Pipe Organ: Under Design

UPDATE:  First pipe design:  Finished!  I completed the design for the CC Pipe on the Principal 8 stop and started on the CC#:

Working on the CC# Pipe - still need foot, languid, and windway.

Working on the CC# Pipe - still need foot, languid, and windway.

And a solid-shaded view of the mouth carving job:

In the 3D camera view (upper right), you can see the nice cutup angle of the two mouths.

In the 3D camera view (upper right), you can see the nice cutup angle of the two mouths.

I knew I was doing something right when the front view matched Audsley’s diagrams:

French Romantic Mouths (10 over 15, straight lip, no ears, no beards)

French Romantic Mouths (10 over 15, straight lip, no ears, no beards)

I’m now to the point where I’m going to be doing the actual design work for the pipe organ on a CAD program.  Here are the specs for the first stop I’m designing, the Principal 8′:

Rank:  Open Diapason
Material:  Wood (Poplar/Walnut)
Division:  Great
Scale:  8′
Wind Pressure:  2″
Ising Number:  2
Halves on:  17
Pipes on stop:  61
Pipes in rank:  85
Compass:  Full

Note # Note Pitch IW ID IL MH WST Flow Rate
1 C 65.4 4.436 5.627 94.46 1.242 0.026 4.52
2 C# 69.3 4.248 5.388 89.03 1.189 0.026 4.27
3 D 73.4 4.068 5.160 83.92 1.139 0.026 4.03
4 D# 77.8 3.895 4.941 79.10 1.091 0.025 3.80
5 E 82.4 3.730 4.732 74.55 1.044 0.025 3.59
6 F 87.3 3.572 4.531 70.26 1.000 0.024 3.39
7 F# 92.5 3.421 4.339 66.22 0.958 0.024 3.20
8 G 98.0 3.276 4.155 62.41 0.917 0.024 3.02
9 G# 103.8 3.137 3.979 58.82 0.878 0.023 2.85
10 A 110.0 3.004 3.810 55.43 0.841 0.023 2.69
11 A# 116.5 2.876 3.649 52.24 0.805 0.023 2.54
12 B 123.5 2.754 3.494 49.23 0.771 0.022 2.40
13 C 130.8 2.638 3.346 46.39 0.739 0.022 2.26
14 C# 138.6 2.526 3.204 43.71 0.707 0.022 2.13
15 D 146.8 2.419 3.068 41.19 0.677 0.021 2.02
16 D# 155.6 2.316 2.938 38.81 0.649 0.021 1.90
17 E 164.8 2.218 2.814 36.57 0.621 0.021 1.80
18 F 174.6 2.124 2.694 34.46 0.595 0.021 1.69
19 F# 185.0 2.034 2.580 32.46 0.569 0.020 1.60
20 G 196.0 1.948 2.471 30.59 0.545 0.020 1.51
21 G# 207.7 1.865 2.366 28.82 0.522 0.020 1.42
22 A 220.0 1.786 2.266 27.15 0.500 0.019 1.34
23 A# 233.1 1.710 2.170 25.57 0.479 0.019 1.27
24 B 246.9 1.638 2.078 24.09 0.459 0.019 1.20
25 C 261.6 1.568 1.989 22.70 0.439 0.019 1.13
26 C# 277.2 1.502 1.905 21.38 0.421 0.018 1.07
27 D 293.7 1.438 1.824 20.14 0.403 0.018 1.01
28 D# 311.1 1.377 1.747 18.97 0.386 0.018 0.95
29 E 329.6 1.319 1.673 17.87 0.369 0.018 0.90
30 F 349.2 1.263 1.602 16.83 0.354 0.017 0.85
31 F# 370.0 1.209 1.534 15.85 0.339 0.017 0.80
32 G 392.0 1.158 1.469 14.92 0.324 0.017 0.75
33 G# 415.3 1.109 1.407 14.06 0.311 0.017 0.71
34 A 440.0 1.062 1.347 13.24 0.297 0.016 0.67
35 A# 466.2 1.017 1.290 12.46 0.285 0.016 0.63
36 B 493.9 0.974 1.235 11.74 0.273 0.016 0.60
37 C 523.3 0.933 1.183 11.05 0.261 0.016 0.57
38 C# 554.4 0.893 1.133 10.40 0.250 0.015 0.53
39 D 587.3 0.855 1.085 9.80 0.239 0.015 0.50
40 D# 622.3 0.819 1.039 9.22 0.229 0.015 0.48
41 E 659.3 0.784 0.995 8.68 0.220 0.015 0.45
42 F 698.5 0.751 0.953 8.17 0.210 0.015 0.42
43 F# 740.0 0.719 0.912 7.69 0.201 0.014 0.40
44 G 784.0 0.689 0.873 7.24 0.193 0.014 0.38
45 G# 830.6 0.659 0.836 6.82 0.185 0.014 0.36
46 A 880.0 0.631 0.801 6.42 0.177 0.014 0.34
47 A# 932.3 0.605 0.767 6.04 0.169 0.014 0.32
48 B 987.8 0.579 0.735 5.68 0.162 0.013 0.30
49 C 1046.5 0.555 0.703 5.35 0.155 0.013 0.28
50 C# 1108.7 0.531 0.674 5.03 0.149 0.013 0.27
51 D 1174.7 0.508 0.645 4.74 0.142 0.013 0.25
52 D# 1244.5 0.487 0.618 4.46 0.136 0.013 0.24
53 E 1318.5 0.466 0.591 4.19 0.131 0.012 0.22
54 F 1396.9 0.447 0.566 3.94 0.125 0.012 0.21
55 F# 1480.0 0.428 0.542 3.71 0.120 0.012 0.20
56 G 1568.0 0.409 0.519 3.49 0.115 0.012 0.19
57 G# 1661.2 0.392 0.497 3.28 0.110 0.012 0.18
58 A 1760.0 0.375 0.476 3.09 0.105 0.012 0.17
59 A# 1864.7 0.360 0.456 2.91 0.101 0.011 0.16
60 B 1975.5 0.344 0.437 2.73 0.096 0.011 0.15
61 C 2093.0 0.330 0.418 2.57 0.092 0.011 0.14

