Blowing machine

[Tunborough]

I promised you another Easter egg from Terry's data. Remember I mentioned a linear relationship (almost) between Strouhal number and X/R? It still holds up, albeit somewhat fuzzy, with the new data:



Except that it still flattens out around St = 0.4:



Now those familiar with the neighbourhood where X/R lives will ask, with good reason, what about phase angle? X/R is the tangent of phase angle, and phase angle actually seems more meaningful in this context, so won't that clean up what happens at larger X/R? Well, it does, except now we end up with two distinct line segments, one for St up to about 0.3, and another above 0.3 that still flattens out a bit for St above 0.4.



To investigate this further, I'm going to have to dust off some modelling software I haven't used in about a decade. Meanwhile, any insights are welcome.

[Terry McGee]

I wonder would one of these work as a universal whistle coupler? https://www.leevalley.com/en-ca/shop/to ... em=03J6109

2 1/2" maximum diameter would be overkill, but it does say it goes down to 1/4".

Woah, I wonder if that's a typo? I can't see how it could close down that small, or wonder why you'd bother. Be good to wander into a leevalley shop and have a fool with it. Not many of them around here unfortunately!

And their's is a vacuum situation, ours is a pressure situation. Maybe they rely on the vacuum to "suck it on"? In which case would our situation "blow it off"?

And they haven't built in a Pressure Take Off point for the Manometer. I guess we could manage that much....

[Terry McGee]

. . . How do we fairly compare tapered and cylinder whistles . . .

One proposal: use the same head on both straight + tapered "test-tubes". The goal: isolate the effects of tapered vs. straight.

And just put up with the probability that the tapered tube is going to sound weak compared to the cylindrical tube, as it will reduce to a much smaller diameter at the bottom. I probably have a reamer made for the 19th century narrow piccolos here somewhere. That might get us in the right ball park.

[trill]

. . . the probability that the tapered tube is going to sound weak compared to the cylindrical tube, as it will reduce to a much smaller diameter at the bottom. . .

Personally, I'd be interested in both volume + spectrum, comparing tapered to straight.

Sort of raises the question: where does a whistle's sound emanate from ? What proportion from the window ? the open holes ? The foot ?

Raises another question: where best to put a microphone in the one-of-kind-whistle-bit-blowing-machine test space ?

Wasn't there a simulation result link posted (here in-thread), which showed pressure-fronts from the foot + windway merging to form an expanding oval ?

[trill]

. . . I mentioned a linear relationship (almost) between Strouhal number and X/R? . . .

For a whistle, what are X, R ?

I'm trying to visualize how the ratio X/R (reactance/resistance) looks.

For a whistle, how is R calculated ? How is X ?

[Terry McGee]

. . . the probability that the tapered tube is going to sound weak compared to the cylindrical tube, as it will reduce to a much smaller diameter at the bottom. . .

Personally, I'd be interested in both volume + spectrum, comparing tapered to straight.

I did a little exploration in the peace and quiet of the office, just mouth blowing a few notes to get a feel for what we might find. That's with a condenser microphone and a good preamp, recording and analysing on Audacity on the PC.

At this point each whistle has its own head. The aim is just to see if we run into any difficulties in recording or analysing. The whistles are my FrankenWhistle (Tapered) and my Highly Tweaked Soodlums Mellow D (Cylindrical).

Code: Select all

D whistles D5		
Partial	Tapered	Cyl
1	-16.6	-16.3
2	-48	-50.5
3	-23	-24.4
4	-49	-44.6
5	-43	-40.7
6	-52	-52.3
7	-60	-58.7
		
		
D whistles, G5		
Partial	Tapered	Cyl
1	-14	-14
2	-35	-35
3	-30.5	-24.9
4	-40.7	-40.5
5	-48.1	-39
6	-58.8	-73
7	-61	-60.9
		
		
D whistles D6		
Partial	Tapered	Cyl
1	-8.7	-13.4
2	-35.3	-25.5
3	-29	-21.5
4	-47.8	-38.8
5	-46.6	-47.7
6	-49.5	-48.2
7	-46.6	-45.2
		
		
D whistles G6		
Partial	Tapered	Cyl
1	-45.3	-50.3
2	-3.2	-6.9
3	-44.5	-42.8
4	-39.2	-40.9
5	-56.8	-59.2
6	-34.2	-30.4
7	-48	-48.6

There wasn't much difference at D5 and G6, the greatest difference noted at D6 where more of the energy of the Tapered whistle is going into the fundamental and less into the upper partials.

Note incidentally with G6 that measurable energy remains in the Fundamental (G5, 1st Partial) even though I'm aiming for the 2nd. We don't see that in D6 because I have hole 1 open, making that partial unviable. Close that top hole and you can hear and see the Fundamental reasserting itself, but around the -54dB level. (Yes, you can try this at home!)

So that all bodes well for recording and analysing, although I'll still have to look into the acoustical environment issues.

[Terry McGee]

Sort of raises the question: where does a whistle's sound emanate from ? What proportion from the window ? the open holes ? The foot ?

In theory, we should be able to measure that. But I imagine it will be complicated, especially depending on how far away you measure from!

Raises another question: where best to put a microphone in the one-of-kind-whistle-bit-blowing-machine test space ?

Traditionally, we tend to measure "at 1 Metre on axis", as this is enough to get out of local effects of both subject and microphone. But say we were investigating the question above, we'd need to get in closer. And I will probably need to get in closer in the lab downstairs to minimise environmental effects. And need to use directional microphones rather than omnidirectional.

[trill]

. . . recording and analysing on Audacity on the PC.

Thank you for posting a "first look" at tapered v. cyl.

I've used Audacity on+off for years. Tons of capability for free.

Favor to ask: could you post the full spectrum for D6 ? Both tapered + cyl if not too much trouble ?

The version of Audacity I've got (3.1.3) has an "export" button in the spectrum window. It dumps to a simple text file.

Very interesting tidbit about D6 w+w/o the top hole. "Top hole open" usually is much more stable for me, though the timbre is noticeably different.

[Terry McGee]

Woah, this could be a test of the system! Here's the tapered whistle playing D6, top hole uncovered:

