Noisemakers

The tones produced by open pipes 1/5, 1/6, 1/7, and 1/8 that long thus produce the 5th, 6th, 7th, and 8th harmonics, respectively.  These represent the 4th, 5th, 6th, and 7th upper partial tones, respectively, vibrate at 5, 6, 7, and 8 times the frequency, respectively, and sound the Seventeenth (Tierce), Nineteenth (Larigot), Flat Twenty-First (Septieme), and Twenty-Second at 1-3/5', 1-1/3', 1-1/7', and 1' pitches, respectively.  The 4 individual stops having fractional numbers which sound the 2nd, 4th, 5th, and 6th upper partial tones, respectively, are sometimes referred to as "mutation stops." The series continues upward from there as incomplete ranks which are part of the compound harmonic-corroborating (mixture) stops of the organ.

Similarly, the unison pitch of the pedals is described as 16', an octave below that, because the lowest C pedal key (which matches the lowest C1 key of the piano keyboard) is sounded by an open pipe 16 feet long.  Since the accepted lower limit of determinate musical sounds the human ear can detect is around 40Hz, and the lowest 16' octave of the organ sounds frequencies in a range of 32Hz-64Hz, this means that all frequencies generated by a musical instrument below low E in the 16' octave (which corresponds to the E1 of the double bass of the orchestra) are felt rather than heard -- that would include the bottom 4 notes (C, C#, D, D#) with a 16' stop drawn.

A sub-octave pedal stop, or "Double," which sounds a whole octave lower, generated by an open pipe 32'  long generating a prime tone on low C1, is sometimes supplied in larger instruments to provide additional gravity.  Such grave stops may be of principal, flute, reed, or non-imitative string tone, and an important organ can, and often does, have more than one.  Sometimes also, we find instruments in which digital stops of 32' pitch supplement the sounds of real pipes in the Pedal division [See blog, "Hybrid" Pipe Organ, Parts I-II]. 

In cases where space or cost considerations will not permit the introduction of the largest pipes of the 32' octave, an independent stop of 16' pitch may be joined with another independent 16' stop wired to play a perfect 5th above it, at 10-2/3' pitch (sometimes the 10-2/3' is introduced as a separate stop called "Quint," which makes possible its combination with any pedal stop of 16' pitch).  This combination, which represents the 2nd and 3rd harmonics (1st and 2nd upper partials) of a 32' prime, generates a differential tone represented by the difference between the frequencies of both pipes and produces a "synthetic 32-foot" sound at that frequency.  This differential or resultant tone is weaker than the sound produced by an independent pipe of 32' but its introduction can be a satisfactory alternative.  Such a stop is properly formed of 2 separate ranks of pipes closely situated to each other in the same chamber and typically is controlled by a drawknob labeled "Acoustic Bass" or "Resultant."

TABLE OF LOWEST FREQUENCIES [A4 = 440Hz]

                  Lower Midrange        80Hz - 160Hz octave / 8-foot E2 to 4-foot E3

               Bass & Upper Bass       40Hz - 80Hz octave / 16-foot E1 to 8-foot E2

                               Deep Bass       32Hz - 40Hz / 16-foot C1 to E1

                         Very Deep Bass       16Hz - 32Hz octave / 32-foot C0 to 16-foot C1

The lower limit of the normal human ear to detect determinate musical pitch is around 40Hz.  This corresponds to the E1 note in the 16-foot octave, the lowest note of the bass guitar, and the lowest note of the upright double bass of the orchestra.  An upright bass with extension goes down to 16-foot C1 [32Hz], and the lowest playable note on the piano is 32-foot A0 [27Hz].  Only the pipe organ and certain electronic instruments produce sound any lower in the very deep bass range [32-foot octave].

NOTE:  The contrabassoon of the orchestra can produce 16-foot C1 [32Hz], but the fundamental on this note is so weak as to be virtually absent.  So the question arises, if the fundamental cannot be heard then why bother to play the note.  The answer is that our ear places the pitch of the note by the interval between the harmonics.  For example, even though on a full length concert grand piano the fundamental of the lowest string sounding on the note A0 [27Hz] is far stronger than with a spinet, a console piano, or a small upright piano, our ear can still detect the pitch on any of these pianos because we hear that string's harmonic structure [octave @ 55Hz, 12th @ 82Hz, 15th @ 110Hz, etc.] even when much of the fundamental it generates is, for all practical purposes, inaudible.