I got the math from here.

Update:  To this I add a 12-pipe extension to make a 4′ octave stop:

Rank:  Open Diapason
Material:  Wood (Poplar/Walnut)
Division:  Great
Scale:  4′
Wind Pressure:  2″
Ising Number:  2
Halves on:  18
Pipes on stop:  12 (lowest 4 octaves shared with highest 4 octaves of Principal)
Pipes in rank:  85
Compass:  Full

49 C 2093.0 0.343 0.436 2.54 0.103 0.015 0.20
50 C# 2217.5 0.330 0.418 2.39 0.099 0.015 0.20
51 D 2349.3 0.317 0.402 2.24 0.095 0.015 0.19
52 D# 2489.0 0.304 0.386 2.11 0.091 0.015 0.18
53 E 2637.0 0.292 0.370 1.98 0.088 0.015 0.17
54 F 2793.8 0.280 0.355 1.86 0.084 0.015 0.16
55 F# 2960.0 0.269 0.341 1.75 0.081 0.015 0.15
56 G 3136.0 0.258 0.327 1.64 0.077 0.015 0.15
57 G# 3322.4 0.248 0.314 1.54 0.074 0.015 0.14
58 A 3520.0 0.238 0.302 1.44 0.071 0.014 0.13
59 A# 3729.3 0.228 0.290 1.36 0.069 0.014 0.13
60 B 3951.1 0.219 0.278 1.27 0.066 0.014 0.12
61 C 4186.0 0.211 0.267 1.19 0.063 0.014 0.12

And a 2′ Superoctave stop:

Rank:  Open Diapason
Material:  Wood (Poplar/Walnut)
Division:  Great
Scale:  2′
Wind Pressure:  2″
Ising Number:  2
Halves on:  18
Pipes on stop:  12 (lowest 3 octaves shared with Principal, penultimate octave shared with Octave stop)
Pipes in rank:  85
Compass:  Full