Code: Select all

Frequency (Hz)	Level (dB)
21.533203	-41.803612
43.066406	-58.925816
64.599609	-63.191994
86.132813	-75.786140
107.666016	-80.496193
129.199219	-80.204514
150.732422	-79.754944
172.265625	-80.963058
193.798828	-82.005592
215.332031	-82.144463
236.865234	-83.055077
258.398438	-84.737289
279.931641	-85.765938
301.464844	-84.648506
322.998047	-84.055023
344.531250	-84.099686
366.064453	-84.493942
387.597656	-84.544518
409.130859	-84.221527
430.664063	-83.682861
452.197266	-82.762840
473.730469	-82.046944
495.263672	-81.328682
516.796875	-79.985268
538.330078	-77.708778
559.863281	-77.079575
581.396484	-77.937065
602.929688	-77.055603
624.462891	-74.950432
645.996094	-74.125595
667.529297	-75.245125
689.062500	-76.802856
710.595703	-74.531059
732.128906	-70.868179
753.662109	-67.096748
775.195313	-65.446724
796.728516	-65.191490
818.261719	-65.207504
839.794922	-63.912254
861.328125	-61.073410
882.861328	-57.942368
904.394531	-53.097313
925.927734	-48.069866
947.460938	-46.888153
968.994141	-51.509731
990.527344	-54.565350
1012.060547	-55.191673
1033.593750	-57.767262
1055.126953	-59.091270
1076.660156	-59.435200
1098.193359	-57.181644
1119.726563	-51.610294
1141.259766	-42.247837
1162.792969	-17.989338
1184.326172	-9.245283
1205.859375	-12.329785
1227.392578	-31.136007
1248.925781	-45.891361
1270.458984	-54.230453
1291.992188	-59.963867
1313.525391	-62.193897
1335.058594	-60.769611
1356.591797	-60.602932
1378.125000	-60.655411
1399.658203	-60.335629
1421.191406	-60.516026
1442.724609	-61.384739
1464.257813	-61.584625
1485.791016	-62.114124
1507.324219	-63.136375
1528.857422	-63.643238
1550.390625	-64.579544
1571.923828	-65.684761
1593.457031	-65.494507
1614.990234	-65.686172
1636.523438	-65.875305
1658.056641	-65.065552
1679.589844	-64.976631
1701.123047	-66.200050
1722.656250	-67.708893
1744.189453	-67.504547
1765.722656	-66.886360
1787.255859	-68.439262
1808.789063	-67.196281
1830.322266	-67.417786
1851.855469	-69.219650
1873.388672	-68.504341
1894.921875	-64.566780
1916.455078	-62.111645
1937.988281	-59.890442
1959.521484	-60.125721
1981.054688	-61.702702
2002.587891	-59.641586
2024.121094	-58.143822
2045.654297	-58.925426
2067.187500	-59.148232
2088.720703	-60.550926
2110.253906	-64.712288
2131.787109	-63.615253
2153.320313	-62.386852
2174.853516	-64.124405
2196.386719	-64.927444
2217.919922	-65.233765
2239.453125	-66.421051
2260.986328	-66.297455
2282.519531	-64.366020
2304.052734	-60.487263
2325.585938	-55.471191
2347.119141	-45.183445
2368.652344	-35.944046
2390.185547	-36.718552
2411.718750	-41.183483
2433.251953	-42.805412
2454.785156	-44.289074
2476.318359	-46.135017
2497.851563	-47.893696
2519.384766	-49.409523
2540.917969	-51.071350
2562.451172	-52.533619
2583.984375	-54.503521
2605.517578	-55.883217
2627.050781	-56.814404
2648.583984	-56.331367
2670.117188	-56.189445
2691.650391	-58.035065
2713.183594	-60.838860
2734.716797	-62.408474
2756.250000	-60.430367
2777.783203	-60.097626
2799.316406	-60.676941
2820.849609	-60.750206
2842.382813	-61.042282
2863.916016	-61.244713
2885.449219	-61.118969
2906.982422	-60.780380
2928.515625	-60.102230
2950.048828	-60.331474
2971.582031	-60.654610
2993.115234	-58.158138
3014.648438	-56.542717
3036.181641	-55.328411
3057.714844	-55.149075
3079.248047	-54.326664
3100.781250	-54.864258
3122.314453	-56.526581
3143.847656	-59.000633
3165.380859	-61.137901
3186.914063	-60.505970
3208.447266	-62.017082
3229.980469	-64.601761
3251.513672	-68.751060
3273.046875	-68.840675
3294.580078	-69.017105
3316.113281	-70.663879
3337.646484	-72.382744
3359.179688	-71.940033
3380.712891	-72.525291
3402.246094	-73.501579
3423.779297	-72.128899
3445.312500	-70.691673
3466.845703	-69.663742
3488.378906	-68.884636
3509.912109	-62.925255
3531.445313	-43.098701
3552.978516	-31.217976
3574.511719	-29.892218
3596.044922	-36.887535
3617.578125	-52.575630
3639.111328	-55.107346
3660.644531	-53.536377
3682.177734	-55.745983
3703.710938	-56.780914
3725.244141	-58.305180
3746.777344	-61.880688
3768.310547	-64.018707
3789.843750	-64.431892
3811.376953	-67.518646
3832.910156	-70.096855
3854.443359	-71.939247
3875.976563	-72.622108
3897.509766	-72.999664
3919.042969	-69.318565
3940.576172	-65.043594
3962.109375	-64.537979
3983.642578	-65.079193
4005.175781	-66.341263
4026.708984	-66.661812
4048.242188	-67.106003
4069.775391	-68.474777
4091.308594	-66.003555
4112.841797	-67.041618
4134.375000	-68.093246
4155.908203	-68.579262
4177.441406	-70.314987
4198.974609	-72.313087
4220.507813	-73.005829
4242.041016	-74.380653
4263.574219	-71.307564
4285.107422	-68.741844
4306.640625	-67.485367
4328.173828	-68.773529
4349.707031	-72.508942
4371.240234	-73.990944
4392.773438	-73.927200
4414.306641	-74.095215
4435.839844	-73.359543
4457.373047	-75.761826
4478.906250	-75.647598
4500.439453	-76.227600
4521.972656	-76.288612
4543.505859	-76.083374
4565.039063	-75.898972
4586.572266	-73.798859
4608.105469	-73.445663
4629.638672	-75.023293
4651.171875	-76.684593
4672.705078	-76.909035
4694.238281	-76.569321
4715.771484	-61.456470
4737.304688	-50.054569
4758.837891	-48.258213
4780.371094	-51.575184
4801.904297	-59.597832
4823.437500	-65.323860
4844.970703	-66.411621
4866.503906	-64.514214
4888.037109	-63.045902
4909.570313	-63.336117
4931.103516	-62.102028
4952.636719	-62.066780
4974.169922	-64.548225
4995.703125	-65.321892
5017.236328	-66.971680
5038.769531	-66.970993
5060.302734	-67.146347
5081.835938	-67.758240
5103.369141	-69.161942
5124.902344	-66.107773
5146.435547	-64.848701
5167.968750	-65.993637
5189.501953	-67.018364
5211.035156	-65.699814
5232.568359	-65.008453
5254.101563	-65.969658
5275.634766	-64.540077
5297.167969	-64.165321
5318.701172	-64.867912
5340.234375	-65.025177
5361.767578	-64.923676
5383.300781	-64.895859
5404.833984	-65.178108
5426.367188	-64.771500
5447.900391	-65.478546
5469.433594	-68.516037
5490.966797	-70.171410
5512.500000	-71.484962
5534.033203	-69.710297
5555.566406	-69.422218
5577.099609	-67.291718
5598.632813	-66.598869
5620.166016	-67.440773
5641.699219	-67.154770
5663.232422	-68.757263
5684.765625	-70.333931
5706.298828	-72.902687
5727.832031	-70.801025
5749.365234	-69.212524
5770.898438	-70.235809
5792.431641	-72.713173
5813.964844	-74.000244
5835.498047	-73.128876
5857.031250	-72.817657
5878.564453	-72.601089
5900.097656	-60.717831
5921.630859	-48.697807
5943.164063	-47.005020
5964.697266	-48.991150
5986.230469	-53.095020
6007.763672	-67.816933
6029.296875	-73.629936
6050.830078	-71.025513
6072.363281	-67.626205
6093.896484	-64.556221
6115.429688	-63.466850
6136.962891	-64.148224
6158.496094	-65.323845
6180.029297	-66.081917
6201.562500	-64.980225
6223.095703	-64.908684
6244.628906	-67.221764
6266.162109	-70.720879
6287.695313	-75.807701
6309.228516	-79.925415
6330.761719	-75.566833
6352.294922	-72.165504
6373.828125	-73.721741
6395.361328	-76.186852
6416.894531	-74.201591
6438.427734	-74.031502
6459.960938	-75.924431
6481.494141	-76.546738
6503.027344	-76.182968
6524.560547	-76.022781
6546.093750	-75.789536
6567.626953	-74.756340
6589.160156	-74.138634
6610.693359	-73.317223
6632.226563	-74.533913
6653.759766	-72.317596
6675.292969	-71.131630
6696.826172	-69.199028
6718.359375	-67.733971
6739.892578	-65.765007
6761.425781	-65.188766
6782.958984	-65.511902
6804.492188	-66.928032
6826.025391	-66.683578
6847.558594	-67.097549
6869.091797	-68.560661
6890.625000	-70.083290
6912.158203	-70.579727
6933.691406	-70.545502
6955.224609	-71.199562
6976.757813	-68.877480
6998.291016	-68.278511
7019.824219	-67.654945
7041.357422	-67.930687
7062.890625	-67.252853
7084.423828	-63.215870
7105.957031	-54.179619
7127.490234	-50.142029
7149.023438	-51.282242
7170.556641	-57.057747
7192.089844	-63.415581
7213.623047	-65.222672
7235.156250	-66.718445
7256.689453	-69.640823
7278.222656	-71.220436
7299.755859	-71.507042
7321.289063	-71.696686
7342.822266	-73.175858
7364.355469	-73.559586
7385.888672	-73.237755
7407.421875	-74.171509
7428.955078	-73.298981
7450.488281	-70.315651
7472.021484	-68.862907
7493.554688	-68.644012
7515.087891	-69.798782