On scientific, practical, and musical grounds, there is no reason to provide an organ with stops any lower in pitch than 32-foot.  People nevertheless are fascinated by extremes.  Monster Pedal stops of 64-foot pitch have been inserted in the very largest pipe and electronic organs which produce real or differential tones having frequencies down to 8Hz on low C.  These have been constructed either of single, individual pipes or 2 pipes wired to each other which sound a perfect 5th apart (at 32-foot and 21-1/3 foot pitches respectively) creating a synthetic, differential 64-foot tone organ builders have labeled Resultant, Vox Gravissima, or simply Gravissima.  The best examples of this stop make use of 2 separate ranks of pipes of similar tone quality, usually a covered flute of medium strength paired with another of subordinate strength wired to play the 5th above.  Since the bottom octave produces differential frequencies in the range of 8Hz-16Hz, and this must be spread over the 12 notes of the chromatic scale, this means that only an 8 Hz difference separates all of those 12 notes.  In the sound tombs of the 64-foot octave it's quite impossible for the ear to determine any difference between one note and another, as all notes are rattling at about the same rate.  All that may be discerned, note to note, is an unmusical, rumbling sound, something akin to a washing machine going through its spin cycle.

No labial pipes of 64' pitch have ever been successfully constructed due to the time it takes for the largest pipes of such a rank to get on speech.  A full length 64' stop labeled Diaphone/Dulzian however was inserted in the Pedal of the Midmer-Losh organ at Boardwalk Convention Hall at Atlantic City, New Jersey with its bottom range constructed of Diaphone pipes.  The longest full length reed pipe on record (the low pedal C1 of the 64' Contra Trombone stop installed in the Thomas Hill organ in the Town Hall at Sydney, New South Wales) has a wooden resonator as long as a 5-story building, weighs 1-1/2 tons, and has a metal reed made to vibrate against a gigantic shallot at a frequency of 8Hz.  On musical grounds, such a curiosity has no real use or value when its sound resembles the alternating banging of 2 wooden drumsticks on a metal washtub.  If such an orchestral effect would be desired, then a real bass drum can be electrically connected to the Pedal and controlled by means of its own pair of  drawknobs or rocker tabs (for single stroke and reiterate) which would take up far less space at considerably less cost.

If the objective is to prove to the world that an organ building firm could construct such a grave, costly, and independent voice and insert it in an organ, then

WHY STOP THERE ? ...

With today's technology, superior materials, skilled construction methods, and increased wind pressures, the next step would be to construct an independent stop of 128-foot pitch [most likely of Diaphone pipes] generating fundamental frequencies in its bottom octave down to 4Hz.  For that matter, once we have that in an organ, the next step would be to extend that rank downward by 12 more pipes, set those 12 pipes on an offset windchest, raise the wind pressure to 200 inches, and unify that rank down to 256-foot pitch with a bottom C pipe 85 yards long weighing 20 tons sounding at only 2 Hz, something no one else's pipe organ in history has ever had.  After that, the next step down this irrational, insane road would be to wire that same rank to play at 256-foot and sub-quint 170-2/3 foot pitches, each note sounding 2 pipes a perfect 5th apart, which would generate a resultant differential tone of 512-foot pitch.  A Vox Magna Sub-Gravissima Absurdus Profunda 512-foot stop like that, with bottom C generating a differential frequency of only 1 Hz, may end up being the 8th Wonder of the World but it would win hands down in any contest for first place as a monument to the beetle-headed stupidity of man. 

We see where all this can lead without calling a halt somewhere.  There's an old dictum in organ playing that applies to organ building as well, and it is this:  "Trust your ear.  Your ear is your best friend.  It will lead your brain.  Brains sometimes work too much, finally."  In the craze to build the biggest and boldest, latest and greatest, largest and loudest musical machine on the face of the earth, at some point builders and acousticians, on all scientific, physiological, musical, and common sense grounds, are faced with drawing the line on such mad sonic pursuits.  When the lower limit of perceptible musical tone is agreed to end around 40Hz represented by the low E1 of a 16-foot Pedal stop, one is left to wonder what can be said of those frequencies which descend into the sound tombs of the 64-foot octave between 8Hz-16Hz.  Such powerful vibrations are not perceptible as musical tones.  Moving chromatically down the frequency spectrum from 32-foot C to 64-foot C we find a difference of only 8Hz over a chromatic scale of 12 notes.  The ear interprets these 12 semitones only as different versions of the same infernal, rattling, unmusical noise.

