Arrangement of harmonics and Hertz frequencies of all the notes in large pipe organs.

[kziss]

Hi everyone.
In Laurens Hammond's patent for the Hammond organ there is a chart with the frequencies in Hertz ( or cycles per second) for all ninety one tonewheel TG notes, and the Hammond organ service manuals have the diagrams showing the numbered arrangement of all the TG notes as they are laid out on all the drawbar footage key contacts and on the bass pedal drawbar footage key contacts so that we can easily see which TG note is located where on all the keyboard notes and on all the bass pedal notes with the corresponding drawbars.

Does anyone know of any equivalent or similar charts showing the Hertz frequencies of all the pipe organ flute notes and reed notes and the numbered arrangement of all these pipe organ notes as they are laid out on the keyboards and on the bass pedal notes with the various draw stop footages of the large full range pipe organs?

As well as that, with the higher draw stop footages of the pipe organs, do the highest frequency treble flute notes or the highest frequency reed notes go "all the way up" in Hertz up to the highest C note of the keyboard, or is there some kind of "treble foldback" arrangement like there is on Hammond organs, whereby a set of treble notes or an octave of treble notes are repeated on the highest octave keyboard notes due to it not being physically possible to create the highest range of treble frequencies with the smallest pipes or the smallest reeds?

Thank you in advance for a reply.
All the best.
Kon.

[toodles]

The book Electronic Musical Instruments by Richard H. Dorf, 3rd edition has a chart that gives the frequencies of notes from the bottom of the 16 ft. octave, to the top of 2 ft. octave. You can create this chart for yourself if you use Excel or other spreadsheet program, knowing that middle A is 440 Hz, and each half-step is related by the 12th root of 2. From this you can multiply out to get all the pitches. The 12th root of 2 is expressed as "=12^(1/12)".

While Hammond, many analog electronic organs, and unit pipe organ stops borrowed non-octavely related pitches from the unison pitches (i.e., fifth sounding stops used G-notes), straight organ stops and most digital organs use exact (correctly tuned) pitches, so the 2-2/3 stop is truly 3 times the pitch of the 8 ft. stop.

A chart such as you suggested isn't really needed, since octavely related stops (32, 16, 8, 4, 2, 1, 1/2, 1/4, etc.) stops are just twice the frequency of the next lower pitch. Likewise for 5-1/3, 2-2/3, 1-1/3, 2/3, etc. stops.

The smallest practical flue (flute and principal, not reed) pipe is usually the top C of a 2 ft stop, sometimes of a 1-3/5 ft stop (Tierce). Smaller than that it becomes impractical to make and tune. Sometimes upper notes are repeated, and sometimes they are just silent. It depends upon the designer and the intended use.

Reed ranks sometimes switch to flue pipes for the upper notes, especially for 4 ft. and higher reed voices. The pitches are often above the formant for the voice, so it is more practical to change over to a flue--the change in voice character isn't very noticeable.

[stefanv]

Just a correction to the above: the 12th root of 2 in Excel is "=2^(1/12)", not "=12^(1/12)".

With the really high pitches, it makes sense to switch to flue pipes, since the harmonics aren't even in the audible range any more (and thus don't affect the perceived character of the sound). A 2' high C is around 8.37kHz, which puts the first harmonic at 16.74kHz (inaudible to most adults), and the second harmonic at 25.12kHz (inaudible to all humans). So a 2' high C will sound the same whether it's a pure sine wave, a square wave, or anything else.

[kziss]

Hi Toodles.
Thank you for your reply.

The book Electronic Musical Instruments by Richard H. Dorf, 3rd edition has a chart that gives the frequencies of notes from the bottom of the 16 ft. octave, to the top of 2 ft. octave.

I actually have a copy of this book, and the chart is shown on page 10.
As well as that, the actual frequencies of all ninety one tonewheel notes are shown on Laurens Hammond's 1934 patent for the Hammond organ, and the tonewheel frequencies are also shown in my TG data spreadsheet.

A chart such as you suggested isn't really needed, since octavely related stops (32, 16, 8, 4, 2, 1, 1/2, 1/4, etc.) stops are just twice the frequency of the next lower pitch. Likewise for 5-1/3, 2-2/3, 1-1/3, 2/3, etc. stops.

It would be very interesting to see a greatly extended full range version of a Hammond organ with several extra drawbar footages including a 64 foot drawbar, a 32 ft drawbar and ultra high drawbars beyond the 1 foot drawbar, as well as drawbars producing third, fourth, fifth and sixth intervals from the main pitch and these extended full range drawbars include a full extended drawbars set for the regular tonewheel flute-ish waveforms, and a full extended drawbars set for the reed waveforms, and that the bass pedals also include the extended flute drawbars and the extended reed drawbars so that both the upper manual, the lower manual and the bass pedals all have the full broad spectrum of organ tones.

As well as that, it would be good for this organ to have the intra manual couplers and octave couplers thus allowing a much more broad sound thus making this organ sound much more like a huge grand pipe organ as well as creating the regular Hammond tonewheel sound that us Hammond enthusiasts love.

The extended range of flute and reed drawbars would allow a full control of all the tones and the harmonics instead of being limited to the preset tonal combinations that many pipe organs and electronic organs have.
With today's digital technology it should be possible to create such an extended range and tonally fully controllable organ.

The smallest practical flue (flute and principal, not reed) pipe is usually the top C of a 2 ft stop, sometimes of a 1-3/5 ft stop (Tierce). Smaller than that it becomes impractical to make and tune.

If the Hammond tonewheel generator had additional extra high frequency tonewheels, then the high C of the 2 foot drawbar would have been numbered as the TG note 97.

Most Hammond tonewheel organ models only go up to the TG note 91 which is the F# below the high C of the 2 foot drawbar, however the H-100 series and the X-77 tonewheel organs do include the additional extra high frequency tonewheels with the TG notes 92 to 96, so therefore the TG note 96 is the highest B note just before the high C of the 2 foot drawbar.

Sometimes upper notes are repeated, and sometimes they are just silent. It depends upon the designer and the intended use.

So this means that some pipe organs do have some kind of a treble foldback system whilst some other pipe organs with the absent high treble notes are somewhat similar to the Hammond spinet organs whose highest keyboard notes with the higher drawbars are all are silent beyond the highest F# TG note 91.

Reed ranks sometimes switch to flue pipes for the upper notes, especially for 4 ft. and higher reed voices. The pitches are often above the formant for the voice, so it is more practical to change over to a flue--the change in voice character isn't very noticeable.

Even with reed harmoniums and accordions, the highest treble notes do sound more like whistles or little pipes instead of having the characteristic reedy or brassy tonality that the lower and the midrange reed tones have so it makes sense to use little flue pipes here.

All the best.
Kon.