7536.621094	-72.126419
7558.154297	-70.950043
7579.687500	-69.650238
7601.220703	-70.148186
7622.753906	-70.301796
7644.287109	-71.273422
7665.820313	-73.172890
7687.353516	-75.265984
7708.886719	-73.546936
7730.419922	-72.424080
7751.953125	-72.055389
7773.486328	-69.572769
7795.019531	-67.518913
7816.552734	-67.941879
7838.085938	-69.453751
7859.619141	-70.326752
7881.152344	-73.452919
7902.685547	-72.507973
7924.218750	-69.862297
7945.751953	-68.525963
7967.285156	-68.994080
7988.818359	-68.958511
8010.351563	-67.854340
8031.884766	-69.282143
8053.417969	-68.631989
8074.951172	-67.216034
8096.484375	-65.909325
8118.017578	-66.848557
8139.550781	-66.970840
8161.083984	-66.552017
8182.617188	-65.999374
8204.150391	-65.983925
8225.683594	-66.164444
8247.216797	-65.302917
8268.750000	-62.172668
8290.283203	-50.939320
8311.816406	-47.276409
8333.349609	-48.184067
8354.882813	-52.360817
8376.416016	-56.034042
8397.949219	-64.908501
8419.482422	-68.545982
8441.015625	-69.386452
8462.548828	-69.723633
8484.082031	-69.280510
8505.615234	-68.830063
8527.148438	-68.775940
8548.681641	-69.258293
8570.214844	-68.581734
8591.748047	-67.272888
8613.281250	-67.112274
8634.814453	-66.736343
8656.347656	-66.033936
8677.880859	-65.750153
8699.414063	-68.042900
8720.947266	-69.310081
8742.480469	-68.416870
8764.013672	-67.777878
8785.546875	-66.897537
8807.080078	-66.986877
8828.613281	-67.157280
8850.146484	-66.580254
8871.679688	-65.280457
8893.212891	-64.482468
8914.746094	-65.071930
8936.279297	-66.328163
8957.812500	-67.921349
8979.345703	-67.228622
9000.878906	-66.647545
9022.412109	-67.292908
9043.945313	-68.153793
9065.478516	-68.225662
9087.011719	-68.517868
9108.544922	-69.110893
9130.078125	-69.556923
9151.611328	-68.711449
9173.144531	-67.654510
9194.677734	-67.941582
9216.210938	-68.161797
9237.744141	-67.968971
9259.277344	-68.698761
9280.810547	-69.788017
9302.343750	-70.645599
9323.876953	-70.449486
9345.410156	-69.558304
9366.943359	-69.057129
9388.476563	-68.394226
9410.009766	-68.478065
9431.542969	-68.684761
9453.076172	-67.406937
9474.609375	-60.980263
9496.142578	-57.222683
9517.675781	-56.040257
9539.208984	-58.522141
9560.742188	-60.509445
9582.275391	-64.748970
9603.808594	-66.784317
9625.341797	-67.192123
9646.875000	-67.378288
9668.408203	-67.688950
9689.941406	-68.424469
9711.474609	-69.952888
9733.007813	-69.918434
9754.541016	-70.717598
9776.074219	-69.583710
9797.607422	-68.287796
9819.140625	-67.908737
9840.673828	-69.806396
9862.207031	-70.652672
9883.740234	-69.533195
9905.273438	-68.730598
9926.806641	-67.859558
9948.339844	-67.423508
9969.873047	-66.981812
9991.406250	-67.073074
10012.939453	-67.948189
10034.472656	-68.934616
10056.005859	-68.457993
10077.539063	-68.283661
10099.072266	-68.894966
10120.605469	-68.931190
10142.138672	-69.233719
10163.671875	-69.151947
10185.205078	-69.852615
10206.738281	-70.613754
10228.271484	-70.408638
10249.804688	-70.478951
10271.337891	-70.559235
10292.871094	-70.158432
10314.404297	-71.170273
10335.937500	-70.831070
10357.470703	-72.256393
10379.003906	-73.067818
10400.537109	-71.641449
10422.070313	-71.434540
10443.603516	-71.472359
10465.136719	-71.724266
10486.669922	-70.938728
10508.203125	-71.296173
10529.736328	-72.603279
10551.269531	-73.069023
10572.802734	-72.994492
10594.335938	-72.172729
10615.869141	-72.598145
10637.402344	-71.281128
10658.935547	-63.877300
10680.468750	-59.801144
10702.001953	-57.361931
10723.535156	-58.922474
10745.068359	-61.589809
10766.601563	-63.787304
10788.134766	-69.586670
10809.667969	-71.717560
10831.201172	-73.293266
10852.734375	-73.378456
10874.267578	-73.533760
10895.800781	-73.607536
10917.333984	-72.758995
10938.867188	-72.575203
10960.400391	-72.059471
10981.933594	-72.657974
11003.466797	-73.388184
11025.000000	-73.050354
11046.533203	-73.413933
11068.066406	-73.314293
11089.599609	-74.881508
11111.132813	-74.514061
11132.666016	-72.883614
11154.199219	-73.246857
11175.732422	-72.932617
11197.265625	-72.715179
11218.798828	-73.011703
11240.332031	-72.835548
11261.865234	-71.639702
11283.398438	-72.111557
11304.931641	-73.445053
11326.464844	-73.509315
11347.998047	-73.469093
11369.531250	-73.264183
11391.064453	-73.606483
11412.597656	-73.566559
11434.130859	-73.264580
11455.664063	-73.226135
11477.197266	-74.083466
11498.730469	-74.470314
11520.263672	-74.107109
11541.796875	-74.105164
11563.330078	-74.608032
11584.863281	-74.651855
11606.396484	-75.087135
11627.929688	-75.060265
11649.462891	-75.669395
11670.996094	-76.079613
11692.529297	-75.927666
11714.062500	-75.777527
11735.595703	-75.679840
11757.128906	-76.702019
11778.662109	-76.470413
11800.195313	-76.100571
11821.728516	-74.830582
11843.261719	-70.497749
11864.794922	-67.209023
11886.328125	-65.920990
11907.861328	-66.670372
11929.394531	-69.069748
11950.927734	-69.860504
11972.460938	-73.714874
11993.994141	-77.242203
12015.527344	-77.750313
12037.060547	-77.368553
12058.593750	-77.687263
12080.126953	-79.639664
12101.660156	-78.908607
12123.193359	-77.676788
12144.726563	-77.259003
12166.259766	-77.260254
12187.792969	-77.811958
12209.326172	-77.081947
12230.859375	-76.973999
12252.392578	-78.003174
12273.925781	-78.585037
12295.458984	-81.426483
12316.992188	-82.270744
12338.525391	-80.834770
12360.058594	-80.587959
12381.591797	-81.691826
12403.125000	-83.123665
12424.658203	-83.097000
12446.191406	-82.170311
12467.724609	-82.089882
12489.257813	-82.382347
12510.791016	-82.657898
12532.324219	-82.792320
12553.857422	-82.963547
12575.390625	-82.889938
12596.923828	-84.416161
12618.457031	-84.094467
12639.990234	-84.902504
12661.523438	-84.060646
12683.056641	-84.511620
12704.589844	-84.806915
12726.123047	-84.135765
12747.656250	-83.593285
12769.189453	-84.832115
12790.722656	-87.033592
12812.255859	-85.961479
12833.789063	-86.166138
12855.322266	-86.820854
12876.855469	-86.589951
12898.388672	-86.192055
12919.921875	-86.109840
12941.455078	-84.299583
12962.988281	-83.845085
12984.521484	-83.657028
13006.054688	-84.988449
13027.587891	-82.791565
13049.121094	-79.474220
13070.654297	-74.877243
13092.187500	-72.863533
13113.720703	-76.409096
13135.253906	-78.588799
13156.787109	-79.954468
13178.320313	-84.430374
13199.853516	-86.823204
13221.386719	-87.709244
13242.919922	-87.314056
13264.453125	-86.807503
13285.986328	-85.930313
13307.519531	-87.018486
13329.052734	-89.908333
13350.585938	-89.482712
13372.119141	-88.072113
13393.652344	-87.791847
13415.185547	-86.348480
13436.718750	-85.698059
13458.251953	-88.380463
13479.785156	-90.472076
13501.318359	-90.140244
13522.851563	-88.750496
13544.384766	-88.115509
13565.917969	-89.789093
13587.451172	-89.883270
13608.984375	-88.819702
13630.517578	-87.255516
13652.050781	-87.306305
13673.583984	-88.829788
13695.117188	-89.694328
13716.650391	-89.235985
13738.183594	-88.532417
13759.716797	-88.605377
13781.250000	-87.362793
13802.783203	-87.263489
13824.316406	-87.000137
13845.849609	-86.061295
13867.382813	-85.668999
13888.916016	-87.014618
13910.449219	-87.741333
13931.982422	-87.740150
13953.515625	-88.536972
13975.048828	-87.709053
13996.582031	-88.185074
14018.115234	-89.640190
14039.648438	-89.600266
14061.181641	-89.164757
14082.714844	-88.211975
14104.248047	-87.108284
14125.781250	-85.718239
14147.314453	-85.751732
14168.847656	-86.584488
14190.380859	-87.193878
14211.914063	-84.937614
14233.447266	-83.123726
14254.980469	-81.294968
14276.513672	-76.499786
14298.046875	-76.300102
14319.580078	-77.246223
14341.113281	-78.160378
14362.646484	-82.316658
14384.179688	-84.491478
14405.712891	-85.245705
14427.246094	-85.596573
14448.779297	-85.262924
14470.312500	-85.039406
14491.845703	-85.199501
14513.378906	-85.431892
14534.912109	-84.815514
14556.445313	-84.381302
14577.978516	-84.052299
14599.511719	-84.187759
14621.044922	-83.368568
14642.578125	-82.652977
14664.111328	-81.371887
14685.644531	-80.911888
14707.177734	-80.991913
14728.710938	-81.071487
14750.244141	-81.629623
14771.777344	-82.529655
14793.310547	-83.412750
14814.843750	-83.850052
14836.376953	-83.985458