In the electronic organ world sound is generated by a speaker cone (woofer) moving in and out.  The distance it travels from the top of its travel to its bottom is called its displacement, or excursion.  For it to move a certain amount of air there are two choices:  1) we can have a larger diameter cone moving in and out over a smaller excursion or displacement, or 2) we can have a smaller diameter cone moving in and out over a greater excursion or displacement.  Generally the former is the preferred method because it will produce less distortion and typically requires less power, but the size of the cone can get to be very large.  The 2nd method does have the benefit of being smaller in size but is more directional and requires a good bit more power to operate.  Since watts are cheap however, this is a very do-able method nowadays, and there are many fine examples.  When a speaker is defined as "long throw" it's referring to the subwoofer using this 2nd method to produce bass.

NOTE:  Not all woofers/subwoofers are created equal.  To get good bass, deep bass, and very deep bass reproduction from an add-on subwoofer it has to move a lot of air, so, the very first thing to look for when contemplating augmenting bass impact in an electronic home practice instrument is not just the sub's cone diameter but also its displacement.  The more displacement there is, the more air is being moved, and, since bass is all about moving air, that means, if everything is done correctly, being louder.  Displacement, as stated, generally means the speaker's linear excursion.  Its so-called Xmax, or maximum linear excursion, is the distance it's voice coil can travel while maintaining within the magnetic gap -- or in other words the distance the cone moves from the center position to all the way forward or all the way back.  To calculate this, you need the voice coil length (sometimes called voice coil height) and the height of the magnetic gap (sometimes also called depth of the gap, or air gap).  The Xmax is first found by subtracting the height of the magnetic gap from the voice coil length, then dividing the result by 2.  For voice coil length, most hi-fi speakers run from .75" up to 2.0" for some long-throw super-pumpers.  The magnetic gap is generally about .25", or 6-8 mm.  For an 8" or larger speaker that gives no specs, the Xmax can be assumed to be around (+ or -) .2"  If it gives the voice coil length, the height of the magnetic gap can be assumed to be either .25" or 6-8 mm.  So, let's say, a speaker with a .75" voice coil can be presumed to have an Xmax of .75 - .25 = .50/2 = (+ or -) .25" -- but if it has a 1" voice coil, the Xmax can be assumed to be 1.00 - .25 = .75/2 = (+ or -) .36", which for bass is even better.  It's better because the amount of cubic inches of air the speaker cone can move is the product of its effective cone area [determined by pi x (r x r), where r is the radius] and its Xmax.  Some manufacturers, chiefly car manufacturers, give the distance the cone moves from all the way back to all the way front, or double the distance from center to front [this is why speaker manufacturers frequently give their Xmax figure as (+ or -) .25", or something similar.  A plus or minus figure means they are measuring from center to front, or center to back, the way they should.  Without a plus or minus, the Xmax figure ends up being inflated].  Hobbyists sometimes start out by adding two 10" subs or two 12" subs to their home instrument when, in actuality [all other things being equal], one 15" sub might move more cubic inches of air and do better than a pair of 10's.  In the same way, one 18" sub may very well move more cubic inches of air and do better than a pair of 12's.  On the other hand, a pair of long throw 10's may actually move about as much air to generate bass as a single 15" -- and a pair of long throw 12's may actually move about as much air to generate bass as a single 18'.

Our ears are less sensitive to extreme low frequencies.  A sound pressure level [SPL] of, let's say, 90 decibels [dB] at 20Hz sounds less loud than a SPL of 90 dB at 40Hz.  More SPL therefore is demanded for the very lowest notes in the Pedal [from around 16-foot E down through and including all of the 32-foot octave] to get them to "sound."  Ordinarily this means employing one or more graphic equalizers to boost the signal stream in deep bass and very deep bass [subsonic] bandwidths possibly with the addition of multiple subs of the long throw type -- this because the speaker cone has to travel further at low frequencies to generate the same SPL as at higher frequencies.  The relationship is that, for the same SPL, cone excursion or displacement is inversely proportional to the square of frequency, i.e., halve the frequency [by playing the same note one octave lower] -- 4 times the cone travel is required.  

Astounding acoustical experiments conducted using the electronic organ at Hammerwood Park, a country residence near east Grinstead, east Sussex, UK, have involved generating fundamental frequencies descending into the 64-foot and even 128-foot octaves.  A full length monster 128-foot stop was created there which made a playable scale down to 4Hz on low C!  The oversized mega-subwoofer specially designed, built, and powered for this demonstration produced an enormous racket, but, if that weren't enough, a "Self-Destruct" button which drew the 128' and 64' frequencies along with the 32' was introduced on this console.  When added to the full organ the effects of this trio of subsonic pitches was of scientific interest and great fun as a noisemaker, but it did nothing really for art.  Deep pockets, an eccentric attitude, plenty of time to waste, and a sophisticated sense of humor all seem part of the requisite equipment for conducting these kinds of probing tests.