49 C 4186.0 0.194 0.246 1.23 0.058 0.011 0.08
50 C# 4434.9 0.186 0.236 1.15 0.056 0.011 0.08
51 D 4698.6 0.179 0.227 1.08 0.054 0.011 0.08
52 D# 4978.0 0.172 0.218 1.01 0.052 0.011 0.07
53 E 5274.0 0.165 0.209 0.95 0.049 0.011 0.07
54 F 5587.7 0.158 0.201 0.89 0.047 0.011 0.07
55 F# 5919.9 0.152 0.193 0.84 0.046 0.011 0.06
56 G 6271.9 0.146 0.185 0.79 0.044 0.011 0.06
57 G# 6644.9 0.140 0.178 0.74 0.042 0.011 0.06
58 A 7040.0 0.134 0.171 0.69 0.040 0.010 0.05
59 A# 7458.6 0.129 0.164 0.65 0.039 0.010 0.05
60 B 7902.1 0.124 0.157 0.61 0.037 0.010 0.05
61 C 8372.0 0.119 0.151 0.57 0.036 0.010 0.05

Audsley says that a super octave should halve on 21. However, all of Laukhuff’s 2′ diapasons halve on 18. Since this is a proven, modern design, it’s what I’m going with.

Here’s the next one (not designing yet – just doing the math):  The Bourdon 16

Rank:  Stopped Flute
Material:  Wood (Poplar/Walnut)
Division:  Pedal
Scale:  16′
Wind Pressure:  2″
Ising Number:  2
Halves on:  17
Pipes on stop:  32
Pipes in rank:  32
Compass:  Partial

The lowest two pipes (CCC and CCC#) will need to be mitered by 6″ since the entire pipe length (with foot, windchest, and stopper) will be 104″ and my ceiling is 99″.

Note # Note Pitch IW ID IL MH WST Flow Rate
1 C 32.7 4.724 5.945 98.60 2.362 0.045 8.28
2 C# 34.6 4.524 5.693 93.00 2.262 0.045 7.82
3 D 36.7 4.332 5.452 87.72 2.166 0.044 7.38
4 D# 38.9 4.148 5.220 82.74 2.074 0.043 6.96
5 E 41.2 3.972 4.999 78.04 1.986 0.043 6.57
6 F 43.7 3.804 4.787 73.60 1.902 0.042 6.20
7 F# 46.2 3.643 4.584 69.42 1.821 0.041 5.86
8 G 49.0 3.488 4.390 65.47 1.744 0.041 5.53
9 G# 51.9 3.340 4.204 61.75 1.670 0.040 5.22
10 A 55.0 3.199 4.026 58.24 1.599 0.040 4.92
11 A# 58.3 3.063 3.855 54.93 1.532 0.039 4.65
12 B 61.7 2.933 3.691 51.80 1.467 0.039 4.39
13 C 65.4 2.809 3.535 48.85 1.404 0.038 4.14
14 C# 69.3 2.690 3.385 46.07 1.345 0.037 3.91
15 D 73.4 2.576 3.242 43.45 1.288 0.037 3.69
16 D# 77.8 2.467 3.104 40.98 1.233 0.036 3.48
17 E 82.4 2.362 2.973 38.64 1.181 0.036 3.29
18 F 87.3 2.262 2.846 36.44 1.131 0.035 3.10
19 F# 92.5 2.166 2.726 34.37 1.083 0.035 2.93
20 G 98.0 2.074 2.610 32.41 1.037 0.034 2.76
21 G# 103.8 1.986 2.500 30.56 0.993 0.034 2.61
22 A 110.0 1.902 2.394 28.82 0.951 0.033 2.46
23 A# 116.5 1.821 2.292 27.17 0.911 0.033 2.32
24 B 123.5 1.744 2.195 25.62 0.872 0.032 2.19
25 C 130.8 1.670 2.102 24.16 0.835 0.032 2.07
26 C# 138.6 1.599 2.013 22.78 0.800 0.032 1.95
27 D 146.8 1.532 1.927 21.48 0.766 0.031 1.84
28 D# 155.6 1.467 1.846 20.26 0.733 0.031 1.74
29 E 164.8 1.404 1.767 19.10 0.702 0.030 1.64
30 F 174.6 1.345 1.693 18.01 0.672 0.030 1.55
31 F# 185.0 1.288 1.621 16.98 0.644 0.029 1.46
32 G 196.0 1.233 1.552 16.01 0.617 0.029 1.38