14857.910156	-84.100365
14879.443359	-83.724083
14900.976563	-83.232269
14922.509766	-82.573700
14944.042969	-82.245438
14965.576172	-82.339180
14987.109375	-82.977654
15008.642578	-83.634766
15030.175781	-84.524406
15051.708984	-85.805290
15073.242188	-86.907455
15094.775391	-87.201897
15116.308594	-86.212212
15137.841797	-85.812271
15159.375000	-87.523262
15180.908203	-88.216568
15202.441406	-88.586952
15223.974609	-89.177826
15245.507813	-90.065331
15267.041016	-88.587982
15288.574219	-87.629219
15310.107422	-87.992638
15331.640625	-88.257240
15353.173828	-88.346169
15374.707031	-88.831673
15396.240234	-87.777977
15417.773438	-84.437538
15439.306641	-84.472000
15460.839844	-80.330124
15482.373047	-78.782967
15503.906250	-80.391632
15525.439453	-80.665421
15546.972656	-81.956398
15568.505859	-84.610840
15590.039063	-84.678459
15611.572266	-83.758804
15633.105469	-82.481186
15654.638672	-81.460892
15676.171875	-81.464493
15697.705078	-81.203392
15719.238281	-80.450943
15740.771484	-80.048485
15762.304688	-80.086075
15783.837891	-79.768166
15805.371094	-79.181328
15826.904297	-79.336258
15848.437500	-79.874672
15869.970703	-80.168457
15891.503906	-80.750755
15913.037109	-80.505013
15934.570313	-80.497429
15956.103516	-80.737915
15977.636719	-80.283455
15999.169922	-80.372673
16020.703125	-80.174736
16042.236328	-80.058182
16063.769531	-80.609528
16085.302734	-81.295090
16106.835938	-81.235893
16128.369141	-82.106697
16149.902344	-82.881088
16171.435547	-83.223160
16192.968750	-83.151566
16214.501953	-83.074234
16236.035156	-83.754280
16257.568359	-84.028198
16279.101563	-84.415367
16300.634766	-85.079025
16322.167969	-85.522858
16343.701172	-85.546745
16365.234375	-85.338593
16386.767578	-85.687538
16408.300781	-86.428864
16429.833984	-87.281006
16451.367188	-87.407410
16472.900391	-87.920883
16494.433594	-88.595154
16515.966797	-89.079849
16537.500000	-88.685486
16559.033203	-88.439194
16580.566406	-88.037277
16602.099609	-87.081955
16623.632813	-88.055443
16645.166016	-88.033058
16666.699219	-88.388031
16688.232422	-90.046654
16709.765625	-90.799484
16731.298828	-90.318108
16752.832031	-90.987175
16774.365234	-90.170692
16795.898438	-90.240608
16817.431641	-90.381638
16838.964844	-88.495308
16860.498047	-87.768600
16882.031250	-87.746147
16903.564453	-86.689087
16925.097656	-86.313103
16946.630859	-87.107155
16968.164063	-87.141785
16989.697266	-87.686676
17011.230469	-88.530228
17032.763672	-88.303658
17054.296875	-88.343239
17075.830078	-88.958817
17097.363281	-89.330429
17118.896484	-90.366882
17140.429688	-91.132362
17161.962891	-91.882866
17183.496094	-91.131615
17205.029297	-90.972435
17226.562500	-91.392746
17248.095703	-91.790329
17269.628906	-91.204498
17291.162109	-91.230164
17312.695313	-91.039688
17334.228516	-90.580467
17355.761719	-89.339592
17377.294922	-89.069481
17398.828125	-88.441093
17420.361328	-87.843712
17441.894531	-87.255653
17463.427734	-86.608345
17484.960938	-85.965462
17506.494141	-85.795403
17528.027344	-85.465378
17549.560547	-85.364426
17571.093750	-84.874626
17592.626953	-86.118324
17614.160156	-86.534454
17635.693359	-86.431076
17657.226563	-86.838478
17678.759766	-87.794563
17700.292969	-88.398758
17721.826172	-88.238243
17743.359375	-88.336365
17764.892578	-87.940948
17786.425781	-86.712471
17807.958984	-86.939873
17829.492188	-85.004196
17851.025391	-84.444328
17872.558594	-87.629448
17894.091797	-88.258911
17915.625000	-88.059967
17937.158203	-90.073013
17958.691406	-92.795464
17980.224609	-93.901627
18001.757813	-94.374794
18023.291016	-94.243240
18044.824219	-94.701622
18066.357422	-95.156090
18087.890625	-95.243553
18109.423828	-95.175903
18130.957031	-95.013741
18152.490234	-94.324814
18174.023438	-93.218544
18195.556641	-92.491791
18217.089844	-93.119629
18238.623047	-93.130417
18260.156250	-91.705902
18281.689453	-90.876488
18303.222656	-91.151398
18324.755859	-92.051857
18346.289063	-92.031281
18367.822266	-91.390617
18389.355469	-92.137825
18410.888672	-93.236412
18432.421875	-93.470398
18453.955078	-93.143166
18475.488281	-93.322136
18497.021484	-93.259247
18518.554688	-93.792503
18540.087891	-94.058945
18561.621094	-93.780312
18583.154297	-92.848389
18604.687500	-92.767082
18626.220703	-93.451523
18647.753906	-93.775681
18669.287109	-93.382751
18690.820313	-93.048477
18712.353516	-92.596680
18733.886719	-93.018654
18755.419922	-93.032181
18776.953125	-94.478630
18798.486328	-94.617256
18820.019531	-94.394356
18841.552734	-94.592834
18863.085938	-93.842255
18884.619141	-93.895897
18906.152344	-94.566742
18927.685547	-95.097221
18949.218750	-93.991913
18970.751953	-91.811539
18992.285156	-92.259140
19013.818359	-92.588623
19035.351563	-91.846397
19056.884766	-93.173935
19078.417969	-93.119316
19099.951172	-93.098419
19121.484375	-93.896584
19143.017578	-93.935211
19164.550781	-93.810112
19186.083984	-95.110077
19207.617188	-95.080978
19229.150391	-95.769882
19250.683594	-96.343491
19272.216797	-96.401031
19293.750000	-96.257217
19315.283203	-96.438538
19336.816406	-96.920395
19358.349609	-97.369675
19379.882813	-98.020065
19401.416016	-98.830833
19422.949219	-98.363808
19444.482422	-97.605179
19466.015625	-97.281540
19487.548828	-97.472000
19509.082031	-97.948593
19530.615234	-97.673187
19552.148438	-97.349632
19573.681641	-97.114296
19595.214844	-97.233917
19616.748047	-97.040367
19638.281250	-95.765556
19659.814453	-95.253212
19681.347656	-95.164291
19702.880859	-95.699356
19724.414063	-96.415085
19745.947266	-96.450424
19767.480469	-95.664238
19789.013672	-95.898987
19810.546875	-96.374626
19832.080078	-97.060570
19853.613281	-96.954338
19875.146484	-96.258308
19896.679688	-96.405800
19918.212891	-95.210907
19939.746094	-95.369850
19961.279297	-95.519791
19982.812500	-96.022438
20004.345703	-95.602638
20025.878906	-95.997215
20047.412109	-96.284126
20068.945313	-95.624054
20090.478516	-94.301292
20112.011719	-94.106682
20133.544922	-94.232216
20155.078125	-93.829262
20176.611328	-93.513618
20198.144531	-93.723412
20219.677734	-92.452446
20241.210938	-93.076660
20262.744141	-94.504776
20284.277344	-94.094528
20305.810547	-94.369461
20327.343750	-95.777924
20348.876953	-95.392128
20370.410156	-95.096001
20391.943359	-94.992264
20413.476563	-94.511658
20435.009766	-94.062790
20456.542969	-93.212158
20478.076172	-93.444427
20499.609375	-94.047028
20521.142578	-93.650848
20542.675781	-93.496284
20564.208984	-93.071198
20585.742188	-93.368355
20607.275391	-93.682648
20628.808594	-92.861397
20650.341797	-93.165596
20671.875000	-91.106293
20693.408203	-92.155243
20714.941406	-93.369774
20736.474609	-93.184914
20758.007813	-90.946587
20779.541016	-88.749100
20801.074219	-92.633392
20822.607422	-94.700874
20844.140625	-94.733093
20865.673828	-93.274147
20887.207031	-93.452377
20908.740234	-95.907295
20930.273438	-95.172653
20951.806641	-95.204956
20973.339844	-91.569344
20994.873047	-93.773827
21016.406250	-96.858177
21037.939453	-96.976669
21059.472656	-94.842438
21081.005859	-92.934303
21102.539063	-96.743011
21124.072266	-97.599213
21145.605469	-98.211540
21167.138672	-98.702354
21188.671875	-98.694084
21210.205078	-99.359306
21231.738281	-98.938095
21253.271484	-99.276077
21274.804688	-99.114029
21296.337891	-99.703690
21317.871094	-99.683701
21339.404297	-98.467606
21360.937500	-98.198845
21382.470703	-98.116173
21404.003906	-97.716759
21425.537109	-98.559418
21447.070313	-99.719429
21468.603516	-99.887146
21490.136719	-99.764328
21511.669922	-99.970360
21533.203125	-100.629906
21554.736328	-100.879883
21576.269531	-100.574814
21597.802734	-99.841255
21619.335938	-99.965614
21640.869141	-99.098167
21662.402344	-97.822655
21683.935547	-98.914757
21705.468750	-98.190971
21727.001953	-98.789429
21748.535156	-99.315430
21770.068359	-99.764832
21791.601563	-99.359299
21813.134766	-99.530258
21834.667969	-100.695442
21856.201172	-100.847389
21877.734375	-99.936821
21899.267578	-100.010574
21920.800781	-99.807541
21942.333984	-100.931190
21963.867188	-100.990997
21985.400391	-100.770348
22006.933594	-101.626923
22028.466797	-101.074432

