27734 20284,28 2,174097665
472 20327,34375 20327,34 2,169491525
473 20370,41016 20370,41 2,164904863
474 20413,47656 20413,48 2,160337553
475 20456,54297 20456,54 2,155789474
476 20499,60938 20499,61 2,151260504
477 20542,67578 20542,68 2,146750524
478 20585,74219 20585,74 2,142259414
479 20628,80859 20628,81 2,137787056
480 20671,875 20671,88 2,133333333
481 20714,94141 20714,94 2,128898129
482 20758,00781 20758,01 2,124481328
483 20801,07422 20801,07 2,120082816
484 20844,14063 20844,14 2,115702479
485 20887,20703 20887,21 2,111340206
486 20930,27344 20930,27 2,106995885
487 20973,33984 20973,34 2,102669405
488 21016,40625 21016,41 2,098360656
489 21059,47266 21059,47 2,09406953
490 21102,53906 21102,54 2,089795918
491 21145,60547 21145,61 2,085539715
492 21188,67188 21188,67 2,081300813
493 21231,73828 21231,74 2,077079108
494 21274,80469 21274,80 2,072874494
495 21317,87109 21317,87 2,068686869
496 21360,9375 21360,94 2,064516129
497 21404,00391 21404,00 2,060362173
498 21447,07031 21447,07 2,0562249
499 21490,13672 21490,14 2,052104208
500 21533,20313 21533,20 2,048
501 21576,26953 21576,27 2,043912176
502 21619,33594 21619,34 2,039840637
503 21662,40234 21662,40 2,035785288
504 21705,46875 21705,47 2,031746032
505 21748,53516 21748,54 2,027722772
506 21791,60156 21791,60 2,023715415
507 21834,66797 21834,67 2,019723866
508 21877,73438 21877,73 2,015748031
509 21920,80078 21920,80 2,011787819
510 21963,86719 21963,87 2,007843137
511 22006,93359 22006,93 2,003913894
512 OCT 22050 22050,00 2