And since the Gedeckt shares a pipe shape with the Bourdon, I’ll do the math for the Gedeckt at the same time:

Rank:  Stopped Flute
Material:  Wood (Poplar/Walnut)
Division:  Solo
Scale:  8′
Wind Pressure:  2″
Ising Number:  2
Halves on:  19
Pipes on stop:  61
Pipes in rank:  73
Compass:  Full

Note # Note Pitch IW ID IL MH WST Flow Rate
1 C 65.4 2.756 3.465 48.91 1.378 0.036 3.84
2 C# 69.3 2.652 3.334 46.11 1.326 0.036 3.69
3 D 73.4 2.552 3.208 43.48 1.276 0.036 3.55
4 D# 77.8 2.455 3.087 40.99 1.228 0.036 3.42
5 E 82.4 2.363 2.970 38.64 1.181 0.036 3.29
6 F 87.3 2.273 2.858 36.43 1.137 0.036 3.17
7 F# 92.5 2.187 2.750 34.34 1.094 0.036 3.05
8 G 98.0 2.105 2.646 32.38 1.052 0.036 2.93
9 G# 103.8 2.025 2.546 30.52 1.013 0.036 2.82
10 A 110.0 1.949 2.450 28.77 0.974 0.036 2.71
11 A# 116.5 1.875 2.358 27.12 0.938 0.036 2.61
12 B 123.5 1.804 2.269 25.56 0.902 0.036 2.51
13 C 130.8 1.736 2.183 24.10 0.868 0.036 2.42
14 C# 138.6 1.671 2.100 22.71 0.835 0.036 2.33
15 D 146.8 1.607 2.021 21.41 0.804 0.036 2.24
16 D# 155.6 1.547 1.945 20.18 0.773 0.036 2.15
17 E 164.8 1.488 1.871 19.01 0.744 0.036 2.07
18 F 174.6 1.432 1.801 17.92 0.716 0.036 1.99
19 F# 185.0 1.378 1.733 16.89 0.689 0.036 1.92
20 G 196.0 1.326 1.667 15.91 0.663 0.036 1.85
21 G# 207.7 1.276 1.604 15.00 0.638 0.036 1.78
22 A 220.0 1.228 1.543 14.13 0.614 0.036 1.71
23 A# 233.1 1.181 1.485 13.32 0.591 0.036 1.65
24 B 246.9 1.137 1.429 12.55 0.568 0.036 1.58
25 C 261.6 1.094 1.375 11.82 0.547 0.036 1.52
26 C# 277.2 1.052 1.323 11.14 0.526 0.036 1.47
27 D 293.7 1.013 1.273 10.49 0.506 0.036 1.41
28 D# 311.1 0.974 1.225 9.89 0.487 0.036 1.36
29 E 329.6 0.938 1.179 9.31 0.469 0.036 1.31
30 F 349.2 0.902 1.134 8.77 0.451 0.036 1.26
31 F# 370.0 0.868 1.091 8.26 0.434 0.036 1.21
32 G 392.0 0.835 1.050 7.79 0.418 0.036 1.16
33 G# 415.3 0.804 1.011 7.33 0.402 0.036 1.12
34 A 440.0 0.773 0.972 6.91 0.387 0.036 1.08
35 A# 466.2 0.744 0.936 6.50 0.372 0.036 1.04
36 B 493.9 0.716 0.900 6.13 0.358 0.036 1.00
37 C 523.3 0.689 0.866 5.77 0.345 0.036 0.96
38 C# 554.4 0.663 0.834 5.43 0.331 0.036 0.92
39 D 587.3 0.638 0.802 5.12 0.319 0.036 0.89
40 D# 622.3 0.614 0.772 4.82 0.307 0.036 0.85
41 E 659.3 0.591 0.743 4.54 0.295 0.036 0.82
42 F 698.5 0.568 0.715 4.27 0.284 0.036 0.79
43 F# 740.0 0.547 0.688 4.02 0.273 0.036 0.76
44 G 784.0 0.526 0.662 3.78 0.263 0.036 0.73
45 G# 830.6 0.506 0.637 3.56 0.253 0.036 0.71
46 A 880.0 0.487 0.613 3.35 0.244 0.036 0.68
47 A# 932.3 0.469 0.589 3.16 0.234 0.036 0.65
48 B 987.8 0.451 0.567 2.97 0.226 0.036 0.63
49 C 1046.5 0.434 0.546 2.79 0.217 0.036 0.60
50 C# 1108.7 0.418 0.525 2.63 0.209 0.036 0.58
51 D 1174.7 0.402 0.505 2.47 0.201 0.036 0.56
52 D# 1244.5 0.387 0.486 2.33 0.193 0.036 0.54
53 E 1318.5 0.372 0.468 2.19 0.186 0.036 0.52
54 F 1396.9 0.358 0.450 2.06 0.179 0.036 0.50
55 F# 1480.0 0.345 0.433 1.94 0.172 0.036 0.48
56 G 1568.0 0.331 0.417 1.82 0.166 0.036 0.46
57 G# 1661.2 0.319 0.401 1.72 0.159 0.036 0.44
58 A 1760.0 0.307 0.386 1.61 0.153 0.036 0.43
59 A# 1864.7 0.295 0.371 1.52 0.148 0.036 0.41
60 B 1975.5 0.284 0.357 1.43 0.142 0.036 0.40
61 C 2093.0 0.273 0.344 1.34 0.137 0.036 0.38