[Terry McGee]

Well, the sky doesn't seem to have fallen in. So here's the cylindrical flute playing D6, top hole uncovered.

Code: Select all

Frequency (Hz)	Level (dB)
21.533203	-53.046284
43.066406	-62.657219
64.599609	-63.660294
86.132813	-75.901398
107.666016	-79.998047
129.199219	-79.358139
150.732422	-79.485626
172.265625	-81.050438
193.798828	-81.569260
215.332031	-81.148003
236.865234	-82.963791
258.398438	-84.472008
279.931641	-84.521690
301.464844	-83.280075
322.998047	-82.556892
344.531250	-83.782944
366.064453	-84.933090
387.597656	-83.585945
409.130859	-83.755821
430.664063	-83.731178
452.197266	-82.404526
473.730469	-81.875130
495.263672	-81.558594
516.796875	-81.117340
538.330078	-77.686996
559.863281	-77.096825
581.396484	-78.289474
602.929688	-76.508827
624.462891	-75.449707
645.996094	-75.131615
667.529297	-75.640381
689.062500	-76.139206
710.595703	-73.278397
732.128906	-70.395844
753.662109	-66.385880
775.195313	-64.362648
796.728516	-64.497009
818.261719	-64.851868
839.794922	-63.285683
861.328125	-59.802364
882.861328	-57.200443
904.394531	-53.495010
925.927734	-51.159100
947.460938	-51.062092
968.994141	-52.688339
990.527344	-52.515808
1012.060547	-53.500736
1033.593750	-56.467010
1055.126953	-58.154064
1076.660156	-57.476219
1098.193359	-52.047054
1119.726563	-44.738907
1141.259766	-25.947584
1162.792969	-14.588010
1184.326172	-15.908422
1205.859375	-31.522171
1227.392578	-44.915222
1248.925781	-53.945091
1270.458984	-60.908440
1291.992188	-64.407478
1313.525391	-62.291580
1335.058594	-60.393826
1356.591797	-59.777779
1378.125000	-59.717194
1399.658203	-60.041985
1421.191406	-61.341930
1442.724609	-62.236183
1464.257813	-61.481304
1485.791016	-62.767860
1507.324219	-63.718529
1528.857422	-64.120613
1550.390625	-65.405685
1571.923828	-66.582115
1593.457031	-66.871277
1614.990234	-65.901566
1636.523438	-64.765388
1658.056641	-65.791992
1679.589844	-67.549286
1701.123047	-68.377014
1722.656250	-69.293640
1744.189453	-70.380905
1765.722656	-70.357491
1787.255859	-70.383621
1808.789063	-68.557655
1830.322266	-68.734612
1851.855469	-67.461403
1873.388672	-64.978935
1894.921875	-61.046955
1916.455078	-59.501873
1937.988281	-58.140598
1959.521484	-60.781830
1981.054688	-60.754955
2002.587891	-59.276054
2024.121094	-58.834396
2045.654297	-60.018303
2067.187500	-60.999130
2088.720703	-62.337425
2110.253906	-63.447559
2131.787109	-61.022926
2153.320313	-59.850540
2174.853516	-60.254246
2196.386719	-59.337307
2217.919922	-58.239689
2239.453125	-57.607422
2260.986328	-53.183666
2282.519531	-49.256733
2304.052734	-40.885647
2325.585938	-28.918976
2347.119141	-25.998516
2368.652344	-32.888241
2390.185547	-45.076675
2411.718750	-49.023621
2433.251953	-53.111141
2454.785156	-53.533333
2476.318359	-54.672020
2497.851563	-55.284874
2519.384766	-55.998520
2540.917969	-56.772915
2562.451172	-57.917465
2583.984375	-59.934334
2605.517578	-60.693825
2627.050781	-61.869137
2648.583984	-61.812885
2670.117188	-61.276451
2691.650391	-63.154194
2713.183594	-65.469429
2734.716797	-67.019638
2756.250000	-64.274017
2777.783203	-63.552765
2799.316406	-64.108879
2820.849609	-64.559761
2842.382813	-64.040726
2863.916016	-64.388084
2885.449219	-64.570976
2906.982422	-63.497131
2928.515625	-61.942074
2950.048828	-59.969803
2971.582031	-58.177929
2993.115234	-55.963421
3014.648438	-54.825809
3036.181641	-53.748302
3057.714844	-51.644032
3079.248047	-50.918659
3100.781250	-52.628777
3122.314453	-55.564907
3143.847656	-57.743076
3165.380859	-57.578907
3186.914063	-58.358387
3208.447266	-60.166359
3229.980469	-63.429550
3251.513672	-66.795670
3273.046875	-66.418724
3294.580078	-67.595764
3316.113281	-69.469154
3337.646484	-69.425423
3359.179688	-66.411674
3380.712891	-65.326057
3402.246094	-64.542244
3423.779297	-62.600376
3445.312500	-60.258617
3466.845703	-53.905205
3488.378906	-29.992397
3509.912109	-22.050200
3531.445313	-23.786840
3552.978516	-35.408749
3574.511719	-48.145958
3596.044922	-55.201023
3617.578125	-57.763947
3639.111328	-59.023087
3660.644531	-61.548199
3682.177734	-62.725052
3703.710938	-62.842651
3725.244141	-64.450096
3746.777344	-65.670273
3768.310547	-67.566643
3789.843750	-70.164253
3811.376953	-73.510788
3832.910156	-72.618332
3854.443359	-72.493637
3875.976563	-72.354645
3897.509766	-71.758453
3919.042969	-70.205795
3940.576172	-67.773682
3962.109375	-68.335640
3983.642578	-67.954247
4005.175781	-69.912117
4026.708984	-70.955795
4048.242188	-70.439400
4069.775391	-68.814819
4091.308594	-68.813240
4112.841797	-71.581696
4134.375000	-70.303459
4155.908203	-69.919601
4177.441406	-72.646416
4198.974609	-71.738129
4220.507813	-70.748596
4242.041016	-73.065918
4263.574219	-72.013580
4285.107422	-69.507301
4306.640625	-69.617264
4328.173828	-71.891541
4349.707031	-76.911438
4371.240234	-78.115570
4392.773438	-76.327606
4414.306641	-77.947716
4435.839844	-79.691132
4457.373047	-80.733582
4478.906250	-78.775429
4500.439453	-78.003899
4521.972656	-76.436951
4543.505859	-75.365257
4565.039063	-75.445694
4586.572266	-73.234146
4608.105469	-71.465462
4629.638672	-66.962280
4651.171875	-51.099461
4672.705078	-40.445477
4694.238281	-39.602047
4715.771484	-45.971390
4737.304688	-59.157784
4758.837891	-65.736099
4780.371094	-71.319946
4801.904297	-74.552238
4823.437500	-79.616745
4844.970703	-78.435081
4866.503906	-75.226280
4888.037109	-74.085709
4909.570313	-71.215584
4931.103516	-69.888672
4952.636719	-71.737465
4974.169922	-71.894363
4995.703125	-72.023186
5017.236328	-74.055023
5038.769531	-72.901321
5060.302734	-74.201813
5081.835938	-76.344643
5103.369141	-72.673058
5124.902344	-69.609863
5146.435547	-69.457962
5167.968750	-69.905785
5189.501953	-69.789848
5211.035156	-68.448227
5232.568359	-68.032677
5254.101563	-68.929054
5275.634766	-69.721741
5297.167969	-69.237633
5318.701172	-69.235405
5340.234375	-69.868233
5361.767578	-68.155930
5383.300781	-66.444244
5404.833984	-66.731255
5426.367188	-68.701279
5447.900391	-71.020004
5469.433594	-73.377647
5490.966797	-73.663315
5512.500000	-72.068596
5534.033203	-70.623909
5555.566406	-69.960320
5577.099609	-68.286079
5598.632813	-68.011276
5620.166016	-68.908028
5641.699219	-70.658310
5663.232422	-72.202980
5684.765625	-74.313644
5706.298828	-72.389221
5727.832031	-70.351204
5749.365234	-69.046761
5770.898438	-70.231209
5792.431641	-70.621902
5813.964844	-62.638046
5835.498047	-50.256054
5857.031250	-48.906208
5878.564453	-55.844242
5900.097656	-63.440338
5921.630859	-70.000259
5943.164063	-70.342400
5964.697266	-75.055458
5986.230469	-75.715218
6007.763672	-73.391808
6029.296875	-73.684799
6050.830078	-74.515900
6072.363281	-72.304939
6093.896484	-72.615334
6115.429688	-75.992424
6136.962891	-78.393272
6158.496094	-77.984123
6180.029297	-77.932556
6201.562500	-79.400475
6223.095703	-82.677155
6244.628906	-79.950027
6266.162109	-76.514671
6287.695313	-75.652832
6309.228516	-75.336891
6330.761719	-75.282021
6352.294922	-75.605095
6373.828125	-75.024139
6395.361328	-72.600151
6416.894531	-73.010994
6438.427734	-74.972641
6459.960938	-75.754021
6481.494141	-74.634621
6503.027344	-76.886551
6524.560547	-78.940735
6546.093750	-77.602859
6567.626953	-76.110764
6589.160156	-74.927315
6610.693359	-73.953957
6632.226563	-72.458755
6653.759766	-72.441505
6675.292969	-71.119331
6696.826172	-70.177971
6718.359375	-69.544594
6739.892578	-69.988533
6761.425781	-69.277969
6782.958984	-69.974754
6804.492188	-70.890266
6826.025391	-71.209351
6847.558594	-71.095573
6869.091797	-69.562744
6890.625000	-68.788010
6912.158203	-69.166405
6933.691406	-68.765877
6955.224609	-67.445755
6976.757813	-63.530151
6998.291016	-54.537262
7019.824219	-49.018539
7041.357422	-49.049530
7062.890625	-53.055656
7084.423828	-60.427525
7105.957031	-62.524097
7127.490234	-64.512703
7149.023438	-67.298622
7170.556641	-67.957405
7192.089844	-68.130424
7213.623047	-69.002571
7235.156250	-69.996445
7256.689453	-70.198975
7278.222656	-70.048615
7299.755859	-70.162735
7321.289063	-69.721001
7342.822266	-69.022346
7364.355469	-70.204094
7385.888672	-69.454956
7407.421875	-68.533020
7428.955078	-68.496666
7450.488281	-69.148720
7472.021484	-69.228096