NOTE:  Subwoofers are sought by owners of digitally sampled organs, obviously, to strengthen the very lowest Pedal sounds in general, and the 32-foot octave in particular.  In the limited and highly competitive world of organ sales, manufacturers are stretched to produce a marketable product in the most cost-efficient way.  It's entirely possible that during the sampling process of fundamentals at subsonic frequencies, when such sounds were recorded from real organ pipes, that something was left to be desired in order to trim down costs ... OR, as mentioned above, these same notes could be cunningly generated by the manufacturer as differential tones.  This can be tested by connecting the instrument to a frequency analyzer that measures fundamentals, setting the cutoff frequency of the analyzer to begin at let's say 30Hz, drawing a 32-foot stop, and stepping on the low C pedal key.  If the analyzer shows nothing, then that note is generating a fundamental below the cutoff frequency.  But if it shows a 16-foot C @ 32Hz along with a 16-foot G @ 48Hz, then that note is derived from the differential tone.  The exact pitch of this resultant tone is determined by subtracting the vibration numbers of any 2 held notes standing a perfect 5th apart.  In this case, the difference between the G @ 48Hz minus the C @ 32Hz = 16Hz, which is the 32-foot C in the octave below.  This differential phenomenon, while weaker and not as obvious above the tenor octave, is nevertheless measurable and demonstrable anywhere on the keyboards and by builders who are, of course, working with real pipes.  The point is, the search for the ideal subwoofer for a digitally sampled organ that strengthens all fundamental frequencies down to 16Hz can be, and very often is, an exercise in futility -- sometimes they're just too weak to amplify -- other times they're not even there.  No subwoofer is able to amplify what the instrument does not, or cannot, send it.  So, the fact is, in many situations, the best that can be expected from a digitally sampled organ is to find one or more high end, long throw subs with very low end reach down in the 20Hz range -- the kind that are housed in smaller cabinets and equipped with big amps pushing a lot of watts -- connect them to play with the Pedal signal, let them search for whatever of a fundamental the manufacturer provided to the bottom-most notes, and, in the end, resolve to be satisfied with the results [See Videos, The Viscount Organ].  

Besides stops of 64-foot pitch, another class of stops might be considered under the heading "noisemakers," or "noise machines."  These are stops of 4-4/7 foot pitch in the Pedal and 2-2/7 foot and 1-1/7 foot pitches in the manual divisions which corroborate the 6th upper partial tones of the 32-foot, 16-foot, and 8-foot harmonic series, respectively, and are represented in the organ by the so-called Septieme (pronounced "set-yem'").  This rank, sometimes labeled "Sharp Twentieth" or "Flat Twenty-First," is formed of open metal, cylindrical pipes voiced to yield a soft principal tone.  When sounded on the note C1 (bottom C in the manuals) the 6th upper partial tone lies between middle A#3 and Bb3 of the physical scale and is therefore slightly out-of-tune with the middle A#/Bb key of the chromatic keyboard tuned in equal temperament.  When this stop has been correctly and scientifically voiced, regulated, and tuned it remains out of sync with the chromatic keyboard, and, being tonally unruly this way, when it is introduced as a complete stop in any organ, it should be the most subdued in tone of any mutation stop and never unduly assertive to keep it from becoming a problem child.  As an element of a complete harmonic structure it is a desirable voice for the foundation work in an important organ, preferably as part of a 4-rank compound (mixture) stop in which it can sound favorably along with the 4th, 5th, and 7th upper partials belonging to the same harmonic series (i.e. the 17th, 19th, and 22nd) and be correctly adjusted tonally.  When such a stop is introduced by itself it is free to combine with any other grouping of stops, lending at times an interesting color when surrounded by other stops closely related in pitch.  The potential is also there for it to become a noisemaker unless caution is exercised with its use.

If it should ever be discovered that certain notes in a Pedal stop of 32-foot pitch are dead or the pipes producing such notes are out-of-tune, poorly regulated, or late to speak, and the music at hand calls for drawing that stop but does not rely particularly heavily upon these same notes, this author is of the opinion that this stop should still be drawn so that the listener does not miss out on hearing some of its sound.  To think of such a voice under these conditions as simply another class of "noisemaker" and keep it retired causes the listener to miss the opportunity of experiencing its sound at all.  Opinions among organists will vary about this, and it can be argued either way, but this author is inclined to put up with a couple of misbehaving notes in such a stop, take what good can be taken, and just go from there.  When the music is showing an appetite for such a voice, half a loaf of bread seems to be better than none.  It's also true that the squeaky hinge gets the oil, and any misbehaving notes are inclined to prick the ears and raise awareness with the right people who are in a position to fund and set in motion whatever restorative measures are needed.