Rank:  Stopped Flute
Material:  Wood (Poplar/Walnut)
Division:  Solo
Scale:  4′
Wind Pressure:  2″
Ising Number:  2
Halves on:  21
Pipes on stop:  12  (lowest 4 octaves shared with Gedeckt 8)
Pipes in rank:  73
Compass:  Full

49 C 2093.0 0.329 0.414 1.29 0.164 0.063 0.80
50 C# 2217.5 0.318 0.400 1.21 0.159 0.063 0.78
51 D 2349.3 0.307 0.386 1.13 0.153 0.064 0.76
52 D# 2489.0 0.296 0.373 1.06 0.148 0.065 0.74
53 E 2637.0 0.286 0.360 1.00 0.143 0.065 0.73
54 F 2793.8 0.277 0.348 0.93 0.138 0.066 0.71
55 F# 2960.0 0.267 0.336 0.87 0.134 0.067 0.69
56 G 3136.0 0.258 0.325 0.82 0.129 0.068 0.68
57 G# 3322.4 0.249 0.313 0.77 0.125 0.069 0.66
58 A 3520.0 0.241 0.303 0.72 0.120 0.069 0.65
59 A# 3729.3 0.233 0.292 0.67 0.116 0.070 0.63
60 B 3951.1 0.225 0.282 0.63 0.112 0.071 0.62
61 C 4186.0 0.217 0.273 0.59 0.109 0.072 0.60

That’s all the math I can do for now. The other ranks require different formulas (harmonics, half-stopped, or string pipes).

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  1. #1 by Joshua on September 6, 2011 - 7:14 AM

    XD – The two pipes above are nice and all but they’re not to spec. I mixed stats from pipes 1 and 13 for the first one and 2 and 14 for the second one. Nice. So it looks like I’ll be starting over on those. At least I know now exactly how to make a French Romantic open diapason: Scale the walls, measure the internal length, set the -10 degree drill so it intersects the inner wall of the pipe at the terminus of the internal length rule, measure the mouth height, set the 15 degree drill so it intersects the inner wall of the pipe at the terminus of the mouth height rule, do boolean difference functions on both drills, remove drills and rules, get a block that 1.75 times the thickness of the pipe base block, cut a 20 degree angle out of it with the languid drill, place this block (the new languid), carve out the windway by boolean difference with a -30 degree drill and a 35 degree drill, grab a block and scale it to the pipe base block dimensions, place this block at the base of the pipe, grab a cylinder and size it to the pipe foot dimension, intersect the pipe base block and do boolean difference to carve the foot out of the base block. Et voila, one French Romantic style open diapason. ^_^

  2. #2 by Joshua on September 6, 2011 - 7:29 AM

    Note to self – re-do math for Bourdon 16 – starting height is too short.

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