7493.554688	-69.707573
7515.087891	-70.983932
7536.621094	-69.312050
7558.154297	-67.256401
7579.687500	-67.621803
7601.220703	-69.201576
7622.753906	-69.622406
7644.287109	-70.471581
7665.820313	-71.720749
7687.353516	-71.871803
7708.886719	-71.726433
7730.419922	-71.758865
7751.953125	-71.599197
7773.486328	-70.774551
7795.019531	-69.272598
7816.552734	-69.068756
7838.085938	-69.740311
7859.619141	-71.292747
7881.152344	-71.237602
7902.685547	-69.125633
7924.218750	-68.616562
7945.751953	-68.090935
7967.285156	-69.173553
7988.818359	-69.139328
8010.351563	-69.413628
8031.884766	-69.685349
8053.417969	-69.413712
8074.951172	-67.651062
8096.484375	-67.003052
8118.017578	-66.308495
8139.550781	-63.934685
8161.083984	-54.061565
8182.617188	-46.516930
8204.150391	-45.453136
8225.683594	-46.386581
8247.216797	-51.770382
8268.750000	-61.190868
8290.283203	-64.677467
8311.816406	-67.869476
8333.349609	-70.632294
8354.882813	-70.604347
8376.416016	-69.341843
8397.949219	-68.689796
8419.482422	-68.799782
8441.015625	-68.689560
8462.548828	-67.975174
8484.082031	-67.215302
8505.615234	-67.123283
8527.148438	-67.458008
8548.681641	-68.231758
8570.214844	-68.920486
8591.748047	-69.810783
8613.281250	-70.898193
8634.814453	-69.360916
8656.347656	-68.587486
8677.880859	-69.028999
8699.414063	-69.778008
8720.947266	-69.187073
8742.480469	-67.910255
8764.013672	-67.341751
8785.546875	-67.721016
8807.080078	-68.650627
8828.613281	-68.193771
8850.146484	-67.588112
8871.679688	-67.739983
8893.212891	-68.277229
8914.746094	-69.077148
8936.279297	-69.339294
8957.812500	-68.704903
8979.345703	-68.644432
9000.878906	-70.470108
9022.412109	-69.987457
9043.945313	-69.830460
9065.478516	-70.802475
9087.011719	-71.042946
9108.544922	-71.097618
9130.078125	-70.416573
9151.611328	-68.815773
9173.144531	-68.199966
9194.677734	-67.546188
9216.210938	-67.539963
9237.744141	-68.087578
9259.277344	-67.535912
9280.810547	-66.576096
9302.343750	-66.117752
9323.876953	-63.813572
9345.410156	-56.183533
9366.943359	-52.517673
9388.476563	-52.158844
9410.009766	-54.584888
9431.542969	-60.520329
9453.076172	-65.188179
9474.609375	-67.602249
9496.142578	-68.627243
9517.675781	-68.888611
9539.208984	-68.538048
9560.742188	-70.307571
9582.275391	-72.258751
9603.808594	-73.441048
9625.341797	-72.529388
9646.875000	-73.247223
9668.408203	-74.805115
9689.941406	-76.783417
9711.474609	-76.037903
9733.007813	-75.444649
9754.541016	-75.344818
9776.074219	-74.850945
9797.607422	-74.399467
9819.140625	-75.926147
9840.673828	-76.863617
9862.207031	-76.126373
9883.740234	-74.432907
9905.273438	-75.443535
9926.806641	-76.508453
9948.339844	-76.549156
9969.873047	-76.197609
9991.406250	-76.469872
10012.939453	-77.431999
10034.472656	-77.800987
10056.005859	-78.285927
10077.539063	-79.472191
10099.072266	-79.883583
10120.605469	-79.332344
10142.138672	-78.752373
10163.671875	-79.515076
10185.205078	-77.926521
10206.738281	-75.878647
10228.271484	-74.826103
10249.804688	-73.251152
10271.337891	-73.226830
10292.871094	-73.774796
10314.404297	-73.901917
10335.937500	-75.212257
10357.470703	-76.129547
10379.003906	-75.443146
10400.537109	-74.281647
10422.070313	-74.585762
10443.603516	-74.823730
10465.136719	-75.193039
10486.669922	-72.185448
10508.203125	-63.621929
10529.736328	-59.262386
10551.269531	-59.729916
10572.802734	-62.108448
10594.335938	-67.226608
10615.869141	-72.880455
10637.402344	-75.129677
10658.935547	-76.201477
10680.468750	-75.888893
10702.001953	-75.274635
10723.535156	-75.480522
10745.068359	-76.116005
10766.601563	-75.965210
10788.134766	-74.521584
10809.667969	-74.576256
10831.201172	-74.583466
10852.734375	-76.001427
10874.267578	-77.145493
10895.800781	-76.559891
10917.333984	-76.285316
10938.867188	-77.224876
10960.400391	-78.056343
10981.933594	-79.110176
11003.466797	-78.989571
11025.000000	-79.800415
11046.533203	-79.158340
11068.066406	-78.611687
11089.599609	-78.898224
11111.132813	-78.251091
11132.666016	-77.875816
11154.199219	-80.219948
11175.732422	-80.835197
11197.265625	-80.550667
11218.798828	-80.356560
11240.332031	-80.049942
11261.865234	-80.949463
11283.398438	-83.273865
11304.931641	-85.285736
11326.464844	-83.906998
11347.998047	-84.585625
11369.531250	-84.283905
11391.064453	-83.016212
11412.597656	-83.847092
11434.130859	-84.452034
11455.664063	-85.364395
11477.197266	-83.257645
11498.730469	-82.217247
11520.263672	-84.672165
11541.796875	-86.961441
11563.330078	-86.091255
11584.863281	-85.980293
11606.396484	-84.805832
11627.929688	-83.380554
11649.462891	-83.009048
11670.996094	-79.809380
11692.529297	-77.026810
11714.062500	-77.001968
11735.595703	-77.123642
11757.128906	-80.123436
11778.662109	-81.433426
11800.195313	-83.290802
11821.728516	-88.289063
11843.261719	-90.858528
11864.794922	-89.107849
11886.328125	-87.131821
11907.861328	-86.412712
11929.394531	-87.906616
11950.927734	-87.034958
11972.460938	-84.759628
11993.994141	-84.422005
12015.527344	-84.709007
12037.060547	-83.358986
12058.593750	-82.859108
12080.126953	-82.209801
12101.660156	-82.033974
12123.193359	-83.320038
12144.726563	-84.350883
12166.259766	-84.721245
12187.792969	-87.022942
12209.326172	-86.930870
12230.859375	-85.454269
12252.392578	-86.705826
12273.925781	-88.244247
12295.458984	-89.354568
12316.992188	-90.207458
12338.525391	-91.053551
12360.058594	-92.978004
12381.591797	-93.269974
12403.125000	-93.160515
12424.658203	-91.218765
12446.191406	-87.889946
12467.724609	-87.762337
12489.257813	-90.102066
12510.791016	-89.206390
12532.324219	-90.768944
12553.857422	-91.346191
12575.390625	-90.766251
12596.923828	-89.541458
12618.457031	-88.047508
12639.990234	-88.569702
12661.523438	-88.919060
12683.056641	-90.903381
12704.589844	-92.162468
12726.123047	-90.893127
12747.656250	-90.162163
12769.189453	-90.009163
12790.722656	-88.650444
12812.255859	-85.964767
12833.789063	-83.062073
12855.322266	-78.244278
12876.855469	-77.567085
12898.388672	-80.839317
12919.921875	-83.606071
12941.455078	-86.100174
12962.988281	-88.817627
12984.521484	-87.752831
13006.054688	-87.116096
13027.587891	-87.944221
13049.121094	-87.768295
13070.654297	-86.740639
13092.187500	-86.652924
13113.720703	-86.303123
13135.253906	-86.800011
13156.787109	-88.459000
13178.320313	-88.826065
13199.853516	-88.101334
13221.386719	-88.261101
13242.919922	-88.725006
13264.453125	-88.547935
13285.986328	-88.347748
13307.519531	-87.387123
13329.052734	-86.530190
13350.585938	-85.420059
13372.119141	-84.525543
13393.652344	-84.350952
13415.185547	-84.677971
13436.718750	-84.720848
13458.251953	-85.209595
13479.785156	-86.022072
13501.318359	-84.458145
13522.851563	-84.084045
13544.384766	-84.222458
13565.917969	-85.548019
13587.451172	-85.842232
13608.984375	-84.769989
13630.517578	-84.737556
13652.050781	-85.065323
13673.583984	-85.367912
13695.117188	-85.860443
13716.650391	-86.708138
13738.183594	-86.703995
13759.716797	-86.213097
13781.250000	-84.177330
13802.783203	-82.715355
13824.316406	-83.293320
13845.849609	-84.878288
13867.382813	-85.710114
13888.916016	-84.426849
13910.449219	-83.832283
13931.982422	-83.915520
13953.515625	-84.575996
13975.048828	-82.634895
13996.582031	-81.070419
14018.115234	-76.826088
14039.648438	-73.785042
14061.181641	-73.900986
14082.714844	-74.261772
14104.248047	-75.601227
14125.781250	-77.839325
14147.314453	-81.095016
14168.847656	-82.925835
14190.380859	-83.407776
14211.914063	-84.501587
14233.447266	-83.404297
14254.980469	-83.682388
14276.513672	-83.428925
14298.046875	-84.625137
14319.580078	-84.377571
14341.113281	-85.249458
14362.646484	-85.714340
14384.179688	-85.903679
14405.712891	-85.479546
14427.246094	-84.925728
14448.779297	-84.734169
14470.312500	-84.828041
14491.845703	-84.959473
14513.378906	-86.158997
14534.912109	-85.671593
14556.445313	-84.675797
14577.978516	-83.846054
14599.511719	-83.785210
14621.044922	-84.047676
14642.578125	-84.413490
14664.111328	-84.788628
14685.644531	-85.914566
14707.177734	-86.446838
14728.710938	-86.381798
14750.244141	-86.145500
14771.777344	-86.211281
14793.310547	-86.550171
14814.843750	-86.816025
14836.376953	-87.676178
14857.910156	-87.789108
14879.443359	-86.867043
14900.976563	-86.842545
14922.509766	-86.327972
14944.042969	-84.852112
14965.576172	-83.872589
14987.109375	-83.584938
15008.642578	-83.001862
15030.175781	-82.364189
15051.708984	-84.004738
15073.242188	-84.856056
15094.775391	-85.563446
15116.308594	-85.815598
15137.841797	-85.397003
15159.375000	-85.060837
15180.908203	-83.242172
15202.441406	-81.683182
15223.974609	-84.132469
15245.507813	-85.527069
15267.041016	-83.778351
15288.574219	-82.413567
15310.107422	-84.019783
15331.640625	-85.132065
15353.173828	-85.465675
15374.707031	-85.680496
15396.240234	-84.145691
15417.773438	-84.026337
15439.306641	-84.479599
15460.839844	-85.207520
15482.373047	-85.689407
15503.906250	-86.114838
15525.439453	-85.493614
15546.972656	-85.997658
15568.505859	-86.659187
15590.039063	-86.672241
15611.572266	-87.944626
15633.105469	-88.283524
15654.638672	-87.807472
15676.171875	-87.075096
15697.705078	-86.167084
15719.238281	-85.582130
15740.771484	-85.764542
15762.304688	-84.709671
15783.837891	-84.870369
15805.371094	-87.079819
15826.904297	-86.792526
15848.437500	-86.304832
15869.970703	-87.289734
15891.503906	-87.376259
15913.037109	-86.864136
15934.570313	-87.439148
15956.103516	-88.430130
15977.636719	-89.363976
15999.169922	-89.472412
16020.703125	-89.887337
16042.236328	-89.938431
16063.769531	-90.827141
16085.302734	-90.499779
16106.835938	-89.384857
16128.369141	-90.246796
16149.902344	-91.302567
16171.435547	-90.857857
16192.968750	-90.659500
16214.501953	-91.504730
16236.035156	-92.155907
16257.568359	-92.468094
16279.101563	-90.767456
16300.634766	-89.975685
16322.167969	-88.949852
16343.701172	-86.950447
16365.234375	-84.230186
16386.767578	-85.075592
16408.300781	-86.342995
16429.833984	-86.217377
16451.367188	-86.036415
16472.900391	-87.444710
16494.433594	-90.052834
16515.966797	-90.659538
16537.500000	-91.334435
16559.033203	-91.623749
16580.566406	-90.739891
16602.099609	-91.832298
16623.632813	-92.854179
16645.166016	-92.879135
16666.699219	-94.069176
16688.232422	-93.839394
16709.765625	-94.267548
16731.298828	-95.556030
16752.832031	-95.532509
16774.365234	-96.413811
16795.898438	-96.905869
16817.431641	-96.385185
16838.964844	-96.120796
16860.498047	-96.101685
16882.031250	-95.405701
16903.564453	-92.981873
16925.097656	-92.160194
16946.630859	-91.792938
16968.164063	-91.533249
16989.697266	-92.146629
17011.230469	-92.324951
17032.763672	-92.984474
17054.296875	-93.542435
17075.830078	-94.630890
17097.363281	-94.924080
17118.896484	-95.498398
17140.429688	-95.744576
17161.962891	-96.401718
17183.496094	-96.678436
17205.029297	-96.659508
17226.562500	-96.972649
17248.095703	-96.628944
17269.628906	-96.971138
17291.162109	-98.284416
17312.695313	-99.246788
17334.228516	-98.926956
17355.761719	-98.082680
17377.294922	-97.718376
17398.828125	-97.613792
17420.361328	-98.347954
17441.894531	-97.971680
17463.427734	-97.423470
17484.960938	-96.303207
17506.494141	-94.404335
17528.027344	-91.916367
17549.560547	-89.843765
17571.093750	-89.598679
17592.626953	-89.104630
17614.160156	-89.204865
17635.693359	-90.199287
17657.226563	-90.654892
17678.759766	-92.449020
17700.292969	-93.862953
17721.826172	-94.776810
17743.359375	-94.613747
17764.892578	-95.462700
17786.425781	-96.439636
17807.958984	-96.406197
17829.492188	-96.138855
17851.025391	-96.073242
17872.558594	-95.743698
17894.091797	-95.064392
17915.625000	-95.881065
17937.158203	-97.714355
17958.691406	-97.636604
17980.224609	-98.059181
18001.757813	-98.111008
18023.291016	-98.416161
18044.824219	-99.299721
18066.357422	-99.329941
18087.890625	-99.071693
18109.423828	-99.275253
18130.957031	-99.937767
18152.490234	-100.253639
18174.023438	-99.690071
18195.556641	-99.440109
18217.089844	-99.607864
18238.623047	-100.222450
18260.156250	-100.108513
18281.689453	-99.647293
18303.222656	-100.248672
18324.755859	-100.354820
18346.289063	-99.956085
18367.822266	-99.263062
18389.355469	-99.090981
18410.888672	-97.466789
18432.421875	-96.344139
18453.955078	-96.773582
18475.488281	-96.900528
18497.021484	-95.940895
18518.554688	-95.254372
18540.087891	-95.524406
18561.621094	-96.661354
18583.154297	-97.819946
18604.687500	-97.757645
18626.220703	-98.817612
18647.753906	-98.741493
18669.287109	-97.943588
18690.820313	-97.755173
18712.353516	-96.945755
18733.886719	-96.913727
18755.419922	-96.077812
18776.953125	-96.597992
18798.486328	-97.729233
18820.019531	-98.325790
18841.552734	-97.539391
18863.085938	-96.586647
18884.619141	-95.428947
18906.152344	-94.518059
18927.685547	-95.237045
18949.218750	-95.454880
18970.751953	-94.550934
18992.285156	-94.060295
19013.818359	-93.836281
19035.351563	-94.243195
19056.884766	-94.947609
19078.417969	-95.658546
19099.951172	-96.134529
19121.484375	-96.765396
19143.017578	-96.821014
19164.550781	-96.640289
19186.083984	-96.719955
19207.617188	-96.996201
19229.150391	-97.349113
19250.683594	-96.525986
19272.216797	-96.966629
19293.750000	-97.653488
19315.283203	-97.514320
19336.816406	-97.093903
19358.349609	-97.780922
19379.882813	-97.683014
19401.416016	-97.108879
19422.949219	-97.765099
19444.482422	-98.936012
19466.015625	-98.976364
19487.548828	-98.642868
19509.082031	-99.603401
19530.615234	-99.975487
19552.148438	-99.755409
19573.681641	-99.496902
19595.214844	-99.908867
19616.748047	-99.828194
19638.281250	-100.144676
19659.814453	-99.972679
19681.347656	-100.237091
19702.880859	-100.238846
19724.414063	-100.013443
19745.947266	-100.756836
19767.480469	-100.384689
19789.013672	-100.821884
19810.546875	-100.664879
19832.080078	-100.729454
19853.613281	-100.152695
19875.146484	-99.360077
19896.679688	-98.742836
19918.212891	-97.410240
19939.746094	-96.211571
19961.279297	-97.157349
19982.812500	-97.750641
20004.345703	-97.921066
20025.878906	-97.989906
20047.412109	-98.978188
20068.945313	-98.768593
20090.478516	-98.404839
20112.011719	-99.311699
20133.544922	-99.654289
20155.078125	-99.764236
20176.611328	-100.704109
20198.144531	-100.195007
20219.677734	-100.812164
20241.210938	-102.429070
20262.744141	-103.170364
20284.277344	-103.887566
20305.810547	-104.094803
20327.343750	-104.068832
20348.876953	-104.338799
20370.410156	-104.215797
20391.943359	-104.388847
20413.476563	-105.329445
20435.009766	-106.193367
20456.542969	-106.260406
20478.076172	-106.464577
20499.609375	-105.406281
20521.142578	-104.154343
20542.675781	-105.107162
20564.208984	-98.275879
20585.742188	-97.401299
20607.275391	-103.077965
20628.808594	-101.431427
20650.341797	-100.867836
20671.875000	-93.495377
20693.408203	-96.198524
20714.941406	-104.162781
20736.474609	-103.887047
20758.007813	-94.717239
20779.541016	-90.568748
20801.074219	-97.592773
20822.607422	-99.029449
20844.140625	-101.036728
20865.673828	-96.613220
20887.207031	-96.479706
20908.740234	-103.887886
20930.273438	-103.006218
20951.806641	-99.851234
20973.339844	-93.121773
20994.873047	-96.136665
21016.406250	-99.399330
21037.939453	-98.287933
21059.472656	-95.488663
21081.005859	-93.038429
21102.539063	-97.042404
21124.072266	-99.622658
21145.605469	-100.094749
21167.138672	-100.716438
21188.671875	-100.601097
21210.205078	-101.237976
21231.738281	-101.308937
21253.271484	-100.812248
21274.804688	-100.203529
21296.337891	-100.583435
21317.871094	-101.347626
21339.404297	-101.330559
21360.937500	-100.512016
21382.470703	-101.333252
21404.003906	-102.918037
21425.537109	-102.385902
21447.070313	-102.685997
21468.603516	-102.673927
21490.136719	-102.126488
21511.669922	-101.404060
21533.203125	-101.519600
21554.736328	-102.359123
21576.269531	-102.502068
21597.802734	-102.718010
21619.335938	-102.806526
21640.869141	-102.785172
21662.402344	-102.441528
21683.935547	-101.905739
21705.468750	-101.121338
21727.001953	-100.693588
21748.535156	-100.642944
21770.068359	-101.127907
21791.601563	-101.640739
21813.134766	-101.931007
21834.667969	-101.959839
21856.201172	-102.441727
21877.734375	-102.993004
21899.267578	-102.593590
21920.800781	-101.276428
21942.333984	-100.638374
21963.867188	-100.779350
21985.400391	-100.426544
22006.933594	-100.239975
22028.466797	-100.250122

[Terry McGee]

Now, you might be a little puzzled about a low peak at around 936-939Hz, Bb5. It occurs in the spectra of both whistles. It's the note that you get if you underblow oxx xxx. I guess best described as c# (ooo ooo) flattened by having all the other holes below it covered. You can try that at home too, just start ooo ooo, then oxo ooo, etc. You notice this most on flutes and whistles with big holes. It's not normally a problem as you tend to blow hard enough to go straight to the D6 note.

It, like the fundamental you see when overblowing xxx xxx, are a reminder that even while you are aiming at a particular note, the partials of any other viable notes are still lurking in there. Waiting for their chance to shine....

Now, trill, those spectra are at a low resolution - 2048. I can easily up the resolution if it doesn't fit your purposes. You name it. And of course can leave out parts of the band with no significance, or that come in below a prescribed level.

Big field test this morning. We went playing Irish music at Grumpy & Sweethearts again this morning, and I mostly played the Tapered Abomination. Plenty of positive comments about the sound. Nobody complimented me on the colour match....

[trill]

Well, the sky doesn't seem to have fallen . . .

Thank you for posting !

I've been digging through old notes+refs on amplitude, power, dB + such, all aimed at interpreting such outputs from Audacity.

Many years ago, I wanted to try and understand why a particular whistle had such a unique voice. I wrote some Matlab scripts to try and find what parts of the spectrum produced the sound. I was hoping it was just the first few harmonics. No..... I was stunned at how high I had to go.

Now, where is that old CD . . .

[trill]

. . . Nobody complimented me on the colour match....

Philistines !

[Terry McGee]

And here's another thing to consider - the actual levels of the notes as played on the two whistles. Notes:
- It's just mouth blown so regard as subjective.
- I'm playing a brief burst on each note starting at 2nd octave B and going down to bottom D
- Tapered whistle on the left, Tweaked Mellow D on right
- I've only shown the top half the envelopes (the bottom half is the mirror image).
- The scale on the left is in dB, so we can get an idea of relative levels.
- Ignore the short burst of low level noise between the two groups, that's just me doing a voice ID.
- It seems to favour the cylindrical, especially on the low notes, but I've become aware I'm not pushing the tapered whistle as hard as I could. I should probably make it a more easy-blowing head!
- And of course these are unweighted figures, I should probably run them through a "loudness" algorithm.

[trill]

And here's another thing to consider - the actual levels of the notes as played on the two whistles.

Very interesting.

2 questions:

1. How do the 2 window areas compare ?

2. How do the 2 bottom diameters compare ?

Also, what is a "loudness" algorithm ?